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Canada
A COMPUTER-BASED MINE DEVELOPMENT
AND PRODUCTION MANAGEMENT GAME
Jacqueline Allison
Department of Mining and Metallurgical Engineering
McGill University, Montreal
August 1994
A thesis submitted to the Faculty of Graduate Studies
and Research in partial fulfillment of
the requirements of the degree of
Doctor of Philosophy
•
~
Jacqueline Allison
1994
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ISBN 0-612-05661-9
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•
•
AB5TRACT
A model of the sequence of decisions required for mine development
and production has been formul ated and i s operated as a computer-based
game. The Mine Manager is an operations research game in which the user
assumes the role of mine management in the exploitation of a mineral
depos it.
Poten t i al app l i cat i ons of the game lie in experi mentat i on,
policy formulation and education in mine economics. The Mine Manager is
described using the terminology of games.
The selection of parameters and of the level of detail in the
model reflects a compromise between realism and simplicity.
At the
development stage, the selection of project specifications concerns the
mining method and capacity installation.
Decisions on cut-off grade
and/or cut-off value, capacity utilization, the sequence of mining,
stockpil ing and expansion are made during the mine l ife.
Deci sion
making takes place within a framework provided by an abstraction of the
operating environment of a mine, and must cemply with a set of rules.
These rules ensure that only feasible decisions are made. Within this
constraint, the model offers a high degree of flexibility in setting the
values of the decision variables.
The Mine Manager combines elements of geology, mining, management
and gaming.
Conditional simulation is used ta generate grades of
copper, zinc and gold in a massive sulphide deposit. Mining operations
in both underground and open-pit mi nes are modell ed, and hypothet i cal
capitaland operat i ng cost functions are devel oped for the mi ne and
mill. A pricing model generates new price series for each run of the
game.
The Mine Manager is operated interactively on a microcomputdr
through the use of modular software. The user interface and a sample
run of the game are described, and the information displays created by
the game are presented .
ii
•
•
RËSUMË
Ce mémoire décrit un modèle de la séquence de décisions prises
lors du développement d'un projet minier ainsi que pendant la période de
production qui suit. Le 'Mine Manager' est un jeu de type recherche
opérationnelle dans lequel l'usager assume le rôle d'un(e) gérant(e) de
mine en prenant des décisions reliées à l'exploitation d'un gîte
minéral.
Le jeu a plusieurs applications intéressantes telles que
l 'expéri mentat ion, l ' anal yse de strat.égi es et tact i ques opérat ionne11 es
d'une mine, et 'l'enseignement. Le modèle e~t décrit en utilisant la
terminologie formelle des jeux.
Le nombre de paramètres considérés dans le modèle et son niveau de
détail reflète un compromis entre le réalisme et la simplicité. Le
choix d'une méthode ainsi que de la capacité d'extraction doit être fait
en premi er lieu, au début de l a période de développement.
Vi ennent
ensuite des décisions relatives à la teneur et/ou valeur de coupure, au
taux ainsi qu'à la séquence d'extraction, au stockage du minerai et à
l'expansion de la capacité d'extraction pendant la vie de la mine. Ces
décisions sont prises dans le cadre d'une structure qui simule
l'environnement opérationnel d'une mine et doivent respecter des règles
qui assurent des activités logiques et réalisables.
Le 'Mine Manager' combine des éléments de géologie, de technologie
mlnlere, d'administration et de jeu. Une simulation conditionnelle est
util isée pour générer les teneurs en cuivre, zinc et or d'un gîte de
sulfures massifs. L'extraction en fosse et en souterrain est possible,
et des fonctions hypothétiques de dépenses en capital et de frais
d'opération sont développées pour la mine et l'usine de traitement. Un
modèle économétrique simple génère des séries de prix à chaque fois que
le logiciel est lancé.
Le logiciel est conçu selon une structure modulaire et opère en
mode interactif sur micro-ordinateur. En plus de décrire l'interface du
logiciel, ce mémoire présente un exemple du déroulement du jeu par
l'intermédiaire de figures et tableaux qui indiquent en détail les
intrants et les résultats .
iii
•
•
STATEMENT OF CONTRIBUTION TO ORIGINAL KNOWLEDGE
This thesis develops a model of the mine environment and of the
sequence of deci si ons for mi ne development and product ion.
Previ ous
work on the mine in economic theory focuses on production rate, cut-off
grade and capital investment decisions either in isolation or in various
combinations, primarily under the assumption of conditions of certainty.
Thosc studies which stress the element of uncertainty provide 1imited
fl exi bil ity in sett ing the val ues of deci si on vari abl es. The proposed
model is based on a comprehensive mining system incorporating
uncertainty and a broader range of mine decision variables than has
previously been addressed. It provides a greater degree of fl exi bil ity
in mine decision making in terms of both the range of permissible values
and the ability to alter the values of decision variables as time
progresses.
The model is operated as an interactive computer-based management
game.
The few mining games which have been developed are either
operated manually or, if computer-based, requi re an admi ni strator for
data input and transfer of feedback to the players. The delays in data
processi ng and transmi ssi on whi ch characteri ze these games have been
avoided by designing the Mine Manager to be fully interactive. Unlike
other mining games, this game addresses mine development and production
management decision making integrated with the technical considerations
of mining. It thus incorporates more of the real ities of mining and
guides the user in the development and operation of a reasonably
realistic mine and mill plant.
The tool which has been developed through this research combines
elements of mining, geology, management and gaming within the framework
of a computer-based system.
This game will find application in
operations research, education and training, and will help to improve
the quality of mine decision making, thereby increasing the benefits to
society from the exploitation of exhaustible mineral resources .
iv
•
ACKNOWLEDGEMENTS
The author would like to thank all who contributed in various ways
to the completion of this research project:
Prof. M. Bilodeau and Dr. R. Dimitrakopoulos for supervising the study
and offering many helpful comments.
Geostat Systems International Inc. for furnishing the geological data
which was used as the basis for deposit simulation.
Mr. D. Tolgyesi (Minnova Inc.) for arranging a visit to the mines of the
Opemiska Division in Chapais, where the staff was most accommodating.
Messrs. Y. Lizotte (CANMET), J. Mossop (McGill University) and G.
McIsaac (Lac Minerals) for providing a wealth of information based on
their experience in mining.
Mr. F. Smith for helping to configure the computer system and debug the
software.
Colleagues for playing the game and providing comments and suggestions.
Finally, my family for providing encouragement and support throughout .
•
v
TABLE OF CONTENTS
~
Page
ABSTRACT
ii
iii
RtSU~lt
STATEMENT OF CONTRIBUTION TO ORIGINAL KNOWLEDGE
ACKNOWLEDGEMENTS
v
TABLE OF CONTENTS
vi
LIST OF FIGURES
ix
LIST OF TABLES
xi i
CHAPTER 1 INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Operating Environment of the Mine
1.2 Mineral Project Development and Production
Decisions
1
1
2
1.3 Modelling, Simulation and Games
5
1.4 Objectives and Scope of the Research
B
CHAPTER 2 LITERATURE REVIEW
10
2.1 Introduction
10
2.2 Optimization Models
11
2.3 Mining Games
22
2.4 The Point of Departure
26
2.5 Elements of the Research
26
CHAPTER 3 GAMING WITH PARTICULAR REFERENCE TO MINING
•
iv
30
3.1 Nature and Purpose of aGame
30
3.2 Concepts in the Decision-Making Process
33
3.3 Components of aGame
34
:l. 4 Game Theory
37
3.5 Mine Management Gaming
3B
vi
•
CHAPTER 4 THE MODEL: A MINE MANAGEMENT GAME
4.1 The Game-World
40
4.1.1 External Factors
40
4.1.1.1 Market for Factors of Production and
Products of a Mine/Mill Operation
4.1.1.2 Geological and Mining Considerations
4.1.1.3 Insta11ed Capacitias
4.1.1.4 Capital Costs
4.1.1.5 Metal Priee and the Value of Mined
Material
4.1.1.6 Operating Costs
4.1.1.7 Stockpiles
4.1.1. 8 Mi 11 ing Parameters
4.1.1.9 Cash Flow Components
4.1.2 The Game-Situation
40
41
47
47
49
49
50
50
53
54
Mineral Deposit
Underground Operation
Open-Pit Operation
Installed Capacities
Capital Costs
Metal Price
Operating Costs
Estimated Value of an Extracted Mining
Unit
4.1.2.9 Stockpiles
4.1.2.10 Milling Parameters
4.1.2.11 Cash Flow Specifications and Financial
Performance
4.1.2.1
4.1.2.2
4.1.2.!
4.1.2.4
4.1.2.5
4.1.2.6
4.1.2.7
4.1.2.8
54
60
76
85
87
92
102
113
118
120
120
4.2 The Sequence of Decisions
124
Overview
124
~.2.1
4.2.2 Open-Pit Operation
126
4.2.3 Underground Operation
130
4.3 Rules of the Game
5. THE MINE MANAGER AT WORK
•
40
132
....................................
138
5.1 Introduction
138
5.2 User Interface
138
5.3 Sample Run
139
6. SUMMARY. LIMITAnONS AND RECOMMENDATIONS
vii
184
•
6.1 Summary
184
6.2 Limitations
188
6.3 Recommendations
191
REFERENCES
193
SELECTED BIBLIOGRAPHY
199
APPENDIX 1 Conditional Simulation
203
APPENDIX 2 Price and Cost Indices, 1973 -
1~87
APPENDIX 3 U.S./Canada Currency Exchange Rates,
1973 - 1987
206
APPENDIX 4 Software Specifications and Design
207
APPENDIX 5 Selected Output from the Sample Run of the Mine
Manager
211
THE MINE MANAGER GAME MANUAL
THE MINE MANAGER GAME DISKETTE -- Available from:
Jacqueline Allison
Department of Mining and Metallurgical Engineering
McGill University
3450 University Street
Montreal, Quebec, H3A 2A7
Telephone: (514) 398-4381 / FAX: (514) 398-7099
•
204
vi i i
•
LI ST OF FIGURES
Fi gure
Page
1.
Interactive Computer-Based Madel
2.
Interactive Computer-Based Madel for Mine Decision-Making
3. A Typo 1ogy of Games
2B
31
4.
Classification of Games for Different Purposes
32
5.
Representation of aGame -- People, Components and the
Conflict Situation......................................
35
6.
Relationship Between Long-Run Capital Cost and Installed
Annua 1 Capac i ty
48
7.
a) Long-Run b) Intermediate-Run c) Short-Run Unit
Operating Cost Curve for the Mine.......................
51
8.
a) Long-Run b) Intermediate-Run c) Short-Run Unit
Operating Cost Curve for the Mill.......................
52
9.
Approximate Shape and Orientation of the Simulated
Mi nera 1 Depos it
56
10.
a) Grade Zonation Pattern for Copper
b) Grade Zonation Pattern for Zinc......................
c) Grade Zonation Pattern for Gold
57
58
59
Il.
Parameters in Sublevel Stoping
63
12.
Development Drifts on Three Sublevels
65
13.
Block Sequencing on a Sublevel Requiring Advancement of
the Development Drift
67
14.
Cross-Section Through a Stope Showing the Relative
Positions of the Western and Eastern Stope Boundaries at
the Base of Each Sublevel
69
Horizontal Projection of Sublevels in a Stope on to a
Longitudinal Section Showing Mining to be More Advanced
on the Lower Sub 1eve 1s
70
16.
Boundaries of the Open-Pit and their Defining Coordinates
78
17.
a) Perpendicular Extension b) Parallel Extension of the
Open-Pit Along the Eastern Boundary
79
15.
•
6
ix
LIST OF FIGURES (CONTINUED)
•
Page
Figure
18.
Block Specification for Paraliel Extension of the OpenPit Along the Eastern Boundary
19. Average Annual LME Prices for a) Copper and Zinc, and
b) Gold (1973 - 1987)
95
20.
Simulated Copper Prices
103
21.
Simulated Zinc Prices
104
22.
Simulated Gold Prices
105
23.
Intermediate-Run Unit Operating Cost Curve as the Locus
of Short-Run Unit Operating Cost Curve Minima for the
a) Mine b) Mill
107
24.
The Sequence of Decisions for Mine Development and
Production -- An Overview
125
25.
Elements of a Mining System -- Open-Pit and Underground
Mine....................................................
127
26.
The Sequence of Decisions During the Open-Pit Mine Life
128
27.
The Sequence of Decisions During the Underground Mine
Life .
131
28.
Delineation Drillhole Locations
142
29.
Outline of the Mineral Deposit Based on Data from the
Delineation Drilling Program
147
30. Cross-Section of the Mineral Deposit
148
31.
Historical Prices of a) Copper and Zinc. and b) Gold for
for the Samp1c Run
150
32.
Price Cycling and the Start of Production in a Period of
a) Recession and b) Recovery
151
33.
Cross-Section of the Portion of the Mineral Deposit to be
Mi ned Underground ................•......................
157
34.
a) Primary Stopes b) Secondary Stopes ..•...............
159
35. Horizontal Projection of Stopes on to a Longitudinal
Section Showing the Planned Underground Mining Sequence
•
81
x
163
•
LIST OF FIGURES (CONTINUED)
Figure
Page
36. Metal Prices and Rates of Inflation During the Period of
Del ay
164
37. Summary of Construction Parameters and Estimated Unit
Operating Costs for the Open-Pit Mine and Mill..........
164
38. Cash Flow -- Years 1 - 3
165
39. Metal Prices -- Years 1 - 3
166
40.
Estimated Grades of Mineralized Mining Units on Level 1
of the Open-Pit.........................................
167
41.
East-West Profile of the Open-Pit at the End of Year 4..
168
42.
Value-Tonnage Distribution -- Year 4
169
43.
Grade-Tonnage Distribution for Copper -- Year 4
170
44.
Grade-Tonnage Distribution for Zinc -- Year 4
170
45. Grade-Tonnage Distribution for Gold -- Year 4
171
46. Summary of Operations -- Year 4
172
47. Stockpile Status Report -. Year 4
173
48.
Currency Report -- Year 4
173
49.
Cash Flow Statement -- Year 4
174
50. Summary of Underground Mine Construction Parameters and
Estimated Unit Operating Costs for the Mine
51.
East-West Profile of the Open-Pit at the End of a) Year 5
b) Year 6 and c) Year 7
52. Summary of the Mill Expansion Program and Estimated Unit
Operat i ng Costs for the Mill
53.
•
Estimated Grades of Mining Units on Level l, Sublevel 1
of Stope l in the Underground Mine
176
176
178
179
54. Horizontal Projection of Stopes on to a Longitudinal
Section Showing the Actual Underground Mining Sequence..
181
55.
183
Financial Performance Report............................
xi
•
LIST OF TABLES
1. Characteristics of Hypothetical Deposit and Host Rock
for Use in Numerical Approach to Mining Technique
Selection...............................................
42
2.
43
Numerical Approach to Mining Technique Selection........
3. Variograms in the Mineral Deposit Simulation
55
4. Constants in the Capital Cost Functions for the Mine and
Mill
89
5. Average Annual LME Priees for Copper, Zinc and Gold
(1973 - 1987)
94
6.
Indices and Factors of the Priee Cycles
97
7.
Formulae for Determining the Starting Position in the
4-Year Priee Cycle Given the Starting Position in the
16-Year Priee Cycle
98
Factors Used to Determine the Relative Limits of the
Triangular Probability Distribution of Priees
98
9. Average Priee Level of Historical Metal Priees and Per
Series of Simulated Metal Priees ...•....................
100
8.
la.
•
Page
Table
Average Priee Change of Historical Metal Priees and Per
Series of Simulated Metal Priees
100
Il. Average Relative Priee Variability of Historical Metal
Priees and per Series of Simulated Metal Priees
101
12. Constants in the Intermediate-Run and Short-Run Average
Operating Cost Functions for the Mine and Mill..........
109
13. Operating Cost Premiums
110
14. Smelter Contract Terms for a Copper Concentrate with ByProduct Gold and a Zinc Concentrate •....................
117
15. Average Intersection Grades of 5-Metre Core Samples from
Vertical Delineation Drillholes
143
16. Historical Priees of Copper, Zinc and Gold for the Sample
Sample Run
149
17.
152
Planned Level of Mine Capacity Utilization ..•...........
xii
•
LIST OF TABLES (CONTINUED)
Table
Page
18. Open-Pit Mine Schedule -- Block Selection by Year and
Level
154
19.
158
Production Targets for the Underground Mine
20. Underground Mine Schedule
•
xiii
161
•
•
CHAPTER l
INTRODUCTION
1.1 Operating Environment of the Mine
The mine environment is defined by geological and economic
parameters.
The geol ogi ,., 1 parameters are those whi ch refer to the
deposit, that is, the quancity and grade of mineral ized material, and
other physical features. The "economic parameters are external to the
depos1t, and are in effect during the period in which decisions are made
with respect to mine development and production. Economie parameters
include metal priees, capital and operating costs, inflation and
exchange rates.
Operating mines are characterized by a depleting raw material,
variable grades and physical properties amongst and within mineral
deposits, poorly-defined cost structures and myriad uncertainties.
Mineral
projects are typically
capital
intensive,
requlrlng
preproduct ion work over several years.
Gi ven the characteri sti cally
long lead times, the market conditions for mineral products at the start
of production may be significantly different from those predicted at the
time of the investment decision. The priees of many mineral products
exhibit marked cyclicity, and are related to the level of industrial
activity in the general economy, the interaction -- real or perceived -between suppl y and demand, and the market for recycled products.
The combined effect of the uncertainties associated with the
various geological and economic parameters is a high level of risk in
mi neral project investment. Dependi ng upon the ri sk preferences of the
firm and its financiers, attempts may be made to reduce the geological,
financial, inflationary, political and market risks to which the firm is
exposed. At any l'ate, it is likely that mine management will alter its
planning decisions as its database improves and uncertainty is resolved
during the life of the mine. The difficulties which are encountered in
decision making wit~ respect to mine development and production point to
a need for systems which enhance the process by which decisions are
made.
These should take into account the sequential nature of the
1
•
decision process and the dynamic features of the mine environment .
1.2 Mineral Project Development and Production Decisions
The profitable exploitation of a mineral deposit requires astute
decisions concerning mine development and production. Sorne of the types
of decisions which must be made are as follows:
1) At the development stage, selection of project specifications.
a) Mining and processing methods.
The methods available for extraction and conversion of ore
into marketable commodities are limited by technology and, thus,
have the potential to change with time. The choice of a method is
influenced by the quality, quantity and location of the ore
reserves, and by the availability of capital.
•
b) Plant capacity.
This refers to the installed mining and milling capacities
which determine the initial requirements of capital expenditure.
At this stage, the planning cut-off grade and corresponding size
of reserves provide the framework for justifying the plant
capacity decision. The cut-off grade is chosen such that there
are sufficient reserves to permit recuperation of the invested
capital, and to provide an acceptable return on the investment.
The calculation of cut-off grade differs from that made at the
production stage by whicn time the plant has been installed and
capital expenditure represents a sunk cost. The exclusion of sunk
costs from subsequent cut-off grade calculations results in a
different estimate of reserves than that used to justify the
initial investment.
Although operating cut-off grades and reserves differ from
those which were generated for planning purposes, future
operations will be constrained by the capacity installations based
on the initial planning decisions. In other words, the chosen
capacities place limitations on the rate at which the mine and
2
•
mill can be operated. The mlnlng capacity and the mi 11 i ng
capacity should be chosen so as to complement each other.
2) At the production stage, decisions concerning operating variables and
the expansion of existing capacity.
a) Capacity utilization.
Capacity utilization decisions are influenced by economic
and technical parameters. For a fixed quantity of ore reserves, a
higher rate of production leads to faster depletion of the
deposit, that is, a shorter mine life.
Short-term shutdown is an extreme form of capacity
underutilization, and may be a favourable alternative to operating
at a loss when the mining firm is facing economic problems. A
mine which is temporarily closed may be maintained in a state of
readiness for resumption of production should conditions improve.
The decision to close the plant on a temporary basis should be
part of a firm's longer-term strategy for survival.
Permanent plant closure is warranted when the ore reserves
are exhausted. Premature closure may become necessary for
economic or technical reasons. A timely curtailment of operations
may mean the difference between survival and bankruptcy of a
mining company.
•
b) Cut-off grade and eut-off value.
The eut-off grade refers to a specifie concentration of an
element of economic interest. The eut-off grade dictates the
amount of mineralized material that will be targeted for recovery.
It is generally used to distinguish between ore and waste and,
thus, determines the size of the ore reserves and, indirectly, the
length of the mine life. In fact, the mineralized material may be
separated into several fractions on the basis of a series of cutoff grades.
The eut-off value refers to a monetary amount which is based
on a eombination of grade, priee and various parameters of
extraction and proeessing. The eut-off value may also be used to
distinguish between ore and waste, and the partitioning of
3
•
mineralized material may be based on a series of eut-off values .
c) Sequence of mining.
Unless the grade is uniform in all parts of the deposit,
financial performance will be affected by the order of extraction
of the mineable units. In many deposits, grades display a zonal
pattern and a firm will select a sequence of mining according to
its operating policy. The sequence of mining may be reconsidered
many times during the production phase because practical
constraints and changes in economic parameters may cause actual
mining to deviate from the existing plans.
d) Stockpiling.
Stockpiles are defined in this study as an inventory of
mined ore at the minesite. It is anticipated that stockpiled
material will be sent to the mill at sorne point in time before
operations cease.
e) Mine and mill expansion.
An expansion of the installed capacity may be considered
advantageous if ore reserves increase or if market conditions are
favourable. An additional capital cost will be associated with an
expansion of productive capacity, and a change in unit operating
costs may result. Deepening of the shaft in an underground mine
may be required during the operating stage.
•
Prior to the commencement of production, the selection of capacity
and eut-off grade applies to the financial decisions of management and
the schedul i ng dec i si ons of the mi ni ng eng i neer.
The dec i sions are
inter-rel ated; the eut-off grade determines the quantity of reserves
which influences the decisions on capacity. In general, attempts are
made to optimize these planning parameters, although the subsequent
operating decisions on capacity and eut-off grade can be expected to
differ.
An organization which is engaged in mining activities will also
have to make decisions about the mining technique to be employed,
manpower requirements, equipment selection and replacement, the
implementation of measures to improve productivity, and other pl anning
4
•
and operational concerns.
The optimization of decision variables is performed with respect
to various economic evaluation criteria. The evaluation techniques are
based on the concepts of cash flow and time value, and therefore, the
purpose of applying optimization techniques is maximization of the value
In
of di scounted cash flow criteri a such as the net present val ua.
practice, Mineral project decision making is also guided by Mineral
policy and overall corporate philosophy which May change over time.
Development and operating decisions control which components exist
in a system and the nature of thei r i nteract ions. Improvements to any
such system, or process in a system, can be brought about by providing
decision-makers with the tools which allow them ta make more timely and
effective decisions throughout the life of a project.
1.3 Modelling, Simulation and Games
•
Modelling and simulation are tools which are applied to increase
the user's understanding of the way a system works, and ultimately to
improve the performance of the system. A model abstracts from real ity
the characteristics of a process or system which are considered to be
relevant given the objectives of the developer. The operation of this
model is referred to as simulation (Lehman, 1977; Gould and Tobochnik,
1988; Kheir, 1988). Computer-based modelling and simulation techniques
have been widely used in the Mineral industry for geological modelling,
ore reserve estimation, mine design and evaluation, Mineral processing
studies and operations research (Weiss, 1978).
Modelling and simulation have been used to investigate the
interaction amongst the components of a system under various conditions,
and to indicate the possible consequences of introducing new systems or
mod ifyi ng exi st ing ones (Loper, 1967, and Morgan et al., 1973). These
analyses can be carried out without the commitment of resources required
by an actual experiment.
Computer-based models are particularly effective because they are
able to perform numerous complex computations on large volumes of data
in short periods of time. This feature allows the developer of a model
5
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to incorporate more parameters and more detai1s concerning their
interactions than might otherwise be practical. By reducing the number
of manua1 calculations required of the user, computer-based mode1s can
a1so reduce the time and tedium involved in the use of the model. This
is particülarly important for mode1s which incorporate a series of
decisions, and provide informati~n about the consecutive st~tes of a
system.
In an interacti',e system, illustrated in figure 1, the user is
provided with preliminary data, and is required to process the data and
make deci si ons for whi ch the re~ults are recei ved. The feedback, in
whatever form, be it co st data, information concerning the market for a
product, production updates or profit information, can assi st the user
in understandi ng concepts, pri nci pl es or the rel at i onshi ps among the
parameters abstracted from the real world.
It should aid the
MICROC0MPUTER
AND
INTERACTIVE SOFTWARE
1
CONSOLE
1
1
1
1
PRINTER
\
Preliminary data
1
Feedback
t
Decisions
•
~igure
USER
1: Interactive Computer-Based Model
6
1
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•
participant in moving toward better decision making.
Computer-based models and simulations are regarded as tools which
help in prediction and explanation (Nenonen et al., 1984).
As
mentioned, the model upon which simulation is based takes account of tha
interactions amongst the elements of the system, and incorporates rules
governing the behaviour of the system as a set of mathematical
expressions. Simulators provide forecasts of the states of a particular
system and, in general, are used to support decision making in specifie
situat ions.
Agame is formally defined as a diversion or pastime on one har.d,
and on the other as a scheme or strategy (Collins Gem Dictionary, 1984).
Alternatively, agame can be described as a plan, or a contest of skill
or luck conducted according to rules; gaming refers to the playing of
games that simulate actual conditions, especially for training or
testing purposes (Webster's Ninth New Collegiate Dictionary, 1990).
In general, game-pl ayi ng has been associ ated wi th enterta inment;
however, models which are presented for operation in a game-type format
may also be of value for learning, teaching and research (Sowen, 1978).
Other uses of games include experimentation, operational analysis and
policy formulation (Stahl, 1983, and Shubik, 1989).
Games for educational or training purposes are described most
appropriately in terms of the scheme, strategy and planning perspectives
of the above definitions. This does not exclude them from the realm of
recreation or competition where they may also find application. The
purpose of these games is to familiarize the user with the features of
the parti cul ar system bei ng modell ed and to reveal the i nherent i nterrelationships which might not be obvious from an observation of similar
real systems in operation. The user is allowed to manipulate the system
and observe the effects of past decisions. The feedback can be used to
develop a rationale for future decision making.
A computer-based game may be similar to a simulator in many
respects vis-a-vis its development based on a model of an operating
system. Depending upon its purpose, the level of realism required of a
game may be lower than that for a simulator. Further, the subject of
the model on which agame is based may be purely hypothetical. The
value of such games does not typically lie in providing direct solutions
7
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to specific problems, but rather in increasing knowledge in a more
general sense, that is, knowledge of the type of system and the
potential benefits and drawbacks of various approaches to the situations
encountered therein.
War games have been used by military organizations for many years
in programs for training personnel and testing mil itary plans. In the
field of management, decision simulations have been developed to
increase the experience factor for business students (Carl son et al.,
1972, and Henshaw, 1984). The number and uses of general business games
has increased rapidly since the introduction in 1957 of the 'Top
Management Deci 5 ion Simul at ion' by the Ameri can Management Assoc i at ion
(Graham et al., 1969).
The term 'game' has become acceptable in
management, education and other fields.
ln the mi neral i ndustry, computer- based model s have been created
and used in simulators largely to aid problem-solving in specific cases.
Few have been developed for training or educational purposes, and more
specifically, in the form of games.
1.4 Objectives and 5cope of the Research
•
The current research aims to develop a computerized model of the
sequence of deci si ons on capaci ty, and cut-off grade and/or val ue made
duri ng the 1i fe of a mi ni ng projed, that i s, from mi ne development
through to production.
The ultimate goal is the creation of a
management game which is based on this model of mine development and
production, and which can be operated on a personal computer.
lt is intended that the mine management game find practical
application in the fields of education and training. Use of the game in
experimentation is also possible, in that it facilitates observation of
the effects of policy implementation in a dynamic and uncertain
environment. Operations research is an area of potential application in
which the game could offer i~sights. into the workings of the mine/mill
system.
A critical review of existing models of mine decision making and
mining games enables identification of the limitations of previous work
8
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and provides a background for the current research. There are three
objectives of this study. The first is to produce an overview of the
subject of gaming, with particular reference to mining; this is
presented as a framework far the description of the mine management game
and the model on which it is based.
The second objective, related to the development of the model of
mine decision making, is to establish those aspects of the mine
environment which are relevant to the type of decisions required of the
user.
From a practical standpoint, it is difficult to justify the
incorporation of all features of the mine environment in the model. It
would become too complex for all but an expert. The excessive detail
would detract from the central theme of the game, and would 1i kely
confuse rather than enl ighten. The approach taken in thi s study i s to
limit the set of features being modelled.
Emphasis is placed on
decision making within a reasonably real istic system. Selection of the
parameters to be included in the model therefore calls for a compromise
between those which are i'"portant given the purpose and scope of the
game and those which increase realism.
A decision is also made
concerning the degree of detail with which the rel ationships between
variables are modelled.
The third objective is the development of interactive, userfriendly software and the use of the game format to present the model of
mi ne deci si on maki ng.
Design of the computer-based management game
strives to meet certain basic requirements. The game must be simple and
pl ayable, yet reali st i c and credi ble. The product shoul d, therefore, be
easy to use, and this attribute increases the likelihood of wide
application in education, training and operations research .
9
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CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
Economie theory has been applied to the mine in order to analyze
the process of decision making with respect to production rate and eutoff grade. Although it is widely recognized that the decisicns on the
rate of production and eut-off grade influence each other, some writers
have restricted their investigation to only one parameter.
Early
studies (Gray, 1914, and Carlisle, 1954) produced static optima for the
decision variables, whereas more recent studies have emphasized the
potential gains to be realized from varying the capacity and/or eut-off
grade throughout the mine life, either on the basis of a predetermined
schedule (Herfindahl, 1955; Scott, 1967; Lane, 1964; Blackwell, 1970;
and Wells, 197B), or in response to resolving uncertainty and changing
perceptions of the future (Ross-Watt et al., 1979; Coylt, 1973; and
El brond et a1., 1977).
The mine and mill capacity installation decision has not received
much attention in the published literature. The conclusions which have
been drawn concerning this parameter have in most cases been impl iciL
In the evaluation of mineral projects involving a constant production
rate throughout the mi nr, l ife, determi nati on of the opt imum value of
this variable is generally assumed to dictate the optimum installed
capacity. In other words, the plant under consideration is assumed to
be operat ing at full capaci ty. If the production schedul e i s one of
declining rates, the installed capacity is assumed to be sufficient to
facilitate operation at the highest scheduled rate of production. Park
(1992) analyzes the effect of varying the initial installed capacity on
the net present value of a mining project.
The optimum size of
installation was found to be dependent upon the discount rate.
In the last two decades, models of sequential decision making in
the mine environment have been developed as training and educational
tools. Documentation concerning mining games is, however, very limited.
The existing games relate to various aspects of the mining industry .
10
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A review of previous work, much of which is focussed on
optimization, draws attention to the parameters affecting decisions on
capacity installation, production rate and cut-off grade, and serves as
a point of departure for modelling the sequence of such decisions.
Although the current model is not based directly on any existing models,
or combination thereof, a review of the progression of the economic
theory of mining and mine decision making aids the understanding of the
types of decisions required and the approaches to problems encountered.
Two types of models are reviewed in this section. The first part
of the di scussion focuses on the optimization of the production rate
and/or cut-off grade, either as static or dynamic variables. This is
followed by a description of several mining games and the models upon
which they are based.
2.2 Optimization Models
•
Hoover (1909) discusses the optimization of mine output per period
in terms of capacity, or rate of production. He states that the
object ive of mi nimi zi ng operat ing costs can be achi eved by 'the most
intensive production', and advocates a higher level of capital
investment to raise plant capacity and reduce total fixed costs over the
mine 1ife.
The increase in production rate is said to be 1imited by the
abil ity of the mine to access capital markets and to recoup capital
costs from future savings in operating costs; practical l imits to the
mine life; technical inefficiency accompanying step-wise expansion; the
effect of overproduction on Metal markets; and the investors' desire for
an investment which is secure, as indicated by the length of the mine
1ife. In addition to the l imitat ions noted by Hoover, mi ne capaci ty May
be influenced by the size and physical characteristics of the deposit,
and by the technical constraints which determine the available working
space in both underground and open-pit mines.
Gray (1914) develops a method for optimizing the rate of
production based on the concept of diminishing marginal returns. He
compares the value of a unit of ore produced now, at higher marginal
11
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cost, to the discounted value of a unit produced in the future at lower
cost. The profitability of operating at alternative production rates is
analyzed in terms of the opportunity cost, that is, the return provided
by a unit of ore mined at the end of the mine life.
Gray concludes that production at the rate of minimum average cost
is justified only by a zero discount rate and that the optimum
production rate would be higher if the discount rate were positive.
This has become the basis of much of the work concerned with optimizing
product ion schedul es. Stat ic opt imi zat ion ignores the fa ct that mi ne
operators may have sorne fl exi bil ity in sett ing the 1evel of use of
existing installations.
In his classic article, Carlisle (1954) stresses the need to
distinguish betwp.en the two important decision variables which apply to
a 'fund' resource. In this case, a 'fund' resource refers to a mineral
inventory in the ground. The two decision variables are the rate of
recovery, that is, the production rate, and the level of recovery. The
latter i s a funct ion of the eut-off grade and refers to the amount of
product to be extracted from the mineralized material.
Carlisle defines unit cost and revenue functions with respect to
the rate of recovery and the l evel of recovery assumi ng a perfect ly
competitive market.
Total undiscounted and discounted profits are
determined for alternative levels of recovery at a fixed rate of
recovery, and for alternative rates of recovery at a fixed level of
recovery. The optimum combination of rate and level of recovery is also
determined.
The static solution is obtained under the assumption of economic
and geologic certainty which, as Carlisle goes on to say, is not
generally appl icable. There are several other drawbacks. Unit costs
are expressed on the basis of a unit of metal produced, although it
would have been more appropriate to base costs on a unit of ore, given
that a mine is designed for the extraction of ore. Static optimization
ignores the fact that mine operators have sorne flexibility in setting
the level of use of existing facilities.
Nevertheless, Carlisle's
introduction of the concept of a eut-off grade is a significant
contribution to the development of economic theory in mining.
Carlisle indicates that short-run economies of scale can be
12
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achieved through the use of blending or 'controlled mining'. A firm may
opt to remove low-grade material which would otherwise have remained in
situ, if it lies adjacent to higher-grade ore for which mine development
was targeted. In addition to increasing the level of recovery, blending
may produce large volumes of uniform mill feed and thus, milling
economies.
Carl i sl e addresses uncerta inty and its effect on the 1evel s of
recovery and installed capacity. He recognizes uncertainties in the
quant i ty and qua1i ty of mi nera1ized materi al, costs and future market
conditions as being typical of mineral projects. The ten":~ncy among
mining firms is to build their plants up gradually, revising the optimum
capacity as more information becomes available.
This conservative
approach impedes the full real izati on of potenti al economies of sca1e.
As the risks associated with operating costs and prices elicit a similar
response, the effect of uncertainty is, in general, to increase costs
and to reduce the total recovery from a deposit.
Hotelling (1931) outlines the 'fundam~ntal principle of the
economics of exhaustible resources'. He states that the social value
of a deposit, that is, its contribution to the general good of a
society, is the present value of future sales of its products after
deduction of extraction and sell ing costs. According to Hotell ing, a
decl i ne in production rates should accompany a ri se in pri ces' as the
resource is depleted over a protracted period.
Herfindahl (1955) and Gordon (1967) build on the framework
establ i shed by Hotell ing. Herfi ndahl deduces that production from a
mineral deposit should begin at the point in time when the profit margin
per unit of production is no longer increasing at a sufficiently high
rate. Deferred production would not be the favoured option unless the
rate of increase in the profit margin is at least as high as the
discount rate.
Herfindahl goes on to discuss the optimum rates of recovery during
the life of a mine. He assumes that all participants in the market have
perfect knowl edge both of the present and future, and that the demand
and production functions are constant through time. Thus at each point
in time, price is such that demand balances production. The selection
of an optimum rate of recovery is made by comparing the present value of
13
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margi nal net returns per peri od to those obta i ned in other peri ods. He
reaches the conclusion that production rates should decline with time as
the deposit is depleted and priee rises.
Based on a similar analysis, Gordon asserts that a firm may be
wi 11 i ng to restrict output and sacri fi ce current profits in order to
obtain future output which is more valuable in present terms. This line
of reasoning may be extended even further to justify a temporary halt in
production should future market conditions appear to be particularly
favourable.
Gordon notes that a consideration of uncertainty would
affect most of the theory, but does not expand on this point.
Scottfs (1967) development of the economic theory of the mine is
based on an assumption that conditions of certainty exist, the size of
the plant is fixed and conditions are constant through time.
If
mineral izati on i s uni form throughout the mi ne, the total present value
will be maximized by operating according to a schedule of declining
production rates over time.
Once the assumption of constant conditions is relaxed, mine
planning must accommodate operations in zones of differing grades. In
this case, several zones may be worked simultaneously and the ores
blended as Carlisle recommends. Alternatively, the zones may be mined
in sequence and maximization of the present value will be achieved
providi ng that the highest grade zones are mi ned fi rst. Scott al so
develops a general approach capable of dealing with complications
produced by shifts in costs and priees with time.
Scott presents oniy a cursory discussion of the basic investment
decision, that is, the size of the plant. The long-run choice of a
plant size is described as a matter of trial and error, although for a
given deposit, there would be a limited range of profitable capacities.
Lane (1964) develops a model of a mining operation comprising
three stages: mining, milling, and refining and marketing. He assumes
that there i s certa inty in and stabil i ty of pri ces and costs, fi xed
installed capacities, full knowledge concerning the grade distribution,
and that ore below the eut-off grade is permanently abandoned. The best
eut-off grade is shvwn to be one of the limiting economic or balancing
eut-off grades.
He concl udes that the optimum eut-off grade to be
applied to a l imi ted resource i s i nfl uenced by the discount rate, the
14
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installed capacities of the several stages and the grade distribution of
the deposi t. He generates a schedul e of decl i ni ng eut-off grades and
rates of production which, given the mining sequence, maximize the
present value of annual profits. The variation of the balancing eut-off
grades, according to the sequence of mining in an irregular orebody, is
recognized as an interesting problem, but one which is beyond the scope
of his study.
Although Lane's analysis is valid given the stated assumptions, it
is uncommon in practice for all three stages of activity to occur in a
single mining operation. It is much more common for a mine and Mill to
be installed for a particular deposit. Small mining operations May not
warrant the construction of on-site milling facilities and May,
therefore, opt for custom-milling at an existing plant. In this case,
the milling rate would be set by contract.
Blackwell (1970) applies Lane's model to construct a decision
framework for a specifie case. He assumes certainty conditions and uses
an heuristic approach to determine the final pit 1imits and optimum
operating strategy subject to various constraints.
The ore reserve
inventory is divided into mining increments and benches, for which the
He observes that within the
grade distributions are specified.
constraints of finance availabil ity and market 1imitations, the optimum
scale of operations is a function of the size of the ore reserves.
Potential marketing difficulties can be avoided through restrained
application of an otherwise optimal eut-off grade policy.
Taylor (1972) clarifies the definitions of concepts commonly used
in the mining industry, and lays the base of a general theory of eut-off
grades.
A eut-off grade is defined as any grade which is used to
separate two courses of action, to truncate a frequency distribution, or
Operating
to separate mineralized material into graded fractions.
control May be exercised through manipulation of the eut-off grade.
Taylor challenges the proposition that the eut-off grade should be
lowered in response to a priee increase.
Strong priees encourage
producers to increase the suppl y of a commodity; in the absence of spare
milling capacity, this can be achieved only by raising the average
grade, and therefore, also the eut-off grade. This May, however, lead
to a lower level of total recovery of the mineralized material .
15
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A signifi cant feature of Taylor' s breakeven calcul at ions i s the
exclusion of the costs of mine development in an underground mine, and
the costs of mining and transportation to the rim of an open-pit. These
are the sunk costs, l ater referred to by Taylor as the 'ore generat i on
costs'. He identifies the points of eut-off in open-pit and underground
mines, and claims that for most mines, the critical eut-off grade is
that which applies between the mining and concentrating stages.
In his follow-up work, Taylor (1985) makes an important
distinction between 'planning' and 'operational' eut-off grades.
The
mine planner makes assumptions about metal priees, uses a eut-off grade
to decide which increments. of the mineral inventory should be included
in the ore reserves, and designs the appropriate installations. On the
other hand, the mine manager must decide which of the available mining
units should be extracted as ore at particular points in time, given the
existing mine and mill plant, and as more information becomes available
In this
concerning the deposit, operating costs and priee patterns.
latter dynamic situation, the original mine plans may be misleading for
eut-off grade decisions.
Taylor refers to the timing of production start-up and the
maintenance of stockpiles as the means by which mining firms can take
advantage of market swings. He also discusses the benefits and problems
of operating at a loss, and asserts that the eut-off criteria which
apply under these circumstances are the same as those which pertain to
profitable operations.
Wells' (1978) model optimizes mine size and eut-off grade
He uses a
simultaneously on the basis of the present value ratio.
hypotheti cal frequency di stri but i on of grades, recovery rate, tax rate
and priee for the product over the life of the mine.
He excludes
uncertainty from his model and mentions only that current expectations
of future events should influence mining strategy.
Based on Wells' optimization model, only a few combinations of
mine size and eut-off grade yield acceptable values of the decision
criterion; however, Wells suggests means by which the present value
ratio of an investment proposal may bEl! improved.
These are 1) by
decreasi ng or postponi ng expenditures, and 2) by i ncreasing revenues,
particularly those in early periods. The latter may be achieved through
16
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a strategy of selective mining which should be planned so that the grade
falls progressively over the life of the mine. Controlled build-up to
full capacity and tactical control of capital expenditure are cited as
possible ways of improving project economics.
Wells discusses in some detail the optimization of the size of the
installation designed to exploit an orebody of finite dimensions. A
larger mine requires more capital investment which is expected to
generate higher annual cash flows over a shorter period of time. He
notes that extremes in mine size, in terms of milling capacity, would
probably be uneconomic. The potential positive cash flow from a small
mine may not provide an adequate discounted return on the fixed capital
investment. At the other extreme, the capital outlay required to bring
a very large mine into production may exceed the value of the unmined
ore. He concl udes that between the two extremes, a pract ical optimum
size of mine exists for a particular deposit.
Ross-Watt and Mackenzie (1979) also identify the installed mining
capacity as an important decision variable, representing a financial
commitment made by management at the mine development stage. Subsequent
adjustments to the installed capacities can be achieved through
expansion during the operating stage; however, this decision variable is
not discussed in their paper.
The ability of mine management to respond to the resolution of
uncertainty is the basis of the mining project evaluation technique
proposed by Ross-Watt and Mackenzie.
Uncertainty is viewed as a
probability distribution of possible values about a single point
estimate of each relevant parameter. The response to the decreasing
geological uncertainty and the evolving environmental parameters is
embodied in a set of operating policies which attempt to simulate the
actual mode of short-term decision making.
The policies which are seen as useful for responding to price and
cost changes are those which control the sequence of mining, cut-off
The
grade, capacity utilization and stockpiling procedure.
effectiveness pf such response is dependent upon the initial level of
uncertainty, the rate at which it is resolved and the availabil ity of
operational flexibility.
Ross-Watt and Mackenzie consider the effect of implementing a
17
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limited number of alternative responses to the priees which occur during
the mine life. The mining project is evaluated in terms of its rate of
return, and the effect of the alternat ive responses on the probabi 1ity
di stri buti on of the rate of return i s exami ned. Exampl es of cut·off
grade policy which may be implemented are:
i) mine to breakeven grade throughout the life of the mine;
ii) mine to 1.6 times the breakeven grade when the priee exceeds the
most-likely value, and mine to the breakeven grade otherwise;
iii) mine to 1.6 times the breakeven grade throughout.
•
Policies i) and iii) are rigid in that the mine is operated at a
single eut-off grade until the reserves are exhausted, regardless of the
The second policy responds to the resolution of
priee level.
uncertainty by allowing adjustment of the eut-off grade according to the
priee level °each year. This results in the most favourable values of
the decision criteria, these being the expected rate of return and the
probabilities of the rate of return falling above or below given values.
The concl usion reached by Ross-Watt and Mackenzie is that
operating policies which allow mine management to respond to the
resolution of uncertainty Nith time can significantly reduce the
perceived and actua1 ri sks of mi nera1 project i nvestment. They al so
concl ude that the deci si on cri teri a deri ved from an eva1uat ion process
which incorporates such poli ci es is likely to be more realistic than
those based on traditional risk analysis techniques.
Ross-Watt and Mackenzie's model reflects the actual mode of short·
term decision making more closely than those described in earlier works.
The poli cies wh i ch they descri be have 1imi ted fl exi bi 1ity; however, i t
would be possible to set more complex policies in terms of the range of
potential responses to improved information about the deposit and
environmental parameters. This could be extended to include a change in
the direction of the policies themselves should mine management decide
to alter some of its objectives during the mine life.
It is unlikely that the various parameters upon which the values
of decision variables are based will be known with certainty at the time
of decision making.
In Ross-Watt and Mackenzie's model, the
environmental parameters are simulated for each year of operation
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following which the values of the decision variables are adjusted
accordi ng to the assumed management poli cy. As the autnors themsel ves
note, uncertainties concerning priees and costs tend to persist up to
the point in time when their predictions become current.
The response of mine management to the resolution of uncertainty
is also inc~~porated in the operating policies evaluated by Coyle
(1973).
Coyle's aim is to show that policy affects the economic
performance of a mine, and that the interactions between pol icy and
performance can be examined through the use of dynamic simulation. He
analyzes the behaviour of a hypothetical mine system which is subject to
a limited number of alternative production and financial policies.
Production policies refer to those which affect the rate of production,
whereas financial policies relate to expenditure in the area of
development.
Coyle stresses the need for simplicity in the development of a
model appropriate to this kind of study.
In his simulation model,
production and financial decisions are set against various geological
and physical constraints. He incorporates a grade distribution which is
assumed to be uniform throughout the mineral deposit, and an artificial
price series which mimics the general type of behaviour displayed by
prices on the London Metal Exchange. The plant capacity i s preset and
there is assumed to be no scope for expansion.
Three production policy options are considered by Coyle; these are
expressed in terms of the divergence of actual priees from some price
which is 'normal' for the particular met al occurring in the deposit.
The policies are of the following type:
i) ignore fluctuations in prices and produce at some nominal
capacity;
ii) increase production up to some limit, for example, twenty percent
over nominal capacity, when price is above normal, and operate
below nominal capacity when price is below normal;
iii) increase production when prices are above normal, but operate at
nominal capacity otherwise.
•
Production policy ii) provides for the greatest degree of response
to the resolution of uncertainty in the price level .
19
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The financial policy is such that the desired development rate is
adjusted in response to the 1evel of cash reserves ava i 1abl e to the
mining firm.
The desired development rate is calculated such that it
ensures replenishment of the depletion caused by current production, and
eliminates any discrepancy between the desired and actual developed
reserves. A cut-back on development expendi ture reduces the number of
weeks of covered production and may eventually re$trict production to a
level below that which is considered desirable.
The normal policy is to cut back development expenditure when
financial reserves fall.
The mixed policy is more aggressive and
initially maintains the original level of expenditure when the cash
position deteriorates; this is followed by a more drastic reduction in
development expenditure.
The best performance as indicated by a five-year cumulative
earnings figure is associated with the 'mixed' financial policy and the
production policy which allows a response to price variations on both
the upside and downside. The results of a series of simulations suggest
that financial policy has at least as much influence as production
policy on the economic performance of a mine.
The use of cumulative
revenues as the performance cri teri on exc1udes the important parameter
of costs from the mine evaluation process.
Coyle's results are obtained using a simple model built on the
assumption of conditions of certainty.
For example, although prices
fl uctuate from year to year, the pri ce seri es i s fi xed and known.
1n
reality, decision making, even if guided by fixed policies, would likely
be affected by uncertainty.
Elbrond and Dowd (1975) describe dynamic optimization, excluding
uncertainty, in the context of the mineral industry, and propose a model
of the sequence of decisions on cut-off grade and rate of production.
Dowd (1976) recognizes that future prices would be known only if they
are set through long-term contracts.
He i ncorporates the el ement of
uncertainty by presenting the problem of optimization as a stochastic
program in whi ch probabil it i es are assigned to poss i bl e future prices.
Elbrond, Lizotte and Plasse (1982) eliminate the constraint of a
•
predetermined end state, such as complete depletion, in the dynamic
programming algorithm which forms the core of an interactive system for
20
•
mine valuation.
Elbrond, Dubois and Daoust (1977) extend the optimization model
of Elbrond and Dowd (1975) into a system which is used to simulate
decision making for a short series of time periods. The system has been
The parameters which describe the
designed as an educational tool.
operational environment include the mineral deposit, defined by size and
grade di stri but ions; the operat i ng costs of mi ni ng and concent rat ion;
prices of the metal; the recovery and the grade of the concentratej and
the permi ssi bl e ranges and i ncrements of production rate and cut-off
grade. Costs and pri ces are i ntroduced as funct ions whi ch i ncorporate
the effects of market variations in time.
The model is capable of
accommodat i ng several production rates and cut-off grades, but fa il s to
take into account many of the technical parameters which are 1ikely to
influence production in a real mine.
The production rate and cut-off grade which apply in any period
are chosen on the basis of limited price and cost data supplied at
beginning of the period in question. The choice of production rate
cut-off grade is restricted to values in a prespecified range,
decision on cut-off grade being subordinate to that on the rate
the
and
the
of
production. In other words, production at a given rate will deplete the
deposit in a fixed length of time regardless of the chosen cut-off
grade. Wh en the ore reserves have been exhausted, the result of stepwise decision making and the optimal result obtained by dynamic
programmi ng are compared. Th i s a11 ows the users to exami ne the effect
of uncertainty on mine decision making.
The system comprises four modules. Module 1 determines the gradetonnage relationship
for a
deposit characterized by lognormally-
di stri buted grades; Modul e 2 cal cul ates the profi tari si ng from mi ne
production at a specified production rate and cut-off grade; Module 3
establishes the optimal sequence of production rates and cut-off grades
during the mine 1ifej and Module 4 establ ishes and prints the possible
sequences of states resulting from decisions on the rate and cut-off
grade for a number of periods.
The system is intended for use in teaching and experimentation,
••
and is designed to reveal some characteristics of the operational
environment of the mine.
The system is not fu11y interactive and its
21
•
operation for teaching purposes requires an administrator.
A major
drawback of the model is the assumption that material below the eut-off
grade is discarded, althoughit can be argued that there are some mining
techniques for which this is a valid approximation.
2.3 Mining Games
•
One of the earliest mine production games is described by Carl sor
and Misshauk (1972).
The participant in the Ashton Mining Game is
expected to pl an production in order to maximize net profits from the
operation of five mines and a single centralized mill. Four of these
mines have been operating for at least eight periods (quarters), whil e
the fifth is due to be brought into production within the next year.
Product ion pl anni ng i s constrai ned by the requi rements of the
concentrator, development costs, the capacity of each mine and the
limitations of a variety of transportation systems.
The pl ayer recei ves hi stori cal informat ion concerni ng the values
per unit of ore extracted from the various mines, and the relative priee
index over the previous eight periods. The ore value per unit is known
to vary from one mine to another as well as within each mine, and is
influenced by the prevailing metal priees.
During the game, the
administrator generates ore values at random using a probability
di stri but ion.
Thus, from the vi ewpoi nt of the pl ayer, there i s an
el ement of uncertai nty. The operat ing costs vary wi th the 1evel of
production, but do not incorporate a random element.
Game-pl ayi ng does not requi re a computer; total costs, revenues
and profits are calculated manually on forms of a suitable format,
provided by the admi ni strator. The game famil i ari zes the pl ayers with
some of the problems of management decision making: game variables
relating to scheduling, production and transportation of a product to a
given market must be ascertained and controlled as much as possible.
Several concerns of mine decision-makers .are not addressed in the
Ashton Mining Game.
Decision making focuses on the problem of
coordinating activities at the various mines under the rather
impractical assumption of certainty of operating costs. There is no
22
•
consideration of the capital investment decision, the techn i cal
constra ints faced by mi ni ng opera tors , nor the possibility of
stockpiling mined ore.
The objective of maxlmlzing net profit per quarter would be
appropriate if the discount rate employed by the Ashton Mining Company
were extremely high, or if the discount rate were of no concern in the
deci sions, as woul d be the case for a typi cal on-goi ng manufacturi ng
firm. It appears that within the time-frame envisioned by the game's
creators, the mineral resources can be viewed as infinite.
This
eliminates a problem faced by most mine operators, namely, depletion.
This type of game may be more suited to other areas of production .and
distribution such as manufacturing concerns, for which resources may be
viewed as unlimited.
Mutmansky and Kim (1973) model the sequence of decisions on
production volume and other variables relevant to the production of base
metals in an oligopolistic market, in order to evaluate competitive
strategies. They use the gaming approach in which participants assume
the role of competitors.
Preliminary information released to the
players includes:
general production information and costs for various modes of
production and inventory levels;
capital expenditures and lag time required to complete an expansion
of productive capacity;
- market conditions at the start of the game.
•
The competitors must analyze the situation as it develops,
formulate a competitive strategy and submit to agame administrator, on
a periodic basis, the values of product price, public relations budget,
product i on vol ume, pl ant i nvestment expendi tures and di vidend amounts.
These values form the basis of the simulation of operations for a 3month period, and each producer is subsequently provided with a
financial statement and market information.
Mutmansky and Kim conclude that gaming is the only effective means
of identifying key elements and evaluating base metals marketing
strategies in an oligopolistic environment.
They feel that market
research would have limited success in this respect given the
23
•
•
peculiarity of the base metal market structure and the unavailability of
useful historical data. Lack of realism and the difficulty in finding
qualified game administl-ators are cited as some of the l imitations of
using the gaming approach.
Mutmansky and Kim claim that. business gaming is useful when there
are several players pitted against each other in an oligopolistic
environment, but is of l ittle value to the participant in a perfectly
competitive market.
While this may be true given an assumption of
perfect knowl edge, there are no cl ear sol ut ions to production probl p.ms
when uncertainty is considered. The inapplicability of a model based on
a perfectly competitive market for evaluating competitive strategies
does not detract from the potent ial useful ness of agame based on a
similar model for simulating decision making in other functional areas
under conditions of uncertainty.
Bodle (1976) reviews the development of the Coll iery Game which
began in 1974 and, since completion, has been used as a computerized
training exercise.
The game is based on a hypothetical pit called
Dukeswood from which about 580 000 tonnes of coal are extracted each
year from three faces.
The pit i s descri bed in terms of the l ocat i ons and l engths of
faces and developments, access routes, geotechnical parameters and
geological structures.
The complexity of the mine geology can be
altered by making modifications to the basic program data. According to
Bodle, mine parameters do not include a random component, thus
eliminating unnecessary complications in an already complex game.
The user inputs a series of operating decisions, and associated
priorities, which defi ne new faces or developments, and which determine
the manner in which the resources -- personnel and machines -- will be
deployed for a twelve-week period. The program can be run several times
to simulate mine operations for up to two and a half years.
The feedback at the end of each simulation provides inf9rm.ation
about the geological structures and cunditions encountered, the state of
the roads and equipment, details of the number of workshifts by task,
advance and product ion for a11 faces and deve1opments worked duri ng the
period, and the financial results of the mining operation.
The Colliery Game has subsequently been tested within the
24
•
Operations Research Executive of the National Co al Board. The game has
been assessed as being broadly realistic, and has made a useful
contribution to the training of mine management. It is intended for use
by either an individual or a team of up to ten players with the
assistance of an operations researcher to verify inputs and to
administer the results. The level of detail in the model makes it
suited for examining short- to medium-term planning problems.
The number of computer-based games which have been developed for
other facets of the mineral industry is very limited. One such game,
'Expl ore', devel oped by Hayes and A11 ard (1981), teaches sorne of the
princjples of exploration drilling for mineral resources. The object of
the exercise is to delineate the simulated sub-surface stri1cture of a
property by deep dri 11 ing on a fi xed budget. Investment and product ion
decision making have not been included in the exercise.
A similar
product called 'Driller -- The Orebody Exploration Game' was çreated by
0011 in 1991In 1994, The Society of Mining Engineers released a shareware set
entitled 'Discover Mining'. Included in this set is a tutorial, 'School
of Mines', which provides an introduction to the concepts and
terminology of the mining industry.
'Explore!' allows the user to
select the location and depth of drillholes, subject to budgetary
constraints, in an attempt to discover sixteen deposits; the location
and size of the deposits are randomly generated such that each run of
the game is different. 'Bonanza Gold' is agame which provides the user
with experience in running an underground gold mine, the objective being
. the maximization of undiscounted profits. The user has no control over
the level of capital investment, the location of stopes, or the cost of
mi ni ng operati ons, but specifi es the sequence of extraction of mi ni ng
units or blasts. Mining is limited to four stopes on each of two
levels, and feedback is available through management reports. Once a
given stope has been opened for mining, its grade and mining costs are
described as high, medium or low, and the gold priee, which varies with
each blast, is available prior to the selection of the mining site.
Increasing the lev~l of real ism is the random occurrence of floods,
cave-ins, labour unrest and the discovery of a bonanza of rich ore. In
'Bonanza Gold' no consideration is given to processing of the ore .
°
O
•
25
•
2.4 The Point of Departure
Previous work follOl'/s a progression from the investigation of
production rate, eut-off grade and capital investment decisions on an
individual basis, to the analysis of various combinations of decision
variables primarily under the assumption of conditions of certainty.
The incorporation of uncertainty adds a new dimension to the study of
mine decision making.
It increases the need for more complex tools
capable of representing not only the intricate inter-relationships in
the mine system, but also the ~çtual mode of decision making.
The few mining games .n existence provide the framework for
assessing alternative approaches to sorne of the problems faced by mine
planners and operators. They allow the participant to gain valuable
management experience in specifie functional areas depending upon the
focus of the game.
Within this realm, there is scope for the development of a mining
game which is based on a more comprehensive mining system rather than on
the more limited spectrum of issues addressed in existing games. With
advances in computer technologies, it is also possible to make games
more interactive, thereby eliminating long lags in the output of
feedback and reducing the need for expert game administrators or
instructors.
By addressing these concerns, mlnlng games could become more
useful tools for mid- to upper-level management, both in terms of their
understanding of the decision-making process and their appreciation of
interests beyond their immediate area of expertise. Management would be
afforded the opportunity to gain perspective, facil itating more
objective analysis and better decision making.
2.5 Elements of the Research
•
The model which has been developed is operated as a game in which
the mine environment and mine decision-making process over a period of
time are simulated. The game is called the Mine Manager and, in the
26
•
•
remaining text, may be referred to simply as the Game.
Earlier models of mine decision making fail to incorporate sorne of
the features consi dered to be characteri st i e of the mi ne envi ronment,
have limited flexibility or are intended for purposes other th an
providing a framework for implementing sequential deeisions.
. For
example, Ross-Watt and Mackenzie (1979) rec09nize the abil ity of mine
management to respond to the reso1ut i on of uncertai nty, but foeus on
mining project evaluation to support the initial investment decision.
Coyle (1973), on the other hand, evaluates a limited number of
product i on and fi nanei al pol ici es under condi ti ons of certai nty. Both
of these studies of operating policies were undertaken for a plant of
The simulation described by Elbrond, Dubois and Daoust
fixed size.
(1971) requires decisions on production rate and eut-off grade given
l imited market information; however, the ehoi ce of values for these
variables is somewhat restricted.
The mode1 wh i ch has been devel oped through th i s research a11 ows
for greater flexibility in setting the installed capacity, level of
capacity utilization and cut-off grade and/or value in response to the
reso1ut i on of uncertai nty as t i me progresses. The Mi ne Manager can be
used for simulating the implementation of individual policies and policy
combinations. It calls for decisions to be made at both the development
and production stages, and reflects the sequential nature of the
decision process from year to year through the mine l ife. It does not,
however, provide the decision schedule which would have been optimal had
the future values been known a priori.
The type of system which is of interest in this study is based on
the interactive approach i11ustrated in figure 2. The user is provided
with preliminary geological information, typical costs functions and
historical metal prices, and is prompted to make a series of decisions.
The input arising from these decisions is validated, and mining and
milling are simulated. The results are available at the console or in
hard-copy format, and may be used to support subsequent decisions.
The geological information which is provided to the user pertains
to a simulated mineral deposit.
The generation of this deposit is
guided by a review of the typical characteristics of the type of
27
•
n
IIi
Priee
Open-Pit Mine
Cost
U"""9'-
Geology
MICROCOMPUTER
~i
AND
INTERACTIVE SOFTWARE
1 CONSOLE
1
1
1
1
1
Data on deposit and historieal
behaviour of priees, eost estimates
1
Feedbaek
Information
reauests
+
USER
Decisions
Figure 2: Interactive Computer-Based Madel
for Mine Decision Making
•
28
PRINTER
1
•
•
deposit. The behaviour of priees, costs and other production-related
parameters, and the uncertai nty associ ated with these parameters, are
also mode11ed.
The model which forms the basis of the Mine Manager is concerned
with the sequence of decisions on capacity utilization and eut-off grade
and/or val ue whi ch are made for operat i onal purposes. Thi s ca11 s for
the selection of mineable units and their intermediate or final
destination -- mi11, stockpile or dump. Consideration is also given to
the mining method, installed capacity, sequence of mining, stockpiling,
and temporary and permanent closure as they infl uence, or are affected
by, the decisions on capacity utilization and eut-off grade and value.
Sorne decision variables are not dealt with explicitly in the
model. It is assumed that trained manpower is available, the equipment
selection and replacement schedule are sound, and an efficient
beneficiation process is employed.
It 'is also assumed that mine
devel cpment in an underground mi ne woul d be suffici ent to accommodate
the specified extraction rate in any period, provided that the mine
capacity is not exceeded. In the case of an open-pit mine, the user is
responsible for ensuring that adequate stripping is carried out.
Project evaluation is based entirely on the financial performance
of the mine/mill plant as part of an integrated company.
The model which has been developed, and its operation, are
described using the terminology of games. The model contains elements
of a real-life situation, but the behaviour of these elements has been
generalized and, therefore, cannot be ascribed to any specifie existing
system. The level of detail and realism in the model is sufficient to
provide verisimilitude, but is less than that which would be required of
a simulator intended for direct use as an aid to management decision
making.
It is possible for several players to 'compete' against each other
in separate runs of the game by simulating the installation and
operation of a mining system within the rules of play. An assessment of
the approach taken to the problems encountered, or a comparison of the
resulting financial performance would determine the 'winner'. Thus, the
game anal ogy is considered to be appropriate to the project .
29
•
•
CHAPTER 3
GAMING WITH PARTICULAR REFERENCE TO MINING
3.1 Nature and Purpose of aGame
Agame is a simplified representation of a real situation in which
participants or players, acting individually or in groups, implement
decisions by milking simultaneous or sequential 'moves'.
In a board
game, a 'MOye' involves the transfer of a player's token from one point
to another. The 'moves' which a player makes in a mining game are
equi val ent to the impl ementati on of the deci si ons of mi ne management,
and therefore, they lead to a change in the state of the system. A
sequence of such decisions could lead to the eventual depletion of the
ore reserves. The sequential nature of the decisions on capacity, and
eut-off grade and/or value, is an important aspect of mine decision
making and can be incorporated in game design.
Stahl
Several schemes exi st for the cl assi fi cat i on of games.
(1983) defines various types of games according to their purpose, and on
the planned usage of the results of game-~laying.
Bowen (1978)
differentiates amongst several types of· games on the basis of their
purpose, the need for·selectivity in choosing game participants, and the
These classification schemes are
level of control over players.
depicted in figures 3 and 4.
The classification of games is not rigid and in Many cases, the
di fference between types of games i s one of degree. Agame May be
constructed as a deliberate cross between two types. The Mine Manager
is MOSt appropriately categorized as an operations research game,
equivalent to the operational research game described by Stahl. lt is
also considered to be an educational game.
An operations research game is similar to an operational game in
that it has the ultimate purpose of being an aid to decision making,
planning and policy implementation. However, rather than focussing on a
single real case, the deposit to be mined is a hypothetical one, and the
Game deals with a specifie type of problem, that is, decision making
with respect to capacity and eut-off grade and/or value during the life
30
•
2. Educatlonal games
Teaching of
5. Operational games
. . . . 1"- Specifie principles or ideas ~
-
--
-
known to game instructor
Learning
Insights not known
to game instructor
Toward subject
taught
...
...JI---
Idea and alternative
generation based on
Toward aspects of
decision problem
Altitude change
..
3. Experimentai games
For basic
research purposes
Demonstration of
Testing of model
For specifie
decision purpose
4. Research games
General increase of
knowledge in broader ...
area
-
----
Forecasts for
"Whal if" answers for
-
~- ~
Specifie decisicns
Dress rehearsal
1. Entertalnment games
Opening lines
of communication
Entertainment
Testing personnel
during recruitment
•
Figure 3: A Typology of Games (Source: Stahl, 1983)
31
•
SELECTION OF PLAYERS
CONTROL
Game designed 10
meellhe needs 01
a specifie group
of people
Suitable people are
lound 10 play the
game
Play conlrolled 10
make the players'
behaviour explicit
TEACHING
RESEARCH
Play unrestricted
subject only to
game rules and
format
LEARNING
FUN
OF
PLAYERS
Figure 4: Classification of Games for Different Purposes
(Source: Bowen, 1978)
•
of a mine.
The decision situation presented in the Game is, in fact, a real
one. The value of the Game lies both ;~ reporting the results of gameplaying to future decision-makers, and in providing players with
experi ence in deal ing wi th the problems of mi ne dec i sion maki ng. The
Game can be used for answering 'what if' questions and for experimenting
with various operating policies in a simulated environment similar to
that in which many mines operate.
The Game has several features which are characteristic of a
learning game. For the player who is unfamiliar with the environment in
which a mine operates or who has .1 imited experience therein, the Game
serves as an introduction to the parameters of the mine environment and
to the types of decisions which must be made. Users who have some
background in geology, mining and management, may find that the Game
32
•
enhances their understanding of the relationships between key variables
and the mining system as a whole. It may also provide useful insights
into the decision-making process associated with the development and
operation of a mine.
Although the player is expected to have a strong 'profit motive',
the objective of playing the Game may simply be to learn something of
the rea l si tuat i on wh i ch i t represents.
Learn i ng ta kes the form of
increased awareness, famil iarity and understanding of critical economic
variables, such as business cycles and inflation; the advantages of
thorough production planning; and the fundamental need to learn from
experience. To a certain extent, the Game al so encourages the pl ayers
to recognize their own attitudes towards uncertainty, and to practice
useful skills in priee forecasting and the analysis of cash flow
statements.
The Game may also be used for teaching. The model is sufficiently
realistic so that the player can be taught about the process and
complexity of mineral project decision making, as well as the types of
pol icies which can be implemented, and their effects. Although it may
be difficult to identify 'right' and 'wrong' decisions, the Game will
reveal, through.the technical and financial reports, the consequences of
successive decisions on capacity and eut-off grade and/or value. Much
can be gained by the participant(s) from a review process in which they
analyze what has occurred.
As an educational tool, the Mine Manager may provide long-term
benefits to its users, as well as indirect benefits to others.
For
example, there are potential long-term benefits from the change in
attitude of game-players towards real-life situations in the workplace,
and the improved efficiency with which they may be able to perform some
of their tasks. This can impact on the job satisfaction of individual
employees and on overall company morale.
3.2 Concepts in the Decision-Making Process
•
The discussion of the concepts involved in the decision-makin9
process follows that presented in Bowen (1978). The need for dec i sion
33
•
making implies that there is a conflict in the situation being modelled
by agame. Confl ict arises from the interaction between two systems
which, in the case of mining, can be thought of as the mine/mill system
and Nature. The concept of 'crisis' may also be relevant in that mine
management may perceive a particular event to be an unusual or
unexpected threat to the financial health of the firm.
The
Conflict and crisis affect the behaviour of a system.
behaviour can be examined in terms of:
1) an aim, which is to bring about a future state of the system or
its environment, for example, to exploit a mineral deposit for
positive net gain (with consideration of the time value of money);
2) a policy, in other words, a plan of action for achieving an aim,
for example, the scheduling of mine production so as to take
advantage of expected price trends;
3) an action, which is part of the process of implementing a policy,
for example, the extraction and processing of ore.
Conflict calls for decisions concerning capacities, cut-off grades
or values, sequence of mining, stockpil ing and so on. An unpredicted
sharp drop in the level of prices may be interpreted as a crisis
situation. During a crisis, a firm may decide to change its aim, policy
or action to better cope with the situation.
3"3 Components of aGame
•
The terminology presented in this section is a combination of the
terms used by Bowen (1978) and Stahl (1983). As shown in figure 5, a
game can be regarded as a model of the real world (the game-world) and a
set of 'oul es whi ch descri be the behavi our of the purposeful system
(mine/mill plant) as the situation develops in the course of time. The
game-situation includes those elements of the game-world which are
The subsystem
thought to have a relevant effect on the systems.
represents the mining firm which is under the control of mine management
(the decision-maker), the role taken by the player. The model may also
include another person -- the experimenter -- who is in full or partial
34
•
•
GAME
GAME-WORLD
GAME-SITUATION
NATURE
..,
1f--
MINEjMlLl.
SYSTEM
SUB-SYSTEM
Decision-maker
U1
1
RULES
1
+
1 PURPOSE 1
e
ê
maker
Figure 5: Representation of aGame -- People, Components and the Conflict Situation
•
•
communi cat ion with the pl ayer.
In thi s study, there i s no separate
experimenter although the player may wish to carry out tests concerning
the economic effects of various decisions on capacity and cut-off grade
and/or value.
The game-situation is described by a set of institutional
assumpti ons whi ch concern physi cal propert ies, such as the amount of
available information, the type and timing of actions, the resulting
The institutional set-up is
payoffs and the time span involved.
provided in the form of scenarios and rules. In the Mine Manager, these
rules cannot be changed from those defined at the start of the game, and
thus, it is an example of a 'rigid-rule' game. Most management games
fa11 i nto thi s category. The behavi oural assumpt ions concerni ng the
thought processes and mode of behaviour of the player are not specified
unless there are means by which the se attributes can be controlled.
Games are associated with two types of decision situations. The
'strategic game-situation' is one which involves at least two decisionmakers who are interdependent in the sense that neither can make an
optimal decision without considering which decision the other player is
likely to make. In 'games against Nature', there is one participant or
group of players acting as one decision-maker, and the decisions of any
others who might be assumed to exist in the particular scenario are
regarded as exogenous variables. This is the case for a mine operating
in a market in which the levels of aggregate demand and supply cannot be
influenced by the decisions of the individual producer who is,
therefore, a price-taker.
Two additional subsystems are the receptors, which take in
i nformat ion of potent i al use to the deci sion-maker, and the effectors,
which carry out the actions prescribed by the decisions, that is, they
put poli cy into act ion. The pl ayer who makes dec i si ons on beha lf of
mine management will have access to economic, geological and mining
data. These can be applied to construct a picture of the game-situation
upon which decisions are based. A distorted picture may result from
errors and faulty deductions in the process of picture-building. In the
Mine Manager, all of the necessary factors of production are assumed to
be available so that the desired actions can be effected .
36
•
3.4 Game Theory
Game theory formalizes the notions of strategy and decision making
and is characterized by the assumption of rational behaviour.
Von
Neumann and Morgenstern (1953) discuss the problem of rational behaviour
and the concept of utility, which has previously been applied to mineral
project decision making (Mackenzie et al., 1974, and Bilodeau, 1978).
lt has been shown that the theory of rational behavi our requi res a
thorough study of the 'games of strategy' .
No attempt has been made in this study to establish or further the
theory of gaming. lt suffi ces to say that a non-zero-sum game, such as
this 'game against Nature', provides a means of generating ideas about a
conflict situation. A non-zero sum game is so called because a gain,
such as a cash inflow to the mining firm, is not necessarily matched by
an equal loss to the opponent. ln the Game, the opponent is considered
to be Nature for whi ch there i s no measure of monetary gai n or l oss.
The player is expected, but not obliged, to use the ideas which have
been generated in an attempt to optimize the economics of the mining
project.
Rational behaviour in the context of the operating mine is defined
as that which seeks to maximize the present value of a series of future
cash flows. This is a restatement of Bellman's (1957) principle of
optimal ity: "An optimal policy has the property that whatever the
initial state and initial decision are, the remaining decisions must
constitute an optimal policy with regard to the state resulting from the
first decision". This principle is the basis of dynamic programming, a
method which has been used for optimization of mineral project decision
variables. If mine management is considering a program of expansion,
then rat ionali ty ca11 s for maximi zat ion of the net present value with
respect to the incremental capital outlay.
Under conditions of uncertainty, the rational player will
select
factual
2) select
satisfy
1)
•
beliefs which appear to be justified by the avail abl e
i nformat ion;
actions, that is, make decisions which appear li kely to
the goals.
37
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Regardless of the desirability of such behaviour, it is imrossible to
ensure that the decisions made by a game-player, or for that matter a
Game-playing is
decision-maker for a real mine, will be rational.
therefore unrestricted, subject only to the rules of the game. The
compl exity of the result i ng si tuat i ons ca11 s for an heu ri st i c approach
to the problem of optimization.
3.5 Mine Management Gaming
•
There are many aspects of mine planning and operation which may be
incorporated into a mining game. The choice of elements to be included
in the game-world and the degree of complexity of their interrelationships are dictated by the purpose and scope of the game. The
issues whi ch the deci si on-maker must address whil e pl ayi ng the Mi ne
Manager were outlined at the end of chapter two. Appropriate and timely
decision making by the player on behalf of mine management requires a
thorough knowledge of the elements of the mine environment and an
understanding of their interactions as represented in the Game.
The elements of the game-world of the Mine Manager are described
in chapter four. General aspects of the various elements are presented
in section 4.1.1 prior to a more detailed discussion of the elements of
the game-situation in section 4.1.2. Included in this latter section
are the assumpt ions upon which the model of the mi ne/mil l system, and
pricing and cost models are based; also included are the relationships,
expressed as mathemat i cal funct ions, that exi st between the parameters
in the model.
Chapter four also contains a description of the flow of decision
making throughout the mine life, that is, for the Game as a whole, and
on an annual basis for mining and milling operations. The rules of the
game, indicating what can or should result from the decisions of mine
management, are listed in the last section in chapter four. The rules
have been divided into groups, each pertaining to a different type of
activity for which decisions must be made: plant development and
expansion, open-pit mining, underground mining, stockpiling and milling,
and permanent closure.
38
•
•
Chapter fi ve focuses on the operat i on of the Mi ne Manager, and
begins with a brief description of the user interface, which is the line
of communication between the computer system and the player. This is
fo11owed by a presentation of the outcome of a sample run of the Mine
Manager which i 11 ustrates the sequence of deci sions facing the pl ayer,
and provides examples of the feedback from decision making. A summary
of the features and potential appl ications of the Game is given in
chapter six along with a discussion of its limitations and sorne
recommendations for further development .
39
•
CHAPTER 4
THE MaDEL: A MINE MANAGEMENT GAME
4.1 The Game-World
4.1.1 External Factors
4.1.1.1 Market for Factors of Production and Products of a Mine/Mill
Operation
•
Business firms operate for the purpose of providing goods or
servi ces. Thi s requi res an i nteract ion wi th outs iders -- ind ividua1s,
other organizations and the government. In order to perform its normal
day-to-day operations, a mining company needs to identify and maintain a
source of inputs to the production process.
Personnel, machinery,
equipment and services are selected from the available pool of resources
provided by the 1abour force, and manufacturi ng and servi ce industri es.
At the other end of operations, customers must be found for the products
of the business. The products of a mining operation take the form of
Even highlyores, mineral concentrates or refined commodities.
integrated companies need to secure a market for their final product.
The envi ronment in whi ch a mi ni ng fi rm operates i s characteri zed
by economic, social, political and regulatory systems of which
management must be cogni zant. Unl ess the production of a part icul ar
mineral commodity is carried out by a single producer (monopolist) or a
few dominant companies (oligopolists), it is unlikely that the
individual producer will be able to have a significant impact on publ ic
policy-making and commodity pricing. A large business enterprise may be
able to dictate the terms of its agreements with its suppliers; however,
this is not the case for most companies. The small to medium-sized firm
is not in a position to control its suppl y of labour and other inputs
and, therefore, has to obtain them at the going rate in the marketplace.
This situation is typical of many base a~d precious metal producers.
In the current model of the real world, a mining firm is assumed
to have full access to, but no control over, capital and labour markets .
40
•
The final products, mineral concentrates, are purchased from the firm at
the market-dictated price as soon as they are produced. The assumption
i s that there are no market constra ints thus a11 owi ng output to be
consumed upon production.
Inventory carrying costs are, therefore,
negligible.
The firm operates in what is similar to a perfectlycompetitive market, except for the existence of uncertainty.
4.1.1.2 Geological and Mining Considerations
•
The extraction of mineralized material can be carried out
underground or from an open-pit.
In the early stages of a mining
project, geological informati on i s very l imi ted and mi ne pl anners must
use the data provided by a del ineation program to determine the shape,
size, location and orientation of the mineral deposit, as well as the
distribution of grades and zonation pattern, if any, in the deposit.
Ore reserves are calcul ated on the basi s of a tonnage factor. Thi s
factor varies with the type of material, that is, mineralized or
In
unmineralized, and with the grade of mineralized material.
conjunction with economic and geotechnical data, the estimates of these
parameters form the basis for a decision on the appropriate mining
method or combination of methods.
The selection of the mining method to be employed for extracting
ore requires a consideration of the structure, competency and stability
of the mineral deposit and host rock, and the geometry and grade
distribution characterizing the deposit. Nicholas (1981) describes a
numeri cal approach to the problem of mi nin9 techn ique select ion. The
geometrical aspects and distribution of grades in the deposit, and the
mechanical characteristics of the mineralized zone, hangingwall and
footwall must be specified; various mining techniques are ranked
according to their ability to accommodate these characteristics.
For each feature, for example, ore thickness, a numerical value
from one to four is assigned to each technique under consideration. A
higher value .is assigned if the technique is highly suited to the
feature. Tabl e 1 contains the parameters whi ch are the basi s for the
numerical example given in table 2. As shown in the example, a high
fracture strength in the m; :1eral i zed zone suggests that the subl evel
41
•
Table 1: Characteristics of Deposit and Host Rock
for use in Numerical Approach to Mining Technique
Selection (Nicholas, 1981)
Characteristics of Deposit
and Host Rock
Description
Geometry/Grade Distribution
General Shape
Ore Thickness
Ore Plunge
Grade Distribution
Tabularjplaty
Intermediate
Intermediate
Gradat i onal
Mechanical Characteristics
Ore Zone
Rock substance strength
Fracture spacing
Fracture strength
Strong
Very weak
Strong
Hanging Wall
Rock substance strength
Fracture spacing
Fracture strength
Moderate
Very weak
Moderate
Footwall
Rock substance strength
Fracture spacing
Fracture strength
•
Strong
Very weak
Moderate
42
•
Table 2: Numerical Approach to Mining Technique Selectlon
(Nicholas, 1981)
Mining Technique'
Characteristics of Deposit
and Host Rock
OP SST R&P BCV SCV
Geometry/Grade Distribution
2
2
1
3
4
2
1
3
2
0
2
2
4
0
1
2
8
10
6
7
4
4
4
4
4
4
4
4
4
1
0
0
3
4
2
12
12
12
1
9
4
4
3
3
4
2
3
4
2
2
0
2
2
1
2
11
9
9
4
5
4
4
1
4
3
3
3
3
3
4
4
2
11
9
la
9
10
Total (mechanical)
34
30
31
14
24
Grand Total
45
38
41
20
31
2
3
3
3
General Shape
Ore Thickness
Ore Plunge
Grade Distribution
11
~echanical
Characteristics
Ore Zone
Rock substance strength
Fracture spacing
Fracture strength
Hanging Wall (andesite)
Rock substance strength
Fracture spacing
Fracture strength
Footwall (rhyolite)
Rock substance strength
Fracture spacing
Fracture strength
•
4
4
3
, OP • open-pit, SST • sublevel stoping,
R&P • room-and-pillar, BCV • block caving,
SCV • sublevel caving
43
•
stoping and room-and-pi 11 ar techni ques are more suitabl e than either
block caving or sublevel caving. The caving techniques receive values
of no more than two, whereas the other techniques are assigned the value
of four.
Once the assignment of values has been completed, the total value
for each techni que i s determi ned.
The techni que associ ated wi th the
highest value
is
regarded as the most efficient given
the
characteristics of the deposit and host rock.
For the assumed
characteristics in the example, the deposit is best mined in an open-pit
or by using the room-and-pi11ar or sublevel stoping technique
underground.
Access from the surface to underground mine workings is via ramp
and/or shaft.
If access to a depth of less than about. 150 metres is
required, a ramp is the appropriate choice given that this mode of
access i s both adequate and cheaper to develop than a shaft.
More
expensive shaft sinking is justified if mining operations are planned at
greater depths.
In this case, shaft pi11ars are maintained as support
structures, and the shaft extends below the deepest level intended for
mining in order to accommodate a loading pocket, sludge and sump. Shaft
deepening is possible should this become desirable.
Mineralized
material which is extracted during ramp construction, shaft sinking or
development dri ft i ng may contri bute to product i on early in the project
1 ife, and to an improved understanding of the meta11urgical properties
of the ore.
In general, the surface opening via which underground workings are
accessed is sited on the basis of a consideration of the centre of
gravity of the ore reserves. Mining may progress laterally in more th an
one direction from the vertical access route provided by the shaft or
ramp.
The more proximal stopes are mined prior to the more di stal
stopes in order to generate early cash inflows while development
proceeds.
An underground mine is divided into levels, the number of which
depends on the geometry of the mineral deposit.
These levels may be
further divided into sublevels. The spacing of levels and sublevels is
•
set so as to a110w adequate grade control and to minimize development
costs, without compromising the stability of the underground openings or
44
•
•
allowing an unacceptable level of blasthole deviation. Stope heights of
up to seventy-five metres can be drilled (longhole) without sublevels
before borehole deviation problems arise (Lizotte, 1989).
Depending upon the mining technique in use, the stability of
underground openings may be maintained through the use of rib and si11
pi 11 ars.
A crown pi 11 ar separates the uppermost underground worki ngs
from the surface. According to Lizotte (1989), experience at the Canada
Centre for Mineral and Energy Technology suggests that sill pillars
between stopes shoul d be of the order of thi rteen to twenty metres
thick. The dimensions of rib pi11ars vary according to the conditions
encountered in the part icul ar mi ne. Subsequent remova1 of ore t i ed up
in ri b pi 11 ars may be performed through secondary stopi ng, provi di ng
that primary stopes are first backfilled.
The mining units which comprise each stope are the smallest blocks
which can be classified as ore or waste. An orebody of narrow width
will be mined in one cut from hangingwall to footwall, and in this case,
the maximum wi dth of a mi ni ng unit i s constrai ned by the wi dth of the
orebody.
Limits to the height and length of a mining unit are
determined by geological and geotechnical parameters. The length of a
mining unit is the minimum advance achievable in a stope, and may be as
low as five metres (Lizotte, 1989). In determining stope boundaries,
economic factors must also be considered.
On each level and sublevel, if the mine is so designed,
development drifts provide platforms from which production drilling can
be performed.
The sublevel drifting pattern is controlled by the
expected location of the ore reserves. This expectation may be based on
del i neat ion dri 11 hol e data, the est imated grades of surroundi ng uni ts
which have previously been drilled, and grade zonation patterns if these
exist and are identified. If the orebody is to be mined in one cut from
hangingwall to footwall, the drifts may be as wide as the orebody.
Different degrees of selectivity with regards to mining units are
associated with the various underground mining techniques. For example,
the cut-and-fill technique, while highly suited to the mining of a
tabular deposit of intermediate dip, severely limits the flexibility of
the mine operator in the sequencing of mining units, and may require
breaks in the extraction process while the fill material is allowed to
45
•
•
set. Sub1eve1 stop ing, on the other hand, wh il e su itable for steep1ydipping orebodies, has successfully been appl ied using incl ined stopes
of only moderate dip (Lizotte, 1989), and pravides greater"flexibility
in mine sequencing.
Open-pit operations may requi re preproduct ion stri ppi ng of rock
and/or soil if the deposit is not exposed on the surface. Once the
overburden has been removed, the extraction of ore and waste from the
open-pit must be timed so as to realize the production goals. Ore
availability at particular points in time is controlled by the pattern
The waste:ore ratio, which may
of removal of the ore and waste.
fluctuate from one production period to the next, should assure good ore
exposure, an adequate variety of grades for blending, if required, and
satisfactory operating conditions.
Open-pit activities are carried out on benches of height equal to
that of the mining units. The sequence of extraction is constrained by
a maximum slope angle. The maximum angle for which slope stabil ity is
ensured is determined by the composition and structure of the material
comprising the pit walls.
The emphasis in pit slope design is on
practir.al stability as defined by safety and economic considerations
(Seegmiller, 1979).
On each level, a minimum mining width must be maintained in arder
that loading and hauling equipment can maneuver.
Depending on the
shovel-haulage truck combination, the minimum working width at the
shovel to provide double spot loading could be thirty to forty-six
If double spotting of haulage trucks for
metres (Crawford, 1979).
loading is prevented by an Inadequate amount of working space, shovel
productivity decreases. According to Bonates (1992), a minimum working
space of the magnitude suggested above would be required in only the
In addition, single truck-shovel
largest of open-pit operations.
interactions are more common at present due to a higher associated
safety factor.
Most open-pits are roughly circular in plan. Slot, wedge, square
and rectangular pit designs, while unconventipnal, do exist and oHer
the potential for simplifying the application of improved haulage
methods (Michaelson, 1979).
The vertical extent of the mineralization determines the ultimate
46
•
depth to which the open-pit would have to be developed for complete
extract ion of the mi nera1ized materi al.
In pract ice, the fi na1 pi t
limits are based on economic as well as technical considerations. The
projected pit 1imits and mi ne 1i fe may therefore be altered as the
estimates of future priees and costs change over the project life.
4.1.1,3 Installed Capacities
The installed mining and milling capacities are the capacities at
which the plant runs most efficiently. The capacity to be installed
must fall withi n the range of techni ca11y acceptabl e insta11 ed an~ua 1
capac it ies for the type and si ze of depos i t to be mi ned. It i s not
uncommon for plants to be capable of operating above their stated
capacity and, therefore, overcapacity production within specified limits
may occur. Capacity underutilization, including temporary closure, or
expansion of the installed capacity may be considered by mine management
at sorne point during the mine life.
Mi ne management may opt to del ay the start-up of preproduct ion
activities.
A study of historical priees will indicate whether a
general upswi ng in future pri ces i s to be expected. lt may be pos si ble
for the mining firm to take advantage of the cycl ical behaviour of
priees by postponing the start-up of production, a function of the
timing and duration of preproduction activities, such that it coincides
with the beginning of a period of priee recovery. If this is achieved,
the project economics will benefit from higher cash inflows in the early
years than would otherwise have been realized.
4.1.1.4 Capital Costs
•
During the preproduction phase of a mining project, initial
capital investment is required to develop the mine and provide physical
facilities such as a mill.
Preproduction activities include the
construction of surface facilities and the provision of mine access and
infNstructure. Some cost items, for example, the cost of constructing
an access road may be independent of the pl anned si ze of the mi ne.
Othel' components have fixed and/or variable components. The size and
47
•
cost of surface installations vary with the size of the mining
operation, but they also contain a fixed co st element. The cost of the
mine equipment and maintenance facilities is likely to be closely
related to the planned rate of production.
In the 1ong-run, when· a range of alternat ive depos it si zes and
mining systems is considered, the behaviour of capital costs can be
described in terms of economies of scale, that is, the capital
investment requi red to deve1op 1arger mi nes increases at a decreas ing
rate. The long-run capital cost curve' is displayed in figure 6. The
long-run capital cost curve for the mill has a similar form.
In the intermediate-run, that is, when the deposit is fixed,
capital costs behave in the same manner as in the long-run. The cost
per unit of insta11ed capacity decreases as the size of the mine and
mi 11 system i ncreases.
Therefore, the intermedi ate-run capi ta1 cost
Inslalled Annual Capacily (1)
Figure 6: Relationship Between Long-Run Capital Cost
and Installed Annual Capacity
•
, The general forms of the cost curves used in this study are those
described in standard microeconomics textbooks such as Thompson (1989).
48
•
curves of the mine and the mill which apply when the deposit is fixed,
are the same as their long-run counterparts. Capital costs need not be
considered in the short-run, that is, within a period of one year, as
the installed capacity of the plant is fixed.
Provision must be made for working capital and sustaining capital.
Working capital is required to bridge the gap between the disbursement
of cash to cover operat ing expenses and the generat ion of revenue from
operations. Sustaining capital is needed on an annual basis for the
replacement of equipment and machines as they become worn-out or
obsolete.
4.1.1.5 Metal Priee and the Value of Mined Material
The priees of the metals contained in the ore concentrates factor
into the calculation of the net smelter return, in a manner 9utlined in
the smelter contract, and ultimately determine the revenue to be
realized from the sale of the concentrates. Metal priees in a perfectly
competitive market behave in a mode similar to that displayed Gn the
London Metal Exchange (LME).
Estimates of metal priees are used to produce an estimate of the
value of the material in a mining unit. Cut-off values can then be
appl ied as the basis for distinguishing between ore and waste, and for
separating mineralized material into various fractions.
4.1.1.6 Operating Costs
•
Operating costs are incurred for the services and consumption of
the factors of production such as labour and materials. In the longrun, neither the deposit nor the plant is fixed and economies of scale,
that is, greater efficiency in the use of variable inputs, can be
achieved as the operating rate of the plant increases. This results in
lower average operating costs and a long-run operating cost curve which
slopes downward as the annual production rate increases.
In the intermediate-run, the deposit is fixed. As the rate of
operation increases from the lower end of the range of possible mining
or mill i ng rates, the average costs per un it of product ion decrease as
49
•
economies of scale are achieved.
If the mine production rate is
increased beyond some value, diseconomies of scale result from the
effects of overcrowding and the, decreased productivity of labour and
machines. Providing that the mill receives its required supply of feed,
the average mill operating cost is not influenced by the physical
characteri st ics of the mi neral depos it bei ng mi ned.
Therefore, the
intermediate-run average operating co st curve of the mill is the same as
the long-run curve.
In the short-run, the plant size is fixed and the average cost is
minimized by operating at a rate which is equal to the installed
capacity. A premium is added to the minimum average cost if production
is at over- or undercapacity. Production at a rate above the stated
capacity may be achi eved through the use of overt ime labour for whi ch
the hourly wage rate i s higher than duri ng the regul ar sh i ft.
The
general form of the long-run, intermediate-run and short-run unit
operating cost curves for the mine and mill is shown in figures 7 and 8.
Operating costs also vary with the haulage distance to the shaft
in an underground mine, and with the depth from which mined material
must be transported to the surface. An i ncrease in un it costs with
depth arises because of the greater distance over which hoisting
underground, or haulage in an open-pit, is required.
4.1.1.7
Stoc~piles
Stockpi l es may be created at the mi ne site for the purpose of
blending ores of different grades. Stockpiles may al so be used for
storing low grade ore until market conditions are considered favourable
for its processi ng and sal e in the form of concentrates. The tonnage
and estimated average grade of the ore in each stockpile is updated as
material is added or transferred to the mill. Some deterioration of the
ore may occur during surface storage for extended periods, and there may
be costs associated with the stockpiling of mined material.
4.1.1.8 Milling Parameters
•
Ore is processed at the mill to produce one or more concentrates
50
•
a)
~
~
Ul
o
Ü
Cl
c:
""!!!
LRoe
~
o
Annual Production Rate (t)
b)
~
~
üi
o
ü
Cl
c:
~
~
o
Annual Production Rate (t)
c)
~
Ul
o
Ü
Cl
.=:
~
al
c3"
Annual Production Rate (t)
•
Figure 7: a) Long-Run b) Intermediate-Run c) Short-Run
Unit Operating Cost Curve for the Mine
51
•
a)
~
<n
o
ü
Cl
c:
~<Il
C-
LRoe
O
Annual Production RaIe (1)
b)
~
~
<Il
o
Ü
Cl
c:
.':::
e
<Il
C-
IRae
O
Annual Production Raie (1)
c)
~
-o
<Il
Ü
Cl
.s
"§
<Il
C-
O
Annual Production RaIe (1)
•
Figure 8: a) Long-Run b) Intermediate-Run c) Short-Run
Unit Operating Cast Curve for the Mill
52
•
which will subsequently undergo smelting and refining. Mill feed is
obtained either directly from the mine or frùm stockpiles, if they
exist. A combination of direct mill feed and stockpiled ore may be
preferable depending on the level of capacity utilization and the grades
of ore available in the mine and stockpiles. The estimated and actual
grades of the mill feed are likely to differ due to uncertainties in the
grade of the material targeted for extraction, and in the levels of mine
recovery and dilution. Given a fixed concentrate grade, the level of
mill recovery is a function of the grade of the mill feed (O'Hara,
1987), but cannot be determined with certainty even if the grade of the
material to be processed is known.
If production above the stated capacity requires a reduction in
the processing time of the mill feed, the level of recovery will l ikely
fall.
If overcapacity production is achieved through the use of
overtime labour then recovery will be unaffected, but unit operating
costs wi 11 i ncrease.
4.1.1.9 Cash Flow Components
The net cash flow which the mlnlng firm reports at the end of each
year is the difference between cash inflows and outflows. Cash inflows
are generated by the sale of mineral concentrates, and cash outflows are
associated with capital investment, the payment of taxes and operating
expenses, including the cost of closure. Cash flow components may be
responsive to inflation' or to changes in exchange rates, if monetary
amounts are expressed in more than one type of currency. Taxes are an
•
1 Inflation
is the change in the current dollar level of a
monetary variable, such as price or cost, the change being aitributable
to factors other than escalation.
Current, or actual, dollars are those which are exchanged on a
daily basis. Thej reflect the impact of inflation on prices or costs.
The components in a project's cash flow statements are generally
expressed in current dollars; net cash flow~ are deflated using a
general inflation rate in order to det:-rmine the net present value or
rate of return associated with the proje~".
Escalation refers to the change in the real (constant dollar)
value of a monetary variable .
53
•
important element in determining project economics. The after-tax cash
flows from mi ni ng operat i ons are cal cul ated on the bas i s of a profit
taxation model.
At the end of the mine life, the sale of as sets and the recovery
of working capital may generate significant cash inflows. Dismantling
and reclamation costs, if incurred when mining operations cease, should
also be included in the calculation of cash flow. The project economics
are determined at the end of the mine life.
4.1.2 The Game-Situation
4.1.2.1 Mineral Deposit
•
The focus of simulated mlnlng activity is a massive sulphide
deposit containing copper, zinc and gold. The products of the mining
and milling operations are copper and zinc concentrates, the former
containing by-product gold.
The mineral deposit is lense-shaped and dips forty-five degrees to
the east.
The deposit has a true thickness of about 17.5 metres,
extends to a depth, of four hundred and twenty metres, and has a strike
, length varying up to one hundred metres. The zone of mineralization has
a sharp boundary with the surrounding host rock. The massive sulphides
are underlain by rhyolite and overlain by andesite, a geological
sequence typical of volcanic environments in which massive sulphides
were deposited over hydrothermal vents (Catallani et al., 1988).
The grades of copper, zinc and gold occurring in the deposit have
been simulated on the basis of prespecified variograms and grade
distributions. The grades thus generated respect the laws of spatial
correlation and randomness.
The grade distributions were selected on the basis of a review of
several massive sulphide deposits in the Abitibi region of' north-western
Quebec, Canada (Knuckey et al., 1982 and Cattalani et al., 1988). The
grade distributions used in the simulation are not intended to be
characteristic of any one deposit, but fall within a range which is
typical of this type of deposit .
54
•
The variograms used in the simulation (table 3) are based on the
logarithmic transformati on of grades from a massi ve sul phide deposit;
the data for the' deposit was provided by Geostat Systems International
Inc. (1990). The simulation was conditioned using a small number of
points in order to replicate zoning patterns found in many massive
sulphide deposits, namely a copper-rich core flanked by a zinc-ri ch zone
(Cattalani et al., 1988).
Conditional simulation is described in
appendix 1.
The simulation produces a three-dimensional grid of points. Each
point represents the centre of a cubic block of five-metre side, and is
assigned a grade which is the average grade of the block. The grid
defi nes a horizontal tabul ar body compri si ng fi ve l ayers of ei ghty by
twenty points on a rectangular grid, oriented such that the long axis
parallels the east-west axis. The grid is subsequently divided into
eighty vertical slices cut parallel to the short horizontal axis;
vertical translation of these slices produces a stepped profile as
viewed to the north, effectively dipping the tabular body forty-five
degrees to the east.
Grid points are removed along the boundaries of the dipping body
in order to produce a more realistic curving outline for the deposit.
Figure 9 shows the approximate shape and orientation of the simul ated
mi neral depos it. Figure 10 di spl ays the grade zonat i on pattGrns for
copper, zinc and gold in the deposit.
Once the deposit had been simulated, the average grades of copper,
Table 3. Variograms in the Mineral Deposit Simulation
Copper
Variogram'
Sill
Nugget effect
Range (horizontal)
Range (vertical)
•
Spherical
1.2
0.3
42 m
7m
Zinc
Gold
Spherical
1.0
0.2
30 m
10 m
Spheri cal
, Based on the natural logarithms of grades .
55
1.1
0.5
25 m
12 m
•
Oepth (m)
w
E
o
100
200
300
400
500
Cross-Section at 475 mN
mN 550
500
450
400
350
100
200
300
400
500 mE
Vertical Projection on to a Plan
•
Figure 9: Approximate Shape and Orientation of the Simulated
Mineral Deposit
56
•
m
100
0
------t0
m
100
Copper Grade
<5.0 %
5.0-10.0 %
10.0-15.0 %
>15.0 %
•
Figure IOa: Grade Zonation Pattern for Copper
57
•
•
:~i'&··
.--
.
m
100
o
o
m
!lW§&,Q:
100
,""":}lpt:
Zinc Grade
<5.0 0/0
5.0-10.0 0/0
10.0-15.0 0/0
15.0-20.0 0/0
>20.0 0/0
•
Figure lOb: Grade Zonation Pattern for Zinc
58
•
:-~-;~:~ .
..... <.>~
.
m
100
0
---""10
ijz..
m
100
<.i:.;;;;s;:. •. . . . . . .
_
Gold Grade
J{ . .• . . .•.
.
•....
<5.0 gft
5.0-10.0 gft
10.0-15.0 gft
15.0-20.0 gft
20.0-25.0 gft
>25.0 gft
•
Figure IDc: Grade Zonation Pattern for Gold
59
e
zinc and gold in each block were raised in order to increase the in situ
value of the mineralized material and improve the potential economics of
its extraction. The final characteristics of the mineral deposit are as
follows:
- mean grade: 4.52 percent copper, 7.46 percent zinc and 6.89 gpt
gol d;
variance of grades: 13.20 percent2 copper, 25.04 percent 2 zinc and
39.50 (grams per tonne)2 gold
- volume: 886 500 cubic metres;
- tonnage: 3 370 722 tonnes, based on a tonnage conversion factor of
0.263 cubic metres per tonne.
The deposit lies on a property with boundaries at 0 metres North
(mN), 0 metres East (mE), 32 765 mN and 32 765 mE.
The surface
topography in the region of the mineral deposit is assumed to be flat.
The geometry and grade di stri but ion of the mi neral depos it, and the
mechanical characteristics of the mineralization and ho st rock are
assumed to be the same as those listed in table l, section 2.5.
At the mine design stage when the initial decision on installed
capacity is made, the information on tonnage and grade is based on the
results of vertical delineation drilling on a forty-by-thirty-metre
grid. For the purpose of providing data to the user, five-metre core
samples from the simulated diamond drillholes are assigned the average
grades of adjacent cubic blocks with five-metre sides. Grade estimation
based on these core samples is l ikely to be less accurate than that
which is subsequently based on data from more closely-spaced blasthole
samples obtained as mining proceeds.
4.1.2.2 Underground Operation
e·
The technique to be employed for underground mlnlng has been
sel ected on the bas i s of the assumed characteri st i cs of the
mineralization and host rock. Given these characteristics, and the need
for flexibility in mine sequencing, sublevel stoping is considered to be
the appropriate technique for mining the ore reserves underground.
While mine design may vary according to the user's preferences,
60
•
'the configuration of stopes and pillars, and mine sequencing, must
fo11ow certain guidel ines intended to ensure a reasonable degree of
realism.
The intervals between levels and sublevels have been preset
based on normal operating practice; however, the working sites each year
are determined by the user.
Vertical access to the mine is provided by a shaft rather than by
a ramp.
It i s not expected that mi ni ng wi 11 be con fi ned to the upper
150 metres of mineral ization for which a ramp would have sufficed. The
shaft depth determines the deepest level which can be developed for
mining; this is the haulage level.
The shaft must ex tend for twenty
metres below the deepest level intended for mining in order to
accommodate a loading pocket, sludge and sump. The minimum shaft depth
is, therefore, 170 metres.
Once the shaft is in place, it is possible to deepen it.
Increments to the shaft depth are mult i pl es of seventy-fi ve metres so
that one or more additional levels are made available for mining.
A
shaft depth of 440 metres permits access to the deepest mineral ized
material.
The maximum depth of the shaft is set at 495 metres; the
lowest level in a mine having a deeper shaft would contain no
mineralized material.
To simplify decision-making, primary and secondary stoping must
In
advance in one direction, northwards alorig strike of the deposit.
the model upon which the Game is based, all stopes must be located at
least as far north as the shaft. The shaft can be sited as far south as
o mN, the southern property boundary. The maximum shaft site northing
is 32 760 mN which allows only one unit to be mined on each sublevel.
Given that there are no requirements regarding shaft pillars in the
Game, this is a technically feasible, though unlikely, situation.
If
open-pit mining precedes the underground operations, the shaft must be
sited outside of the pit. The shaft site easting is not made explicit
and i s assumed to be appropri ate to the i ntended l ocat i on of stopi ng
activity.
Stopes dip forty-five degrees to the east, paralleling the dip of
the deposit. The vertical interval between levels and sublevels is set
•
at seventy-five metres and twenty metres, respectively.
The maximum
number of sublevels per level is three, and levels are separated by sill
61
•
•
pillars fifteen metres in thickness.
The crown pillar is at least
fifteen metres thick .
The deposit is of moderate width and is, therefore, to be mined in
one cut from hangingwal1 to footwall.
Figure 11 shows some of the
parameters of the sublevel stoping technique.
A mining unit has a
length of five metres, a vertical height equal to the sublevel interval
of twenty metres, and a width equal to the selected stope width. The
width of a stope is a multiple of five metres and is no more th an
twenty-five metres. The maximum length of stopes and the minimum length
of intervening rib pillars is twenty-five metres. All of the material
extracted from the underground mine is regarded as ore, and is either
processed at the mill or diverted to a stockpile.
Mining can take place on several sublevels and levels in a given
year. Mine sequencing is possible, and selectivity is limited only to
ensure that mine sequencing is reasonably realistic.
The major
cC'1straints to sequencing in the underground mine are that primary and
secondary stopi ng must advance northwards, and that the advance al ong
the various subl evel s of a l evel be coordinated such that bl asted rock
fragments can fall to the base of the stope. This requires that mining
on lower sublevels be more advanced than on upper sublevels.
The number of l evel s avail abl e for mi ni ng i s a fun ct i on of the
mineable depth which is determined by the shaft depth, thickness of the
crown pillar and pit depth, if an open-pit exists. The mineable depth
is the vertical interval between the base of a crown pillar of minimum
thickness and the limit to mining at depth, that is, twenty metres above
the foot of the shaft. Assuming that the underground operations which
follow open-pit mining will take place below the deepest level reached
in the pi t, the thi ckness of the crown pi 11 ar i s measured from the
bottom of the pit. If no open-pit mining has taken place, the top of
the crown pillar is at ground level.
For a shaft depth of 420 metres, including a twenty-metre
extension for the loading pocket, and a crown pillar of minimum
thickness (fifteen metres) at ground level, the mineable depth is
calculated as follows:
mineable depth
=
420 - 20 - 15
= 385m
62
•
,
'.
'.
Sublevel
interval
20m
!
,
'.
,,
,,
,
,
,
,
, 2
,,
,
,
,,
,,
,,
,
,
,
'.
Mining
units
,
,
, 3
,,
,
'.
,
,
,
'.
",
..
Stope width
(maximum 25 m)
Figure Il: Parameters in Sublevel Stoping
•
ci3
,
'.
•
With the possible exception of the shallowest level, all of the levels
into which the deposit is divided contain three sublevels. The number
of such levels is the whole number resulting from the division of the
mineable depth by the vertical interval between levels (seventy-five
metres) :
Number of levels = 385 / 75
= 5 (remainder 10 metres)
•
The remainder from the above division (ten metres) is the vertical
interval between the base of a crown pillar of minimum thickness and the
top of the hi ghest l evel conta in i ng three subl eve l s. The magn itude of
the vertical interval determines whether or not an additional level can
be considered available for mlnlng.
Such a level would be the
sha110west in the mine. If the vertical interval is between twenty and
thirty-nine metres, the additional level contains one sublevel.
A
vert i cal i nterva l of between fort y and fi fty-ni ne metres a11 ows for two
sublevels in the additional level. Given the remainder of ten metres in
this example, the number of levels is unchanged at five, and the crown
pillar has a thickness of at least twenty-five metres.
Level sin the underground mi ne are numbered in sequence with
The reverse applies to the
depth, the shallowest being Level 1.
numbering of the sublevels, Sublevel 1 being the deepest on any level.
Development drifts are driven on the three sublevels as shown in
figure 12. These drifts run northwards and should be located so as to
follow the mineralization because they are used as platforms for
drilling which may lead to production. Given that the vertical interval
between sublevels is twenty metres and that the deposit dips forty-five
degrees to the east, an upper development drift must be displaced twenty
As mining must
metres to the west of the drift immediately below.
commence on lower sublevels before upper sublevels, it is necessary to
specify the western and eastern boundaries of the development drift at
the bas~ of a level. The eastings of the boundaries of the development
drift on upper sublevels are automatically calculated.
If the development drift on the lowest sublevel has been poorly
located, as evidenced by a lack of mineralization in the mining units
selected for drilling, it is possible to begin a new development drift
64
•
Figure 12', Development Drifts on Three Sublevels
•
65
•
•
in a different location.
This is conditional upon the fact that no
extraction has occurred; otherwise, it is assumed that the drift has
been satisfactorily sited. There must be no overlap in the boundaries
of the original and new drifts. Modification of the location of the
development drift is allowed once per level, upon selection of the level
number; the geol ogy i s not cons i dered to be suffi ci ent l y compl ex to
warrant additional relocations.
A development drift has a height of three metres, and a width
determined by the user-specified coordinates of the western and eastern
The deve l opment
boundari es, up to a maximum of twenty- fi ve metres.
drift on each sublevel is assumed to begin at the northing of the shaft
and advance northwards as mining progresses.
The dimensions of a
development drift, including the length of the drift, are the basis for
calculating the volume of material excavated for costing purposes. The
void which would be created by drifting, and the material removed, which
might in reality contribute to production, are ignored. Therefore, in a
given level, the uppermost material on the first or second sublevel is
assumed to be contiguous with the material at the base of the sublevel
above.
Once mining has begun on a particular sublevel, the need for
additional drifting northwards is dependent upon the stope boundary
specifications.
At any point in time, the development drift on a
particular sublevel has been driven as far north as the most northerly
drilling site (figure 13), whether or not the drilling was followed by
extraction.
If a selected block is more northerly than the existing
northern l imit of the development drift, then additional drifting is
required. The drift is extended the entire distance between the currerli.
northern limit of the development drift and the northern boundary of the
selected block.
Stope selection follows the specification of the level and
sublevel on which mining is to occur.
A stope comprises up to five
mining units which may be extracted in different years, or in the same
year either througr a single st ope selection, grouping the units as a
block, or by repeat i ng the select i on procedure up to fi ve t i mes. The
block of one or more mining units to be drilled and possibly extracted
from a stope is delimited by the coordinates of its northern, southern,
66
•
•
N
S
Jil1
a,
....,
Shaft
Most-northerly
drilling site
Block selected for
drilling and/or extraction
....-Development drift
.
Additional drifting
required
....
Northern limit of
development drifting
Figur'? 13: Black Sequencing on a Sublevel Requiring Advancement of the Develapment Drift
•
•
western and eastern boundaries at its base.
The eastings delimiting a stope are specified only for the base of
the first sublevel of a new stope, and must be the same as or within the
The
eastings of the boundaries selected for the development drift.
wi dth of a stope, set upon commencement of extract i on on the fi rst
sublevel, remains unchanged when mining takes place on the second and
th i rd subl evel s above. The western and eastern boundari es of blocks
being mined from these upper sublevels are automatically set according
to the boundaries of the stope on the first sublevel, with an adjustment
reflecting the forty-five degree dip of the stope (figure 14). This
reduces the number of decisions which would otherwise have to be made,
and ensures that the fall of material from upper sublevels to the base
of the stope is not impeded. Although the width of a single stope
cannot be changed once it has been set, stope width can be varied from
stope to stope.
In the sel ect i on of the northern and southern boundari es of a
block ta be extracted, consideration must be given to the property
boundaries, the maximum length of a stope, the minimum length of a rib
pillar and the condition that mining advances northwards. For mining on
upper sublevelsthere is an additional constraint imposed by the mining
technique with regards to the correct positioning of a selected block
relative to the stope boundaries on the sublevel below. The northern
and southern boundari es of the sel ected bl ock must be the same as or
within the corresponding boundaries of the stope on the sublevel below.
In other words, mining on an upper sublevel cannot extend beyond the
stope limits on a lower sublevel. As shown in figure 15, mining must be
at least as advanced on a lower sublevel as on an upper sublevel; this
desi gn permi ts the free fa11 of bl asted materi alto the base of the
stope.
Blocks mined from the second or third sublevels of a stope must
be contiguous. Assuming that ~ome extraction has already taken place on
an upper sublevel of a stope, the southern boundary of the selected
block must be the same as the northern boundary of the stope on the
particular sublevel.
If the block is the first to be mined from an
upper subl evel of the stope, its southern boundary must be at 1east as
far north as the southern boundary of the stope on the sublevel below .
68
•
w
E
Sill pillar
1
~-~---"""-
75 m
-----
Sublevel3
SOm
Sublevel2
r------------ ------------ ----t
20
230 mE
255 mE
m
Sublevel 1
250 mE
275 mE
Figure 14: Cross-Section Through a Stope Showing the
Relative Positions of the Western and Eastern
Stope Boundaries at the Base of Each Sublevel
•
69
•
s
N
SiI\ pil\ar
- - - - - - - -
-
-
,.------,- -
-
- -
- - - - - -
-
-
-
- -
-
Sublevel3
- - - - - - ,....
J..
_L.
-. -
_
Sublevel2
Stope
- - - - - - - - - - .1..-_ _--.- - - - --
Sublevel1
(mined out)
Direction of advance --..
Figure 15: Horizontal Projection of Sublevels in a Stope
on to a longitudinal Section Showing Mining ta
be More Advanced on the lower Sublevels
•
70
•
•
The northings selected for a block on the first sublevel determine
whether mi ni ng i s to be started in a new primary stope or in a new
secondary stope, or cont inued in an exi st i ng stope, Secondary stopi ng
takes place in the rib pillars separating primary stopes, One secondary
stope can be developed in each of these pillars. A secondary stope may
al so be developed in the southern wall of the most southerly primary
stope.
If the southern boundary of the selected block is at least twentyfive metres north of the most northerly stope, then mining is taking
place in a new primary stope. If the selected block is contiguous with'
the most northerly primary or secondary stope,.then that stope is being
extended.
. Once mining units have been selected on the first sublevel of a
new stope, operat ions in a more southerly stope of the same type are
assumed to have been completedj further mining on the level is carried
out in the new stope or in a more northerly stope. In other words, the
most northerly primary stope is the active primary stope; the same holds
true for secondary stopes. If mining takes place in the pillar south of
the most northerly primary stope, extraction in the primary stope is
assumed to have been completed, and primary stoping may be resumed in a
new stope.
It is assumed that backfilling of a primary stope is carried out
immediately following the termination of mining operations in the
part icul ar stope. It i s al so assumed tiiat the curi ng peri od i s short
enough to a110w extraction in a secondary stope to begin in the same
year in which mining of the adjdcent primary stope or stopes has ended.
Val idation of the coordinates of the boundaries of a selected
block also requires a comparison of the maximum amount of material which
could become available from mining the block with the amount which can
be mined given the remaining mine capacity. The mine capacity remaining
at any poi nt duri ng a year i s cal culated as the maximum overcapacity
product ion l evel l ess the capacity ut il i zed for mini ng and expl oratory
drilling activities.
Drill ing which does l:ot lead to extraction is consi~ered to be
exploratory. A unit of exploratory drilling is assumed to be equivalent
to two-thirds of a unit of mining, that is, each unit of exploratory
71
•
drilling reduces the remalnlng mine capacity by two-thirds of a unit .
This assumption is based on estimates for a 1000-tonne-per-day operation
which has a twelve to tenratio of development manpower to miners. If
all miners worked in development at a seventy percent level of
efficiency, the rate of development would increase to about 150 percent
of the design level. Exploratory drilling is not production-related,
but consumes sorne of the resources whi ch woul d otherwi se be ava il abl e
for mine production.
If the amount of material which is available from mining ~
selected block is more than can be extracted given the remaining mine
capacity, the boundaries of the block must be modified so as to reduce
its size.
Providing that the coordinates delimiting a block are
acceptable, estimates of the grade of copper, zinc and gold in each in
situ mining unit are generated through a two-step procedure:
1) the true grade of each element of economic interest is calculated
as the mean grade of up to twenty constituent cubic blocks of
five-metre side.
2) random deviates of the grades of the three elements are generated
from normal distributions, each having a most-likely value equal
to the true grade, and a coefficient of variation' of 1.15 for
copper, 0.90 for zinc and 0.86 for gold. The coefficient of
variation is the square root of the relative kriging variance
determined using KRIVAR, by Geostat Systems International Inc.
(1989), with relative variogram input. Kriging is based on three
drillholes per five-metre width of a mining unit, five-metre row
spacing and a four-by-four-by-four-block grid definition.
The random deviates thus generated are used as the estimates of
the grade of copper, zinc and gold in a mining unit, as would be
•
, For the purpose of this study, the coefficient of variation of a
parameter i s defi ned as the standard devi at ion of the di stri but ion of
values as a proportion of the most-likely value. To model uncertainty
in a parameter for which the true value is unknown and which is
characterized by an asymmetrical distribution of possible values, the
initial estimate is taken as the most-likely value and the lower and
upper coefficients of variation are specified relative to this value.
72
•
produced from blasthole sample data. These estimates of grade may be
used by the plaver to support decisions concerning the selection of
mininc units for extraction. On the basis of the grade estimates, the
user may decide to extrdct sorne or all of the mining units delimited by
the specified coordinates, or to leave the block in situ.
Stope boundari es can be modifi ed from those previ ously sel ected
Any material which is in a block under
prior to extraction.
consideration, and which is external to any others selected in the
current stope speci fi cat ion, has to be dri 11 ed for purpose of grade
estimatfon and blasting.
Reselection of previously drilled, but
unextracted, material from a separate stope specification results in
redrilling and the production of new estimates. This occurs even if the
selection is repeated in the same year. If more than one set of grade
estimates is produced for a given mining unit, it is the most recent set
whi ch i s used in any subsequent computations. The amount of materi al
which has been drilled is cumulated throughout the year.
A block of material which has been drilled may be extracted
without further modification of its boundaries, or may be left in place.
At the end of a year, the total amount of material drilled is compared
to the amount of material which was targeted for extraction during the
year. Any drilling in excess of that require~ for current production is
consiCÎered to be exploratory drill ing.
ln Qrder to ensure that the actual amount of material mined does
not exceed the limit of overcapacity, several assumptions are made with
regards to the levels of mine recovery and dilution1, and the tonnage
factor to be appl ied to mined material. In estimating the amount of
material which could be mined for any given block specification, it is
assumed that there is full recovery and that dilution is at a maximum.
The maximum rate of dilution is set at twenty percent which is double
the typical dilution rate for blasthole open stoping (Mackenzie, 1987).
, Unless otherwise specified,
external dilution, that is, material
boundaries of the selected in situ
along with the targeted material.
the hangingwall and footwall.
73
the term 'dilution' refers here to
lying adjacent to, but beyond, the
mining unit(s), and which is mined
The diluting material derives from
•
•
The tonnage factor for massive sulphides, 0.263 cubic metres per tonne,
is used in estimating the amount of material available from mining
because a block of maximum dimensions could lie entirely within the
boundaries of the deposit.
For any mining unit specification, the actual amount of material
mined during a particular year is a function of the average annual rates
of dilution and mine recovery; these rates are unknown to the user until
mi ni ng operat ions have been compl eted for the year. The uncerta inty
associated with these parameters is incorporated in the model by
simulating their actual values from normal probability distributions.
The distributions are characterized by most-likely values of fifteen
percent for di l ut i on and ei ghty-seven percent for mi ne recovery, and
coefficients of variation of 0.14 for dilution and 0.05 for mine
recovery. Simulated values are l imited on the upper side at twenty
percent for dilution and one hundred percent for mine recovery.
The amount of material which is extracted from the mine is also a
function of the composition of the selected mining units. A factor of
0.263 cubic metres per tonne is used to convert from volume to weight of
mineralized material. The andesites and rhyolites hosting the deposit
have a higher tonnage factor of 0.370 cubic metres per tonne, typical of
more silica-rich rocks. The amount of material to be mined is increased
by dil ut ion. Dependi ng upon where the stope wa11 sare l ocated, the
additional material associated with dilution may be mineralized or
barren, and therefore, does not necessarily reduce the mined grade. The
cumulative amount of material mined, updated after each st ope selection,
is the basis for calculating the remaining mine capacity.
The di fference between the assumed and actllal rates of mi ne
recovery and dilution may lead to a situation in which there appear to
be conflicting messages. If the underground mine is operating at a rate
which is close to the limit of overcapacity, it may appear, for example,
that only one additional nlining unit can be accommodated by the
remaining capacity. Once extraction of the unit has been completed and
the actual rates of mine recovery and dilution have been applied instead
of the assumed maximum rates, further extraction may be possible.
Mining activities for a given year have been completed if at least
on~ of the following conditions is met:
74
•
1) all levels have been mined out between the northern and southern
limits to mining as determined by the northern property boundary
and the shaft site, respectively. A level is deemed to be mined
out if neither primary nor secondary stoping can take place.
Primary stoping has been completed if the third sublevel of the
northernmost stope has a) advanced to the northern boundary, or b)
the maximum allowable stope length, and the distance from the
northern stope boundary north to the property boundary is
insufficient to accommodate a rib pillar and a new stope of
minimum length. Secondary stoping has been terminated if the
third sublevel of the secondary stope in the most northerly pillar
has a) advanced to the northern boundary of the pillar, or b) the
maximum allowable stope length.
2) there is insufficient mine capacity remaining for the extraction
of the smallest available mining unit.
3) the user decides to terminate mining activities.
Should a decision be taken to continue mining, it may be necessary
to reselect the level and sublevel. The specified parameters must meet
certain criteria for acceptability.
Mining can take place on the
selected level providing that all of .he following are true:
1) the level exists, that is, the level number lies between 1 and the
number of levels.
2) the level is not mined out, and at least one mining unit is
currently available for extraction.
3) the minimum mineable increment on the level is acceptable in terms
of the remaining mine capacity.
On an acceptable level, mining can take place on a selected
sublevel if two conditions are met:
•
1) the sublevel exists, that is, the sublevel number lies between one
and the number of sublevels on :he particular level. All levels
have three sublevels with the possible exception of Level 1.
2) extraction has nct been suspended on the selected sublevel of both
primary and secondary stopes.
Extraction cannot proceed on
75
•
Sublevel 1 of a primary stope if mining has advanced to the
northern property boundary, or if the stope has the maximum
allowable length and the distance from the northern stope boundary
north to the property boundary is insufficient to accommodate a
rib pillar and new stope of minimum leogth. Extraction cannot
proceed on Sublevel 1 of a secondary stope if mining has advanced
to the northern pillar boundary, or if the stope has the maximum
allowable length.
On the second and third sublevels of either a primary or a
secondary stope, extraction is suspended if the northern boundary
of the northernmost stope is in vertical continuity with the
corresponding stope boundary of the sublevel below. This arises
from the rule that mining must advance northwards and be more
advanced on a lower sublevel than on a higher one.
4.1.2.3 Open-Pit Operation
•
As shown in section 4.1.1.2, open-pit mlnlng is an appropriate
alternative to sublevel stoping as a means of extracting the ore
reserves. The order of removal of ore and waste i s set by the user
within certain constraints. These constraints are intended to increase
the level of realism in the simulation of open-pit operations. The
minimum mining width has been preset based on a consideration of normal
operating practice.
The mining units are cubic blocks with a length of ten metres.
The hei ght of each bench i s, therefore, ten metres, and ben ch wi dth i s
also a multiple of ten metres. A minimum mining width of twenty metres
applies to mining on a new level. This width is less th an that required
for double spotting (Crawford, 1979) and in very large mining operations
(Sonates, 1992), but is assumed to be adequate for an open-pit designed
to operate within the allowable range of capacities. It is also assumed
that a maximum pit slope angle of forty-five degrees will ensure
stability and safety in the open-pit.
Mining takes place in a pit which is approximately square or
rectangular in plan.
This pit shape, while uncommon in practice,
reduces the compl exi ty in the specifi cat i on of pit i ncrements by the
76
•
user, and simplifies the software development.
There are four
boundari es, each referri ng to a si de of the pi t. A boundary may be
straight over its entire length or divided into segments which parallel
the north-south or east-west axes. As shown in figure 16, each boundary
is defined by three coordinates which del imit the outermost section of
the pit along the boundary:
northern boundary
southern boundary
western boundary
eastern boundary
•
northern, western
southern, western
western, northern
eastern, northern
and
and
and
and
eastern coordinates
eastern coordinates
southern coordinates
southern coordinates
The northern boundary, for example, is considered to be straight
if its western coordinate is the same as that of the western boundary,
and its eastern coordinate is the same as that of- the eastern boundary.
Similar criteria must be met for other boundaries to be considered
straight. On the pit level outl ined in figure 16, the northern and
western boundaries are straight. A side of the pit may be segmented
into as many as three parallel sections, depending upon the selection of
pit increments.
The limits of the open-pit are extended in two ways. A block of
one or more mining units may be removed from a straight boundary, th us
extending the pit limit, or part thereuf, in a direction perpendicular
to the sel ected boundary. Thi s process i s therefore referred to as
perpendicular extension, and is illustrated in figure 17a with reference
to the eastern pit boundary.
At least one block of mining units may be removed from a boundary
which is not straight. Along the selected boundary, the oucer limit of
the pit, as defined by its coordinate, for example, the eastern
coordinate of the eastern boundary, remains unchanged after the pit
extension.
The block or blocks removed parallel the selected pit
boundary. This type of extension, termed parallel extension, is shown
in figure 17b for the eastern pit boundary.
To produce a perpendi cul ar extensi on, the coordi nates del imit ing
the block to be mined must be specified. If the extension takes place
along a section of the eastern boundary, as in figure 17a, the eastern
pit limit is extended by ten m<;tres, the length of a mining unit.
77
•
Northern boundary
--1"-----------.-
Western
boundary
Eastern
boundary
....----~- Es
Sg, Ws -
.1------'
1
1
1
SE
Southern boundary
LEGEND
AB: Boundary Coordinats
•
Figure 16: Boundaries of the Open-Pit and their Delimiting
Coordinates
78
•
a)
N
t
Exi sting pitlimits
••,.
1
Block to be
extracted
-
-..
b)
Directi on of extension
N
t
Existing pitlimits
t
1
rection
DI of
extension
i
•
Block to be extracted
Figure 17: a) Perpendicular Extension b) Parallel Extension
of the Open-Pit Along the Eastern Boundary
79
•
•
Following such a perpendicular extension, the boundary is no longer
straight and can be extended further through a parallel extension.
If a perpendicular extension affects the entire length of a
boundary, the pit l imit can be extended, in one specification, by
several rows of units, that is, for distances which are multiples of ten
The distance by which the pit limit can be extended is,
metres.
however, constrained by the maximum pit slope angle or, on the first
level, by the property boundaries.
If underground mine construction is being carried out during openpit operations, perpendicular pit extension on the first level is also
constrained by the location of the shaft. If the shaft site northing
lies between the outermost pit l imits on the northern and southern
boundaries of the pit, the shaft is assumed to be sited ta the east or
the west of the pit and, therefore, the eastern and western pit
boundaries cannot both be extended to their corresponding property
The alternative case is that in which the shaft is
boundaries.
originally sited to the north or south of the open-pit. If the eastern
and western pit boundaries are subsequently extended to the property
boundaries, the northern or southern pit limit can be extended towards,
but not as far as, the shaft.
To effect a parallel extension, the user specifies the coordinates
which will define the boundary after the pit increment. As shown in
figure 18, the block delimited must include all of the mining units
which have previ ously been extracted from the boundary bei ng extended.
Drilling is simulated for only those units remaining in situ.
Given the bench height of ten metres, the maintenance of a pit
slope angle of forty-five degrees or less requires that the minimum
hori zontal di stance between the correspondi ng boundari es on two
consecutive levels of the pit be ten metres. If the boundaries are not
straight and parallel extension is under consideration, it is the
position of the inner segment of the boundary on the upper level
relative to the position of the outer segment of the boundary on the
lower level which is relevant.
In a parallel extension southwards along the eastern boundary, for
example, the block being removed cannot extend further south than the
southern limit of the pit on the southern boundary. This ensures that
80
•
N
r - - - - Previously cxtracted
t
mining units
Existing pit limits
t
Direction
of
extension
Mining units to
be extracted
LEGEND
Block delimited for
parallel extension
Figure 18: Block Specification for Parallel Extension of
the Open-Pit Along the Eastern Boundary
•
81
•
the plan of the pit on each level is approximately square or
rectangular.
Validation of the coordinates bounding a block selected in the
open-pit is similar to that performed for blocks in the underground
mine. The maximum amount tif material which could become available from
mining the block is compared with the amount which can be mined given
the remaining capacity. It may be necessary to modify the boundaries of
the block so that mining of the incremental material is possible given
the remaining capacity.
Providing that the coordinates del imiting the block are
acceptable, grade estimates for the selected mining units are generated.
Estimates of the grade of copper, zinc and gold are produced through a
two-step procedure simil ar to that used to generate grades for mining
units in an underground mine:
1) the true grade of each element of economic interest in a mlnlng
unit is calculated as the mean grade of eight constituent cubic
blocks of five-metre length.
2) random deviates of the grades of the three elements are generated
from normal distributions, each characterized by a most-likely
value equal to the true grade, ~nd a· coefficient of variation of
0.78 for copper, 0.53 for zinc and 0.61 for gold. The coefficient
of variation is the square root of the relative kriging variance
determined using KRIVAR with relative variogram input. Kriging is
based on four drillholes per mining unit, an eight-metre spacing
between drillholes, and a four-by-four-by-four-block grid
defi nit ion.
•
The random deviates th us generated are used as the estimates of
the grade of copper, zinc and gold in a mining unit, as would be
produced from blasthole sample data.
On the basis of the grade
estimates for the selected mining units, the user may decide to extract
sorne or all of the mining units delimited by the specified coordinates,
or to leave the entire block of units in the ground.
Block boundaries can be modified prior to extraction, as is
permitted in the model of underground mining operations. Any material
wh ich i sin the bl ock under cons iderat ion, and wh ich 'i s external to any
82
•
other blocks selected in the current block specification, has to be
dri 11 ed for purpose of grade est imat i on and poss i bly al so product i on .
Reselection of previously drilled, but unextracted, material from a
previous block specification results in redrilling of the material and
the generation of new grade estimates.
sel ect ion i s repeated in the same year.
Redrilling occurs Even if the
If more than one set of grade
estimates is produced for a given mining unit, it is the most recent set
whi ch i s used in any subsequent computations.
The amount of materi al
which has been drilled is cumulated throughout the year, and the amount
of exploratory drilling determined as described in section 4.1.2.2.
The calculation of the amount of material mined in a given year is
based on the assumption of full recovery and no dilution.
In practice,
open-pi t recovery rates are high, and the amount of dil ut i on i slow in
relation to the amount of material being mined.
The assumption that
dilution and mining losses are insignificant is therefore considered to
be a close approximation to reality.
In estimating the amount of
materi al associ ated with a proposed pi t i ncrement, it i s assumed that
mineral ized materi al consti tutes the maximum possi bl e volume for the
proposed pit extension.
The appropriate tonnage factors -- 0.263 cubic
metres per tonne for mi nera1i zed materi al and 0.370 cubi c metres per
tonne for the host materi al -- are appl i ed to the respective calcul ated
volumes.
This ensures that the actual amount cf material mined in a
year does not exceed the limit of overcapacity production.
A drawback
of this assumption is that the estimate of the amount of material to be
mined is higher than the actual amount associated with any pit increment
in which the volume of mineral ized material is lower than the maximum
volume.
The assumption is unlikely to affect block selection unless the
mine is operating at a rate close to the limit of overcapacity.
Mining activities in the open-pit have been completed for a given
year if at least one of the following conditions is met:
1) all
the
pit
cannot be extended further than the four property boundaries.
On
a
levels
•
been mined out.
On the first
level,
lower level, a lack of accessible mining units at a
point
for
have
in time does not necessal'ily render the
level
particular
unavailable
future mining; subsequent removal of material from the
above may make extraction possible.
83
level
A lower level is mined out if
•
there is no materlal available for extraction from it or from any
of the levels above.
2) there is insufficient mine capacity remaining for the smallest
allowable pit increment from a technical standpoint.
3) the user decides to terminate mining activities.
a decision be ta ken to continue mining, it may be necessary
or desirable to select a pit level and boundary which differ from those
l ast speci fi ed. The sel ected parameters have to meet certai n criteri a
Mining can take place on the ~elected level
for acceptability.
providing that all of the following conditions are satisfied:
S~Quld
1) the l evel exi sts, that i s, mi ni ng operat i ons have al ready
commenced on the level, or mining is to begin on a new level. A
new level is considered to be acceptable if it is the first level
in ·the pit or if the level number is the next in sequence after
the number of the deepest level in the pit.
2) the level is not mined out and material is currently available for
removal. In other words, mining must be possible on at least one
of the four boundaries on the selected level.
3) the minimum tonnage to be mined on the level is acceptable in
terms of the remaining mine capacity.
On an acceptable level, a boundary can be selected for mining
operations if two conditions are met:
•
1) the boundary eXists, that is, the northern, southern, western or
eastern boundary is selected.
2) a parallel or perpendicular extension can take place along the
boundary. Any boundary is acceptable for the first cut on Level
1. On a level on which some extraction has taken place, at least
one unit must be available for mining on the specified boundary.
If mining is to take place on a new level below Level 1, the
acceptability of the chosen boundary is dependent upon the
configuration of the pit 011 the level above. It must allow access
on the selected level to at least two mining units 1ying adjacent
to each other such that, as a who1e, they paralle1 thl~ specified
boundary. The minimum number of mining units which must be
84
•
•
accessible is higher for a new level
constraint of a mi~lmum minlng width.
in order to meet the
4.1.2.4 Installed Capacities
The choice of an installed mlnlng capacity and an installed
milling capacity may be based on an analysis of preliminary information.
The results of simulated delineation diamond drilling, historical prices
and cost estimates are available to support decisions.
The range of techni ca11y acceptabl e i nsta11 ed annua1 capac it ies
for the underground mine and mill installations is from 75 000 tonnes to
675 000 tonnes. Assumi ng that extracti on of only mi nera1i zed materi al
takes place without any temporary mine closures or underutil ization of
capacity, the minimum and maximum mine life are five and forty-five
The range of technically acceptable installed
years, respectively.
annual capacities for the open-pit mine is from 227 000 tonnes to 11.34
mill ion tonnes; thi 5 i s the normal range of operat i ng capacit ies of
open-pit mines (O'Hara, 1987).
Given the simulated mineral deposit, underground mine production
at a rate of 300 000 tonnes could lead to depletion of the deposit in
about ten years. This is a reasonable length of operation, and should
be manageable in terms of the time requi'rements for game-playing. The
maximum project life is set at forty-five years, as the game would
become tedious were the mine·life longer.
The installed capacity of the underground mine and mill shoul d be
simi lar, based on an assumpt ion that no waste i 5 extracted from the
underground mine. The planned use of stockpiles may, however, influence
the choice of an appropriate mine-mill combination.
Production rates which are up te twenty percent in excess of the
installed capacity are considered to be attainable through the use of
overtime. It is also possible for the mine and mill to be operated
below full capacity. Hence, within the bounds of overcapacity, the
player is allowed to determine the level of capacity utilization for
each year of operation.
The player also has the option to shut down the plant on a
temporary basis, and to expand the product ive capacity of the mine
85
•
and/or mi11 during the operating stage of the project.
There is a
minimum feasible capacity by which the installed capacity can be
expanded.
For the underground mine and mill, the minimum annual
capacity by wh ich the i nsta11 at ion can be expanded i s 75 000 tonnes.
The minimum annual capacity by which an open-pit mine can be expanded is
227 000 tonnes. An expansion of the minimum magnitude would lead to a
doubling of capacity in the case of a mine or mill of minimw~ size.
The length of the preproduction period of the underground mine or
mi11 is dependent on the insta11ed capacity.
The function used to
determine the preproduction period is based on data in Mackenzie (1987),
and is as follows:
pp
=
O. 84Qo.22
where:
pp is the preproduction period (rounded to the nearest whole
number of years)
Q is the installed annual capacity of the underground mine or
mi 11 (/000 tonnes)
A plant comprising an underground mine and mill with an installed
annual capacity of 300 000 tonnes requires three years of preproduction
work. Th.:! longest preproduction period which can be expected for an
underground mine or mill of maximum allowable installed capacity is four
years. The preproduction period for ..n open-pit mine designed within
the range of technically-feasible installed capacities is two years. If
there is a difference between the preproduction period determined on the
basis of the mine design and that calculated for the mill, the
preproduction period is taken as the longer of the two oeriods.
The time needed to complete a capacity expansion program for an
underground mine or the mill is a function of the difference between the
preproduction period required for the mine or mill of the former
installed capacity and that required for a new installation of the
expanded capacity:
•
EP
=
1.15 (0.84QxO.22 - 0.84Qo.22)
86
•
where:
EP is the period required for expansion (rounded to the nearest
positive whole number of years)
Q is the former installed annual capacity of the underground
mi ne or the mill (' 000 tonnes)
Qx
is the expanded annual capacity of the underground mine or
the mi 11 (' 000 tonnes)
The difference in the l engths of the preproduct i on peri od
associated with the two capacities is multipl ied by a factor which is
Th i s refl ects the i neffi ci enc ies ari sing in the
greater than one.
selection and installation of additional equipment as a separate project
following the initial capacity installation. Expansion of the installed
capacity of an open-pit mine l'equires one year.
The commencement of preproduction work can be delayed for a period
of up to fifteen years, thus providing the user with some flexibility in
timing the start-up of operations. As is discussed further in section
4.1.2.6, metal prices display cyclical behaviour, a four-year price
cycle being superimposed upon a sixteen-year cycle. Provided that the
player is able to match project start-up correctly with cycle position,
the mining firm may be able to benefit from a delay in the start of
For example, if the start of production is timed to
production.
coincide with a period of price recovery, the firm has the potential to
In
increase early cash inflows and thus improve project economics.
making a decision with respect to project postponement, the player
should bear in mind that inflation during a period of delay will raise
the level of capital and operating costs (sections 4.1.2.5 and 4.1.2.7).
4.1.'-.5 Capital Costs
•
ln the model on which The Mine Manager is based, the deposit
cannot be varied, and therefore, it is the intermediate-run capital
costs which are relevant. The capital outlay required °to set up a mine
and mill is assumed to have a fixed cost component and a variable cost
component related to the level of installed capacity. The general form
of the functions which relate capital costs to the installed capacity of
87
•
the mine or mill is:
cc = a
+ bQc
where:
CC is the capital cost of the mine or mill ($'000)
Q is the installed annual capacity ('000 tonnes)
a, band c are constants
The values of the constants in the hypothetical capital co st
functions used in the model are given in table 4. These values give
ri se to i ntermedi ate-run capital cost curves of the form di scussed in
section 4.1.1.4, with costs which are close to 1990 levels.
Capital costs may also arise in connection with functions other
than mining and milling. It is assumed that other cèpital 'costs, such
as those associated with the provision of access and power, are included
in the capital costs of the mine and mill. This simpl ifying assumption
eliminates the need to generate a separate function relating other
capital costs to the level of the installed capacities of the mine and
mill. The total capital cost is:
CCtotal
•
=
CC rnin• + CCrni II
The capital cest of an underground mine developed while the openpit is in operation is assumed to be seventy percent of the value
obtained using the capital cost function. This assumption is based on
the fact that sorne of the costs of providing infrastructure and general
plant services would already have been incurred at the time of
development of the open-pit mine.
The capital cost of an expansion program is the difference between
the capi tal cost of the mi ne or mill of the former capacity and the
capital cost associated with a new installation of the expanded
capacity, multiplied by an adjusting factor. The factor has a value of
1.15, and rEsults' in an upward adjustment to the difference in capital
costs. This reflects the fact that additional capacity is l ikely to
cost more if it is put in place after completion of the plant.
88
•
Table 4: Constants in the Capital Co st
Functions for the Mine and Mill
Capital
Cost
Function
Constant
Value
Underground mine
a
b
c
3226.3109
233.31596
0.7662613
Open-pit mine
a
b
c
475.40508
132.44452
0.6088922
Mill
a
b
c
5767.6280
229.91615
0.7093054
Calculation of the capital cost of shaft sinking is based on the
following relationship' and an assumption of competent host rock
conditions:
SOCC
=
307252SAo. 25 + 1259. 223S01.'SAo. 25
where:
SOCC is the capital cost of the shaft ($)
SA is the cross-sectional area of the shaft (square metres)
SO is the shaft depth (metres)
The cross-sectional area of the shaft, which is appropriate given
the assumed host rock conditions, is calculated as follows:
SA
•
=
1.682Qo.4
, The capital cast relationships presented here are based on those
generated by Mackenzie (1987) and Q'Hara (1987).
89
•
where:
Q is the installed
an~ual
capacity ('000 tonnes)
The cost of shaft deepening is the difference in the capital costs
of shaft sinking to the original depth and to the proposed depth,
mult i pl ied by a factor of 1.15. The use of thi 5 adjustment factor
results in a higher unit cost for an increase in shaft depth after
completion of the initial shaft sinking. A shaft deepening project can
be completed in one year.
The amount of working capital which must be available at the end
of a year is the estimated working capital requirement of the following
year. Working capital is typically calculated as a proportiJn of the
operating costs ta be incurred during a yeal':
wc
=
0.25 (Expected annual operating costs)
where:
WC is the working capital investment ($)
The annual operat ing costs referred to are those expected to be
incurred for operation at the installed capacity, or for maintaining a
mine or mnl which is temporarily closed. The values of the installrd
capacity and operating co st variables may change from year to year and,
therefore, the working capital requirements can al 50 be expected to
vary. The working capital recovered each year is the amount which was
investe'.! at the end of the previ ous year. The net effect on cash fl ow
in any given year is the difference between the amount invested and the
amount recovered; this is referred to as the net working capital.
The annual sustaining capital required for the mine is a function
of the installed mine capacity:
open-pit mine
underground mine
ASC mine
ASC.
mme
=
=
0.2638Q + 132.124
223. 39Qo.6791
where:
•
ASCmine is the annual sustainin9 capital for the mine ($)
Q is the installed annual mine capacity ('000 tonnes)
90
•
The annual sustaining capital required for the mill 15 one percent
of direct milling plant costs. Although the direct milling plant costs
are not itemized for the purpose of determin1ng the capital cost of the
mill in the Game, it is assumed that the direct milling plant costs are
approximately one third of the total mill capital costs. Recall ing the
above assumption that other capital costs are included in the value of
CC mill , the direct milling plant costs are a lower proportion of the
total mill capital costs. The annual sustaining capital for the mill is
calculated as:
ASC milL
=
0.01 (1/4.5) CC mill
where:
ASC~ll
•
is the annual sustaining capital for the mill ($'0001
The sustaining capital costs are adjusted if the operation is expanded.
If an installation has been shut down, no sustaining capital is required
for the period of closure. In anticipation of permanent closure, no
expenditure of sustaining capital takes place in the final y~ar of
operation of the mine or mill.
There are two sources of uncertainty which may affect the
est imat i on of capi tal costs. One source rel ates to the suitabi 1ity of
the installed mining and processing systems, and the infrastructure.
Uncertainty also arises from possible variations in the costs of
It is assumed that the uncertainty in the total
individual items.
capital expenditure is of the latter type.
The capital costs, excluding working capital, are simulated on the
basis of assumed probability distributions.
Each distribution 15
characterized by a most-likely value generated using the appropriate
capital cost function.
The lower and upper coefficients of variation
used in the simulation of the capital expenditures for plant
The
construction and expansion are 0.04 and 0.07, respectively.
simulation of annual sustaining capital required for the mine and mil 1
is based on lower and upper coefficients of variation of 0.06 and 0.09,
respect i vely. The capi tal costs associ ated with the i nsta11 at ion or
expansion of mining and mill ing capacit.v are spread evenly, in constant
dollar terms, over the construction period .
91
•
The value generated by a capital cost funct ion i sin constant
dollars of the last year for which historical prices are given. The end
of the historical period coincides with the beginning of the
preproduction period (Time Zero) only if there is no delay in the start
of preproduct i on act i vi t i es.
Capita1 costs are fully respons i ve to
inflation.
The annual cost inflation rate is simulated from a
distribution characterized by a most-likely value equal to 4.70 percent,
and a coefficient of variation of 0.10.
The most-likely rate of cost
inflation is taken as the mean annual percentage change in the Marshall
and Swift mine/mill equipment co st indices between 1973 and 1987. Rates
of change over ten percent are eliminated from the calculation so the
resulting mean does not fully reflect the rapid inflation characterizing
this period. The indices from which the rates of change are determined
are listed in appendix 2.
lnfl at ion al so i nfl uences the requi rements for worki ng capital.
The amount of working capital which must be available at the end of a
year i s based on the expectat ion that i nfl at ion wi 11 continue in the
foll owing year.
For the purpose of cal cul at ing the worki ng capital
requirements, it is assumed that cost inflation will occur at the mostli kely rate.
Therefore, the worki ng capital investment refl ects the
actual annual cost inflation rates up to the current year, and a rate of
4.70 percent for the following year.
4.1.2.6 Metal Priee
A prieing model is required to generate eopper, zinc and gold
prices for the maximum possible duration of the Game in terms of periods
of pl ay.
Each average annual price i s assumed to be the pri ce at whi ch
the suppl y and demand for the particular met al are balanced throughout
the year.
The series of simulated average annual metal
period of eighty years, including fifteen years for
prices are provided, fifteen years by which the start
work may be del ayed, four years for the completi on
•
prices covers a
which historical
of preproduction
of preproduct ion
aetivities, and a forty-five year period during which the plant may
operate.
The pri ces of copper, zinc and go l d have been generated in
92
•
•
eurrent U.S. dollars .
No attempt has been made to develop a prlelng model for eopper.
zinc and gold whieh replieates the aetual sequence of spot priees on the
LME; however, a study of the historieal priee behaviour between 1973 and
1987 serves as a guide to modelling priees i~ terms of average priee
levels and the degree of priee variability. Priees prior to this period
were not ineluded in the study beea~se 1973 was the first complete year
in whieh world eurreney values were on a floating basis, and the priee
of gold determined by the free market. The priees of eopper and zinc
were reviewed for the same period.
The historieal LME eurrent dollar spot priees for eopper, zinc and
gold are listed in table 5, and displayed graphieally in figure 19.
Average priees are quoted for Good Ordinary Brand zinc from 1973 to
1984.
Trading of zinc began on a distinct Highgrade eontraet in
September, 1984, and the priees from 1985 onwards thus refer to
Highgrade zinc. The eopper priees also span trading on several types of
eontraets.
During the 1970s trading took place on the wire bar
eontraet. The eopper cathode high grade eontraet was introdueed in late
1981, and Grade A eopper eontracts started in April 1986. Gold priee
quotations refer to Engelhard Industries' fabrieated gold.
The historieal behaviour of metal priees ean be deseribed in terms
of a trend, eyel ieal ity and a random eomponent. These features have
been ineorporated into the prieing model in order to depiet the type of
behaviour exhibited by priees on the free market.
It assumed that priee trends in the reeent past will continue into
the future. It is possible, therefore, to prediet the most-likely value
of a future priee based on the weighted average of preeeding historieal
priees.
Given that more reeent occurrences are expeeted to have a
stronger influence on eurrent priees, the most reeent priee is the most
heavily weighted. This method is similar to the smoothing method of
popular use in foreeasting.
The prieing model generates the most-likely value of the priee in
a given year as the weighted average of the priees in the three previous
years:
93
•
Table 5. Average Annual LME Prices for Copper, Zinc and Gold
(1973 -1987)
Meta1 Pri ces 1
Year
Copper (US$/lb)
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
0.81
0.93
0.56
0.64
0.59
0.62
0.90
0.99
0.79
0.67
0.72
0.63
0.65
0.64
0.80
Zinc (US$/lb)
0.38
0.56
0.34
0.32
0.27
0.27
0.34
0.34
0.39
0.34
0.35
0.40
0.36
0.34
0.26
Gold (US$/oz)
97.96
159.74
161.49
124.83
147.71
193.65
307.36
612.56
459.64
375.91
424.00
360.66
317 .66
368.24
447.95
, Current dollars
(Sources: Metal Statistics, 1989;
Non-Ferrous Metal Data, 1975,
1980, 1984)
•
94
•
a)
'ê
c:
"
.e-
0.8
Coppe<
0
<F>
en
22l
'C
a.
0.6
Zinc
0.4
02
o.l.,--...--............1973
1974
1975
1976
......1977
.....__.-_._-.,........,-......1978
1979
1980
1981
1982
1983
......1984
............-,..,J
1985
1986
1987
Year
b)
700
600
Q)
"c:
500
<F>
.e"
400
<Il
300
en
2.9
~
a.
200
100
0.1.0--_-..._.......- ....- ..........,-_._-......- .............- ....- .....__.--'
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
Year
•
Figure 19: Average Annual LME Priees fo,' a) Copper and Zinc, and
b) Gold (1973 - 1987)
95
1987
•
where:
MLV(P T) is the most-likely price in year T
PT-3 is the price in year T-3
PT.2 is the price in year T-2
PT"
is the price in year T-l
The coefficients of 0.65, 0.25 and 0.1 weight the historical
pri ces and refl ect the assumed rel at i ve i nfl uence of recent events on
the current price. The application of an unequal set of weights to past
data i s si mi 1ar to exponent i al smoothi ng methods used in forecast i ng
(Makridakis and Wheelwright, 1989).
The prices used to generate the
first weighted average in a simulated price series are the average
annual LME prices in 1973, 1974 and 1975.
The periodicity exhibited by metal prices has been attributed to
the existence of economic cycles (Grandison, 1976).
Of the various
cycles which have been recognized, the shortest is the Kitchin cycle.
It has a 1ength, from recess ion to recess i on, of 42 +/ - 2 months, or
close to four years. The Kitchin cycle, commonly known as the business
cycle, is based on changes in the Gross National Product and is
reflected in the stock markets, bank clearings and interest rates.
Forecasts of the peaks and troughs of this cycle have been very useful
in business planning. The Wardwell cycle is particular to the mining
industry and has a length of sixteen years.
Other cycles of varying
length have been suggested, but it is assumed that they do not
significantly affect the prices of mineral commodities.
Tiit! seri es of simul ated pri ces refl ects a short economi c cycl e
(four years) superimposed on a cycle of greater length (sixteen years).
The indices and factors representing the various positions in the two
cycles are given in table 6. The compounded effect of the cycles is to
alter prices by up to 32.25 percent of their most-likely values. The
difference between the most-likely price and the value which results
from its multipl ication by the cycl iog factors is referred to as the
cycling effect.
•
16.
The position in the long cycle is indicated by an index of 1 to
The index corresponding to the first year of the price series is
96
•
Table 6. Indices and Factors of the Priee Cycles
4-Year Cycle
16-Year Cycle
Index
Factor
1
2
3
4
0.85
1.00
1.15
1.00
Index
Factor
1
0.85
0.89
0.93
0.96
1.00
1.04
1.08
1.11
1.15
1.11
1.08
1.04
1.00
0.96
0.93
0.89
2
3
4
5
6
7
8
9
10
11
12
13
14
1·5
16
•
chosen at random.
The two cycles are assumed to be dependent;
therefore, the position in the short cycle (indicated by an index of 1
to 4) in the first year of the series is selected such that each peak in
the long cycle is coincident with a peak in the short cycle. Given the
randomly-selected starting position in the longer cycle, the starting
position in the short cycle is determined as indicated in table 7. The
cycles are repeated throughout the project life.
The random component of priees is incorporated by simulating
values from an assumed triangular probability distribution having the
following parameters: a most-likely value which is the weighted average
priee for the current year, and lower and upper relative limits
described below. The average annual metal priee is the sum of the
simulated value and the cycle effect. Therefore, the random variability
of priees is not directly influenced by the priee cycles.
A relative limit of a triangular probability distribution is
produced by multiplying the most-likely priee by the appropriate factor
from table 8. The levels of uncertainty associated with the priees of
97
•
Table 7. Formulae for Determining the Starting Position
in the 4-Year Price Cycle Given the Starting Position
in the 16-Year Price Cycle
Starting Position in
the 4-Year Cycle
Starting Position in
the 16-Year Cycle (J)
1
2 - 5
J
J
J
J
6 - 9
la - 13
14 - 16
4
-
1
5
9
13
Table 8. Factors Used to Determine the Relative Limits
of the Triangular Probability Distribution of Prices
Relative Limit
Price Range
Lower
Upper
Copper (US$/lb)
<0.62
0.62 - 1.00
>1.00
0.80
0.80
0.30
2.00
1.20
1.20
Zinc (US$/lb)
<0.32
0.32 - 0.60
>0.60
0.75
0.75
0.30
2.00
1.25
1.25
Gold (US$/oz)
<300
300 - 615
>615
0.50
0.50
0.30
2.00
1.50
1.50
Metal
•
98
•
•
eopper and zinc are approximately equal. The factors refleet a greater
uneertainty in the priee of gold, partieularly within its intermediate
priee range.
For eaeh metal, the factor to be used varies aeeording to the
range within whieh the most-likely vah.e falls.
If the most-likely
priee of eopper is in the normal priee rar,ge, that is, between SO.62 and
SI. 00 per pound, the factors used to determi ne the lower and upper
limits of the triangular probability distribution are 0.8 and 1.2,
respeetively. Therefore, if the most-l ikely priee is SO.96 per pound,
the random eomponent of priee variability is ineorporated by simulating
a value from a triangular distribution eharaeterized by a relative lower
limit of SO.77 per pound, and a relative upper limit of SI.15 per pound.
A priee SO.62 per pound of eopper has been seleeted as the lower
bound of the range of \ norma l' pri ces beeause the average annua l LME
priee has been above this level for most of the study period. The upper
bound of the normal priee range, SI.00 per pound, is close to the
highest reeorded average annual spot priee for eopper between 1973 and
1987. The normal priee ranges for zinc and gold have been selected on
the same basis.
If the most-likely priee of a metal is below the normal range, the
factor used to determine the relative upper l imit of the probabil ity
distribution inereases.
In the case of eopper, the factor to be used
wh en the most-likely priee is below SO.62 per pound is 2.00.
This
results in a relative upper limit that is higrer than it would normally
be, and there is an inerease in the probability that the simulated value
is higher than the most-likely priee.
An adjustment is also made if the most-likely priee is above the
normal range.
The factor used to determine the lower l imit of the
probabil ity di stri buti on deereases, eausi ng the l imit to be lower th an
i t woul d normally be. The result i s an i nereased probabil ity that the
simulated value is lower than the most-likely priee. If the most-likely
eopper pri ce i s above $1. 00, a factor of 0.3 i s used to determi ne the
value of the lower limit. The variation in the values of the factors
has the tendeney to central ize the simulated priees and reduees the
frequeney of extremely high or low priees.
The average level of priees in a series has been determined using
99
•
3000 independently simulated series per metal. The simulations were
repeated for seri es of fi fteen years and ei ghty years. The average
abso1ute pri ee ehange from year to year was al so eomputed for eaeh
seri es. The average pri ee 1evel s and average pri ee ehanges for the
simulated priee series appear in tables 9 and 10, respeetively, along
with those for the historieal priees in the study period.
The average priee levels and average priee ehanges in the fifteenyear series of simulated priees are elose to the values obtained for the
fifteen-year series of historieal priees. The values are almost doubled
for the eighty-year series of simulated priees. During a longer period
of simulation, priee eyeling and random eomponents may interplay in sueh
a way that the resulting priees are signifieantly higher than their
historieal levels.
Table 9. Average Priee Level of Historieal Metal Priees and per
Series of Simulated Metal Priees
Metal
Copper (US$/lb)
Zine (US$/lb)
Gold (US$/oz)
Historical
Priees
(1973 - 1987)
Simulated Priees
15-Year Series
0.80
0.47
418.54
0.73
0.35
303.96
80-Year Series
1.44·
0.89
711. 57
Table 10. Average Priee Change of Historieal Metal Priees and per
Series of Simulated Metal Priees
Metal
COP!ler (US$/lb)
Zine (US$/lb)
Gold (US$/oz)
•
Historieal
Simulated Priees
Priees
(1973 - 1987) 15-Year Series 80-Year Series
0.10
0.06
70.41
0.12
0.06
79.24
100
0.18
0.12
122.80
•
The average rel at ive vari abil ity measures the average abso1ute
magni tude of pri ce changes i n ~ pri ce seri es as a proport i on of the
average 1eve1 of priees in the series. The average relative variabi1ity
has been determined for 3000 simu1ated priee series of fifteen years and
eighty years (table 11). The variabil ity of historiea1 LME priees for
eopper, zinc and gold during the fifteen-year study period has a1so been
determined for comparative purposes.
The values in table Il revea1 that the average relative
vari abil ity of simu1 ated pri ces i s of the same order of magni tude as
that of the aetua1 priees. The variability of simulated gold priees is,
however, somewhat lower than that of the aetual priees oeeurring between
1973 and 1987. Although the average priee leve1s are higher for the
ei ghty-year seri es of pri ces, the average rel ati ve vari abi lit ies are
similar to those for the fifteen-year priee series due to the higher
average priee changes.
Priee series whieh eontain extremely high or low priees are not
eonsidered acceptable for use in the Game. Priee series are regenerated
until all average annual priees are within a reasonab1e range. A priee
series is rejeeted if it eontains more than one priee outside of the
following ranges:
- SO.30 to S10.00 per pound of eopper;
- SO.10 to S6.00 per pound of zinc;
- S150.00 to S6150.00 per ounce of gold.
Table Il. Average Relative Variabi1ity of Historieal Metal
Priees and per Series of Simulated Metal Priees
Metal
Copper
Zinc
Gold
•
Hi stori cal
Simulated Priees
Priees
(1973 - 1987) 15-Year Series 80-Year Series
0.1639
0.1734
0.2607
0.1239
0.1241
0.1531
101
0.1255
0.1281
0.1594
•
The minimum priees were seleeted on the basis of a review of the
historieal metal priees. The minimum priees of eopper and zine are
lower than the average annual priees sinee at least 1973. The priee of
gold fell below $150.00 per ounee only twiee during the study period, in
1973 and 1976. It is reasonable to expeet that priees will remain above
these levels. The maximum priee for eaeh metal is aroitrarily seleeted
to be ten times the upper limit of the normal priee range.
Figures 20, 21 and 22 show eighty-year simulated priee series for
eopper, zine and gold produeed using the prieing model. The long-run
trends are vari abl e and resuli: from the parti eul ar sequenees of most1i kely pri ees, eyel i ng faetors and random eomponents whi eh were
generated.
The simulated priee series for eopper is eharaeterized by low
to average priees, by historieal standards, for the first forty-five
years after whieh the long-term trend is toward higher priees, peaking
at $5.38 per pound of eopper in the fi na1 year of the seri es. Zine
priees undulate between highs of just over $0.60 per pound and lows of
about $0.23 per pound; there isas1ow ri se in the genera1 1eve1 of
priees. The simulated gold priees are elose to the average historieal
level, exeept for a major upswing in priees between years 15 and 20, and
in the 1ast few years of the seri es. The pri ee of go1d reaehes over
$700 per ounee on both oeeasions. The long-term trend in priees is one
of stabil ity.
The priees seri es i neorporate four- and si xteen-year
Any wide variations in
eyeles and show fairly well-defined peaks.
priees ean be attributed to extreme values of the random eomponent.
A new series of priees is generated for eaeh run of the Game. The
positions of the peaks and troughs of the priee eyeles ean be expeeted
to ehange from one run to the next.
4.1.2.7 Operating Costs
•
For the purpose of developing operating eost funetions, the mining
firm is viewed as operating in the intermediate- to short-run. The
deposit is fixed, but the firm ean ehoose any feasible installed
eapaeity for the mine and mill, and operate the plant within a range of
102
•
~
1:!
lB
III
10
...on
<Il
Q)
fa
u
'C:
Cl.
...'"
~
2i.
a.
~
0
~
:i
...
'"
l:l
!ll
~
N
~
~
'"
on
'"
•
...
'"
'"
(punod/$snl aOPd
103
0
ni
Q)
>-
CJ
~
:>
E
èii
ë(\J
CIl
~
:>
.2'
U-
•
•
2
1
1
1.6
'ô
c
:>
0
Q.
1.2
fi>
....0
...
en
24>
0
.::
a.
0.8
0.4
1
0'.
il
'l
'l'
5
9
13
1"1
17
21
j
1
25
29
1"1
33
37
1
1
41
45
1"1
49
53
Year
Figure 21: Simulated Zinc Priees
l'
57
1"'1'
61
65
111
69
73
n
•
•
1400
1200
éD
0
1000
en
IF>
800
l'l
600
-
"5.
....o
U1
2-
.:::
Q..
400
200
0
5
9
13
17
21
25
29
33
37
41
45
49
53
Year
Figure 22: Simulated Gold Priees
57
61
65
69
73
77
•
rates dependent upon the chosen installations.
The i ntermedi ate-run average operat i ng cost curve i s defi ned for
modelling purposes as the locus of short-run average operating cost
minima.
It differs from the theoretical intermediate-run cost curve
which is the envelope of -a11 short-run curves (Thompson, 1989). The
rel ati onshi p between the i ntermedi ate- and short-run average operat i n9
cost curves for the mi ne and for the mill are shown in figure 23. The
intermediate-run average 'cost curve for the mine and the short-run
average cost curves for the mine and mi11 are generated using functions
of the general form:
De
=
aQ2 - bQ + c + d / Q
where:
De is the average operating cost
intermediate-run average operating
underground or open-pit mine, or
ooerating cost (SROe) associated with
(S/tonne),
i.e.
the
cost (IROe) of the
the short-run average
the mine or mill
Q is the annual production rate ('000 tonnes)
a, b, c and d are constants
The i ntermedi ate-run average operat i ng cost cUl've for the mi 11 i s
generated using a function of the form:
IRoe = a + bQ"C
where:
IRoe is the intermediate-run average operating co st ($/tonne)
Q is the an nual production rate ('000 tonnes)
a, b, and c are constants
•
The cost functions which have been developed yield values which
are close to 1990 operating cost levels (Scales, 1991), but are purely
Each mine or mill which could be installed for the
hypothetical.
exploitation of the deposit has a different minimum average operating
cost for full capacity operations; a series of these costs defines the
i ntermedi ate-run average operati ng cost curve. A di fferent short-run
106
•
a)
~
~
-
~
Ul
o
Q
.="§
Cl
Ql
Cl.
o
Annual Production RaIe (1)
b)
IROC
Annual Production RaIe (1)
•
Figure 23: Intermediate-Run Unit Operating Cast Curve as
the Locus of Short-Run Unit Operating Cast
Minima for the a) Mine b) Mill
107
•
average operating cost curve is associated with each installation.
The values generated using the IROC and SROC functions for the
underground mine and the SROC function for the mill are assumed to reach
their minima at an annual production rate of 300 000 tonnes. The minima
generated us i ng the IROC and SROC funct i ons for the open-pi t mi ne are
assumed to occur when the annual production rate is 3.3 million tonnes.
The values of the constants in the IROC and SROC functions for the
underground and open-pit mines and the mill are given in table 12. The
IROC function for the mill does not yield a minimum value, but rather a
series of decreasing values as the installed annual capacity increases.
The constants in the other intermedi ate- and short-run cost funct ions
are such that the cost premiums in table 13 are observed for production
rates above and below the cost-minimizing rate.
An underground mi ne/mi 11 pl ant operat i ng at a rate equal to the
i nstall ed capacity of 300 000 tonnes i s expected to i ncur operat i n9
costs of $20.15' per tonne mined and $18.00 per tonne processed through
the mi 11 :
1ROC mine = SROC mine = 20 .15
IROCmill = SROC mill = 18.00
If the plant operates at eighty percent of its installed capacity, the
short-run operating costs would rise to $21.56 per tonne mined and
$19.26 per tonne milled.
Assuming that the form of the short-run average operating cost
curve is constant regardl ess of its posi t i on on the i ntermedi ate-run
cost curve, the SROC function can be used to determine the premium which
must be added to the intermediate-run operating cost for any size of
installation.
The minimum short-run operating cost is achieved by
operating at a rate which is equal to the installed capacity of the mine
or the mill. The actual production rate is expressed as a proportion of
this short-run cost-minimizing rate. Since the SROC function is valid
•
, Unless otherwise indicated, monetary values are in Canadian
dollars.
lOS
•
Table 12: Constants in the Intermediate-Run and Short-Run
Average Operating Cost Functions for the Mine and Mill
Operating Cost Function
Installation
Constant
Underground mine
a
b
c
d
Open-pit mine
a
b
c
d
Mill
a
b
c
d
IROC
SROC'
2.1279619 x 10'4 2.8693481 X 10'4
0.1165666
0.1670942
32.634990
39.934133
1000.0000
906.00000
1.2453014 x 10'7 1.6710645 X 10- 7
7.5761974 X 10'4 1.0392662 X 10- 3
2.3318907
2.7997892
700.00000
693.00000
2.0002226
164.48033
0.4085363
2.5624317 x 10'4
0.1447459
35.661884
810.00000
, For an installed annual capacity of 300 000 tonnes
for the underground mine and mill, and 3.3 million
tonnes for the open-pit mine
•
109
•
Table 13: Operating Cost Premiums
Production Rate as
Proportion of Operating
Cost-Minimizing Rate
Operating Cost as Proportion
of Minimum Cost
Intermediate-Run
1. 10
1.05
1.02
1.00
1.02
1.05
0.7
0.8
0.9
1.0
1.1
1.2
Short-Run
1.12
1.07
1.03
1.00
1.03
1.07
only for an installed annual capacity of 300 000 tonnes, the proportion
obtained above is multiplied by 300 000 to arrive at an adjusted
production rate. The premium is the difference in the values derived
from the SROC funct ion wi th Q equal to 300, and wi th Q based on the
adjusted production rate.
For example, if the installed annual capacity of the underground
mine is 250 000 tonnes, the intermediate-run average operating cost is
$21.62 per tonne mined. If the mine produces 275 000 tonnes in a given
year, the adj usted product ion rate to be used in the SROC funct ion i s
calculated as follows:
Q = (275/250) 300 000
= 330 000
The short-run operating cost function yields a value of 20.44 when
Q is based on this adjusted production rate. The addition of a premium
of $0.29 (SROCCQ:330l - SROCCQ:300l) to the intermediate-run operating cost
results in a short-run operating cost of $21.91 per tonne mined.
The underground operating cost functi ons are val id when hoi st i ng
takes place from a depth of 170 metres. Given that unit hoisting costs
increase by 0.33 cents per metre, the unit operating costs incraase with
the shaft depth as follows:
•
oc •
value from functions + [0.0033 (shaft depth - 170)]
110
•
The open-pit cost functions are valid for mining operations on the
first level. Unit haulage costs increase by two cents per bench, and
the weighted average increase in unit operating costs' with depth is
based on the proportion (p) of material mined from each level:
Increase in OC
= ~
{p [0.02 (level number - 1)])
A cost of $1 per tonne of drilling is the basis for determining
the cost of exploratory drilling. Assuming that the unit drilling cost
of $1 applies to mineralized material, the drilling cost per cubic metre
i s the inverse of the tonnage factor of 0.263 cubi c metres per tonne.
The cost of drilling is rounded to $4 per cubic metre.
Drifting costs are $72 per cubic metre based on the following
parameters and an assumption that labour cost is one third of the total
cost of drifting:
Rate of advance in drift = la cubic metres/personshift
Shifts per day = 2
Persons per shift = 2
Advance per day = la x 2 x 2
= 40 cubic metres
Salary = $30/hour or $240/personshift
Total cost of drifting = 240 x 2 x 2 x 3
= $2880/day
Drifting cost per cubic metre = 2880 / 40
= $72
•
As drifting and exploratory drill ing are costed on the basis of
volume, the composition of the material through which drifting or
drilling takes place is irre1evant to the ca1cu1ation of their
respective costs.
The ma intenance cost for the mi ne or mil l i s defi ned for the
purpose of the Game as the cost of care and upkeep of the installation
on a stand-by basis.
These costs are incurred in the event of a
temporary cl osure. The annual mai ntenance costs are $100 000 for the
underground mine and $70 000 each for the open-pit mine and the mill .
111
•
•
If drifting and/or exploratory drill ing ar~ carried out without any
extraction of material, the costs of these activities are added to the
maintenance costs to producE Ule total annual mine 'operating' cost.
The cost of permanent closure is included with the operating costs
in the final year of the project.
At this time, the dismantling,
reclamation and severance costs associated with permanent closure of the
plant are assumed to exceed the proceeds from the sale of assets by the
amount of two million dollars.
The costs of drifting, drilling and plant closure, and the values
generated using the operating cost functions are the most-likely costs.
The actual operating costs incurred by the mining firm are influenced by
the economic cycles described in section 4.1.2.6 on metal prices. The
generalized description of the interplay between prices and unit
operating costs in the private economy (Moore, 1980), indicates,
however, that a lag of a few years can be expected between the peaks in
price cycles and those in cost cycles.
In the model on which the Game is based, the cycle effect on
operating costs is determined by multiplying the most-likely operating
costs by the same cycling factors affecting metal prices, but with a lag
of two years. That is, cost cycles lag two years behind price cycles.
In practice, this lag is observed because of the timing of changes in
the levels of productivity and labour costs as prices cycle.
At the bottom of a price cycle, productivity increases rapidly,
only to slow once prices start to rise. Concurrent with this is an
increase in labour costs from the moderate levels maintained during the
initial phase of the upswing in prices. Other operating costs exhibit a
similar pattern of behaviour so that at the start of a price expansion,
costs rise less rapidly than prices whereas at the close, the situation
is reversed.
A random component is incorporated in the generatiJn of costs by
simulating an operating cost from a probability distribution
characterized by a most-likely cost derived from the cost functions.
The lower and upper coefficients of variation are, respectively, 0.06
and 0.08 for mine operating costs, including the costs of temporary
closure, 0.06 and 0.09 for the cost of permanent closure, and 0.05 and
0.07 for mill operating costs. The operating cost which is reported is
112
•
the result of addition of the cycle effect to the simulated value.
The operating cost functions yield values which are in dollars of
the l ast year of the hi stori cal peri od.
Operat i ng costs are fully
responsive ta inflation. The annual inflation rate applied to operating
The rate is
costs is the same as that applied to capital costs.
simulated from a distribution characterized by a most-likely value equal
to 4.70 percent, and a coefficient of variaticn of 0.10.
4.1.2.8 Estimated Value of an Extracted Hining Unit
The material mined as a single mining unit is assigned an average
dollar value per tonne. The estimate of value is a function of the
estimates of the grade of copper, zinc and gold in the unit, the priees
of the three metals, the net smelter return and the mill recovery rate
for each metal. The estimated average value per tonne of material in a
mining unit is the estimated total revenue to be derived from the sale
of its constituent metals divided by the number of tonnes of material
extracted as the single unit:
Estimated Average Value per Tonne =
(Revenue copper + Revenue Zinc + Revenue GOld )
/
Tonnes mined
The estimated revenue generated by each metal is a product of the
estimates of four variables:
RevenueMetal
=
Metal content x NSR x MR x Metal pri ce
where:
Metal content refers to the mass of metal (tonnes of copper and
zinc, or grams of gold)
NSR is the net smelter return
MR is the rate of mill recovery
Metal priee is in current dollars per unit of mass of the metal
•
In the open-pit operation, it is assumed that there is full
Therefore, a mining unit selected for
recovery and no dilution.
extraction is removed in its entirety. The situation differs in the
113
•
underground mi ne in that the materi al sel ected for extract ion may be
augmented by dilution and/or reduced by lncomplete mine recovery. For
the purpose of determini n9 the est imated average value of the mi ned
material, it assumed that any diluting material is unmineralized. The
metal content is therefore determined on the basis of the estimated
grades and the estimate of the amount of material comprising the
undiluted mining unit.
The net smelter return at the smelter i s the proporti on of the
value of the metal in the concentrate which is received by the mine.
The value of the metal in the concentrate is determined using a
generalized net smelter relationship:
NSV
=
(CG p
-
UO) / 100 (PR / 100) (P - RC) . [TC a + e(P - Pa)] + CR - PN
where:
NSV is the net smelter value per tonne of concentrate
CG p is the concentrate grade of the product, e.g., percent zinc
UO is the unit deduction
PR is the proportion of the metal content paid for (percent)
P - RC is the settlement metal price less the refining charge
TC a is the base treatment charge
P - ~a is the settlement price less the smelter contract base
prlce
e is the treatment charge adjustment factor
CR refers to credits for by-products ($/tonne of concentrate)
PN refers to penalties for deleterious elements
concentrate)
($/tonne of
The credits for by-products are calculated as follows:
CR • (CGa - UO) (PR / 100) (P - RC)
where:
•
CG a
is the concentrate grade of the
grams/tonne)
114
by-product
(e.g.,
•
The concentrate grade of by-product gol dis cal cul ated in two
steps. The mass of the concentrate of the product, that i s, copper,
which is produced in a given period of time is determined as a function
of the grade of the ore processed through the mill:
where:
CV p is the mass of the concentrate
GRp is the grade of the ore, i.e., percent copper
MRp is the mill recovery of the product
ORE is the amol:nt of ore (tonnes) processed during the given
period of time
The concentrate grade of by-product gold is the mass of gold in
the copper concentrate divided by the mass of the concentrate:
where:
GRa is the grade of the by-product in the ore (grams/tonne)
MRa is the mill recovery of the by-product
The net smelter return at the minesite is the net smelter value,
including any penalties, but excluding by-product credits, less the
transportation costs from the mill to the smelter, divided by the value
of the metal in the concentrate:
NSR
z
(NSV - TR) / [(CG p
/
100) Pl
where:
TR is cost of transporting the concentrate from the mill to the
smelter ($/tonne)
•
The contract between the smelter and the mlnlng firm is the basis
for calculating the net smelter return associated with each metal. The
details of the smelter schedules for copper, zinc and gold are given in
115
•
table 14. The terms of the selected schedules are typical for the
smelting of a copper concentrate with gold credits, and a zinc
concentrate (Mackenzi e, 1987; 0' Hara, 1987; and Schumacher, 1988) . It
i s assumed that nei ther of the two concentrates contai n del eteri ous
elements, and that no penalty is impossd for their moi sture content.
The copper concentrate is transported ninety kilometres by truck,
and the zinc concentrate 580 kilometres by rail, to the nearest
smelters. Freight charges arising from truck and rail haulage are $0.14
and $0.04 per tonne-kilometre, respectively. Freight charges are based
on cost estimates in U.S. doll ars (Smith, 1992), and the average of
annual U.S./Canada currency exchange rates between 1973 and 1987
(appendix 3), that is, 0.86 U.S. dollars per Canadian dollar. Freight
charges are assumed to be fixed by long-term contract.
The net smelter return is a function of the metal priee. At the
stage at which a decision is required concerning the destination of an
extracted mining unit, the average annual metal priees are not yet known
with certainty. The user is responsible for providing the estimates of
copper, zinc and gold priees, in U.S. dollars, along with an estimate of
the annual average exchange rate between the U.S. dollar and the
Canadian dollar. These inputs are used to estimate the net smelter
return and the revenue to be generated by each metal in a mining unit.
For concentrates of constant grade produced in a mill of a given
design, the mill recoveries of copper and zinc from copper-zinc ore vary
with the ore grade according to O'Hara's (1987) formulae:
MRcopper
MRzinc
=
=
1 - 0.16 (GR Copper ),0.8
) '0.6
1 - 0.45 (GR.
Zlnc
where:
MRcopper is the mill recovery of copper
GRcopper is the grade of copper in the ore (percent)
MRzinc is the mill recovery of zinc
GRzinc is the grade of zinc in the ore (percent)
•
O'Hara's (1987) recovery formula for gold in base metal ores
requires a minimum gold grade of 6.28 grams per tonne for recovery of
116
•
Table 14. Smelter Contract Terms for a Copper Concentrate
with By-Product Gold and a Zinc Concentrate
Smelter Contract Term
Copper
Zinc
Gold
25.5%
52%
CG B
Unit deduction
1.0
0.15(CG)
1.0
Proportion of content
paid for
99%
85%
95%
Concentrate grade
Refining charge
S150/t
SO .18/g
Base treatment charge
S80/t
$l80/t
Smelter contract base
price
S2000/t
S1l50/t
0.025
(P>=2000)
0.01
(P<2000)
0.1
(P>=1l50)
0.05
(P<1l50)
Treatment charge
adjustment factor
•
Metal
117
•
gold by flotation. Given that the average grade of gold in the mineral
deposit is only margina11y higher than this minimum value, a single
. typical recovery rate of 0.60 (Mackenzie, 1987) is used for gold in a
copper-zinc mill.
Following the simulation of mlnlng activities, decisions
concerni ng the a11 ocat ion of mi ned materi al amongst the waste dump,
stockpiles and mill are based on the estimated value and/or grade of the
material in each mining unit.
4.1.2.9 Stockpiles
•
Four stockpiles can be created at the minesite. The tonnage of
material in each stockpile is monitored, but no upper limit is placed on
the size of stockpiles. The material in each stockpile is assumed to be
thoroughly mi xed such that homogeneity of grade i s achi eved.
Thus,
there is an estimated average grade and a true average grade which apply
throughout each stockpile.
The calculation of the estimated grades of copper, zinc and gold
in a stockpi lei s based on the estimated grades of the const ituent
mining units. The true grades of the mining units are the basis for
determining the true average grades in the stockpile. The total weight
of metal, estimated or true, derived from the constituent units is
divided by the number of tonnes of material in the stockpile in order to
arrive at an average grade.
The transfer of stockpi 1ed materi al to the mill requi res the
specification of the number of the stockpile, from 1 to 4, which is to
suppl y the mi11 feed. The user is provided with information on the
tonnage and estimated average grades of copper, zinc and gold in the
stockpil e. The amount of materi al whi ch i s to be transferred to the
mill feed is then specified.
For tonnage verification, values are rounded to the nearest whole
number cf tonnes. Providing that the amount of material selected for
transfer does not exceed the si ze of the stockpil e, or the remai ni ng
mill capacity, transfer of the material is simulated and the size of the
stockpile reduced accordingly. It is possible to select a tonnes from a
stockpile; this feature allows the user to reverse a previous decision
118
•
•
to mill stockpiled material before it is transferred from the s~ockpile.
The process of selecting stockpiled material for mill feed can be
repeated as long as there is remaining mill capacity and at least one
stockpile exists.
Subsequent to underground or open-pit mlnlng operations,
stockpil ing deci si ons al so determi ne the immedi ate dest i nat ion of the
mined units which are regarded as ore. All of the material which has
been extracted from an underground mi ne i s handl ed as if it were ore,
that is, the material which is not allocated to a stockpile is sent to
the mill for processing in the current year.· Of the material mined from
an open-pit, the amount of mineral ized material to be considered as
waste, and dumped along with unmineralized mined material, is determined
by a combination of the eut-off grade and eut-off value specified by the
user. A mining unit is dumped if its estimated grade or value falls
below any one of the selected cut-offs. Any remaining material from the
open-pit is considered to be ore, and must be assigned to one or more of
the stockpil es or to the mi 11, as i s the case for materi al from the
underground mine.
Mining units are chosen for stockpiling on the basis of their
estimated grade and/or value per tonne. Following the selection of a
stockpile, eut-off grades and/or values are applied in order to
distinguish the mining units which are to be stored from those which
will constitute the direct mill feed.
A grade or value range is
del imited by an upper and lower eut-off. If the user selects on ly a
value range, those mining units having estimated values which are
greater than or equal to the lower limit and less than the upper limit
of a specified value range are sent to the designated stockpile
regardless of their grade. If the user also selects grade ranges, the
uni ts are stockpil ed provi di ng that thei r est imated grades of copper,
zinc and gold fall within the selected grade ranges. In other words, in
order to be stockpiled, a mining unit must meet all of the grade and
val ue criteri a whi ch have been set. If no grade and value ranges are
specified after the selection of the stockpile number, then no material
i s stockpil ed.
After a value range and/or grade ranges for copper, zinc or gold
have been specified, the user is informed of the amount of material, if
119
•
any, by which the selected stockpile has been augmented. An update of
the quantity of unallocated mined material is also provided: the
stockpil ing procedure can be repeated until this quantity, rounded to
the nearest whole number, has been reduced to zero.
4.1.2.10 Hilling Parameters
It is assumed that the mill receives feed of a uniform grade
The sel ecti on of mi ni ng uni ts and stockpil ed
throughout the year.
material for mill feed is based on estimates of grades, and establishes
the annual production rate at the mill. It is, however, the true milled
grades which determine the most-l ikely mil l recoveries of copper and
zinc, and net smelter return of gold as described in section 4.1.2.8.
The true grades are the average grades of the materi al arri vi ng at the
mill from all sources, that is, directly from the mine, and from the
stockpil es.
Uncertainty in the level of mill recovery is incorporated by
simulating the actual mill recovery rate for each metal from a normal
probability distribution characterized by the most-likely rate of
recovery and a coefficient of variation of 0.03. The mill recovery of
copper is required for the calculation of the net smelter value of gold.
The net smelter return for each metal at the mfnesite is determined
following the simulation of mining and milling operations for the year.
At this time, the average price for each metal during the year is
available as an input in the net smelter relationship.
4.1.2.11 Cash Flow Specifications and Financial Performance
•
The cash flow associated with the mining project is calculated on
an annual basis. The cash flow components are revenue, operating costs,
capital expenditures and taxes.
Revenue is generated by the sale of copper and zinc concentrates.
The annual revenue ascri babl e to each metal in the concentrates i s a
funct ion of the average grade and amount of ore whi ch i s processed
during a year, the average annual price of the metal, the level of mill
recovery and the net smelter return:
120
•
REV p
=
GR p x ORE x P x MR x N5R
where:
REV p is the annual revenue from the product (metal)
zinc or gold ($)
-- copper,
GRp is the grade of the product in the milled ore
copper or zinc; grams/tonne gold)
(percent/IOO
ORE is the tonnage of ore milled
P is the metal price ($/tonne copper or zinc; $/gram gold)
MR is the mill recovery
N5R is the net smelter return
•
Metal prices are expressed in U. 5. doll ars, and revenue i s
converted from U. 5. to Canadi an currency on the bas i s of the annual
exchange rate. The most-l ikely exchange rate throughout the project
life is assumed to be 0.86 U.5. dollars per Canadian dollar, the average
annual exchange rate between 1973 and 1987.
The exchange rate
prevailing each year is simulated based on a probability distribution
characterized by the most-likely value of 0.86, and a coefficient of
variation of 0.06.
The annual operating costs are related to the type of activities
which have been carried out in the mine and mill during the year. If no
extraction occurred, mine operating costs may or may not be incurred.
If the mine has been closed on a permanent basis either by management
decision, or because no extraction is possible given the constraints of
the mining method, no mine-related costs are incurred. The mine can no
longer be operated and, therefore, need not be maintained in a state of
readiness for resumption of mining activities.
If extraction was
technically possible, but no extraction took place, the operating costs
for the mine comprise the cost of maintaining it on d stand-by basis and
the expenses associated with drifting and exploratory drilling, if these
have been carried out. If material has been extracted from the mine,
the operating costs are determined by multiplying the unit mine
operating costs by the number of tonnes mined, and adding the costs
which may have been incurred for drifting and exploratory drilling.
121
•
•
The annual operat) ng costs of the mi 11 are its mai ntli!nance costs
while temporarily closed, or the product of the unit mill operating
costs and the number of tonnes milled during the year. At the end of
the project life, the net costs of permanent plant closure are added to
any costs directly related to operations or the maintenance of
installations closed on what was originally a temporary basis.
Tax a11 owances are determi ned by applyi ng a fi xed depreci at ion
rate to a declining-balance pool of mine and mill plant assets'. The
pool of depreciable assets is generated by capital expenditure
associated with the initial installation, and any subsequent expansion,
of mine and mill capacity, deepening of the shaft in an underground
mine, and the replacement of worn-out or obsolete machinery and
equipment. In order to determine the depreciation allowance, a rate of
fifteen percent is applied to the balance remaining in the pool at yearend, including all capital expenditures on fixed as sets during the year.
Depreciation allowances are claimed as soon as they are available,
that i s, from the fi rst year of the preproduct i on peri od. The company
is assumed to be integrated and to have enough other sources of
operating profits to allow it to benefit from a flow-through form of tax
allowances. Thus, any excess allowances related to the mineral project
are absorbed.
Corporate income taxes are based on a simple profit taxation
model. Taxes are thirty percent of the taxable income, and are payable
in full each year.
Tax credits whi ch ari se beyond the end of the
project life due to undepreciated book balances are ignored. The aftertax cash flow is the operating profit less the tax payments and capital
costs, including the annual sustaining capital and the net working
capital. As no profits are generated while preproduction activities are
being carried out, the cash flows during this period reflect the capital
expenditures for the initial installation of mine and mill capacity, the
tax credits arising from the depreciation of plant as sets starting in
the year of their acquisition, and the investment of working capital
, For tax purposes, all plant as sets are assu:ned to be in the same
depreciable pool.
122
•
prior to the start of production.
The financial performance of the mineral project is measured using
discounted casi. flow techniques. The current dollar cash flows of the
project are fi rst defl ated usi ng a series of genera1 i nfl at i on rates
from the start of ths preproduction period to the end of the project
1i fe.
The most- 1i ke1y genera1 i nfl at i on ra te throughout the proj ect
life is the me an annual rate of change in the Consumer Price Index (CPI)
for Canada between 1973 and 1987. Rates of change above ten percent are
considered to be extraordinarily high, and are excluded from the
conlputation. The Consumer Price Indices for which the annual rates of
change are cillcl dted are given in appendix 2.
The average rate of
growth in the CPI is 6.4 percent.
The general inflation rate each year is the most-l ikely general
inflation rate multiplied by the proportion of the simulated cost
i nfl at i on rate to the most-l i kely cost i nfl at i on rate. Therefore, ~he
direction and degree of change in the general infl ation rate from year
to year is the same as for the cost inflation rate.
Based on the project's constant dollar cash flow distribution, the
rate of return i s determi ned and the net present value computed for
discount rates of five, ten, fifteen, twenty and twenty-five percent.
The success, or failure, of the mineral project can be measured in terms
of these criteria. If the project economics of two separate runs of the
Game are to be compared on the basis of an equivalent monetary value, a
future equivalent or present equivalent, other than the net present
value as calculated in the Game, could be used.
Such a comparison
requires that the values pertain to the same point in time. This is not
necessarily the case for the net present value supplied by the Game; all
cash flows are discounted to Time Zero which is the beginning of the
preproducti on peri od. A user has the option of del ayi ng the start of
preproduction activities, and therefore, Time Zero may not refer to the
same poi nt in t ime in di fferent runs of the Game.
The end of the
historical period is the point in time at which the first decision is
taken -- to start preproduction work immediately or to delay its start-
•
up. This is a common point. in time for all players and could be used as
a reference poi nt for compari son of project economi cs. Mi ni ng projects
coul d al so be compared on the bas i s of the future equi va1ent of cash
123
•
fl ows at the end of the project 1i fe if, in a11 runs of the Game,
permanent plant closure occurs at a set point in time, for example,
twenty years from the end of the historical period.
4.2 The Sequence of Decisions
4.2.1 Overview
•
The sequence of decisions for mine development and production is
displayed in flow chart format in figure 24. At the development stage,
the player decides which method, underground or open-pit, will be used
to mi ne the ore reserves. Although not ind i cated in the di agram, a
decision must be made concerning the length of delay, if any, in the
start-up of the preproduction activities. These activities lead to the
installation of the annual mining and milling capacities which are
selected by the player.
If an open-pit mine is developed and operated, a decision may be
made to convert to underground mining operations.
Should such a
decision be taken, the installed underground mining capacity must be
selected, and conversion of the mining method would be due to occur at
the end of the underground mine construction period.
The development of underground mining facilities, whether for
conversion from open-pit operations or as the sole means of extracting
the ore reserves, requires specification of the shaft site northing and
the depth to which the shaft is to be sunk. Further decision-making
takes place during the operating life of the underground mine.
The decisions which are required for mine and mill production are
dependent upon the choice of mining method and insta11ed mining and
milling capacities. Decisions concerning grade control and the level of
util ization of mine capacity are made indirectly through selection of
the blocks to be extracted in a particular year. The level of mill
capacity utilization is determined by the amount of ore assigned to the
mill from the stockpiles and by grade- and/or value-range selection with
respect to the mining units extracted in a given year.
Upon completion of mining and mil1 ing operations, the pl ant is
124
•
START
Development
Stage
Select mining method
Select installed
mining and
milling capacities
Production
F
T
Open-pit mine
Stage - ,
Select shaft
sequencing
Select installed
depth and site
underground
mining capacity
Underground mine
T
'
sequencing
,
-,
Financial
Evaluation
END
•
Figure 24: The Sequence of Decisions for Mine Development
and Production -- An Overview
12.5
•
closed on a permanent basis. The financial evaluation of the project is
the final step in the Game .
Figure 25 shows elements of a generalized mining system with both
open-pit and underground operations, such as might be produced from a
similar sequence of decisions. The open-pit mine is divided into levels
from which ore and waste are extracted. A crown pillar lies between the
open-pi t and the underground mi ne worki ngs.
There are three 1evel s
separated by si 11 pi 11 ars in the underground mi ne; Level 1 i s composed
of two sublevels, and Levels 2 and 3 have three sublevels each. Mining
takes place in stopes which are separated by rib pi11ars, and mined
material is hoisted to the surface from the deepest level.
4.2.2 Open-Pit Operation
•
The sequence of decisions made during the open-pit mine 1ife is
shown in figure 26. Production can begin immediately following mine and
mill installation. The player may, however, decide to delay the st art
of operations. This is not reflected in figure 26 in which it is
assumed that production begins immediately after the preproduction
period. As shown, mining sites in the open-pit are to be specified in
terms of the level and boundary on which they are located. The player
must select the appropriate block limits according to whether the first
cut is being made on the level, or a parallel or perpendicular pit
extension is being carried out. Providing that there are mineable ore
reserves remaining and that mine production has not reached the limit of
overcapacity, the player has the option of selecting more material for
extraction; otherwise, no further specification of mining sites is
possible.
When the player has completed the selection of mlnlng units for
extraction in the current year, the stockpiling decisions which are made
control the flow of mined material into and out of the stockpiles.
Stockpiled material, if it exists, may be selected for processing as a
supplement to or substitute for direct mill feed.
At this stage,
decisions must also be made concerning the allocation of mined material
to the mil l, stockpi l es and dump. Thus., the mil l i ng and stockpil ing
126
•
Open-Pit Mine
Level 1
"
~;rI'~~~~!J~Mining
unit
in waste "
~
"
"
\
\
Underground Mine \
\
LEVEL 1
Hangingwall
\
\
SîII pillar
\
,
----"--~~~\
_
Sublevel 2 ~~~~~~~~~~~~~~~Mining
unit
Sublevel 3 ------...-
\
LEVEL2
Sublevel1 -~~
SîII pillar
,
-->;""
Development \
drift
F"'~
\
\
Footwall
LEVEL3
Limit of ore
Haulage level
•
Figure 25: Elements of a Mining System -- Open-Pit and Underground Mine
127
•
START
Selecdtlevelkb.ou,ndary
an bloc hmlts
T
F
T~
-.:...J
Select stockpiled material
for milling and allocate
mined material to mill
L__a_n_dJ..;o_r..;,st,:o:;Ck~p=i1=es==::!...._..JSelect stockpiled
material for milling
F
Consider nex! year's mine and mill aclivilies,
change of mining melhod, and expansion or
permanent ciosure of mine and mill
T
F
F
Increment year
Increment year
RETURN
•
Figure 26: The Sequence of Decisions During the Open-Pit Mine Life
128
•
•
decisions are interlinked.
The user shoul d not plan future open-pi t product i on incerta i n
situat ions. If the project 1ife has been extended for forty-fi ve years
beyond the end of the preproduct i on peri od, the plant i s cl osed on a
permanent basi s. Open-pi t operat ions cease if the open-pit cannot be
extended at depth or wi dened on any 1evel, or if a dec i sion has been
taken to change the mining method, and underground development work has
been completed.
In the latter case, mine sequencing can begin
underground the following year.
Providing that open-pit mine production is possible, the user can
opt to mine and mill.
If mill feed is available from one or more
stockpiles, the mill can be operated while the mine is closed. If no
operations are planned for either of the installations, the player must
indicate whether the closure of the mine at the end of the current year
i s expected to be temporary, or i s permanent. If the mi ne i s clos i ng
temporarily, then mill closure must also be temporary, and both
facilities are maintained on stand-by.
If the mine is closed on a
permanent basis, the player must indicate whether or not the plant
closure is permanent.
At the end of each year of the open-pit life, the player has the
option of starting underground mine construction during the following
year if 1) the plant is not closing permanently, 2) at least one of the
pit boundaries has not been extended to a property boundary, 3) a shaft
can be sunk to a depth whi~h allows at least one level containing at
least one sublevel to be devç,oped, and 4) a decision has not previously
been made to convert from open-pi t to underground operat ions.
The
second condition ensures that the mine shaft can be sited on the
property.
The player is also given the opportunity to initiate an
expansion program for the mine or mill, providing that there is no
expansion of the installation already underway, and the maximum feasible
size would not be axceeded.
In the case of an open-pit operation,
provision of the option to begin a mine expansion program is contingent
upon the fact that no underground.mine development work is taking place
or due to start the following year.
If the plant is closing permanently, no further decisions are to
be made, otherwise decision making continues the following year.
If
129
•
open-pit mlnlng is to take place, the player repeats the process of
decision making, beginning with the selection of one or more mining
sites. If at the end of the previous year, the player took the decision
to carry out mi" ing operations without mining, stockpiled material can
be selected as mill feed; if no material is actually dispatched from the
stockpiles, the mill is closed for the year.
4.2.3 Underground Operation
•
The sequence of decisions made during the undergrQund mine life is
shown in figure 27.
Underground production can begin when mine
development work has been completed.
The sequence of decisions
displayed in the figure is based on the assumption that although the
player has the option of delaying the start-up of mine operations, the
decision is taken to start mining activities during the year following
the completion of mine development. As shown, an underground mining
site is selected by specifying the level and sublevel on which mining is
to take place.
When the first mining site is being selected on a
particular level, the eastern and western limits of the development
drift at the base of the level must also be specified.
The player
chooses the coordinates which delimit a block in a stope and thus
determines whether primary or secondary stoping is to take place, and
which mining units may be extracted. If the reserves of the mine are
not exhausted and the overcapacity limit of the mine has not been
reached, further mine production is possible.
The selection of material for extraction has been completed when
no further extraction from the mine is possible, there is no remaining
mine capacity or the player elects not to continue mining in the current
year. The player can select any previously stockpiled material to feed
the mill, and must allocate material which has been mined in the current
year amongst the stockpiles and mill.
If the underground mine cannot be extended on any of the existing
levels and no stockpiles exist, the underground mine and the mi" are
closed permanently. Providing that there are ore reserves available for
extraction, or there is at least one stockpile of mined material, the
130
START
•
Select level, sublevel
and black Iimits
T
F
T.J:oooIf--
.:...J
Select stockpiled material
for milling and allocate
mined material ta mill
and/or stockpiles
F
Select stockpiled
material for milling
T
T
Consider next yea~s mine and mill activilies
change of mining melhod, and expansion or
permanent closure of mine and mill
F
F
•
•
Increment year
Increment year
Figure 27: The Sequence of Decisions During the Underground Mine Life
131
•
player selects the course of action in the following year
mlnlng and
milling, temporary shut-down of the mine and/or the mill, permanent mine
closure, or no operations consequent to a decision to close the entire
plant on a permanent basis at the end of the current year.
Unless the plant has been closed permanently, decision making
cont inues the fo 11 owi ng year.
1f the underground mi ne i s to be in
operation, the process is repeated beginning with the selection of
mining units at one or more sites.
A decision to mill without
concurrent mine production requires that at least one stockpile be
selected as the source of mill feed; however, it is possible to leave
the stockpiled material intact, and the mill, therefore, remains closed
for the year.
At the end of each year, the player is given the opportunity to
initiate an expansion program for the mine or mill, providing that there
is no expansion of the installation already underway, and the maximum
feasible size would not be exceeded. The option of deepening the shaft
is given at the end of each year beginning the year after completion of
underground mine construction. A positive outcome to decision making
concerning shaft deepening or the expansion of installed capacity
results in implementation commencing the year after the decision is
taken.
4.3 Rules of the Game
•
The development and operation of a mine and mill plant are
simulated according to the series of decisions made by the player,
provided that the rules of the game are respected. The rules are set
according to the scope and degree of detail of the model upon which the
Game is based.
The rules govern the behaviour of the player in
assigning values to the decision variables, and adherence to the rules
ensures that only feasible decisions are made. Most of the operational
rules pertain to the constraints of the mining method •
. The rul es are li sted accordi ng to the type of act i vitY to whi ch
they apply •
132
•
•
Development and expansion:
1) an open-pit or underground mine is to be developed; should an
open-pit mine be selected initially, the development of an
underground mine for conversion of operations may subsequently be
possible;
2) the installed annual capacities of the mine and mill must fall
within a range of feasible values -- 75 000 to 675 000 tonnes for
the underground mine and mill, and 227 000 to Il 340 000 tonnes
for the open-pit mine;
3) a period of delay in the start-up of preproduction activities can
be specified, but must not exceed fifteen years;
4) the shaft must be sited between 0 mN and 32 760 mN; if the
selected northing is not a multiple of five, the value is
automatically rounded to the nearest multiple;
5) the shaft depth in an underground mine must be at least 170
metres, no more than 495 metres, and a multiple of five metres; a
value which is not a multiple of five is automatically rounded to
the nearest multiple;
6) if conversion from open-pit to underground mining is planned, the
shaft must be deep enough to provide access to at least one
sublevel beneath a crown pillar at the base of the pit;
7) increments to the shaft depth must be multiples of seventy-five
metres;
8) an expansion of the underground mine or mill must increase the
installed annual capacity by a minimum of 75 000 tonnes;
9) an expansion of the open-pit mine must increase the installed
annual capacity by at least 227 000 tonnes;
10) underground mine construction work can be initiated while open-pit
operations are taking place, providing that at least one of the
pit boundaries has not been extended to the corresponding property
boundary, and the shaft can be sunk deep enough to allow the
development of at least one sublevel below a crown pillar at the
base of the pit .
133
•
Open-pit mining:
1) open-pit mining must be carried out within the limits of
overcapacity associated with the existing mine design; in any
given year, the mine may be temporarily closed, or operated at a
rate of up to twenty percent over the stated capacity.
2) the four boundaries of the pit must be parallel to the north-south
and east-west axes, and can be segmented;
3) the levels of the open-pit are to be developed in sequence of
depth;
4) the pit slope angle cannot exceed forty-five degrees;
5) a mining site is to be specified in terms of the level and
boundary on which it is located;
6) a minimum mining width of twenty metres is required;
7) exploratory drilling and/or extraction can be carried out on
several benches in a single year providing that technical and
capacity constraints are met;
8) the open-pit can be expanded in two ways: a) parallel extension
along a segmented boundary, and b) perpendicular extension of a
straight boundary;
9) mining units are cubic blocks which have a height equal to the
bench height, that is, ten metres;
10) block selection for lateral pit expansion or pit deepening cannot
lead to fragmentation of mining units, that is, mining units
cannot be subdivided into smaller blocks.
Il) blocks selected for mining must lie within the property
boundaries, in other words, the coordinates delimiting blocks of
one or more mining units must lie between 0 mN and 32 765 mN, and
between 0 mE and 32 765 mE; northings and eastings which are not
multiples of five are automatically rounded to the nearest
multiple.
Underground mining:
•
1) underground mining must be carried out within the limits of
overcapacity associated with the existing mine design; in any
given year, the mine may be temporarily closed, or operated at a
134
•
2)
3)
4)
5)
6)
7)
8)
9)
10)
Il)
12)
•
13)
rate of up to twenty percent over the stated capacity;
the maximum depth of mining is dictated by the shaft depth; the
deepest level at which mining can take place is twenty metres
above the base of the shaft;
mining can take place within a vertical interval determined by the
depth of the open-pit, if one exists, the thickness of the crown
pillar, and the depth of the shaft (refer to rule 2);
the deposit is to be accessed from drifts on levels at seventyfive-metre intervals, and on sublevels at twenty-metre intervals
of depth;
the deposit is to be mined in one cut from the hangingwall to the
footwall;
a mining site is to be specified in terms of the level and
sublevel on which it is located;
the western and eastern boundaries of the development drift on the
first sublevel of a new level are to be specified prior to stope
selection, and must be no more than twenty-five metres apart;
providing that no extraction has taken place, the development
drift may be relocated once such that the drifts are at least five
metres apart;
mining units are selected by specifying the coordinates which
delimit the base of the block containing them;
exploratory drilling and/or extraction can take place at several
sites in a single year providing that technical and capacity
constraints are met;
mine sequencing must respect the constraints imposed by the use of
sublevel stoping as the mining technique;
rib pillal's have a minimum length of twenty-five metres and extend
the full height of the stope; the crown pillar and the sill pillar
between two levels should be at least fifteen metres in vertical
thickness;
mining which takes place in a pillar between primary stopes or in
the southern wall of the most southerly primary stope is to be
considered secondary stoping;
primary and secondary stopes must be located at least as far north
as the shaft site;
135
•
14) primary and secondary stoping must advance northwards;
15) mining unit selection in a new stope on a level where there eXlsts
a more southerly stope of the same type, that is, primary or
secondary, signifies that mining activities in the more southerly
stope have been completed;
16) mining in the pillar adjacent to the most northerly primary stope
signifies that mining in that primary stope has been terminated,
and further primary stoping on the level will have to take place
in a new stope;
17) extraction can begin in a secondary stope once mining and
backfilling of the adjacent primary stope(s) have been completed;
18) stopes dip forty-five degrees to the east;
19) stopes must be no more than sixty metres in vertical height, and
no more than twenty-five metres in width and length; stope width
may vary from stope to stope but must be uniform within a single
stope;
20) mining units have a length of five metres, a height equal to the
sublevel interval of twenty metres, and a width equal to or less
than that of the development drift;
21) the minimum advance in any stope is five metresj
22) blocks selected for mining must lie within the property
boundaries, in other words, the coordinates selected to delimit
blocks of mining units must lie between a mN and 32 765 mN, and
between a mE and 32 765 mE; northings and eastings which are not
multiples of five are automatically rounded to the nearest
multiple.
Stockpiling and milling:
•
1) up to four stockpiles of mined material can be created at the
minesite;
2) a stockpile can be augme~ted in any year in which material
considered to be mineralized has been extracted from the mine;
3) the allocation of mined material to the stockpiles, mill or dump
is by mining unit, and is based on the estimated grade and/or
average value per tonne of material extracted as a unit;
4) all of the material mined underground must be stockpiled or milled
136
•
in the year in which it is extracted;
5) material from an open-pit is dumped, stockpiled or milled in the
year of extraction;
6) mill feed is to be obtained directly from the mine and/or from
stockpilesj
7) milling is to be carried out within the limits of overcapacity
associated with the existing mill design; in any given year, the
mill may be temporarily closed, or operated at a rate of up to
twenty percent over the stated capacity.
Permanent closure:
1) the
open-pit or underground mine is closed when the mineable ore
reserves have been fully depleted;
2) if conversion to underground mining is planned, the open-pit mine
is closed at the time originally scheduled for the start of
underground operations;
3) the mill is closed if there is no stockpiled material when the
underground mine closes, that is, the entire plant is shut down;
4) the mine/mill plant is closed when the project life has been
extended for forty-five years beyond the end of the preproduction
period .
•
137
CHAPTER 5
THE MINE MANAGER AT WORK
•
5.1 Introduction
This chapter addresses the operational aspects of the Mine
Manager, that is, issues pertaining to the actual running of the Game.
In sect ion 5.2, the user interface i s descri bed, thus reveali ng the
manner in which communication is achieved between the user and the
computer system. Examples are given of the types of decisions facing
the user and of the appropriate input to be made by the user.
Documentation of a sample run of the Game (section 5.3) begins
with a statement of the operating pol icies which are in effect. Mine
planning is performed on the basis of preliminary data, and the
resulting plant size and mine schedules for both an open-pit and
underground mi ne are presented.
Foll ow; nr; the impl ementat i on of
management's mine development and production decisions, feedback is
obtained and is used to update mine plans.
Technical and financial
reports are shown for each year of the mine life.
5.2 User Interface
•
The user interface is that part of an interactive system directly
concerned with end-user interaction (Newman, 1991).
According to
Newman, the user interface supports the two-way flow of information
between the user and the system by providing a command language and
information display. The command language is the medium through which
the user expresses actions to be performed. The information display
shows the state of the stored information.
The user interface of the Mine Manager controls the display of
information,. prompts and messages, and to a certain extent, guides the
user in the selection of inputs. The interface design allows a high
degree of interactivity between the user and the computer system.
In the Game, a command consists of a single character, in either
138
•
upper or lower case, to be entered in response to a prompt. The actions
to be performed are expressed in terms which are meaningful in the
context of a mining project. For example, in response to the prompt
'Continue mining on the current level?', the user may enter 'Y'I'y' or
'N'l'n' at the console, depending on the decision that is taken.
The user i s prompted to make deci si ons requi ri n9 the input of
numerical values, for example, the annual mining capacity ta be
installed. In such cases, if a numerical value is not entered, or is
entered incorrectly, the user is informed of the entry error, and lll"'st
reenter the value. Providing that a numerical value is input by the
user, its acceptabil ity can be verified according to the constraints of
the model. If the value is found to be unacceptable, a screen message
indicates that the value should be changed.
The information displays generated by the Game include delineation
drillhole data, a list of historical priees, a summary of construction
parameters and estimated unit operating costs, a statement of cash flows
and pri ces during the preproduct i on peri od, a li st of est imated grades
of mining units selected as a single block on a given level or sublevel,
reports on the grade- and val ue-tonnage rel ati onshi ps for units mi ned
during a given year, a stockpile status report, a summary of operations
and cash flow statement for each year of the production period, and the
financial performance report.
The user has sorne control over the display of preliminary
i nformat ion and feedback. Through the response to vari ous prompts, the
user may choose to recsive or forgo sorne of the information which is
available. By using the on-screen menu, a hard-copy of the information
displayed on the screen can be obtained.
Further di scuss ion of the computeri zat ion of the model of mi ne
development and production is presented in appendix 4.
5.3 Sample Run
•
The sample run of the Mine Manager is described in a step-by step
manner, from mine planning on the basis of preliminary information to
mine and mill plant operations, leading to one of many possible outcomes
139
•
in terms of financial performance and mine configuration. The sample
run is based on a sequence of decisions made in accordance with the
rul es of the Game, and provi des exampl es of the informat i on. di spl ays
which it generates.
The Implementation of operating policies is
demonstrated and, through exercise of the option to convert the mining
method, sequencing in both the open-pit and underground mine is shown.
The operating policies which can be used in the Mine Manager are
those which control the level of capacity util ization, the grade or
value of mined material, and stockpiling activities. Mine sequencing is
set in accordance with these policies and within the constraints of the
mining method. The operating policies which have been selected for the
sample run of the Game are not necessarily optimal policies.
In the sample run, the plant capacity utilization policy is:
i) operate the plant at overcapacity if the priee forecasts for at
least two of the three metals -- copper, zinc and gold -- are
higher than normal. The 'normal' priee level is determined from
regression of historical priees and is updated on an annual basis.
The open-pit mine is operated at seventeen percent overcapacity',
and the underground mine and mill at twenty percent overcapacity.
ii) close the plant on a temporary basis if the priee forecasts for
all three metals are lower than normal.
Iii) operate the plant at a rate equal to the installed annual capacity
in all other cases.
In reality, temporary plant closure would be justified if the cash
flow position would be improved over that resulting from operation of
•
, The open-pit is scheduled to operate below the limit of
overcapacity so as to reduce the probabil ity that capacity constraints
prevent the planned final pit Increment from being mined in its
entirety. Such a situation could arise if the pit slope is the maximum
permissible (forty-five degrees), and the proportion of mineralized
material has been underestimated, such that the tonnage associated with
a given volume of mined material is higher than expected. Extraction of
mineral ized material from the deeper pit level s would require further
stripping on the levels above. If the mine is operating at a rate which
is close to the limit of overcapacity, it may not be possible to perform
sufficient stripping to allow access to the mineralized material.
140
•
the plant; however, for the purpose of the sample run, the plant
capacity policy is implemented without further analysis.
Stockpiling decisions are based on the estimated unit mill
operating costs. All mining units having an estimated average value of
l ess than the est imated uni t mi 1"1 operat i ng costs are pl aced in
Stockpile 1.
If the mill capacity is insufficient to accommodate the
remaining mined material, excluding waste from an open-pit mine which is
dumped, units having the lowest value are stockpiled.
In the sample
run, up to two more stockpiles are created if necessary; mining units
wi th an est imated average val ue of l ess than twi ce the unit mi 11 i ng
costs are assigned to Stockpile 2, and units of higher estimated value
are allocated to Stockpile 3. If there is inadequate direct mill feed,
stockpiled material may be used to supplement mill feed.
The aim of the open-pit operation is to extract all of the
mineralized material within the ultimate pit depth with a minimum of
internal dilution. Mine planning seeks to ensure adequate access to ore
for direct mill feed through advanced stripping.
The grade policy
implemented underground is one of blending higher- and lower-grade ore
in order to restrict the range of grades received by the mill.
The preliminary data which the user can obtain are the results of
the del ineation drill ing program, historical prices, and cost functions
which are used to generate capital and ope rat i ng cost est imates. The
locations
of
thirty
del ineation
drillholes
which
intersected
mineral ization are shown in figure 28. The average intersection grades
of five-metre core sampl es from these dri 11 hol es are al so ava i labl e to
the user; these grades are given in table 15.
Figure 29 shows a horizontal section (down dip) of the deposit
which has been projected to the surface. The outline of the deposit is
based on the assumption of an equal are a of influence for each
drillhole. The length along strike of the deposit is ninety metres (430
mN to 520 mN). Also presented in figure 29 is a cross-section of the
deposit at 475 mN. It shows that the deposit dips forty-five degrees to
the east, the projected limit of the mineralization is at a depth of
•
about 400 metres, and the vertical and horizontal thickness of the
deposit is a maximum of twenty-five metres. Mineral ization may extend
towards the surface between 25 mN and 50 mN. The del ineation, drill ing
141
•
50mE
150mE
250mE
350mE
450mE
+
+
+
+
+
535mN+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1
505mN+1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1
475mN+1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+.
0
-+-
0
-+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1
445mN+-
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
415mN+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
o : Drillhole
Figure 28: Delineation Drillhole Locations
•
142
•
•
Table 15. Average Intersection Grades of 5-Metre Core Samples
from Vertical Delineation Drillholes
Average Intersection Grade
Northing Easting Depth of Base
(mN)
(mE) of Sample (m) Copper(%) Zinc(%) Gold(g/t)
445
70
25
30
35
40
1.95
3.35
3.39
4.94
5.83
12.33
19.70
4.98
3.25
4.76
5.64
6.81
445
110
60
65
70
75
80
2.46
2.26
5.25
10.25
1. 74
5.18
4.45
7.72
4.96
21. 72
3.69
2.54
3.28
2.63
7.42
445
150
100
105
110
115
120
4.87
3.39
1.94
8.24
10.05
8.16
3.80
3.66
2.69
5.42
6.65
7.49
9.67
7.63
5.26
445
190
150
155
160
3.96
3.65
2.74
7.45
4.86
4.10
2.53
3.14
7.07
445
230
180
185
190
195
200
3.16
5.41
3.54
2.27
21.04
2.30
4.13
3.61
4.92
3.07
2.69
3.03
5.53
4.46
4.45
445
270
220
225
230
235
240
9.81
4.99
7.94
11.89
9.59
2.76
4.00
3.31
2.11
4.94
3.27
4.60
9.75
3.35
3.89
445
310
260
265
270
275
280
5.48
4.18
3.58
12.12
4.73
3.14
3.50
7.84
4.42
6.52
3.13
4.19
18.59
6.05
20.06
445
350
300
305
310
315
320
3.47
6.27
4.77
4.10
10.07
5.72
5.19
8.59
7.76
12.04
5.81
3.20
5.44
8.19
2.65
143
•
•
Table 15 . (continued)
Average Intersection Grade
Northing Easting Depth of Base
(mN)
(mE) of Sample (m) Copper(%) Zinc(%) Gold(g/t)
445
390
340
345
350
355
360
2.24
2.15
1.93
2.40
3.68
19.63
7.08
5.34
2.56
3.06
13.30
4.56
5.68
6.93
17.59
445
430
380
385
390
395
2.97
1. 79
2.59
1.71
19.11
5.76
3.41
4.67
28.90
7.42
8.89
5.20
475
70
20
25
30
35
40
1.65
1.67
1.49
3.27
1.64
21. 72
7.10
12.21
14.24
21. 72
4.26
2.28
10.77
28.90
5.93
475
110
60
65
70
75
80
2.55
3.50
3.94
2.12
1.91
10.07
5.28
12.47
21. 72
13.30
12.69
7.18
4.15
3.54
3.77
475
150
100
105
110
115
120
1.94
5.99
3.24
4.14
2.51
4.26
6.93
11.85
15.22
4.28
2.15
1.54
2.38
3.88
6.12
475
190
150
155
160
6.47
3.49
4.58
3.48
3.09
3.99
4.73
4.78
8.02
475
230
180
185
190
195
200
21.04
17.37
2.71
2.61
6.21
9.64
9.66
4.62
2.97
4.43
2.93
1.84
1.27
1.45
3.60
475
270
220
225
230
235
240
2.79
2.18
4.12
13.97
12.46
2.86
3.64
7.02
2.33
4.48
4.45
3.79
1.97
2.08
1.43
144
•
•
Table 15. (continued)
Average Intersection Grade
Northing Easting Depth of Base
(mN)
(mE) of Sample (m) Copper(%) Zinc(%) Gol d( gft)
475
310
260
265
270
275
280
4.21
3.88
2.92
3.91
2.58
10.61
21.72
5.14
2.16
3.96
7.66
4.54
8.94
3.77
5.63
475
350
300
305
310
315
320
1.88
3.45
2.26
3.41
3.47
19.30
8.25
4.13
17.66
5.97
13.27
11.25
20.70
5.40
1. 79
475
390
340
345
350
355
360
1.92
3.04
4.02
2.79
2.08
2.54
4.28
21. 72
20.15
18.77
5.04
3.18
4.27
1.80
3.88
475
430
380
385
390
395
400
1.27
1.81
1.53
1.59
2.19
5.20
6.16
21. 72
21. 72
17.39
7.16
10.46
10.36
6.83
2.81
505
70
20
25
30
35
40
1.42
2.22
1.57
1.17
2.76
10.38
20.98
14.01
21. 72
21. 72
7.63
13.77
4.99
8.22
12.59
505
110
60
65
70
75
80
2.60
2.77
1. 79
2.58
1.58
12.58
19.84
9.16
5.15
9.37
7.26
4.46
7.21
1.68
1. 78
505
150
100
105
110
115
120
3.70
2.83
4.52
3.02
2.39
8.60
4.10
2.31
2.20
3.69
2.98
1.85
4.95
3.42
1.08
505
190
150
155
160
1.97
2.42
4.99
5.57
12.42
10.31
5.15
5.43
3.27
145
•
•
Table 15 . (continued)
Average Intersection Grade
Northing Easting Depth of Base
of Sample (m) Copper(%) Zinc(%) Gold(g/t)
(mN)
(mE)
505
230
180
185
190
195
200
8.06
3.84
3.89
6.44
16.94
5.06
6.86
7.92
3.19
5.79
1.16
1.50
1.77
1.37
1. 73
505
270
220
225
230
235
240
4.12
3.46
1. 78
3.67
2.52
4.65
4.07
3.31
3.68
7.86
2.93
8.05
20.69
18.48
5.92
505
310
260
265
270
275
280
4.16
5.28
3.50
1.58
4.69
5.53
4.42
3.66
6.52
21. 72
7.57
2.03
2.98
10.14
3.88
505
350
300
305
310
315
320
9.70
2.54
1.64
6.79
10.57
5.15
2.96
13.22
13.51
13.99
4.25
8.56
2.01
4.01
2.15
505
390
340
345
350
355
360
2.14
1.61
2.30
1. 78
2.76
13.78
5.78
3.76
6.47
11.29
11.47
3.31
3.07
3.00
6.42
505
430
380
385
390
395
400
1.12
5.87
3.30
1.50
1.32
21. 72
7.02
3.34
21. 72
5.91
12.65
28.90
6.76
15.78
5.23
146
•
SOOmN
550mN
0
500mN
0
0
0
0
0
0
0
0
0
Delineation drillholes
450mN
0
0
0
0
0
0
0
0
0
0
0
0
0
0
o.
0
0
0
0
0
400mN
/
Outlîne of deposit
(vertical projection to surface),
350mN
W
Depth (m)
70 mE
E
190 mE
310 mE
430 mE
0
Delineation drillholes
100
200
Outlîne of deposit /
(cross-section at 475 mN)
300
400
•
Figure 29: Outline of the Mineral Deposit Based on Data from the
Delineation Drilling Program
147
•
data reveal grade zonation: a central zone of higher copper grades and
lower zi ne grades fl anked by areas of lower copper grades and higher
zinc grades.
Based on a cross-sectional shape of the deposit as shown in figure
30, a stri ke l ength of ni nety metres, a eut-off grade of zero, and a
tonnage factor of 0.263 for massive sulphides, there are 3 422 053
tonnes of ore reserves. An estimate of the length of the production
period associated with the deposit can be produced at this stage.
Assuming that mill production each year is 300 000 tonnes -- the
intermediate-run operating cost-minimizing rate -- the reserves would be
depleted in about eleven years. In practice, more detailed geological
modelling and reserves estimation would be performed.
The user is informed of the average annual metal priees during the
The
fifteen-year period prior to mine development decision making.
historical priees of copper, zinc and gold (table 16 and figure 31)
display cycles of several years duration.
Copper and zinc priees
exhibit peaks in Years 2, 7, 10 and 15. Gold priees peak in Years 5, Il
and 14. The average cycle length is four years, and peaks centre around
Years 2, 6, 10 and 14. If preproduction activities were to begin
w
E
-25m-
400m
•
Figure 30: Cross-Section of the Mineral Deposit
148
•
Table 16. Historical Prices of Copper, Zlnc and Gold for the
Sample Run
Metal Prices
Year
1
2
3
4
5
6
7
8
9
la
11
12
13
14
15
•
Copper (USS/lb)
Zinc (USS/lb)
Gold (USS/oz)
0.74
0.75
0.66
0.57
0.61
0.73
0.76
0.63
0.72
0.94
0.79
0.60
0.58
0.55
0.67
0.33
0.42
0.36
0.39
0.44
0.51
0.59
0.50
0.67
0.61
0.41
0.36
0.31
0.28
0.23
220.59
161.41
276.05
265.56
364.99
349.13
393.51
419.53
483.87
628.61
696.19
249.71
399.26
421.57
258.43
immediately and continue for three years, for example, early mine
production would coincide with a period of recession (figure 32a).
Production will be timeo instead to start in a period of recovery
(fi gure 32b). Th i sis accompli sh!ld by schedul i ng preproduct ion work
such that i t i s compl eted in fi ve years t ime, that i s, the si xth year
from now is the first year of operation. Given that the maximum length
of the preproduct ion peri od i s four years, the start of preproduct ion
activities will have to be delayed. The length of this period of delay
is known only when the installed annual mine capacity and corresponding
preproduction period have been determined.
Initial mine planning is performed on the basis of the specified
operating policies, and prices which are forecast prior to the start of
the project. Once the project is underway, mine plans are likely to be
altered as forecasts change. In the sample run, it is assumed that the
forecasts which are available at the initial planning stage lead to the
same decisions with respect to production rate as do subsequent
149
•
a)
b)
eoo
700
~
<>
c:
600
::l
.!2
fi>
500
CIl
2Q)
<>
'c
400
0..
300
200
2
3
4
5
6
7
B
9
10
11
12
13
Year
•
Figure 31: Historical Priees of a) CORper and Zinc, and b) Gold
for the Sample Run
150
14
15
•
4-year cycle
a)
'\
\
fi
/
Present:
\
4·yea~ cycle
b)
,:
/
1
7
End 01 Ilrst year
of op$ration
Present:
TIME
Figure 32: Price Cycling and the Start of Production in a Period of
a) Recession and b) Recovery
•
151
•
forecasts'. This eliminates the need to change the original plan due to
changing price forecasts; however, there remains uncertainty as to the
actual prices which will prevail in any year. Therefore, there is no
guarantee that an operating policy will be effective.
In the
underground operation where dilution and mine recovery can significantly
impact the level of mine production, and where exploration takes place
along the outer border of peripheral stopes, the mine plan is altered in
response to any deviation from planned production.
Table 17 shows the operating years in which the forecast prices
for each metal are higher than normal. Operating Year 1 i 5 the year
following the completion of preproduction work. The final column
Table 17. Planned Level of Mine Capacity Utilization
Operating
Year
1
2
3
4
5
6
7
8
9
10
11
Price Forecast Higher than Normal
Copper
Zinc
Gold
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Level of Mine
Capacity
Util ization'
0
0
0
0
0
0
0
S
0
S
= production at stated capacity
o = production at overcapacity
, S
--._--
•
, Price forecasts are generated by the user. In the sample run,
the final price forecasts produced prior to operation are the
one-period-ahead forecasts determined from Holt's exponential smoothing
(Makridakis and Wheelwright, 1989).
152
•
•
indicates the level of mine capacity utilization planned according to
the operating policy. Mining will take place at overcapacitj during the
first seven operating years. The mine will then be closed for a year,
reopening to operate at the stated capacity for one year. This will be
followed by operation at overcapacity during Year la, and at the stated
capacity in the final year of operations.
The final pit depth is 120 metres, the greatest depth for which
the actual stripping ratio of 9 does not exceed the transition stripping
ratio of la'. Ore is mined from three new levels each year, and thus pit
deepening occurs at a rate of thirty metres per year for four years.
The scheduled rate of ore extraction in the first three years of openpit operation is 256 654 tonnes per annum.
In the fin.ll year, the
amount of ore to be mined is reduced to 254 515 tonnes; the pit width on
the deepest bench is twenty metres which is just less than the maximum
width of the deposit. Widening of the pit to thirty metres on the
deepest bench was not performed as the additional stripping which would
have been required could not be justified by the incremental ore.
Production is at approximately seventeen percent overcapacity
during the open-pit mine l ife, and therefore an installed annual mine
capacity of 2 200 000 tonnes is required. The installed annual mill
capacity is 213 900 tonnes, and the preproduction period is three years.
The commencement of preproduction work must therefore be delayed for two
years. The start of the preproduct ion peri od i s Time Zero, and the
first year of open-pit operation is Year 4 of the project.
The coordinates which delimit the blocks selected for open-pit
mining are grouped by year and level in table 18.
The blocks are
scheduled such that only perpendicular pit extension is carried out.
The number of block specifications required each year is thus kept to a
minimum, although extraction of the same material could have been
, The stripping ratio indicates the number of units of waste which
are removed to mine a unit of ·ore. The purpose of calculating the
transition stripping ratio is to determine the number of units of waste
which can be removed per unit of ore mined in an open-pit such that the
total stri ppi ng cost per unit of ore pl us the mi ni ng cost per un it of
ore equals the underground mining cost per unit of ore. This ratio
establishes the point at which underground mining is more profitable.
153
•
Table 18. Open-Pit Mine Schedu1e -- B10ck Selection by
Year and Leve1
Project Year
Leve1
1
2
3
4
B10ck
Bou~d- Pit Boundary
ary
West
N
S
W
E
N
S
W
E
N
S
W
E
5
Pit Boundary
West East North South
590
370
30
220
590
370
220
270
630
590
30
270
580
380
40
210
580
380
210
260
620 380
580 330
40. 40
260
260
550
400
50
160
550
400
160
210
580
550
50
210
4
540
410
60
130
5
530
420
70
120
6
520
430
80
110
370
320
30
270
, Coordinates defining b10ck boundaries on the north
~Nt and south (S) are in metres North. Coordinates
e ining b10ck boundaries on the west (W.) and east
(E) are in metres East .
•
154
•
Table 18. (continued)
Project Year
Level
3
Block
Boundary
6
Pi t Boundary
West
N
S
W
E
4
N
S
W
E
5
N
S
W
E
6
N
S
W
E
7
8
610
580
50
250
400
340
50
250
540
410
130
210
600
540
60
210
410
370
60
210
600
370
210
240
530
420
120
180
560
530
70
180
420
390
70
180
560
390
180
230
590
560
70
230
390
360
70
230
520
430
110
170
550
520
80
170
430
400
80
170
550
400
170
220
580
550
80
220
400
370
80
220
570
540
90
210
410
380
90
210
N
530
420
100
150
530
420
150
200
560
530
100
200
420
390
100
200
520
430
110
140
520
430
140
190
550
520
110
190
430
400
110
190
S
N
S
540
410
120
180
N
N
S
530
420
130
170
N
S
520
430
140
160
W
E
•
370
350
60
240
540
410
160
210
W
E
12
East North South
580
400
210
250
S
11
West
540
410
90
160
W
E
10
East North South
N
S
W
E
W
E
9
7
Pit Boundary
W
E
155
•
achi eved through many combi nat ions of perpendi cul ar and para11 el pit
extensions. A forty-five degree slope is maintained on the western pit
wall which is located at the contact between the deposit and the
underlying rhyolites. On levels where mining has been started in a
previous year and is being resumed, the pit is expanded along the
eastern, northern and southern boundaries. The final pit limits on each
level have been selected such that the pit walls on all sides have the
maximum slope of forty-five degrees.
Conversion to underground mining is scheduled to take place at the
end of Year 7. Underground operations are also planned on the basis of
the prel iminary data. Given that the deposit extends to a depth of
about 400 metres, a shaft sunk to 420 metres provides access to all of
the mineralized inaterial. The crown pi11ar lies beneath the open-pit,
and the base of the pi 11 ar i s at a depth of at l east 135 metres. The
base of the mineable interval associated' with a. shaft of 420 metres is
at a depth of 400 metres. The mineable interval and the number of
levels in the mine -- based on an interval between levels of 75 metres
are determined as follows:
Mineable interval = 400 - 135
= 265 metres
Number of levels = 265 / 75
= 3.53
•
The shallowest level has a vertical height of forty metres and is
composed of two subl eve l s. There are four l eve l sin the underground
mine; Level 4, the deepest level, is the haulage level.
The reserves of the underground mine are calculated with
consideration of the three fifteen-metre thick sill pi11ars which are
required to separate the four levels (figure 33). These pillars reduce
the vertical interval of the mineable reserves from 265 metres to 220
metres. Based on a mining width of twenty-five metres, strike length of
ninety metres, and mine recovery and dilution at their most-likely rates
of ninety-three percent and fifteen percent, the underground mine
reser~es are 2 012 937 tonnes.
The installed capacity of the underground mine is 300 000 tonnes
the intermediate-run unit operating cost-minimizing rate.
156
•
w
E
_25m_
Sili pillar
265 - 45
= 220 m
Figure 33: Cross-Section of the Portion of the Mineral Deposit
to be Mined Underground
•
Underground mine development requires three years. The capacity of the
mill is expanded during the year prior to start-up of underground
operat ions to match the i nsta11 ed underground mi ne capacity. Assumi ng
that the mine achieves the production targets (table 19) which have been
set in accordance with the capacity util ization policy, 360 000 tonnes
of ore are extracted in Years 8 to 10, and in Year 13 of the project.
The mine is shut down on a temporary basis for Year Il, produces 300 000
tonnes in Year 12, and util izes ninety-one percent of capacity in the
final project year to produce 272 937 tonnes.
The number of mining units to be targeted each year is determined
by dividing the planned production rate by the estimated number of
tonnes in a mining unit. Calculation of the amount of material in a
mining unit is based on a length of five metres, a vertical height of
twenty metres and a width of twenty- fi ve metres.
Mi ne recovery and
dilution are assumed to occur at their most-likely rates of ninety-three
percent and fi fteen percent, respect i vely, and the tonnage factor for
157
•
Table 19 . Production Targets for the Underground Mine
Project Year
Target Production
Rate (Tonnes/Year)
Number of Units
Targeted
8
9
10
360 000
360 000
360 000
35
35
35
300 000
360 000
272 937
30
35
28
Il
12
13
14
massive sulphides is applied:
Estimated amount of material
in a mining unit
= (5 x
=
•
20 x 25 / 0.263) x 1.15 x 0.93
10 166 tonnes
The positioning of development drifts takes into account the
forty-five degree dip of the deposit and the probable western limit of
mineral ization at 25 mE. Therefore, on Level 4, where the base of
Sublevel 1 is at a depth of 400 metres, the coordinates of the western
and eastern boundaries of the development drift are 425 mE and 450 mE,
resp6ctively. The development drifts on higher levels are positioned in
a similar manner. The shaft is sited at 425 mN, allowing exploration to
take place both north and south of the outlined reserves in regions of
possible mineralization.
Mining takes j)lace in four stopes on each level; primary and
secondary stopes on one level are shown in figure 34. Two primary
stopes are mined in sequence progressing northwards. The more southerly
stope, from 450 mN to 475 mN, has a length of twenty-five metres and is
referred to as Stope 1. Stope 2, which lies between 500 mN and 520 mN,
has a planned length of twenty metres. Should peripheral mining units
prove to be mi nerali zed, the l ength of the stope wi 11 be extended to
twenty-five metres. The stope length will be adjusted as necessary to
eliminate unmineralized mining units .
158
•
a)
Slrike length
90 m
- - - - - - -......
S
Slope 1
430mN
b)
Rib pillar
450mN
s
475mN
Slope 2
500 mN
Slope 3
430mN
F1
iii
450mN
475mN
- - - - - - -.......
159
N
.;
$%~,#.%jX;;,.;t:if;>':
W$T~t0ftf${ffi:r4;?%;
~~u:j/;,;;1/i;;'j/;f;j/
w0!~;w#;;:::Z:;hù":wfÔ
Slope 4
\1 Backfilled
~g
i%1i
'tf/'c
§{J'fff/1W4iW/f,io/:::<&/";-;fJ$J~!l#ff~~ti:~,
_»Pl?;ii~0~f%
500mN
Figure 34: a) Primary Stopes b) Secondary Stopes
•
520mN
Slrike lenglh
90 m
N
520mN
•
•
Two secondary stopes are mined on each subl evel after primary
stoping and backfilling have been completed. The more southerly, Stope
3, extends from 430 mN to 450 mN, in the southern wall of Stope l.
Stope 4 is developed in the rib pillar between the two primary stopes,
from 475 mN to 500 mN. The pl anned l ength of Stope 3 i s l ess than the
maximum permissible stope length; the length can be extended to twentyfive metres if mineralized material is found along the southern boundary
of the stope.
Given the zonation of grades in the deposit, blending can be
achieved by selecting mining units on each of the four levels of the
mine. The sublevel stoping technique provides the flexibil ity to allow
a fairly equitable division of mining units amongst the levels and
sublevels. Thus, material from the central zone of the deposit, which
is rich in copper and relatively poor in zinc, can be mixed with
material of lower copper grade and higher zinc grade from greater depth.
The underground mine schedule developed at the planning stage is given
in table 20.
The western and eastern bounding coordinates of the
development drift at the base of each level are shown below the level
number. All development drifts and stopes are twenty-five metres wide.
For each combi nat ion of l evel, stope and subl evel, the southern and
northern coordi nates defi ne the boundari es of the block of sel ected
mining units. Figure 35 is a projection of the sublevel stopes on to a
longitudinal section; it shows the planned sequence of underground
mining, and indicates the areas of potential mineralization along the
northern boundary of Stope 2, and south of the periphery of Stope 3 on
each level.
The mine plans are followed as closely as possible during the
sample run of the Mine Manager. At the appropriate prompts, the openpit mining method is selected with a delay of two years in the start of
preproduction work. The metal priees and rates of cost and general
inflation during the period of delay are reported to the user through an
information display as shown in figure 36. At the start of the project,
Time Zero, the user specifies the installed annual mine and mill
capacities, and receives information about the estimated capital costs
of plant construction, in current dollars, in a summary report of
construction parameters (figure 37). Total capital expenditure for the
160
•
a
Sublevel : southern boundary of block (mN) - northern boundary
of block (mNl
b
Coordinate (mE) of the western boundary of the development drift
at the base of the level
C
Coordinate (mE) of the eastern boundary of the development drift
at the base of the level
161
•
Table 20 . (continued)
Project Year
Level
Stope
1
1
W200
E 225
2
3
12
1
W275
E 300
2
3
1:475-500
2:475-500
1: 440-450
2:430-450
3:430-450
4
3
1
W350
E 375
2
3
1:475-500
2:475-485
1:430-450
2:430-450
4
4
1
W350
E 375
2
3
1:430-450
2:430-450
2:475-500
3:475-500
3:430-450
1:475-500
162
2:485-500
3:475-500
3:430-450
1:475-500
4
•
14
2:430-450
4
2
13
2:475-500
3:475-500
•
s
N
Level I-.-------~
1
1
1
?
h====m
: . 1111,111"","\1
1
1
1
1
2
?
I?
1
1
1
: 1\'lllli
3
4
1
1
1
1
I?
1
1
1
1
1
1
1
?
1
1
1
1
1
1
1
1
1 ?
1
1
1
1
1
1
1
1
?
1
1
1
450 mN
475mN
Project year
Mining unils
targeted
8
35
9
35
.~û111
10
35
Closed
11
••
;,
•
1
1
430 mN
LEGEND
1
1
.
500mN
0
••
?
520mN
Projecl jear
Mining units
largeled
12
30
13
35
14
28
Possible mineralization
Figure 35: Horizontal Projection of Stopes on to a Longitudinal Section
Showing the Planned Underground Mining Sequence
163
•
The start of prepr~uctian wark has been postponed for 2 years.
Ouri.nQ t(lis period. the average aIYlual free narket priees for
capper, zinc and goLd, and the rates of cost and generat inflation
are as fat Law:
YEAR
1
2
Fl~Print
--------------COPPER (S/lB)
PRICE (USS)
ZIHC (S/lB)
0.74
0.75
0.33
0.42
sereen and continue
------------GOlO (S/OZ)
220.59
161.41
IHFlATIOH OD
COST GEHERAl
4.0
3.6
5.5
5.0
<EHTER)-Continue
Figure 36: Metal Priees and Rates of Inflation During the
Period of Delay
•
SUHHARY OF COHSTRUCTIOH PARAHETERS AHO ESTIHATEO UHIT OPERATIHG COSTS
Installed open-pit Rine capacity (tpa): 2200000
Installed Rill capacitu (tpal: 213900
Preproduction period (years): 3
Capital costs (thousand S):
Hine:
Hill:
~(1E?5.400
14249.144
16426.337
Estinated unit operatlng costa for
full capacity operations (S/tonne)
Hine:
Hill:
1. 71
21.95
Fl-Print screen and continue <EHTER>-Continue
•
Figure 37: Summary of Construction Parameters and Estimated
Unit Dperating Costs for the Dpen-Pit Mine and Mill
164
•
mine and mill is estimated at $30.7 million. The report confirms the
selected initial mine and mill capacities and states the length of the
preproduction period.
The estimated operating costs at full capacity
are $1.71 per tonne mined and $21.95 per tonne milled.
The cash flows in each year of the preproduction period are shown
in current dollars in a single statement (figure 38) following the
selection of the initial plant construction parameters. As production
has not yet begun, no revenue has been generated and operating costs
have not been incurred.
Tax al 1owances are claimed during the
preproduction period resulting in Immediate tax credits which help to
offset the impact of capital expenditures on cash flow.
The capital
expenditures for the plant increase each year due to inflation. Working
capital of $2.5 million is required at the end of Year 3 of the project.
The rates of i nfl at ion duri ng the preproduct i on years appear in the
statement, and are used in subsequent cost est imat ion.
The user i s
informed of the metal priees during this three year period (figure 39):
CASH FLOU -- YEARS 1-3 (thou.
Year
$)
1
Revenue
Operating Costs
TaK Allowances
Taxabll! Inca""
laMes
Capital EKpl!nditurl!
Working capital
2
3
0.000
0.000
1593.591
-1593.591
-418.077
10623.941
0.000
0.000
O.UOO
3026.230
-3026.230
-901.869
11144.514
0.000
0.000
0.000
4325.885
-4325.885
-1291.165
11690.596
2530.085
-10145.864
-tO'-35.646
-12922.915
----------------------------------------------------------
Cash Flow
Inflation Ratl!S
Cost
General
3.9~
5.4~
FI-Print screen and continue
•
4.9~
6.1%
4.9%
6.1%
<EHTER>-Cmltinue
Figure 38: Cash Flow -- Years 1 - 3
165
•
The aueraQe annual free ~arket priees for copper,
durina the preproduction period are shaun below.
YEAR
---------- •• --COPPER (S/LB)
0.60
0.60
0.72
1
2
3
Fl-Print screen and continue
PRICE (USS)
ZIHC (S/LB)
zinc
and
Qold
------------GOLO (SI OZ)
0.41
0.40
0.36
467.42
356.00
418.69
<EHTER>-Continue
Figure 39: Metal Priees -- Years 1 - 3
•
these priees are incorporated in the priee forecasting model.
Production begins as scheduled in Year 4.
In each production
year, prior to the selection of material for mining and milling, the
user provides estimates of the average priees, in U.S. dollars, of
copper, zinc and gold, and an estimate of the U.S.·Canadian dollar
exchange rate which will prevail in the current year.
The priee
estimates used are the one-period-ahead forecasts from Holt's
exponential smoothing: $0.91 per pound of copper, $0.50 per pound of
zinc, and $635.12 per ounce of gold in Year 4. The most-likely currency
exchange rate of $0.86 U.S. dollars per Canadian dollar is taken as the
estimate of the exchange rate for each production year of the sample
run.
Bl ocks, or groups of mi ni ng uni ts, are sel ected for dri 11 i ng and
extraction by specifying the level and the pit boundary on which mining
is to take place, and the block boundary coordinates according to the
mine schedule in table 18. In Year 4, mining takes place on Levels 1 to
3 of the open-pit. The grades of mineralized mining units, estimated on
the basis of drillhole samples, are available to the user. Figure 40
166
•
GRnDES OF HIHERnLIZEO HIHIHG UHITS ESTIHnTEO FRDH BLOSTHDlE SAHPLES
-------------------------------------------------------------------
HO. OF HIHIHG UHITS SELECTED: 418
HO. OF HIHERALlZED HIHIHG UHITS: 5
LEVEL 1. UESTERH PIT BOUHOARY
UESTERH COORDIHnTE OF HIHIHG UHIT(S) (ME): 50
SOUTHERH
COORDIHATE
OF HINIHG
UHIT (MH)
H
UHIT
UHIT
UHIT
UHIT
UHIT
5
4
3
2
1
ESTIHATED GRADE
--------------------------------------
COPPER
(~)
GOLO
(DIT)
-----------------------------------------------------490
0.32
460
470
460
450
FI-Print sereen and continue
2.25
1.23
5.26
1.65
3.27
3.34
1.22
3.51
0.99
4.66
3.45
1.60
4.01
0.67
<EHTER>-Continue
Figure 40: Estimated Grades of Mineralized Mining Units
on Level 1 of the Open-Pit
•
shows the estimated grades of mineralized mlnlng units drilled on Level
1. The grades are listed with their corresponding mining unit numbers.
These are placed in sequence from north to south for units to be mined
along the western or eastern boundaries, and from east to west for units
to be mined along the northern or southern boundaries. If more th an one
row of units had been selected for mining, the estimated grades of units
in the most westerly row or the most southerly row would be 1isted
first.
The level, and the coordinates of the southern and western
boundaries of each mining unit are also listed, th us providing the exact
This information display
location of each unit in the open-pit.
indicates that of the mining units selected on Level 1, none of those
west of 50 mE or east of 60 mE are mineralized. The deposit tapers off
towards the surface, and has a stri ke 1ength of no more th an fi ft y
metres within the first ten metres of depth.
After each pit increment, an update is given regarding the number
of units mined and the actual amount of material extracted. When mining
of the targeted units on the first three levels of the open-pit has been
completed in Year 4, the total mine production is approximately 40 000
167
•
tonnes less than that expected according to the mlnlng plan (2 568 816
tonnes). The user has the option of continuing mining operations in the
current year.
Ore extraction could be started on Level 4, but this
would reduce ore production in at least one subsequent year. Additional
stripping would increase operating costs without generating revenue.
Ci ven that pri ces have not yet peaked in the current peri od of pri ce
recovery, pl anned ore product i on for the upcomi ng years shoul d not be
decreased as this would reduce the potential for the firm to benefit
from an expected ri se in pri ces.
Incremental stri pp; ng costs can be
postponed without loss of revenue, and therefore the decision is taken
not to continue mining.
The east-west pit profile aftel' the first year
of mining is shown in figure 41.
Informat i on about the grade- and val ue-tonnage rel at i onshi ps of
mined units is provided each year after mining activities have been
completed.
Figure 42 shows the value-tonnage distribution
the
tonnage and est imated average value of extracted materi al havi ng an
estimated value greater than or equal to a series of cut-off values.
The
cut-off values
intervals
within
are
the
calculated
such
that
range of estimated values
there
are
associated
five
with
equal
the
w
E
~'------------..
evell
30 mE
Level2
220 mE
Level3
..
...
•
110m
•
170m
•
190m
Figure 41: East-West Profile of the Open-Pit at the End of Year 4
168
•
•
VALUE - TOHHAGE RElATIOHSHIP -- YEAR 4
The tonnage - value per tonne relationship for the units l'dned tllis
year is shown in the table below. Average values represent the
esti~ated net reatizable revenue per tonne nilled, i.e., nining and
estiAated Rilling losses, dilution and estinated net snelter relurn
have been accounted for.
eUT-OFF VALUE
ISlTOHHE)
26.01
156.84
287.67
418.49
549.32
TOHHAGE ASOVE
eUT-OFF
166519
80118
17912
7055
3527
AVERRGE VALUE RSOVE
CUT-OFF ISlTOHHE)
176.56
265.43
402.50
550.40
680.15
Hate: 2362162 tonnes of nined "atertal, assuned to be unnineratized. are not reflected in the value-tonnage retatiol'lShip,
Fi-Print sereen and continue
<EHTER>·Continue
Figure 42: Value-Tonnage Relationship -- Year 4
mineralized mlnlng units removed from an open-pit, or with all of the
mining units extracted from an underground mine.
The grade-tonnage
45) are
relationships for copper, zinc and gold (figures 43
established in a similar manner and are based on the estimated grades.
In each year of open-pit mining, only the mining units which are
cons idered ta be unmi neral i zed are dumped.
Th i sis accomp l i shed by
selecting a cut-off value and cut-off grades of zero ta distinguish
between ore and waste. Stockpil ing decisions are guided by policy and
requi re an est imate of the unit mill c.perat i ng cost for the current
year. The estimate is produced by inflating the value obtained from the
mill operating cost functions'. The actual cast inflation rates during
the period of delay before the start of preproduction work, and during
the project itself, are combined with an estimate of the rate of
inflation for the current year. The most-likely rate of cost inflation
•
1 The cast functions yield values which are in dollars of the end
of the fifteen-year historical period.
169
•
GRADE - TOHHAGE RELATIOHSHIP -- YEAR 4
•
Th~
copper grade - tonnage relationship for the units
uear 15 shmm in the table below .
Ained
CUT-OFF GRADE
(l( CDPPER)
TOHHAGE ABDUE
CUT-OFF
AVERAGE GRADE ABOVE
CUT-OFF (l( CDPPER)
0.10
1.14
166519
118419
67845
21714
3527
1. 90
2.40
2.11
3.21
4.24
this
3.03
3.96
5.28
Hote: 2362162 tonnes of nined ~aterial, assu~ed to ~e unAineralized, are not reflected in the value-tonnage relationship.
FI-Print sereen and continue
(EHfER>-Continue
Figure 43: Grade-Tonnage Relationship for Copper -- Year 4
GRADE - TOHHAGE RELATIOHSHIP .- YEAR 4
The zinc grade - tonnage relationship for the
uear 15 shown in the table below.
units
Ained
CUT-IIFF GRADE
(l( 2IHC)
TOHHAGE ABOUE
CUT-OFF
AVERAGE GRADE ABOVE
CUT-OFF (l( 2IHC)
0.28
3.88
7.40
11.08
14.68
166519
108387
73938
35824
24967
7.23
10.01
this
12.03
15.14
16.23
Hote: 2362162 tonnes of Mined Material, assûMed to be unMineralized, are nDt reflected in the value-tonnage relationship.
FI-Print screen and continue
•
<EHTER>-Continue
Figure 44: Grade-Tonnage Relationship for Zinc -- Year 4
170
•
GRADE - TOHHAGE RElATIOHSHIP -- YEAR 4
The
QOl.d
grade - tonn""Oe relations,'lip for the
year i5 shown in the tabLe below.
eUT -lIFF GRAOE
(GIT DOlO)
0.46
8.71
16.97
25.22
33.47
TOHHADE ASOVE
CUT-DFF
ooit5
rdned
this
AVERAGE GRACE ASOUE
CUT-OFF (OIT DOlO)
166519
66058
10582
7055
3527
8.71
15.49
29.06
34.75
41.72
Hate: 2362162 tonnes of ~ined naterial. assuned to be unninerali2ed. are oot reflected in the value-tonnage relationship.
&
Fl-Print screen and continue
<EHTER>-Continue
Figure 45: Grade-Tonnage Relationship for Gold -- Year 4
•
is used in the sample run as an estimate of the rate of cost inflation.
In Year 4, all mineralized mining units which have an estimated average
value of less than $27.58 per tonne, the unit mill operating cost, are
stockpiled. Thus Stockpile 1 is created, and contains 2 978 tonnes at
an estimated grade of 0.17 percent copper, 2.50 percent zinc and 1.17
grams per tonne gold at the end of Year 4. The remaining mineral ized
material is supplied to the mill.
Figure 46 shows a report summarizing the annual operations of the
plant. It states the number of tonnes r,lined and milled, and the mill
feed grade. In Year 4, mi ne production was 2 528 682 tonnes and mi 11
throughput was 163 542 tonnes.
Mill production was lower th an
originally expected because many of the mining units which were thought
to be mineral ized were, in fact, barren. In the years in which mining
operations take place underground, the rates of dilution and mine
recovery al St' appear in the operat ing summary. The mill recovery and
net smelter return for eaçh metal and the unit operating costs of the
mine and mill are stated in the report. If either the mine or the mill
had been closed on a temporary basis, the costs of maintainin9 the
171
•
SUHHARY OF OPERATIOHS (OPEH-PIT HIHElHILL) -- YEAR 4
Tonnes Mined:
Tonn~
Ftilled:
Hitle<! grades:
Hill recovery:
Het BRetter return:
2528682
163542
1. 76 YoCu
9.11 y,zn
8.64 g/t Au
eu
zn
Au
eu
zn
------
92Y.
87r.
60%
71Y.
38%
93Y.
Hine operating cast:
SI.79/tonne
Hill operating cast:
$l7.38/tonne
Ho eKploratory dril1ing was carried out.
Au --
FI-Print screen and continue
<EHTER>-Continue
Figure 46: Summary of Operations -- Year 4
•
facility on a stand-by basis would be provided.
The user is also
informed of the costs, when incurred, of drifting underground and of
exploratory drilling in the open-pit or underground mine.
After stockpiling operations have been completed, a report on the
status of the stockpiles is available (figure 47). This report contains
information on the tonnage of stored material, and the estimated average
grades of copper, zi ne and gol d associ ated wi th each stockpil e. The
user also has the option of viewing the stockpile status report in a
year in which no stockpiling operations were carricd out.
To aid the planning of future mining and milling operations, a
currency report is available at the end of each operating year. The
report discloses the free market priees for copper, zinc and gold, the
rates of cost and general inflation, and the exchange rate for the
current year. The currency report for Year 4 i s shown in figure 48 .
.The actual priees for copper and zinc are close to their respective
forecasts, but the priee of gold is much lower than the fo~ecast priee.
The actual exchange rate is higher than the estimate used.
Before the net cash flow for the year can be calculated,
172
•
STOCKPILE STATUS
REPO~T
- YERR 4
ESTIMATED GRADE
STDCKPILE
HUMBER
TOHHAGE
1
2976
CDPPER (lIl
0.169
o
o
o
2
3
4
FI-Print seree" and continue
ZIHC (:1)
GOLO (G/Tl
Z.499
1.167
<~TER>-Continue
Figure 47: Stockpile Status Report -- Year 4
PRICE AHD CURREHCY REPORT -- YERA 4
Price
capper (US$! lb)
Gold (USS/oz)
Zinc (USS/lb)
Inflation Rate
cast
General
EMchange Rate (US$/Cdn$)
0.69
416.95
0.46
4.0:1
5.4:1
0.91
FI-Print screen and continue
•
<EHTER>-Continue
Figure 48: Currency Report -- Year 4
173
•
management's plans for the mine and mill must be specified: closure on a
temporary or permanent bas i s, or operation the fo 11 owi ng year.
The
specified plans determine the amount of working capital, if any,
required for the fo11owing year, and th us the level of net working
capital -- the difference between working capital recovery and input.
At the end of Year 4, the user indicates that mining activities are
planned for the next year. It is not necessary to specify that the mi)l
will also be operating; this is assumed to be the case whenever the mine
is in operation.
During the operating phase of the project, cash flow statements
are produced on an annual basis.
The items listed in a cash flow
statement, such as is shown in figure 49 for Year 4, are the revenues,
operating costs, tax allowances, taxable income, corporate income taxes,
capital expenditure and working capital. Each source of revenue in the
ore concentrates i s i terni zed, mi ne operat i ng costs are di sti ngui shed
From mill operating costs, and the annual sustaining capital is shown.
CASH FLOU -- YEAR 4 (thou.
$)
----------------------------Revenue
concentrate (USSO.89/Ib Cu)
:
credits in Cu cone (US$416.95/oz Ru):
zn coneentrate (USSO.48/Ib Zn)
:
Operating Costs
Hine
Hill
PerAanent plant closure
TaM Allowances
Cu
Au
4065.500
11594.236
5828.092
4514.203
4476.992
Il.000
raMaille Irx:one
TaMes
Capital EKpenditure
Annual Sustaining capital
Hine
Hill
Het UorkinQ capital
140.272
58.601
Cash Flow
8991.195
3T06.833
8789.800
2636.940
0.000
198.873
lOI. 2113
9559.616
Annual Rates -EMchange: Il.91 USS/CdnS
Cost Inflation: 4.11%
FI-Print screen and continue
•
2148T.828
Gen. Inflation: 5.4%
~EHTER>-Continue
Figure 49: Cash Flow Statement -- Year 4
174
•
•
The term 'maintenance' appears under the operating co st heading if the
mi ne or mi 11 has been closed on a temporary bas i s for the gi ven year .
'Mine (closed)' signifies that the mine has been closed on a permanent
basis. The net cash flow for Year 4 is about $9.6 million.
The ~nnual cost inflation rates and general inflation rates are
appended to all cash flow statements. The annual exchange rate between
the U.S. dollar and the Canadian dollar is appended to each cash flow
statement during the operating life of the plant. It is during this
peri od that revenue i s generated from the sal e of metal concentrates .
The amount of revenue, in Canadian dollars, is influenced not only by
the market for metals, but also by the currency exchange rate given that
the annual prices are expressed in U.S. dollars.
At the end of Year 4, the user indicates that conversion of the
mining method is planned, and that underground mine development must be
started in Year 5. This ensures that conversion of the mining method
can take pl ace as pl anned at the start of Year 8. The user spec ifi es
the parameters of the underground mine, and receives a summary of
construct ion parameters and est imated uni t operat i ng costs for the mi ne
(figure 50).
A capital expenditure of about $17.4 million is
anti ci pated for underground mi ne development. The est imated operat ing
costs at full capacity are $25.81 per tonne mined.
These monetary
amounts are in current dollars.
The current prices for copper, zinc and gold are incorporated in
the price forecasting model to produce the forecasts for Year 5: $1.03
per pound of copper, $0.56 per pound of zinc and $346.82 per ounce of
gol d. The mi ne plan refl ects the updated i nformat ion j overcapac ity
production will take place with block selection as indicated in table
18. The value-tonnage relationship, summary of operations, stockpile
status report and cash flow statement for Years 5, 6 and 7 are shown in
appendix 5. Mine production and mill production are close to their
respective targeted levels in the last three years of the open-pit mine
li fe. East-west pi t profil es at the end of each of the se years appear
in figure 51.
Stockpiling operations lead to the augmentation of Stockpile l,
and the creation of Stockpiles 2 and 3 in Year 5. ln Year 6, material
is added to Stockpiles 2 and 3, and in Year 7, the amount of material in
175
•
SUHHAPY OF CONSTRUCTION PARAHETERS AND ESTIHATEO UNIT OPERATING COSTS
Installed underground Aine capacity (tpa); 300000
Shaft depth (A): 420
Shaft site northing
(~H):
425
Preproduction period (years): 3
Capital costs (thousand
$) --
underground Aine
17381.484
Estinated unit operating costs for
full capacity operations at
underground hine (S/tonne):
~I-Print
screen and continue
25.81
<EHTER>-Continue
Figure 50: Summary of Underground Mine Construction Parameters
and Estimated Unit Operating Costs for the Mine
a)
w
E
30 mE
~70mE
..
..
•
~
30 m
160 m
240m
Figure 51: a) East-West Profile of the Open-Pit at the End of Year 5
176
•
b)
w
E
30mE
270 mE
30m
...
c)
150 m
240m
w
E
:!<l mE
270mE
20m
160m - - -....~
...
•
240m
Figure 51 (continued): East-West Profile of the Open-Pit at
the End of b) Year 6 and c) Year 7
177
•
Stockpiles 1 and 2 is increased. The creation of Stockpi1es Z and 3 is
necessary because in Years 5 to 7, more mineralized material is
extracted from the open-pit mine th an can be accommodated by the mi 11.
This may be due in part to underestimation of the size of the deposit.
An increase in ore reserves results from internal dilution; the sides of
the mining units are vertical and therefore can not be aligned perfect1y
with the inclined deposit-host rock contact.
At the end of Year 6, the parameters of a mill expansion program
are specified.
The expansion of the mill to an installed annual
capacity of 300 000 tonnes, i s to be compl eted by the end of Year 7.
The expansion proyram has an estimated capital cost, in current dollars,
of $3.8 million (figure 52).
Cash flows are positive in Years 5 and 6 in spi te of the capital
expenditure associated with the development of the underground mine. In
Year 7, when metal priees are depressed and an additional capital
expendi ture i s requi red for expans i on of the mi 11, the cash fl ow i s
SUHHARY CF COHSTRUCTIOH PARAHETERS AHO ESTIHATED UHIT OPERATIHG COSTS
EKpanded "i11 capacity (tpa): 300000
Period required for
~il1
expansion (years): 1
Capital costs (thousand S) -- ni11 ewpansion:
3784.442
Estinated unit operating costs for full capacity
operations at eKpanded ni11 (S/tonne): 25.45
Fl-Print screen and continue
•
<EHTER>·Continu~
Figure 52: Summary of the Mill Expansion Program and Estimated
Unit Operating Costs for the Mill
178
•
negative. At the end of Year 7, the open-pit mine is closed.
In the first year of underground operations, Year 8, material is
extracted from Stope 1 on Levels 1 to 4. Figure 53 is an information
display of the estimated grades of mining units selected on Sublevel 1
of Level 1. The grades are l isted with the corresponding mining unit
numbers in sequence from north to south.
The level and sllblevel
numbers, the coordinates of the southern boundaries of the mining units,
and the coordinates of the western and eastern stope boundaries at the
base of the mining units are also given.
Mining is completed on
Subl evel s 1 and 2 on every l Evel except for Level 4. The select i on of
blocks of mining units according to the mine plan leads to extraction of
325 979 tonnes of material. The remaining mine capacity is calculated
as follows:
Remaining mine capacity = limit of overcapacity production tonnes mined
= 360 000 - 325 979
= 34 021 tonnes
HIHIHG UHIT GRADES ESTIHATED FROH BLASTHDlE SAHPLES
LEVEL 1
SUBLEVEL 1
WESTERH COORDIHATE OF BASE OF HIHIHG UHIT(S) (AE): 200
EASTERH CDORDIHATE OF BASE OF HIHIHG UHIT(S) (AE): 225
SOUTHERH
COORDlHATE
OF HIHIHG
UHIT (AH)
H
UHIT
UHIT
UHIT
UHIT
UHIT
5
4
3
2
1
470
465
460
455
450
ESTIHATED GRADE
CoPPER
on
18.32
8.77
2.15
5.13
4.50
2IHC (r.)
7.28
14.75
8.1~
9.86
4.18
GOLO (G/Tl
5.82
7.02
4.93
10.73
4.94
FI-Print screen and continue <EHTER>-Continue
•
Figure 53: Estimated Grades of Mining Units on Level 1,
Sublevel 1 of Stope 1 in the Underground Mine
179
•
•
The minimum number of mining units which can be extracted is a
function of the remaining mine capacity and the maximum amount of
material which can be mined as a unit. This maximum amount of material,
11 407 tonnes, is calculated on the assumption of full mine recovery,
twenty percent dilution, and a completely mineral ized mining unit of
twenty-five-metre width. The minimum number of mining units which can
be extracted is therefore 2.98, or 2 whole units.
After extraction of two mining units from Sublevel 2 of Stope 2 on
Level 4, the remaining mine capacity is recalculated at 15 120 tonnes.
The amount of material mined per unit is less than the maximum amount of
11 407 tonnes, determi ned as above.
The rema in ing mi ne capac ity i s
utilizecl ta extract an additional mining unit on Sublevel 2, bringing
the total amount of materi al mi ned in Year 8 ta 354 330 tonnes from
thirty-eight mining units.
The stockpiling policy is the same as that implemented during the
open-pit mine l ife, but does not lead ta stockpil ing of material from
the underground mine in Year 8. The value-tonnage relationship, summary
of operations and cash flow statement for Year 8 and the remaining years
of the project appear in appendix 5. The stockpile status report is not
given Years 8 to 13; there was no transfer of material into or out of
the stockpiles during this period, and therefore the status of the
stockpiles remains unchanged from that reported in Year 7. The summary
of operations shows that the actual rates of mine recovery and dilution
in Year 8 are ei ghty-ei ght percent and thi rteen percent, respect i ve l y.
These rates are less than those used in calculating the amount of
material to be mined as a unit for planning purposes, and this accounts
for the fa ct that more mining units can be extracted than originally
planned. Costs are incurred for drifting from 425 mN, the shaft site
northing, to 475 mN, the northern limit of Stope 1.
In Year 9, on each level, mining is completed in Stope 1, and
blocks of five mining units are selected in Stope 2 on Sublevel 1 of
each level. All of the drilled mining units are extracted except on
Level 2 where the peripheral mining unit is unmineralized. The maximum
leng~h of Stoole 2 on this level is therefore twenty metres.
As shown in
figure 54, the length of the same stope on Sublevel 3 is only fifteen
metres; the deci si on to reduce the stope l ength from that pl anned i s
180
•
s
N
Level
1
1
IX
1
2
1
X,
1
3
1
IX
1
4
430mN
LEGEND
•
475mN
450mN
••
500 mN
Mining un~s
Project year ex1racled
8
38
9
36
Il
10
35
Closed
11
D
Il
II
X
520 mN
Mining units
Project year ex1racled
33
12
13
37
14
32
Samples unmineralized
Figure 54: Horizontal Projection of Stopes en to a Longitudinal Section
Showing the Actual Underground Mining Sequence
181
•
•
based on drilling results: the samples retrieved from the most northerly
mining unit on the sublevel are unmineral ized. On Level s 1 and 3, Stope
3 also has a length of less than twenty-five metre. In Years la and 12,
unmineralized drill core samples are retrieved from the peripheral
mining unit on Sublevel lof these two levels, and therefore the stope
is not extended to its maximum length. The corresponding mining units
on upper sublevels are not dri11ed as they can not be extracted given
the constraints of the mining technique.
Mine and mill production falls below target in Years 9 and la when
sorne of the drilled mining units prove to be unmineralized. In both of
these years, the rema ini ng mi ne capaci ty i s over 9 000 tonnes but i s
insufficient for further extraction given that stope width i s twentyfive metres.
The plant is closed for Year Il as planned, and
maintenance costs are incurred for the mine and mi11.
In Year 12,
policy dictates that the mine should operate at the stated capacity,
that is, 300 000 tonnes should be produced. Management has the ability
to override policy, and in light of the increased reserves in peripheral
zones, a decision is taken to raise the level of production by
extracti ng three addit iona1 mi ni ng units. Thi s reduces the chance of
reserves remaining in the ground at the end of the planned project life
of fourteen years.
Given the assumption that mining and processing
occur at a uniform rate throughout th'=! year, a sma11 amount of ore is
associated with a low rate of capacity utilization and high unit
operating costs. An attempt is made to avoid the situation in which a
choice must be made between a low level of capacity utilization and the
abandonment of mineralized material. The existing stockpiling policy is
implemented in Year 12 and, as no material is added to the stockpiles,
the mill receives 319 000 tonnes of direct feed, exceeding its
requirements by six percent.
Plant production is close to the limit of overcapacity at 355 584
tonnes in Year 13. In the final year of operations, Year 14, mine
production exceeds the target in the mine plan as Stope 4 is mined out
and the mi ne reserves are exhausted. Based on the two-peri ods-ahead
pri ce forecasts, mi 11 i ng of the stockpil ed materi al in Year 15 i s not
economically justifiable. In Year 14, the estimated average value of
material in Stockpile 3 is greater than the estimated unit mill
182
•
operating cost, and a decision is taken to supplement the direct mill
feed of 321 152 tonnes with 38 847 tonnes from this stockpile. The mill
therefore operates at twenty percent over the stated capacity in Year
14. The option still exists for the mill to remain open in Y2ar 15 to
process the remaining stockpiled material; however, this proves to be
un justifiable on the basis of the one-period-ahead forecasts which are
generated when the actual priees for Year 14 become available.
The financial performance report (figure 55) shows the results of
the financial evaluation of the mining project. The total cash flow is
over $62 million constant dollars.
A rate of return of twenty-four
percent is achieved in spite of negative cash flows in two years of the
production period: Year 7 in which a capital expenditure was associated
with expansion of the mill in addition to underground mine development,
and Year Il in which the mine and mill were closed on a temporary basis.
The net present val ue at the start of the preproduct i on peri od ranges
from $35.4 million dollars at a discount rate of five percent, down to
-$683 900 at a discount rate of twenty-five percent.
FIHAHCIAL PERFORHAHCE REPORT
Honetaru values are in Tine 0 constant dollars
Total cash flow:
Rate of return:
Discount
Rate
62044.833 thousand $
24.00 1.
Het Present Value
(thou.
5 1.
101.
15 1.
20 1.
25 1.
FI-Print screen and continue
•
$)
35438.219
19504.609
9642.092
3315.619
-683.900
<EHTER>-Continue
Figure 55: Financial Performance Report
183
•
•
CHAPTER 6
SUMMARY. LIMITATIONS AND RECOMMENDATIONS
6.1 Summary
Most of the previous studies of the mine in economic theory focus
on decision making under conditions of certainty.
In reality,
uncertai nty characteri zes the mi ne envi ronment, and its i ncorporat ion
into the study of mine decisions increases the need for more complex
tools capable of representing the actual mode of decision making.
There are few mining games in existence.
ïhey provide
participants with the opportunity to gain management experience in
functional areas such as metal marketing, production scheduling and
product transportation.
The models which have been used as the basis for previous studies
on the mine in economic theory or for earl ier mining games have been
limited in some respects. For example, decision making with respect to
the cut-off grade and/or production rate has been exami ned without
consideration of the capacity installation dEcision, conditions of
certainty have been assumed, or decision making has been restricted to
certain functional areas of management while ignoring the technical
aspects of mining operations.
A model of the sequence of decisions required for mine development
and production has been formul ated through the current research and i s
operated as a computer-based game, thus meeting the goal of the project.
The Mine Manager is an operations research game in which the mine
envi ronment and the mi ne deci sion-maki ng process over a peri od of t ime
are simulated. The Mine Manager may also find application in education
and training in mine economics. It can be used for experimentation with
individual operating policies or policy combinations. Potential us ers
are students at the university level, and mine decision-makers from the
operational ta upper management levels. The Mine Manager is described
using the terminology of games.
The Game is based on a comprehensive mining system rather than on
the more limited spectrum of issues addressed in other mining games. It
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ca11 5 for decisions to be made at both the development and production
stages, and reflects the sequential nature of the decision process
throughvut the project life. The selection of parameters to be included
and of the l evel of deta il in the model requi red a compromi se between
realism and simplicity. Decisions must be made with respect to the
mi ni ng method -- open-pit and/or underground, capaci ty i nsta11 at ion and
utilization, eut-off grade and/or eut-off value, the sequence of mining,
stockpiling and mine closure.
The model offers a high degree of
flexibility in setting the values of decision variables in terms of both
the range of permissible values and the fact that values can be varied
during the mine life.
The Mine Manager is fu11y interactive, providing immediate
feedback of the results of decisions and eliminating the need for agame
administrator. Due to its interactive user-friendly nature, training is
unnecessary for users; however, it is advisable that the game manual be
read before play begins.
The player is provided with preliminary geological data, typical
cost functions and historical metal priees. The user inputs data based
on the decisions which have been made, the input is validated and mining
activities simulated.
The focus of simulated mining activity is a massive sulphide
deposit containing copper, zinc and gold.
The selection of the
characteristics of the mineral deposit was guided by a review of massive
sulphide deposits in the Abitibi region of Quebec.
The grades of
copper, zinc and gold in the deposit were generated on the basis of
prespecified vari ograms and grade di stri buti ons.
The si mul at ion was
conditioned in order to replicate zoning patterns found in many deposits
of this type, that is, a copper-rich core flanked by a zinc-rich zone.
Transformation of the three-dimensional grid produced by the simulation
resulte~ in a moderately-dipping lense-shaped deposit.
Mining operations in an underground and open-pit mine have been
modelled. The technical aspects of mining which have been incorporated
in the Game reflect some simpl ification, but significantly increase the
level of realism over models in which there is no consideration of the
mining sf'quence at the mlnlng unit level. The degree of complexity of
game-playing is also raised but not to such an extent as to be
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considered unmanageable for the user.
Mine sequencing, and the
result i ng configurat ion of underground· stopes and pill ars and of openpit boundaries, follow certain guidel ines intended to ensure a
reasonable approximation to normal operating practice.
Any mine
designed within these constraints is considered to be feasible.
Th~ size of the plant to be installed determines the length of the
preproduction period. A delay in the start-up of preproduction work is
possible, and production at a rate which is above or below the stated
installed capacity is considered feasible. It is assumed that a gradual
build-up to full capacity operation is unnecessary.
The installed
capacity can be expanded during the production period which l asts a
maximum of forty-five years.
Given that the dsposit is fixed, it is the intermediate-run
capital costs which are relevant in the Game.
The initial capital
investment is a function of the level of installed capacity.
The
hypothetical capital cost functions for the open-pit mine, underground
mine and mill generate costs which are close to 1990 cost levels. In
addition to the initial capital investment, working capital, annual
sustaining capital and the capital required for an expansion of capacity
are considered.
The model of capital cost behaviour incorporates
uncertainty as well as the effect of inflation on the level of costs.
A pricing model is used to generate series of copper, zinc and
gold prices for the Game. The behaviour of the simulated metal prices
is similar to that of prices on the London Metal Exchange between 1973
and 1987. Price behaviour is described in terms of a trend, cyclicality
and a random component. The simulation of prices is designed so as to
central ize priees and reduce the frequency of extremely low or high
priees.
Hypothetical intermediate- and short-run operating cost functions
have been developed for the mine and mill. The intermediate-run average
operating cost curve is defined as the locus of short-run operating cost
minima, and thus, differs from the theoretical curve which is the
envelope of. short-run cost curves. The short-run unit operating costs
are rel ated to the 1evel of capacity ut il izat ion. The operat i ng cost
functions yield values which are of a similar level to actual operating
costs in 1990. Uncertai nty and infl at ion have been inel uded in the
186
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operating co st model.
The selection of extracted mlnlng units for stockpiling, milling
or dumping is facilitated by the provision of information on their
va1ue-tonnage and grade-tonnage rel at i onshi ps. The est imated average
value of the mined material can be compared directly to estimated cost
of ore processing.
The other parameters of the mine envi ronment which have been
modelled are dilution, mine and mill recovery, and the net smelter
relationship. The most·likely values of dilution and mine recovery have
been assigned on the basis of average mine operating conditions. The
mill recoveries of copper and zinc are functions of the mill head grades
while a typical recovery rate for gold is assumed.
The after-tax cash flow of the mine/mill plant is calculated
annually, and is based on a simple profit taxation model.
For tax
purposes, the mi ni ng fi rm i s treated as part of an i ntegrated company.
Project evaluation is based on financial performance, and discounted
cash flow techniques are applied to the constant (Time Zero) dollar cash
flow distribution associated with the project. Time Zero is the start
of the preproduction period.
The sequence of decisions determines th~ consecutive states of the
mini ng system from year to year throughout the project 1ife, that i s,
from the development period until the end of the production period. The
simulated mining and milling activities arising from the decisions of
mine management are assumed to occur at a uniform rate during a given
year. The sequence of deci si ons for underground mi ne operat ions i s
simiiar to the sequence for open-pit operations except that mining units
are selected on sublevels in stopes rather than along boundaries of
specified levels. If underground mining is chosen there is no option to
convert to a different mining method, but shaft deepening may be
possible.
The rul es of the Game govern the behavi our of the pl ayer in
choosing values for decision variables. Rules have been set for the
various types of decisions required of the user: development and
expansion, open-pit mining, underground mining, stockpiling and milling,
and permanent cl osure. Most of the rul es rel ate to the constrai nts of
the mining method .
187
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The sampl e run of the Mi ne Manager i11 ustrates the sequence of
decisions facing the player, and provides examples of the feedback -information displays -- generated at various stages in the project life.
Open-pit and underground mine sequencing is demonstrated, and o~erating
policies are implemented with respect to capacity-utilization, grade and
stockpiling.
The sample run also confirms the high degree of
selectivity associated with the sublevel stoping technique.
6.2 Limitations
•
The development of the Mine Manager required a compromise between
simpl i city and real i sm. Abstracti on from reali ty has been performed
with a view to producing a reasonably realistic game. The Mine Manager
has several limitations arising from the required compromise.
The
geology is relatively simple and structural features such as faults and
folds have not been mode11ed. It is also assumed that any permissible
mine configuration is stable, and therefore, there has been no attempt
to model technical problems such as slope failure or rockburst which may
afflict real mines.
At the development stage, the choice of mine and mill capacity is
restricted to a specified range, the limits of which have been set based
on a consideration of normal operating practice and of the resource
base, that is, the massive sulphide deposit. In reality, small-scale
mi ni ng takes pl ace at rates whi ch are bel ow the lower l imi t of the
capacity range used in the Mine Manager; however, small-scale rrlÎnes have
different characteri st i cs from the type of operat i on mode11 ed in the
Game.
There is a lack of realism in the assumption that previously
dri 11 ed, but unmi ned, materi al must be redri 11 e,j for the p~rp()se of
grade estimation and, possibly, extraction. This arises from the fact
that the software does not maintain an inventory of estimated grades of
mi ni ng uni ts, but rather, produces est imates as needed based on the
stope limits specified by the user. Given the flexibility in mining
unit selection, it is impossible to predict the boundaries of each unit
to Ile mined. If a mining unit for which an estimate of grade has been
188
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generated is left in situ, the drilling which took place is therefore
described as exploratory, and drill ing of blastholes will be required
before extraction can take place.
In order to avoid excessive complexity and tedium in the
specification of mining units to be extracted from the open-pit, the
shape of the pit in plan view has been simplified to approximate a
square or rectangl e. Although the four boundari es do not have to be
straight, a limitation of the simplified mining unit selection process
is that the open-pit cannot assume a smoothly curving outline as do many
real mines.
A single tonnage factor has been assigned to mineralized material
regaréless of its grade.
The tonnage factor for pyrite, a common
mineraI in massive sulphide deposits, is 0.21 cubic metres per tonne
which is slightly lower than that of chalcopyrite and sphalerite (0.24
to 0.26 cubic metres per tonne). Therefore, in reality, the number of
tonnes associated with a fixed volume of massive sulphides is higher for
material which has a lower grade of copper and zinc and a higher
proportion of pyrite than for higher grade material with a lower
proportion of pyrite.
Mining can advance in only one direction in the underground mine,
that is, northwards. The Game would be more realistic if mining could
advance both northwards and southwards from a shaft located centra11 y
along the strike length of the deposit. However, the decisions facing
the user would remain the same: given the constraints of the mining
technique, the operating policy, if any, and the current information
about priees and costs, in which sequence should the mining units be
extracted? It is assumed that primary stopes are backfilled if adjacent
secondary stopes are to be mi ned, but. the cost of backfi 11 i ng has not
been mode11 ed.
Mining units are the basis for selecting material for extraction,
stockpiling and direct mill feed. In reality, there may be sorne mixing
of matei' i il 1 in ore passes, but th i sis not taken i nto account in the
Game; instead it is assumed that material originating from one w.ining
unit can be distinguished from that associated with another unit until
the material is delivered to the mill or until stockpiling takes place.
The mill recovery functions used in the Game do not take into
189
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•
account improved milling methods which may facilitate process control as
a function of varying grade input. New technologies in both mining and
processing can be expected and would alter the inter-relationships
amongst variables in the system.
Operating periods of less than one ypar are not considered in the
Game, and therefore, mine or mill closure can take place only at the end
of a year.
Due to the assump' i on that product i on takes place at a
uniform rate throughout each year, mining or processing of a small
amount of material leads to high unit operating costs, a situation which
may be avoided with proper production planning. Conversion from openpit to underground mi ni ng must take pl ace at the end of the year in
which underground mine development work is completed. In a real system,
the option ta continue mining in the open-pit may exist beyond the point
in time at which underground mining becomes possible.
In the Game,
there i s no cons i derat i on of the co st associ ated with the process of
closing a mine nor of reopening a mine which has been temporarily
closed. It is assumed that the mine is maintained on a stand-by basis,
and therefore the costs of reverting the mine to an operational state
would be minimal.
The Mi ne Manager must be pl ayed from start to fi ni sh without
interrupting the execution of the code by breaking the run of the Game
or turning off the computer. As it is not possible to stop the Game
until the end of the project 1He, mine planning, if carried out, must
take place concurrently.
If the player requires the use of other
software on the same computer system, the Mine Manager should be run in
a DOS window.
In its current form, the Game serves to inform the user about the
characteri st i cs of the mi ne envi ronment and the rel at i onsh i ps amongst
its parameters. In pl aying the Game, the user has the opportunity to
experience the decision-making process. The Game also provides answers
to 'what if ... ' type questions by allowing the user to implement and
assess alternat ive operat i ng pol i ci es without the commitment of
resources that would be required in a real system.
According to Sage's (1991) classification of support systems, a
system which answers a 'what is the ... ' type question, focuses on data
processing and generates summary reports for the user i s a management
190
•
information system (MIS). One which can provide an 'iL .. then' type of
response is referred to as a predictive management information system
(PMIS). A decision support system (DSS) goes even further by attempting
to answer the question 'which alternative is best?'.
Under Sage's classification scheme, the Mine Manager lies between
an MIS and a PMIS. The reports generated by the Game answer quest ions
such as 'what is the net smelter return for copper at the minesite?'.
The information provided with the Game' answers questions like 'what is
the typical mil1 recovery rate for gold?'. The Mine Manager also has
predi ct ive capabil it ies. "Through the use of a mi croeconomi c model, it
Rrovides the user with an estimate of the production costs associated
with full-capacity operations. This is equivalent to the statement 'if
the plant operates at full capacity, the operating costs would be
approximately ... '. The Mine Manager cannot, however, accommodate direct
'what if' type questions. Although the Game creates a situation in
which the user can learn about the impact of various mine development
and production-related decisions, it is the responsibility of the user
to apply the knowledge gained correctly to decision making for a real
project.
6.3 Recommendations
•
The Mine Manager lies towards one end of a continuum from MIS to
DOS. The Game could be developed further to include a forecasting model
for prices ilnd a risk analysis model which could assist the user in
maki ng appropri ate deci sions. The development of a DSS i s not simple
and the effort required would only be justified for a real operation
rather than the hypothetical one on which the Game is based.
The addi t ion of sophi st i cated graphi cs woul d enhance the vi sual
impact of the Game.
The display of sections, plans and threedimensional images of the mine would facilitate mine sequencing.
In the field of education, the Mine Manager is considered to be a
self-instructional programmed learning tool.
As an educational or
training tool, the Game could be developed in several directions
depending upon the particular subject of interest. The geological data-
191
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base could be adapted to a real deposit for which mine development is
being considered, underway or already completed.
The option of
employing underground mining techniques other th an sublevel stoping
could be added, and the inclusion of events such as floods and
rockbursts would increase realism.
Human aspects such as public
relations, labour management and the learning curve could be
incorporated by establishing a relationship between community investment
or training expenditure, and the rate of employee turnover or the level
of operating efficiency.
ln spite of the limitations of the Mine Manager, it is a practical
tool for operations research and educat i onal purposes.
1t i ntegrates
aspects of geology, mining and management and presents them in a format
which is easy to use. As a computerized mine management game, it has
the potential to be developed further in various directions with farreaching benefits .
192
•
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•
•
Webster's Ninth New Collegiate Dictionary, 1990, Merriam-Webster, Mass.,
1564 p.
Weiss,
A., 1978, 'New Concepts and Tools in Decision-Making for the
Mining Industry', Mining Engineering. November, pp. 1555-1561.
Wells,
H.M., 1978, 'Optimization of Mining Engineering Design in
Mineral Valuation', Mining Engineering, December, pp. 1676-1684 .
198
•
SELECTED BIBLiOGRAPHY
Anderson, M.N. and Scheye, K.G., 1987, 'The World Mining Industry.
Turnaround -- Its Implications', The Northern Miner, vol. 73, no.
16, June 29, 1987, pp. 25.
Bossan,
R. and Varon, B., 1977, 'Mineral Priee Behaviour', in The
Mineral Industry and the Developing Countries, Oxford University
Press, pp. 103-131.
Cal l away, H.M., 19S8, 'Economie Relation of Mining Rate to Grade of
Ore', Mining Engineering, April, pp. 470-472.
Carlilse, D., 1964, 'Economie Aspects of the Definition of Ore', Trans.,
IMM, vol. 64, December, pp. 89-99.
Coyle,
R.G. and Montaldo, M., 1977, 'Dynamic Control of an Operating
Mine', paper in the proceedings of the 14th International
Symposium on the Application of Computer Methods in the Mineral
Industry, University Park, Pennsylvania, October, 1976, pp. 357360.
Dale,
L., 1984, 'Mine Capacity and Mineral Priee',
September, pp. 153-162.
Resources Pol icy,
Douglass, E.J., 1971, 'How to Make the Most of a Mining
Mining Engineering, October, pp. 64-67.
Investment',
Erskine, J.C., 1978, 'The Effect on Ore Reserves of Rising Costs and
Falling Priees', Australian Mineral Industry Quarterly, vol. 31,
pp. 53-66.
Fitzgibbons, A. and Cochrane, S., 1978, 'Optimal Rate of Natural
Resource Depletion', Resources Policy, September, pp. 166-171.
Garg, O. and Piche, A., 1979, 'Computer Applications in Open-Pit Mine
Planning', CIM Bulletin, vol. 72, no. 805, May, pp. 69-75.
Gauthier, F.J. and Gray, R.G., 1971, 'Pit Design by Computer at Gaspe
Copper Mines, Limited', CIM Bulletin, vol. 64, no. 715, November,
pp. 95-102.
Halls, J.L., Bellum, D.P. and Lewis, C.K., 1969, 'Determination of
Optimum Ore Reserves and Plant Size by Incremental Analysis',
Trans., IMM, vol. 78, pp. A20-A26.
Hamrin,
•
H., 1982, 'Choosing an Underground Mining Method', Underground
Mining Methods Handbook, ed. W.A. Hustrulid, AIME, New York, pp.
88-112.
Hayes, A.G.B. and Renzoni, C.L., 1977, 'Cyclical Trends and the Metal
Market Outlook', CIM Bulletin, vol. 70, no. 778, February, pp. 8390.
199
•
Henley,
S. and Stokes, W.P.C., 1984, 'Improved Geol09ical Modelling
Techniques for Mine Planning', paper in the proceedings of the
18th International Symposium on the Application of Computers and
Mathematics in the Mineral Industries, London, England, March, pp.
265-268.
Henning, U., 1963, 'Calculati::n of Cut-Off' Grade',
Journal, vol. 84, March, pp. 54-57.
Canadian Mining
Hufford, G.A., 1986, 'Selection of a Cutoff Grade Strategy for an Open
Pit Mine', paper presented at the SME Annual Meeting, New Orleans,
March.
John, H.T., 1985, 'Cutoff Grade Calculations for an Open-Pit Mine',
Bulletin, vol. 78, no. 879, July, pp. 73-75.
CIM
Kaufmann, A., 1967, Graphs, Dynamic Programming and Finite Games,
Academie Press, Inc., N.Y., 484p.
Kaufmann, T.D., 1987, 'The Witchcraft and Logic of Gold Pricing
Politics, Inflation, Speculation and the Value of the Dollar are
All Contributing Factors', Mining Engineering, vol. 39, no. 9, pp.
857-858.
Kelsey,
R.D., 1979, 'Cutoff Grade Economies', paper in the proceedings
of the 16th International Symposium on the Application of
Computers and Operations Research in the Mineral Industry, Tucson,
Arizona, October, pp. 286-291.
Lane, K.F., 1979, 'Commercial Aspects of Choosing Cutoff Grades', paper
in the proceedings of the 16th International Symposium on the
Application of Computers and Operations Research in the Mineral
Industry, Tucson, Arizona, October, pp. 280-285.
Lane, K. F. , 1984, 'Cutoff Grades for Two Mi neral s', paper in the
proceedings of the IBth International Symposium on the Application
of Computers and Mathematics in the Mineral Industries, London,
England, M?rch, pp. 485- 491.
Lemieux, M., 1977, 'A Different Method of Modelling a Mineral Deposit
for a Three-Dimensional Open Pit Computer Design Application',
paper in the proceedings of the 14th International Symposium on
the AppHcation of Computer Methods in the Mineral Industry,
University Park, Pennsylvania, October, 1976, pp. 557-572.
Lillico, LM., 1973, 'How to Maximize Return on Capital
Open Pit Mines', World Mining, June, pp. 26-31.
When Planning
Lipkewich, M.P. and Borgman, L., 1969, 'Two and Three Dimensional Pit
Design Optimization Techniques', A Decade of Digital Computing in
the Mineral Industry, AIME, pp. 505-524.
•
Lizotte, Y. and Elbrond, J., 1982, 'Choice of Mine-Mill Capacities and
Production Schedules using Open-Ended Dynamic Programming', CIM
200
•
Bulletin, vol. 75, no. 839, March, pp. 154-163.
Lizotte, V., 1988, 'The Economies of Computerized Open-Pit Desi9n',
International Journal cf Surface Mining, pp. 133-152.
Maleas, A., 1983, 'Optimum Depletion of Exhaustible Resources with
Particular Reference to Mining', M.Eng. Thesis, McGill University,
Montreal, 211p.
Mason, P.M., 1984, 'Capital and Operational Planning for Open- Pits in a
Modern Economy', paper in the proceedings of the 18th
International Symposium on the Application of Computers and
Mathematics in the Mineral Industries, London, England, March, pp.
791-801.
McKnight, B.K., 1984, 'The New H-W Orebody -- Cut-Off Grades and Mine
Economies', paper presented at the 86th Annual General Meeting of
CIM, Ottawa, Aptil.
Napier, J.A.L., 1981, 'Investment Criteria and Choice of Production Rate
in the Planning of Gold-Mine Production', Journal of the South
African Institute of Mining and Metallurgy, July, pp. 221-228.
O'Neil, T.J., 1973, 'Estimating Minimum Copper Priee Levels Through
Production Cost Projections', paper in the proceedings of the I1th
Symposium on Computer Applications in the Minerals Industry,
Tucson, Arizona, April, pp. GI-G30.
Pana, M.T., 1965, 'The Simulation Approach to Open-Pit Design', paper in
the proceedings of the Short Course and Symposium on Computers and
Computer Applications in Mining and Exploration, Tucson, Arizona,
March, pp. III -ll23.
Pasieska, A.R. and Sotirow, G.V., 1985, 'Planning and Operational Cutoff
Grades Based on Computerized Net Present Value and Net Cash Flow',
CIM Bulletin, vol. 78, no. 878, June, pp. 47-54.
Petersen, U. and Maxwell, R.S., 1979, 'Historical Mineral Production and
Priee Trends', IMM, January, pp. 25-34.
•
Ramos,
H.C., 1977, 'Impact of Grade Management on Project Economies',
paper presented at the Mining Economies Symposium, School of
Mining Engineering, University of New South Wales, September.
Recny,
C.J., 1982, 'The Influence of Geologie Characteristics on
Production Capacity and Their Relation to Costs and Profitability
of Mining Projects' in Mineral Industry Cost, ed. J.R. Hoskins,
Northwest Mining Association, Spokane, WA.
Rich,
E.A., 1986,
'Rationality and Creativity in Artificial
Intelligence', in Expert Systems and Knowledge Engineering, ed. T.
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Roman, R.J., 1973, 'The Use of Dynamic Programming for Determining MineMill Production Schedules', paper in the proceedings volume of the
201
•
10th International Symposium on the Application of Computer
Methods in the Mineral Industry, Johannesburg, RSA, April, 1972,
pp. 165-169 .
Rudenno, V., 1979, 'Determination of Optimum Cutoff Grades', paper in
the proceedings of the 16th International Symposium on the
Application of Computers and Operations Research in the Mineral
Industry, Tucson, Arizona, October, pp. 261-268.
Rychkun, E.A., 1980, 'Economie Depression Cycle 13: 1929-1984?', CIM
Bulletin, vol. 73, no. 824, December, pp. 131-143.
Shen,
Y., 1988, 'Risk Analysis and Its Application in Mining Project
Evaluation', M.Eng. Thesis, McGill University, Montreal, 213p.
Solow,
R.M., 1974, 'The Economies of Resources or the Resources of
Economies', American Economie Review, vol. 64, pp. 1-14.
Spencer, 0.0., 1975, Game Playing with Computers, Hayden Book Co.
312p.
Inc.,
Strongman, J.E., 1985, 'Sorne Notes on Mineral Markets' for the
International Mining Agreement Negotiation Seminar, Washington,
D.C., April.
Thomas,
E.G., 1976, 'Justification of the Concept of High-Grading
Metalliferous Orebodies', Mining Engineering, May, pp. 393-397.
Verner,
W.J. and Shurtz, R.F., 1966, 'For Mine Evaluation -- A Fresh
Model', Mining Engineering, November, pp. 65-71.
Vickers, LL., 1961, 'Marginal Analysis -- Its Appl ication in
Determining Cut-Off Grade', Mining Engineering, June, pp. 578-582.
Williams, C.E., 1974, 'Computerized Year-By-Year Open-Pit Mine
Scheduling', SME of AIME Trans., December, vol. 256, pp. 309-317.
Yu,
T.R. and Counter, D.B., 1983, 'Backfill Practice and Technology at
Kidd Creek Mines, CIM Bulletin, vol. 76, no. 856, August.
, 1986, 'Use of Fly Ash in Backfill at Kidd Creek Mines', paper
presented at the 86th Annual General Meeting of CIM, Ottawa,
April .
•
202
•
APPENDIX 1
Conditional Simulation
This outline of cOilditional simulation follows that given by
Journel and Huijbregts (1978) and Dimitrakopoulos (1990).
Conditional simulation is used to generate values at grid points
These values are realizations of
representing grades in a deposit.
random variables, the set of which, Z(x), constitutes a random function.
This random function honours the mean, variance and variogram of a real
deposit. Conditional simulation yields values which match the available
grades at specified locations, and thus, conditioning adds robustness to
the simulation.
Conditional simulation of Z(x) is expressed as
where:
Ze.(x) is the defined random function with the properties as
described above
Z· is an estimate at a grid point based on the original data
Z.(x) - Z;(x) is an error, i.e., the difference between a
realization of Z(x) and its estimate, kriged as if the
simulated values were known only at the sample points
Conditional simulation requires four steps:
1) simulation of a regular grid of values with the same variogram as the
sample data;
2) estimation of the grid points using the sample data;
3) estimation of the grid points using the simulated values at the
sample points;
4) at each grid point, addition of the value from step 2) to the
difference betwe2n the values from steps 1) and 3)
•
203
•
APPENDIX 2
Priee and Cost Indices, 1972 - 1987
According to Statistics Canada, the Consumer Priee Index (CP!) is
an indicator of changes in consumer priees, as experienced by the target
population. The CPI is generally defined as a measure of priee change
obtained by comparing, throug h time, the cost of a basket of
commodities, specified according to purchases made by the target
population in a certain reference period. Since the basket contains
commodities of unchanging or equivalent quantity and qual~ty, the index
reflects only pure priee movement.
The Consumer priee Indices from 1972 to 1987 are listed below.
CPI
33.4
36.0
39.9
44.2
47.5
51.3
55.9
61.0
67.2
75.5
83.7
88.5
92.4
96.0
100.0
104.4
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
(Source: Statistics Canada, 1991)
•
The Marshall and Swift (M & S) Equipment Cost Index is generated
in much the same way as the CPI, except that industrial equipment and
services rather than consumer goods and servi ces are eva1uated. The
evaluation involves a fixed spectrum of equipment classifications purchased by a fi xed spectrum of industri es; equi pment install at ion costs
are al so accounted for, so that the M & S index refl ects changes in
construction labour costs as well (Valle-Riestra, 1983) .
204
...
The M & S mi ne/mi 11 i ndi ces from 1972 ta 1987 are 1i sted bel ow.
The base for the M &S index is 100 for the year 1926.
Year
M &S
Index
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
332.0
343.0
394.0
451.0
482.9
520.8
564.7
619.2
683.5
750.3
783.8
799.3
816.5
822.6
827.1
837.1
(Source: CIM Special Vol. 25, 1982;
Chemical Engineering, 1981-88)
...
205
•
APPENDIX 3
U.S.jCanada Currency Exchange Rates, 1973 - 1987
The rates of exchange between the U. S. and Canadi an currenci es
from 1973 to 1987 are listed below.
U.S.S/CdnS
1973
1974
1975
1.976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1.00
1.02
0.98
1. 01
0.94
0.88
0.85
0.86
0.83
0.81
0.81
0.77
0.73
0.72
0.75
(Source: Bank of Canada Review, 1980, 1991)
•
206
•
•
APPENDIX 4
Software Specifications and Design
Software Specifications
The Mi ne Manager i s a standal one app li cat i on wh i ch requ ires an
IBM-compatible personal computer using the DOS operating system, version
3.0 or higher. The Mine Manager game package consists of a single 5.25
inch 1.2 Mb or 3.5 inch 1.44 Mb floppy disk lnd a user's manual. The
diskette contains program and data files, some of which have been
compressed using the archive creation shareware PKPAK, version 3.61, by
PKWARE, Inc.
The Game is to be run on an IBM XT-, AT- or PS/2-compatible having
a floppy disk drive, but not necessarily a hard disk.
The software
requires 640 K of random access memory, and supports most standard video
modes, for example, Hercules mo,;ochrome, and IBM-CGA, -EGA and -VGA.
If the Game is to be run from a hard disk, installation is
required.
Prior to the installation, there must be at least 600 K
available on the selected drive. This ensures that sufficient space is
available for decompression of individual data files as needed. Hard
disk users have the option of decompressing all of the data files at the
start of the Game. Complete decompression avoids subsequent delays wh en
data must be accessed. At least 5 Mb must be available on the selected
drive if complete decompression is to be performed.
No installation package has been designed for the Mine Manager
because the installation procedure is simple. It is advisable that the
user create a directory on the hard drive to which all files from the
program diskette should be copied; only Game files should exist in this
directory.
The Game directory should contain twenty files: two .EXE files,
including the main executable file for the Game; one .OVR file; and
seventeen. data files having .DAT or .ARC extensions. The PKUNPAK.EXE
file is part of the shareware package developed by PKWARE, Inc., and is
used to decompress data fi l es duri ng the operat i on of the Game. A11
data files which have been decompressed are deleted prior to normal
207
•
termination of the Game.
If the Game is stopped prematurely, for
example, by using Ctrl<Break>, decompressed data files with names
beginning with 'level' may remain on the drive in use, and should be
deleted before any subsequent runs of the Game.
The Game must be run from the directory containing all of the
files listed above. To start the Game, the user types 'mg' at the DOS
prompt.
Software Design
•
The software for the Mi ne Manager i s written in Turbo Pascal,
versi on 6.0. The top-down approach to programmi ng, as shown on the
following page, was appl ied in the development of this computer-based
Game.
The mai~ program is divided into a series of modules through which
three types of activities are carried out: performance of prel iminary
tasks, simulation of mine development and mine/mill production, and
financi al eval uat ion at the end of the project l ife.
The flow of
control through the main program is represented in part by figure 24 in
section 4.2.1. Although this figure is primarily intended to show the
sequence of decisions during the project life, it reveals some of the
components of the main program.
The preliminary tasks performed by modules referred to directly in
the main program are to display the title of the Game; provide a brief
introduction to the Game; decompress data files, if appropriate;
generate annual metal prices and inflation rates; display delineation
drillhole data and historical prices; and prompt the selection of the
mining method and the length of delay, if any, in the start of
preproduction work. The selection of the mining method determines whiçh
of the modules for simulating mine and mill production is to be
executed.
The two largest modules of the program are used for simulating
open-pit and underground mine development and production, and are
themselves composed of a number of lower-level modules. Sorne of the se
lower-level modules are used to simulate mine development and mill
construction based on the capacity installation decisions of the user .
208
•
•
Top-Down Approach ID Program Development
lHE MINE MANAGER
Main Program
l
r.--------------------,.r------- --------r'----------------"
N
o
ID
Simulation of open pit
mine development and
mine/mill operations
Performance of
preliminary tasks
e.g. file decompression
generation of prices
dis
1 and
formation
tian
pro
ad
Simulation of underground
mine development and
mine/mill operations
Financial evaluation
1
1
Planning of
activities for
the following
year
Expar sion of
insIal ations
and shaH
dee~ ening
(under ground)
1
Installat' ln of the
selected mine and
. millcal acities;
calculati ln of the
associaI id capital
expenditure
Extraction of
matarial
Drifting (underground),
drilling and estimation
of grades of selected
mining units
Addition to and
transfer from
stockpiles
Calculatian of total
tonnage mined during
a given year and
computation of mine
operating costs
Production of copper
and zinc concentmtes;
computation of mill
operating costs
Calculatian of
annualcash
flows
•
•
Dther modules are needed for the simulation of production-related
activities, and the calculation of costs and the values of other cash
flow components. Further subdivision of some of these modules has been
carried out where mine decision making and verification of user inputs
are required.
With the exception of the main program, the code for the Mine
Manager has been di vi ded i nto more manageab1e segments referred to as
units. The multi-unit setup increased the program code-size limit and
helped in organizing the many statements of the program.
Each unit
occupies a memory segment which can be as large as 64 K. The units are
compiled individually into .TPU files, but cannot be run independently.
Several units are overlaid in that, when loaded into random access
memory, they share the same address. The memory requi rements of the
program are thus reduced.
Compilation produces a .DVR file which
contair.s the overlay code. The use of overlays is possible because the
units which have been converted into overlay modules are not required
concurrently by the main program .
210
•
APPENDIX 5
Selected Output from the Sample Run
The information displays generated in the sample run of the Mine
Manager are presented according to the project year:
Years 5, 6, and 7 -- Value-tonnage relationship, Summary of operations,
Stockpile status report and Cash flow statement;
Years 8, 9 and 10 -- Value-tonnage relationship, Summary of operations
and Cash flow statement;
Year Il -- Summary of operations and Cash flow statement;
Years 12 and 13 -- Value-tonnage relationship, Summary of operations and
Cash flow statement;
Year 14 -- Value-tonnage relationship, Summary of operations, Stockpile
status report and Cash flow statement.
The title of each statement appears at the top of the report .
•
211
•
Year5
UALUE - TOHNAGE RELATIOHSHIP -- YEAR 5
The tonna~e - value per tonne relationship for the units Ained this
year is shawn in the table below. Average values represent the
estiftated net realizabte revenue per tonne A1tled, i.e., Mining and
estiRated ~illing losses, dilution and estlMated net snelter return
have been accounted for.
CUT -OFF VALUE
($/TOIlllEI
27.96
63.66
139.79
195.70
251. 60
ASDUE
CUT-OFF
TOIHlGE
AVERAGE UALUE ASOUE
CUT-OFF (SlTDIlIlEI
330364
262997
16762D
76412
26066
146.10
166.09
202.03
240.66
265.55
NDte: 2235135 tDnnes Df Ained Aateria1, assUAed tD be unAinerallzed, are nDt reflected in the value-tonnage relatlonship.
F1-Print screen and cDntinue
<EHTER>-CDntinue
SUHHARY OF OPERATIOHS (OPEN-PIT HINElHILLI -- YEAR 5
TDnnes Ained:
TDnnes Ailled:
Hilled grades:
2565519
255942
2.59 1.cu
9.91 1.zn
9.11 glt Au
eu
94l(
zn -- 90l(
Au -- 63l(
Net snelter return:
eu -- 74l(
zn -- 41l(
Au -- 93%
Hine Dperating CDst:
SI.76/tDnne
Hill Dperating CDst:
S22.ODItonne
ND e.p1DratDry drilling was carried out.
Hill rec"""ry:
F1-Print screen and cDntinue
•
<EHTER>-CDntinue
212
•
STOCKPILE STATUS REPORT - YEAR 5
STOCKPILE
HUHBER
1
2
3
ESTIHATEO GRADE
TOHHAliE
COPPER (Y.)
5818
23180
48421
0.215
0.835
1.521
4
o
F1-Print screen and continue
CASH FLOU -- YEAR 5 (thou.
ZIHC
(li)
2.781
3.041
6.039
1.353
2.040
2.611
<EHTER>-Continue
$)
RevenJe
eu conœntrate (USS1.08/1b Cu)
:
Au credits in eu cone (05$563.03/02 Au):
zn coneentrate (USSO.57/1b Zn)
Operating Costs
Hine
Hill
Pernanent plant closure
TaK Allowances
12252.079
27783.624
13179.549
4521. 960
5631.306
0.000
TaKable IncaN!'
T~es
Capital EKpenditure
Annual Sustaining capital
Hine
Hill
Het Uorking capital
164.609
53.619
Cash Flow
Annual Rates -E~change: 0.89 US$lCdn$
53215.252
10153.266
4091. 725
·38970.261
11691. 078
6054.550
218.228
118.408
24979.722
Cost Inflation: 4.5Y.
F1-Print screen and continue
•
GOLO (G/Tl
<EHTER>-Continue
213
lien. Inflation: 6.2Y.
•
Year6
UALUE - TONNAGE RELATIONSHIP -- YEAR
&
The tonnage - value per tonne relationship for the units Ained this
year 15 shown in the table below. Average values represent the
estiftated net realtzable revenue per tonne AitIed, i.e., Aining and
estiRated Ailling losses. dilution and estlAated net snelter return
have been accounted for.
CUT-lFF UALUE
($/TOHHEI
TONNAGE ASOUE
38.19
117.34
195.88
274.43
352.97
34U553
24U183
123180
48055
29594
CUT-OFF
AVERAGE UALUE ASOUE
CUT -lIFF ($ITOHHEI
183.&2
224.57
283.14
3&0.84
401. 31
Note: 2224324 tonnes of nined naterial, assuned to be unnineralized. a~ not reflected in the value-tonnage relationshlp.
FI-Print screen and continue
<EHTER>-Continue
SUNMARY OF OPERATIONS (OPEN-PIT HINElMILLI -- YEAR 6
Tonnes nined:
Tonnes nilled:
Mi lied grades:
2564818
254293
3.60 Y.cu
8.25 y.zn
Mill recovery:
6.13 glt Au
Cu -- 98Y.
Net BAelter return:
zn
Au
eu --
zn --
90Y.
57:'.
14?
43Y.
Au -- 91:'.
Mine operating cast:
S2.32/tonne
Mill operating cast:
S29.53/tonne
Ho eKP\oratory drilling was carried out.
F1-Print screen and continue
•
<EHTER>-Continue
214
•
STOCKPILE STATUS REPORT - YEAR 6
STOCKPILE
NUMBER
ESTIHATEO GRACE
TONNAGE
COPPER (Y.)
ZINC
(Y.)
GOLD lü/Tl
0.215
2.781
1.353
1
5818
1.117
1.518
2.552
2
43932
1.573
5.539
2.617
3
113930
4
o
--------------------~-------------------------------------------
FI-Print screen and continue
<EHTER>-Continue
CASH FlOW -- YEAR 6 (thou. $)
Revenu!
eu concentrate (USSI.05/lb Cu)
:
Au credits in eu cane (USS572.38/oz Au):
zn coneentrate (USSO.62/1b Zn)
Operating Costs
Mine
Mill
Per~anent plant ctosure
TaM Allowances
52914.912
19079.760
20177.031
13658.122
5954.058
7510.417
0.000
TaKable IncoN!'
laMes
capital EMpenditure
Annual Sustaininu capital
Mine
179.655
50.926
Mill
Net WOrkina capital
cast Inflation: 5.6Y.
FI-Print screen and continue
•
4471. 594
34978.843
10493.653
6393.605
230.582
153.983
22178.614
Cash Flow
Annual Rates -EMchange: 0.81 US$/Cdn$
13464.475
<EHTER>-Continue
215
üen. Inflation: 7.6Y.
•
Year7
VALUE - TOHNAGE RELATIONSHIP -- YEAR 7
The tonnage - value pe~ tonne relationship for the units ~ined this
uear is shoun in the table below. Average values represent the
estiftated net realizable revenue per tonne nilled, i.e., ninino and
est~ted ~illing
losses, dilution and
have been accounted for.
CUT-OFF VALUE
(SlTOHllEI
5.57
107.75
209.92
312.09
414.26
TOHHAGE ABOlIE
CUT-OFF
esti~ated
net snelter return
AVERAGE VALUE ABOUE
CUT -OFF (SlTOHHEI
287505
184158
65142
10582
7055
148.87
193.54
276.12
443.58
475.99
Hote: 2294595 tonnes of nined naterial, assuned to be unnineralized. are not reflected in the value-tonnage relationship.
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SUHHARY OF OPERATIOHS (OPEN-PIT HIHElHILLI -- YEAR 7
Tonnes nined:
Tonnes nilled:
Hilled grades:
Hill recovery:
Het snelter return:
2582100
254705
J.87 Y.cu
5.65 y,zn
5.66 olt Au
eu
95Y.
Zn
85Y.
Au
58Y.
eu
11 y.
Zn
Au
38Y.
90Y.
Hine operating cost:
53. 27/tonne
Hill operating cost:
536. 37/tonne
No exploratory drilling was carried out.
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•
216
•
STOCKPIlE STATUS REPORT - YEAR 7
STOCKPIlE
HUMBER
1
2
3
4
ESTIHATEO CRADE
TONNAGE
COPPER (r.)
ZIHC (:\)
0.313
1.213
1.573
14888
67661
113930
o
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GOLO (G/Tl
0.759
1.196
2.617
1.541
2.733
5.539
<EH7ER>-Continue_
CASH flOW -- YEAR 7 (thou. $)
Revenue
Cu conœnt rate (USSO.871lb Cu)
:
Au credits in Cu cone (US$363.85/oz Au):
zn concentrate (USSO.46/lb Zn)
Operating Costs
Hine
Hill
Pernanent plant closure
Tax Allowancl!S
Taxable Ineo""
14526.655
10046.946
5428.348
8450.327
9264.465
0.000
laMes
Capital EllpendituM!
Annual Susta1ning capital
Hine
Hill
Met WOrking capital
0.000
68.135
cash Flow
Rnnual Rates -EMchange: 0.88 US$lCdn$
17714.792
5421.751
6865.406
2059.622
10737.840
68.135
1564.501
-2142.941
l:Dst Inflation: 5.5r.
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•
30001.948
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217
Den. Inflation: 7.6::
•
Year8
VALUE - TONHAGE RElATIOHSHIP -- YEAR 6
The ~onnage - value per tonne retationship fOf the units Ained this
year 1s shawn in the table below. Average values represent the
estiAated net reati2able revenue per tonne "itted, i.e., Aining and
estiAated Rilling losses, dilution and estiAated net snelter return
have been accounted for.
CUT-OFF VALUE
IS!TOHHEI
TOHHAGE ABOUE
CUT-OFF
AUERAGE VAlUE AOOVE
CUT-OFF (S/TONNEI
55.09
115.96
176.03
237.71
290.50
354410
251390
149109
75346
26357
170.37
201. 51
239.59
263.35
332.40
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SUHHAAY IF OPERATIONS (UHOERGROUlll HIHE/HILL) - - YERR 6
Tonnes nined:
Tonnes l'Iilled:
Hilll!d grades:
354410
354410
3.09 r.cu
6.25
Oilution:
Mine recoveru:
Hill recovery:
Het snelter return:
r.zn
5.92 g/t Ru
13%
00%
eu
90Y.
zn
84%
eu
73%
Ru
zn
61Y.
42Y.
90Y.
Hine operating cost:
$37. 06/tome
Hill operating cost:
531.04/tome
Orifting/eHploratory drilllng costs totalled 53562043.
Ru
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•
218
•
CASH FLOU -- YEAR 8 (thou. $)
Revenue
eu coneentrate (USS1.05!lb Cu)
:
Au credits in eu cone (USS374.40!oz Ru):
zn concentrate (USSO.64!lb Zn)
Operating Costs
Mine
Mill
Pernanent plant ctosure
Jax Allowances
, axable Inc:one
Taxes
Capital Expenditure
Rnnual Sustaining Capital
Mine
51633.042
24754.874
14934.085
11944.083
16698.695
11282.798
0.000
13.727
74.242
Mill
Het Uorking capital
COst Inflation: 5.4%
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•
4621. 684
19029.866
5708.960
0.000
87.969
241.282
17613.340
Cash Flow
Annual Rates
E~change: 0.92 US$!Cdn$
27981.493
<EHTER>-Continue
219
Gen. Inflation: 7.3%
•
Year9
VALUE - TOHHAGE RElATIOHSHIP -- YEAR 9
The tonnage - value per tonne retationship for the units ~ined this
year is shawn in the table below. Averaoe values represent the
estiRated net realizable revenue per tonne nilled, i.e., nining and
estiRated Rilling losses, dilution and esti~ated net snelter rcturn
have been accounted for.
CUT -OFF VALUE
($/TOHllEI
TOHHAGE ASOVE
euT-OFF
AVERAGE VALUE ABOUE
euT -OFF (S1TOHllEI
03.41
.35
344261
239946
144103
61462
19215
220.69
269.62
326.00
318.53
452.46
2::.5.29
321.23
401.16
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SUHHARY OF OPERATIOHS (UHOERGROUHO HIHE/HILLI -- YEAR 9
Tonnes n:ined:
Tonnes l'Iilled:
Hilled grades:
Oilution:
Mine recoveru:
Hill recovery:
344261
344261
3.31 %Cu
6.04 r,zn
4.98 git Au
16Y.
89Y.
eu
zn
Het snelter return:
Au
eu
zn
gO:!.
82Y.
60Y.
11 Y.
44Y.
90Y.
Mine operating cast:
$34. 801t ome
Mill operatina cast:
$28. 19/tome
Orifting/eKploratory drilling costs totalled 53148844.
Au
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•
<EHTER>-Continue
220
•
CASH FLOU -- YEAR 9 (thou.
$)
Revenue
Cu concentrate (USSI.36/lb Cu)
:
Ru credits in Cu cone (US$351.45/02 Au):
zn concentrate (USSO.71/lb Zn)
55244.341
28436.271
12556.942
14251.128
Operating COsts
15128.800
9912.982
0.000
Mine
MiU
Per"anent plant closure
TaK AUowances
TaMable Incane
laMes
Capital EKpenditure
Annual Sustaining capital
Mine
13.892
85.931
MiU
Het UOrking capital
Cost Inflation: 4.3r.
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•
3943.405
26259.155
7877.746
0.000
99.823
202.507
22022.483
Cash Flow
Annual Rates -EKchange: 0.83 US$/Cdn$
25041. 782
<EHTER>-Continue
221
Gen. Inflation: 5.9r.
•
Year10
UALUE - TOHNAGE
-- YEAR 10
P~ATIDHSHIP
The tonnage - value per tonne retationship for the units "ined this
year 1s shawn in the table below. Aueraoe values represent the
estinated net re~t12able revenue per tonne "il\ed, i.e., "1n1no and
estinated ~illing tosses, dilution and esti"ated net snelter return
have been accounted for.
CUT -OFF VALUE
($/TOHHE)
-------- .. ----
TOHHAGE RBOUE
CUT-OFF
AUERRGE UALUE RBOUE
CUT-OFF (SITOHHE)
72.25
203.56
334.88
466.19
597.51
341881
196964
228.99
309.32
577 .47
728.82
728.82
------------1~896
-"110
':31;_
9949
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<EHTER>-Continue
SUHHRRY IF OPERATIOHS (UNDERGROlJHD HINE/HILL) -- YERR 10
Tonl1l!8 l'l1ned:
Tonl1l!8 l'litled:
Hille<! grades:
Oilution:
Hine recoveru:
Hill recovery:
341881
341881
3.60 Y.cu
6.60 Y02n
5.15 g/t Ru
13%
93%
Cu
94:'.
zn
Ru
87:'.
57:'.
Het snelter return:
eu
Hine operating cast:
Hill operating cast:
Ru
90:'.
$42. D2/tllfV1e
531. 171 tllfV1e
zn
Drirting/eKplora"~ry drilling
16%
27:'.
costs totalled 53622445.
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•
222
•
CASH FLOU -- YEAR 10 (thou. $)
Revenue
44493.117
eu concentrate (US$I.25/Ib Cu)
:
Au credits in eu conc (US$381.57/o2 Au):
zn concentrate (USSO.31/Ib Zn)
27675.712
12636.978
4180.426
Hine
Hill
Pernanent plant closure
17988.637
10657.338
0.000
Operating COsts
, aM: Allowances
TaKable Inca...
laMen
Capital EKpenditure
Annual Sustaining capital
Hine
Hill
Het Uorkina capital
-4606.119
16611.934
cast Inflation: 4.8%
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•
3366.462
12488.679
3744.284
0.000
97.123
14.523
82.600
Cash Flow
Annual Rates
EKchange: 8.87 USSlCdnS
28645.975
<~ER>-Continue
223
Gen. Inflation: 6.6%
•
Year 11
SUHHARY OF OPERATIOHS (UHOERGROUHD MIHE/MILL) -- YEAR Il
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - __ r
_
Mine closed tenporarily and Aaintained on a stand-bu
basis at an annual cost of $229523.
Hitl closed tenporarily and Aaintained on a stand-bu
basis at an annual cast of $156323.
Ho driftinglexploratory drilling was carried out.
FI-Print screen and continue
<EHTER>-Continue
CASH FLOW -- YEAR Il (thou. S)
ReveRJe
Cu concentrate (USSO.19/1b Cu)
Au credits in Cu cone (USS348.31/02 Au):
zn concentrate (USSO.31/1b Zn)
Operating Costs
Mine ( intenance)
Mill ( intenancel
PerManent plant closure
Tail Allowances
0.000
0.000
0.000
0.000
229.523
156.323
0.000
Tal<ab le Incoœ
TaMes
Capital Expenditure
Annual Sustaining capital
Mine
Mill
Het Workina capital
0.000
0.000
Cash Flow
Annual Rates -Exchange: 0.82 US$/Cdn$
2861. 493
-3241.339
-914.202
0.000
0.000
51114.429
-4516.013
CDst Inflation: 5.1r.
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•
385.846
<EHTER>-Continue
224
Gen. Inflation: 1.0r.
•
Year12
UALUE - TDHHAGE RELATIDHSHIP -- YEAR 12
The tonnage - value pe~ tonne retationship for the units Ained this
uear ls shawn in the table below. Average values represent the
estiftated net realizable revenue per tonne nilled, i.e., ninlng and
estiRated "illing losses, dilution and estiAated net snelter return
have been accountoo for.
CUT -OFF VALUE
($/TOHllEl
TOtlHAGE AllOUE
CUT-OFF
AVERAGE UALUE ABOUE
CUT-OFF ($/TOHllEl
42.23
90.83
139.43
188.04
236.64
318958
234824
116226
68894
29818
139.05
166.36
184.39
232.11
211.48
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SOMHARY OF OPERATIOHS IUHOERGROUtll HIHE/HILLl -- YEAR 12
Tonnes nined:
Tonnes ..illed:
Mille<! grades:
Dilution:
Mine recoveru:
"ill reClM!ry:
Het sne\ter
318958
318958
4.25 %Cu
4.88 Yoln
6.12 olt Au
16%
91%
eu -- 90%
zn -- 85%
Au -- 61%
return~
eu -- 13%
zn --
29%
90Y.
"Ine operating cast:
S41.12/tonne
"Ill operating cast:
538. 94/tonne
Oriftlng/exploratory drilling costs totalled S19181.
Au --
FI-Print screen and contin... <EHTER>-Continue
•
225
•
CASH FLOW -- YEAR 12 (thou.
$)
Revenue
eu concentrate (USSO.93/lb Cu)
Au credits in eu cone (US$447.12/02 Ru):
zn concentrate (USSO.31/lb Zn)
Operating Costs
Hine
Hill
Per~anent plant closure
Ta.. Rllowances
Taxable Incone
TaMes
Capital Ellpenditure
Annual Sustaining capital
Hine
Hill
Het Uorking capital
22293.934
18963.600
3191. 746
2447.342
16275.995
4662.799
0.000
IDD.466
18.804
81. 664
254.263
13465.766
Cost Inflation: 4.7%
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•
25746.142
13325.513
12420.629
0.000
Cash Flow
Annual Rates -Ellchange: 0.62 US$/CdnS
44469.460
<EHTER>-Continue
226
Gen. Inflation: 6.5%
•
Year 13
VALUE - TOHHAGE RELATIOHSHIP -- YEAR 13
The tonnage - value pe~ tonne retationship for the units Ained this
year 1s shawn in the table below. Average values represent the
eS1iRated net real12able revenue per tonne Ml11ed, i.e., Ainlng and
estiAated Rilling losses, dilution and esti~ated net snelter return
have been accounted for.
eUT -IIFF VALUE
TOHllAGE ABOUE
AVERAGE VALUE ABOVE
(SlTOHIl!:)
CUT-OFF
CUT-lIFF (SITOHHE)
65.57
155.60
245.63
335.66
425.68
355584
251555
115787
57823
19274
221.48
269.22
344.50
411.04
495.54
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and continue
<EHTER>-eontinu~
SUHHARY OF OPERATIOHS (UHDERGROUHD HIHE/HILL) -- YEAR 13
355584
355584
4.72 %Cu
5.85 %Zn
5.47 glt Au
14%
90%
eu
94%
zn 84%
T0I'lIll!lI "in<!d :
Tonnes" i l i"d:
HillE!d
g~ad"s:
Dilution:
Mine recoveru:
Hill ~~c"""ru:
Het sneiter return:
Hine
Hill
Ho
op~~ating
op~~ating
d~iftinQ/eKPlo~atoru
FI-P~int sc~een
•
cost:
cost:
Au
64?
zn
74%
29%
90Y.
eu
Au
$JO. 86/tonn"
$J4.99/tonn"
d~illing
and continue
was
car~ied
out.
<EHTER>-eontinu~
227
•
CASH FLOU -- YEAR 13 (thou. $)
Revenue
eu concentrate (USSO.99/1b Cu)
:
Ru credits in eu cone (USS605.38/02 Au):
zn concentrate (USSO.31/1b Zn)
Operating Costs
Hine
Hilt
PerAanent plant closure
TaK Altowances
Taxat;Jle Incone
30619.666
26395.828
4096.903
13818.262
12440.361
0.000
Taxes
Capital EKpenditure
Annual Sustaining capital
Hine
Hill
Het Uorking capital
19.294
88.153
cast Inflation: 4.3%
FI-Print screen and continue
•
26258.623
2096.358
32757.416
9821.225
0.000
101.441
243.576
24675.526
Cash Flow
Annual Rates -.
EKchange: 0.83 USS/CdnS
61112.397
<EH7ER>-Continue
228
Gen. Inflation: 5.9%
•
Year14
VALUE - TOHHAGE RELATIOHSHIP -- YEAR 14
The tonnage - value per tome relationship for the units lTIined this
year is shawn in the table below. Average values represent the
estiRated net realizable revenue per tonne Milled, i.e., Mining and
estiRated Ailling losses. dilution and estiMated net s~elter return
have been accounted for.
CUT-OFF VALUE
(S1TOHllE)
TOHHAGE ASOUE
CUT-OFF
AVERAGE VALUE ASOVE
CUT-OFF ($ITONNE)
62.68
149.80
236.93
324.06
411.18
321152
220123
49782
39942
29810
204.19
244.31
408.60
438.42
458.22
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SUHHARY OF OPERATIIIHS lUHOERGROUlll HIHE/HILL) -- YEAR 14
Tonnes Mined:
Tonnes ..illed:
Hilled grades:
321152
359999
4.24 %Cu
6.19
Dilution:
Mine recoveru:
Hill recOYerg:
Het SAelter return:
r.zn
5.90 glt Au
14%
94%
eu -- 95%
2n -- 83%
Au -- 59%
CU .. - 61%
2n -- 34%
Au -- 90Y.
Hine operating cast:
$42. 201tome
Hill operating cast:
$42.99/tome
Ho drifting/eKPloratorg drilling was carried out.
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•
<EHTER>-Continue
229
•
STOCKPILE STATUS REPORT - YEAR 14
STOCKPILE
NUHBER
1
2
3
4
ESTIHATEO GRADE
TONNAGE
COPPER
(%)
ZINC
0.313
1.213
1.573
14888
67661
75083
o
GOLO (G/Tl
(%)
1.541
2.733
5.539
0.759
1.196
2.617
---------------------------------------------~------------------
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<ENTER>-Continue
CASH FLOW -- YEAR 14 (thou. S)
Revenue
eu concentrate (USSO.79/lb Cu)
:
Au credits in eu conc (US$444.81/o2 Au):
zn concentrate (USSO.43/lb Zn)
Operating costs
Mine
Mill
Per~anent plant closure
TaN Allowances
TaNable. Inco"",
laMes
Capital EKpenditure
Annual Sustaining capital
17580.788
16471.195
6137.682
13553.515
15476.977
4204.580
Mine
Mill
Net Wcrking capital
Cost Inflation: 4.5%
F1-Print screen and continue
•
33235.071
1781.904
5172.690
1551.807
0.000
0.000
-5908 .137
11310.925
Cash Flow
Annual Rates -ENchange: 0.97 US$lCdnS
0.000
0.000
40189.666
<ENTER>-Continue
230
Gen. Inflation: 6.2%
•
THE MINE MANAGER
GAME MANUAL
© JACQUELINE ALLI SON
McGILL UNIVERSITY
AUGUST 1994
•
CONTENTS
•
•
Page
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
.
.
.
1. INTRODUCTION
1.1 Mine Management Gaming
1.2 Operating Environment of the Mine
1.3 Mineral Project Development and Production
Decisions
1.4 Purpose of the Game
.
2. ELEMENTS OF THE MINING PROJECT
2.1 Preliminary Geological Information
2.2 Underground Operation
2.3 Open-Pit Operation
2.4 Preproduction Period
2.5 Capital Costs
2.6 Metal Price
2.7 Operating Costs
2.8 Estimated Value of an Extracted Mining Unit
2.9 Stockpil es
2.10 Milling Parameters
2.11 Cash Flow and Financial Performance
.
3. THE MINE MANAGER AT WORK
3.1 The Sequence of Decisions
3.1.1 Overvi ew
3.1.2 Open-Pit Operation
3.1.3 Underground Operation
3.2 Rules of the Game
3.2.1 Development and Expansion
3.2.2 Open-Pit Mining
.
ii
ii
iv
v
1
1
3
4
B
10
10
16
31
40
42
46
47
53
58
60
61
64
64
64
68
71
74
74
76
•
3.2.3 Underground Mining
3.2.4 Stockpiling and Milling
3.2.5 Permanent Closure
3.3 Getting Started (at Last)
REFERENCES .................................•....•.•............
•
iii
77
79
80
81
83
•
LIST OF FIGURES
Figure
1.
Delineation Drillhole Locations
Il
2.
Parameters in Sublevel Stoping
18
3.
Development Drifts on Three Sublevels
20
4.
Block Sequencing on a Sublevel Requiring
Advancement of the Development Drift
22
5.
Cross-Section through a Stope Showing the
Relative Positions of the Western and Eastern
Stope Boundaries at the Base of Each Sublevel
24
Horizontal Projection of Sublevels in a Stope
on to a Longitudinal Section Showing Mining to
be More Advanced on the Lower Sublevels
25
Boundaries of the Open-Pit and their
Delimiting Coordinates
32
a) Perpendicular Extension b) Parallel
Extension of the Open-Pit Along the Eastern
Boundary
34
Block Specification for Parallel Extension of
the Open-Pit Along the Eastern Boundary
36
Intermediate-Run Unit Operating Cost Curve as
the Locus of Short-Run Unit Operating Cost Curve
Minima for the a) Mine b) Mill
48
The Sequence of Decisions for Mine Development
and Production -- An Overview
65
Elements of a Mining System -- Open-Pit and
Underground Mi ne
67
The Sequence of Decisions during the Open-Pit
Mine Life
69
The Sequence of Decisions during the
Underground Mi ne Li fe
72
6.
7.
8.
9.
10.
Il.
12.
13.
14.
•
Page
iv
•
LIST OF TABLES
Page
Table
1. Average Intersection Grades of 5-Metre Core
Samples from Vertical Delineation Drillholes
2.
Constants in the Capital Cost Functions for
the Mi ne and Mi 11
3. Constants in the Intermediate-Run and ShortRun Average Operating Cost Functions for the
Mine and Mill
4.
•
Smelter Contract Terms for a Copper
Concentrate with By-Product Gold and a Zinc
Concentrate
v
12
43
50
56
•
1. INTRODUCTION
1.1 Mine Management Gaming
The Mine Manager is an interactive operations research game in
which the mine operating environment and the mine decision-making
It can be used for
process over a period of time are simulated.
experimentation with individual mine or mill operating polici~s or
policy combinations, and may find application in education and training
in mine economics.
Potential users are students at the university
level, and mine decision-makers from the operational to upper management
levels.
In this manu al , the Mine Manager is also referred to as the
'Game', and the terms 'user' and 'player' are applied interchangeably.
The Game is based on a comprehensive mining system. It calls for
decisions to be made at both the development and production stages, and
reflects the sequential nature of the decision process throughout the
project life.
The user is provided with preliminary geological
information generated from a simulated Noranda-type massive sulphide
copper-zinc-gold deposit, typical cost functions and the historical
pattern of copper, zi nc and go1d pri ces. The user i s then prompted to
make a series of decisions concerning the installation and operation of
a mine/mill system, and to enter data such as the selected mining and
mill ing capacities, estimates of metal prices and the level on which
mining is to take place.
The input is validated and the results of
mining and/or milling activities are displayed. Decisions are made on
an annual basis, and periodic operating and financial reports are
available to support subsequent decisions.
•
The mining firm is viewed as operating in the intermediate- to
short-run, that is, the deposit is fixed, but the firm can choose any
feasible capacity for the mine and mill, and operate the plant within a
range of rates constrai ned by the chosen i nsta11 at ions. The fi rm has
full access to, but no control over, capital and labour markets. The
fi na1 products, copper concentrate contai ni ng by-product go l d, and zinc
1
•
concentrate, are sold by the firm at the market-dictated price as soon
as they are produced.
The firm operates in what is similar to a
perfectly-compet it ive market envi ronment, except for the exi stence of
unceïtainty.
The Mine Manager offers a high degree of flexibil ity in setting
the values of decision variables in terms of the range of acceptable
values and the fact that values can be varied during the mine life. For
example, it allows for changes in the installed capacity and level of
capacity utilization, and in the cut-off grade and/or value, in response
It does not,
to the resolution of uncertainty as tim~ progresses.
however, provide the decision schedule which would have been optimal had
the future values been known a priori.
The select ion of parameters to be i nc1uded and of the 1eve1 of
detail in the model required a compromise between realism and
simplicity. Appropriate and timely decision making by the player on
behalf of mine management requires a thorough knowledge of the elements
of the mine operating environment and an understanding of their
interactions as represented in the Game.
The Game can be completed in a few hours, but may require a full
day of play depending upon the player's familiarity with the mine
environment, mine management and the model upon which the Game is based;
the efforts of the player in arriving at sound decisions; the operating
policies being implemented and the annual outcome of the simulated mine
and mill operations .
•
2
•
1.2 Operating Environment of the Mine
The mine environment is defined by geological and economic
parameters. The geol ogi cal parameters are those whi ch refer to the
deposit, that is, the quantity and grade of mineral ized material, and
other phys ical features. The economi c parameters are external to the
deposit, and aY'e in effect during the period in which decisions are made
wi th respect to mi ne development and product ion. Economi c parameters
include metal prices, capital and operating costs, inflation, and
exchange rates.
Operating mines are characterized by a depleting raw material,
variable grades and physical properties within the mineral deposit, and
myriad uncertainties. Mineral projects are typically capital intensive,
Given the
requlrlng preproduction work over several years.
characteri st i cally long l ead t imes, the market conditions for mi neral
products at the start of production may be significantly different from
those predicted at the time of the investment decision. The prices of
many mi neral products exhi bit marked cycl icity, and are rel ated to the
level of industrial activity in the general economy, the interaction -real or perceived -- between suppl y and demand, and the market for
recycled products.
The combined effect of the uncertainties associated with the
various geological and economic parameters is a high level of risk in
mineral project investment.
It is likely that mine management will
alter its planning decisions as its database improves and uncertainty is
resolved during the life of the mine. Decision-making is a sequential
process which should take into account the dynamic features of the mine
environment .
•
3
•
1.3 Mineral Project Development and Production Decisions
This section addresses in more detail the types of decisions to be
made in the Mine Manager, and clarifies some the terms used throughout
this document.
The profitable exploitation of a mineral deposit
requi res astute deci sions concerni ng mi ne development and production.
Some of the types of decisions which must be made are as follows:
1) At the development stage, selection of project specifications.
a) Mining and processing methods.
The methods available for extraction and conversion of ore
into marketable commodities are limited by technology and, thus,
have the potential to change with time. The choice of a method is
influenced by the qualitY,.quantity and location of the ore
reserves and by the availability of capital.
•
b) Plani capacity.
This refers to the installed mining and milling capacities
which determine the initial requirements of capital expenditure.
At this stage, the planning eut-off grade and corresponding size
of reserves provide the framework for justifying the plant
capacity decision. The eut-off grade is chosen such that there
are sufficient reserves to permit recuperation of the invested
capital, and to provide an acceptable return on the investment.
The calculation of eut-off grade differs from that made at the
production stage by which time the plant has been installed and
capital expenditure represents a sunk cost. The exclusion of sunk
costs from subsequent eut-off grade calculations results in a
different estimate of reserves than that used to justify the
initial investment.
Although operating eut-off grades and reserves differ from
those which were generated for planning purposes, future
operations will be constrained by the capacity installations based
on the initial planning decisions. In other words, the chosen
capacities place limitations on the rate at which the mine and
mill can be operated. The mining capacity and the milling
4
•
(apacity should be chosen so as to complement each other .
2) At the production stage, decisions concerning operating variables and
the expansion of existing capacity.
a) Capacity utilization.
Capacity utilization decisions are influenced by economic
and technical parameters. For a fixed quantity of ore reserves, a
higher rate of production leads to faster depletion of the
deposit, that is, a shorter mine life.
Short-term shutdown is an extreme form of capacity
underutilization, and may be a favourable alternative to operating
at a loss when the mining firm is facing economic problems. A
mine which is temporarily closed may be maintained in a state of
readiness for resumption of production should conditions improve.
The decision to close the plant on a temporary basis should be
part of a firm's longer-term strategy for survival.
Permanent plant closure is warranted when the ore reserves
are exhausted. Premature closure may become necessary for
economic or technical reasons. A timely curtailment of operations
may mean the difference between survival and bankruptcy of a
mining company.
•
b) Cut-off grade and eut-off value.
The eut-off grade refers to a specifie concentration of an
element of economic interest. The eut-off grade dictates the
amount of mineralized material that will be targeted for recovery.
It is generally used to distinguish between ore and waste and,
thus, determines the size of the ore reserves and, indirectly, the
length of the mine life. Mineralized material may be separated
into several fractions on the basis of a series of eut-off grades.
The eut-off value refers to a monetary amount which is based
on a combination of grade, priee and various parameters of
extraction and processing. The eut-off value may also be used to
distinguish between ore and waste, and the partitioning of
mineralized material may be based on a series of eut-off values .
5
•
c) Sequence of mining.
Unless the grade is uniform throughout the deposit,
financial performance will be affected by the order of extraction
of the mineable units. In many deposits, grades display a zonal
pattern and a firm will select a sequence of mining according to
its operating policy. The sequence of mining may be reconsidered
many times during the production phase because practical
constraints and changes in economic parameters may cause actual
mining to deviate from the existing plans.
d) Stockpiling.
Stockpi l es are defi ned in th i s sl'Ay as an i nventory of
mined ore at the minesite. It is anticipated that stockpiled
material will be sent to the mill at sorne point in time before
operations cease.
e) Mine and mill expansion.
An expansion of the installed capacity may be considered
advantageous if ore reserves increase or if market conditions are
favourable. An additional capital expenditure will be associated
with an expansion of productive capacity, and a change in unit
operating costs may result. Deepening of the shaft in an
underground mine is also an option during the operating stage.
An organization which is engaged in mlOlng activities will also
have to make decisions about the mining technique to be employed, for
example, sublevel stoping or cut-and-fill; manpower requirements;
equipment selection and replacement; the implementation of measures to
improve productivity; and other planning and operational concerns. It
is assumed that trained manpower is available, the equipment selection
and replacement schedule are sound, and an efficient beneficiation
The mining technique decision variable is not
process is employed.
dealt with explicitly in the Game; given the characteristics of the
simulated deposit, and the need for flexibility in mine sequencing, the
appropriate underground mining technique is sublevel stoping .
•
The optimization of decision variables is performed with respect
6
•
•
to various economic evaluation criteria. The evaluation techniques are
based on the concepts of cash flow and time val ue, and therefore, the
purpose of applying optimization techniques is maximization of the value
of discounted cash flow criteria such as net present value.
In
practice, mineral project decision making is also guided by mineral
policy and overall corporate philosophy which may change over time .
7
•
1.4 Purpose of the Game
The Mine Manager has the ultimate purpose of being an aid to
decision making, planning and policy implementation. However, rather
than focussing on a single real case, the deposit to be mined is a
hypothetical one, and the Game deals with a specifie type of problem,
that is, decision making with respect to capacity and eut-off grade
and/or value during the life of a mine.
The decision situation
presented in the Game is, therefore, a real one.
As an operations research game, the value of the Mine Manager lies
both in reporting the results of game-playing to future decision-makers,
and in providing players with experience in dealing with the problems of
mine decision making. The Game can be used for answering 'what if'
questions, in an indirect manner, and for implementing various operating
policies in a simulated environment similar to that in which many mines
operate.
The Mine Manager has several features which are characteristic of
a l earni ng game. Although the pl ayer i s expected to have a strong
'profit motive', the objective of playing the Game may simply be to
Learning
learn something of the real situation which it represents.
takes the form of increased awareness, familiarity and understanding of
critical economic variables, such as business cycles and inflation; the
advantages of thorough production planning; and the need to learn from
experience. To a certain extent, the Game also encourages the players
to recognize their own attitudes towards uncertainty and risk-taking,
and to practice useful skills in priee forecasting and the analysis of
cash flow statements.
•
For the player who is unfamiliar with the environment in which a
mine operates or who has limited experience therein, the Game serves as
an i ntroduct i on to the parameters of the mi ne envi ronment and to the
types of decisions which must be made. Users who have some background
in geology, mining and management, may find that the Game enhances their
understanding of the relationships between key variables and the mining
8
•
system as a whole.
It can also provide useful insights into the
decision-making process associated with the development and operation of
a mine. Game-playing by mine managers may increase their appreciation
of interests beyond their immediate area of expertise. Management would
be afforded the opportunity to gain perspective, facilitating more
objective analysis and better decision making.
The Game may also be used for teaching. The model is sufficiently
realistic so that the player can be taught about the process and
complexity of decision making for an operating mine, as well as the
types of policies which can be implemented and their effects. Although
it may be difficult to identify 'right' and 'wrong' decisions, the Game
will reveal, through the technical and financial reports, the
consequences of successive decisions on capacity and cut-off grade
and/or value. Much can be gained by the participant(s) from a review
process in which they analyze what has occurred.
As an educational tool, the Mine Manager may provide long-term
benefits to its users, as well as indirect benefits to others. For
example, there are potential long-term benefits from the change in
attitude of game-players towards real-life situations in the workplace,
and the improved efficiency with which they may be able to perform some
of their tasks. This can impact on the job satisfaction of individual
employees and on overall company morale .
•
9
•
2. ELEMENTS OF THE MINING PROJECT
The elements of the mlmng project which are discussed in this
section are those which either are not addressed in the rules (section
3.2) or require elaboration. The details presented here are crucial to
a thorough understanding of how the economic variables and elements of
the mine/mill system are represented in the Game.
2.1 Preliminary Geological Information
The focus of simulated mining activity is a massive sulphide
deposit containing copper, zinc and gold. The zone of mineralization
has a sharp boundary with the surround i ng host rock -- rhyolite in the
footwall and andesite in the hangingwall. The surface topography in the
region of the deposit is flat. The deposit 1ies on a property with
boundaries at 0 metres north (mN), 0 metres east (mE), 32 765 mN and
32 765 mE.
The tonnage factor associated with the massive· sulphides is 0.263
cubic metres per tonne. A higher tonnage factor for the host material,
0.370 cubic metres per tonne, is typical of more silica-rich rocks.
The locations of thirty vertical delineation drillholes which
intersected mineral ization are shown in figure 1.
The average
intersection grades of five-metre core samples from these drillholes are
given in table 1.
•
10
•
SOmE
lS0mE
2S0mE
3S0mE
4S0mE
+
+
+
+
+
S3SmN+--+--+--+--+--+--+--+--+--+__ +__+__ +__ +__+__ +__ +__ +__ +__ +__ +
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1
SOSmN+1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
47SmN+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1
44SmN+1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+-
0
-+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
41SmN+--+--+--+--+--+--+--+--+--+-_+__
+__ +__ +__ +__ +__ +__ +__ +__ +__ +
o : Dri 11 hole
Figure 1: Delineation Drillhole Locations
•
11
•
•
Table 1. Average Intersection Grades of 5-Metre Core Samples
from Vertical Delineation Drillholes
Average Intersection Grade
Northing Easting Depth of Base
(mN)
(mE) of Sample (m) Copper(%) Zinc(%) Gold(g/t)
445
70
25
30
35
40
1.95
3.35
3.39
4.94
5.83
12.33
19.70
4.98
3.25
4.76
5.64
6.81
445
110
60
65
70
75
80
2.46
2.26
5.25
10.25
1. 74
5.18
4.45
7.72
4.96
21. 72
3.69
2.54
3.28
2.63
7.42
445
150
100
105
110
115
120
4.87
3.39
1.94
8.24
10.05
8.16
3.80
3.66
2.69
5.42
6.65
7.49
9.67
7.63
5.26
445
190
150
155
160
3.96
3.65
2.74
7.45
4.86
4.10
2.53
3.14
7.07
445
230
180
185
190
195
200
3.16
5.41
3.54
2.27
21.04
2.30
4.13
3.61
4.92
3.07
2.69
3.03
5.53
4.46
4.45
445
270
220
225
230
235
240
9.81
4.99
7.94
11.89
9.59
2.76
4.00
3.31
2.11
4.94
3.27
4.60
9.75
3.35
3.89
445
310
260
265
270
275
280
5.48
4.18
3.58
12.12
4.73
3.14
3.50
7.84
4.42
6.52
3.13
4.19
18.59
6.05
20.06
445
350
300
305
310
315
320
3.47
6.27
4.77
4.10
10.07
5.72
5.19
8.59
7.76
12.04
5.81
3.20
5.44
8.19
2.65
12
•
•
Table 1. (continued)
Average Intersection Grade
Northing Easting Depth of Base
of Sample (m) Copper(%) Zinc(%) Gold(gjt)
(mN)
(mE)
445
390
340
345
350
355
360
2.24
2.15
1.93
2.40
3.68
19.63
7.0B
5.34
2.56
3.06
13.30
4.56
5.6B
6.93
17.59
445
430
380
385
390
395
2.97
1.79
2.59
1.71
19.11
5.76
3.41
4.67
28.90
7.42
8.89
5.20
475
70
20
25
30
35
40
1.65
1.67
1.49
3.27
1.64
21.72
7.10
12.21
14.24
21. 72
4.26
2.28
10.77
28.90
5.93
475
110
60
65
70
75
80
2.55
3.50
3.94
2.12
1. 91
10.07
5.28
12.47
21.72
13.30
12.69
7.18
4.15
3.54
3.77
475
150
100
105
110
115
120
1.94
5.99
3.24
4.14
2.51
4.26
6.93
11.85
15.22
4.28
2.15
1.54
2.38
3.88
6.12
475
190
150
155
160
6.47
3.49
4.58
3.48
3.09
3.99
4.73
4.78
8.02
475
230
180
185
190
195
200
21.04
17.37
2.71
2.61
6.21
9.64
9.66
4.62
2.97
4.43
2.93
1.84
1. 27
1.45
3.60
475
270
220
225
230
235
240
2.79
2.18
4.12
13.97
12.46
2.86
3.64
7.02
2.33
4.48
4.45
3.79
1.97
2.08
1.43
13
•
•
Table 1. (continued)
Average Intersection Grade
Northing Easting Depth of Base
(mN)
(mE) of Sample (m) Copper(%) Zinc(%) Gold(g/t)
475
310
260
265
270
275
280
4.21
3.88
2.92
3.91
2.58
10.61
21. 72
5.14
2.16
3.96
7.66
4.54
8.94
3.77
5.63
475
350
300
305
310
315
320
1.88
3.45
2.26
3.41
3.47
19.30
8.25
4.13
17.66
5.97
13.27
Il.25
20.70
5.40
1. 79
475
390
340
345
350
355
360
1.92
3.04
4.02
2.79
2.08
2.54
4.28
21. 72
20.15
18.77
5.04
3.18
4.27
1.80
3.88
475
430
380
385
390
395
400
1.27
1.81
1.53
1.59
2.19
5.20
6.16
21. 72
21. 72
17.39
7.16
10.46
10.36
6.83
2.81
505
70
20
25
30
35
40
1.42
2.22
1. 57
1.17
2.76
10.38
20.98
14.01
21. 72
21. 72
7.63
13.77
4.99
8.22
12.59
505
110
60
65
70
75
80
2.60
2.77
1. 79
2.58
1.58
12.58
19.84
9.16
5.15
9.37
7.26
4.46
7.21
1.68
1. 78
505
ISO
100
105
110
115
120
3.70
2.83
4.52
3.02
2.39
8.60
4.10
2.31
2.20
3.69
2.98
1.85
4.95
3.42
1.08
505
190
ISO
1.97
2.42
4.99
5.57
12.42
10.31
5.15
5.43
3.27
155
160
14
•
•
Tabl e 1. (continued)
Northing Easting
(mN)
(mE)
Average Intersection Grade
Oepth of Base
of Sample (m) Copper(%) Zinc(%) Go1d(g/t)
505
230
180
185
190
195
200
8.06
3.84
3.89
6.44
16.94
5.06
6.86
7.92
3.19
5.79
1.16
1.50
1.77
1.37
1. 73
505
270
220
225
230
235
240
4.12
3.46
1. 78
3.67
2.52
4.65
4.07
3.31
3.68
7.86
2.93
8.05
20.69
18.48
5.92
505
310
260
265
270
275
280
4.16
5.28
3.50
1.58
4.69
5.53
4.42
3.66
6.52
21. 72
7.57
2.03
2.98
10.14
3.88
505
350
300
305
310
315
320
9.70
2.54
1.64
6.79
10.57
5.15
2.96
13.22
13.51
13.99
4.25
8.56
2.01
4.01
2.15
505
390
340
345
350
355
360
2.14
1.61
2.30
1. 78
2.76
13.78
5.78
3.76
6.47
Il.29
11.47
3.31
3.07
3.00
6.42
505
430
380
385
390
395
400
1.12
5.87
3.30
1.50
1.32
21.72
7.02
3.34
21.72
5.91
12.65
28.90
6.76
15.78
5.23
15
•
2.2 Underground Operation
While mine design may vary according to the user's preferences,
the configuration of stopes and pillars, and mine sequencing, must
follow certain guidelines intended to ensure a reasonable degree of
realism. The mining technique used is sublevel stoping. The intervals
between levels and sublevels have been preset based on normal operating
practice; however, the working sites at any point in time are determined
by the user.
Vertical access to the mine is provided by a shaft. The shaft
must extend for twenty metres below the deepest levp.l intended for
mining in order to accommodate a loading pocket, sludge and sump. The
minimum shaft depth is 170 metres. Once the shaft is in place, it is
possible to deepen it. Increments to the shaft depth are multiples of
seventy-five metres. The maximum shaft depth is set at 495 metres.
To simpl ify decision making, primary and secondary stoping must
advance in one di;-ection -- northwards. All stopes must therefore be
located at least as far north as the shaft. The shaft can be sited as
far south 0 mN, and as far north as 32 760 mN.
There are no
requirements regarding shaft pillars in the Game.
The shaft site
easting is not made explicit and is assumed to be appropriate to the
intended location of stoping activity.
Stopes dip forty-five degrees to the east. The vertical interval
between levels and sublevels is set at seventy-five metres and twenty
The maximum number of sublevels per level is
metres, respectively.
three, and levels are separated by sill pillars fifteen metres in
thickness. The crown pillar is at least fifteen metres thick.
•
The deposit is to be mined in one cut from hangingwall to
footwall. A mining unit has a length of five metres, a height equal to
the sublevel interval of twenty metres, and a width equal to the
selected stope width. The width of a stope is a multiple of five metres
and is no more than twenty-five metres. The maximum length of stopes
16
•
and the minimum length of rib
shows sorne of the parameters
deepest level is the haulage
extracted i s regarded as ore,
diverted to a stockpile.
pi11ars is twenty-five metres. Figure 2
of the sublevel stoping technique.
The
level.
A11 of the material which is
and i s either processed at the mi 11 or
Mining can take place on several sublevels and levels in a given
year. Mine seqllencing is possible, and selectivity is limited only to
ensure that mine sequencing is reasonably realistic.
The major
constraints to sequencing in the underground mine are that primary and
secondary stopi ng must advance northwards, and that the advance al ong
the various sublevels of a level be coordinated such that blasted rock
fragments can fall to the base of the stope. This requires that mining
on lower sublevels be more advanced than on upper sublevels.
The number of levels available for mining is a function of the
mineable depth which is determined by the shaft depth, thickness of the
crown pi11ar and pit depth, if an open-pit exists. The mineable depth
is the vertical interval between the base of a crown pillar of minimum
thickness and the l imit to mining at depth, i.e., twenty metres above
the foot of the shaft. Assumi ng that the underground operat i ons wh ich
follow open-pit mining will take place below the deepest level reached
in the pit, the thickness of the crown pi11ar is measured from the
bot tom of the pit. 1f no open-pi t mi ni ng has taken place, the top of
the crown pillar is at ground level.
For a shaft depth of 420 metres, including a twenty-metre
extension for the loading pocket, and a minimum thickness of fifteen
metres for a crown pi11ar at grollnd level, the mineable depth is
calculated as follows:
mineable depth = 420 - 20 - 15
= 385m
•
With the possible exception of the shallowest level, all of the
levels into which the deposit is divided contain three sublevels. The
number of such levels is the whole number resulting from the division of
17
•
\
\
\
\
~
\ 5 \
\
\
\
\
\
\
\
,
\
Sublevel
interval
20m
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
~\'O ~ \ \
?\\.-~
\
\
\
\
\
\
(fi> ~ ~
\..:&.'
__
...
Stope width
(maximum 25 m)
Figure 2: Parameters in Sublevel Stoping
•
\
\
\
18
~\'O c
\ \ ?\\.-\.-\'-'P
\
\
\
1
\
\\
2 \\3
\
\
4
Mining
units
\
•
the mineable depth by the vertical interval between levels (seventy-five
metres) :
Number of levels = 385 1 75
= 5 (remainder la metres)
The remainder from the above division (ten metres) is the vertical
interval between the base of a crown pillar of minimum thickness and the
top of the shallowest level containing three sublevels.
The magnitude of the vertical interval determines whether or not
an additional level can be considered available for mining.
Such a
level would be the shallowest in the mine. If the vertical interval is
between twenty and thirty-nine metres, the additional level contains one
sublevel. A vertical interval of between fort y and fifty-nine metres
allows for two sublevels in the additional level. Given the remainder
of ten in this example, the number of levels is unchanged at five, and
the crown pillar has a thickness of at least twenty-five metres.
Levels in the underground mine are numbered in sequence with
depth, the shallowest being Level 1.
The reverse appl ies to the
numbering of the sublevels, the first sublevel being the deepest on any
1evel .
Development drifts are driven on the three sublevels as shown in
figure 3. These drifts run northwards and should be located so as to
follow the mineralization bec au se they are used as platforms for
drilling which may lead to production. Given that the vertical interval
between sublevels is twenty metres and that the stopes dip forty-five
degrees to the east, an upper development drift must be displaced twenty
As mining must
metres to the west of the drift immediately below.
commence on lower subl eve l s before upper sub1eve1s, it i s necessary to
speci fy the western and eastern boundari es of the deve l opment dri ft at
the base of a level. The eastings of the boundaries of the development
drift on upper sublevels are automatically calculated .
•
If the development drift on the lowest sublevel has been poorly
19
•
Figure 3: Development Drifts on Three Sublevels
•
20
•
located, as evidenced by a lack of mineral ization in the mlnlng units
selected for dril'ling,
it is possible to begin a new development drift
in a different location.
This is conditional
upon the fact that no
extraction has occurred; otherwise, it is assumed that the drift has
been satisfactorily sited.
There must be no overlap in the boundaries
of the original and new drifts.
development
drift
is
allowed
Modification of the location of the
once
per
level;
the
geology
is
not
considered to be sufficiently complex to warrant additional relocations.
A development drift has a height of three metres, and a width
determined by the user-specified coordinates of the western and eastern
boundari es,
up to a maximum of twenty- fi ve metres.
The development
drift on each sublevel is assumed to begin at the northing of the shaft
and
advance
northwards
as mining
progresses.
The
dimensio~s
of a
development drift, including the length of the drift, are the basls for
calculating the volume of material excavated.
The void which would be
created by drifting, and the material removed, which might in real ity
contribute to production, are ignored.
Therefore, in a given level, the
uppermost material on the first or second sublevel
is assumed to be
contiguous with the material at the base of the sublevel above.
Once mining has begun on a particular sublevel,
additional
drlftlng northwards
specifications.
At
is dependent upon the
any point in time,
the need for
stope
boundary
the development drift on
a
particular sublevel has been driven as far north as the most northerly
dri 11 i ng site (fi gure 4), whether or not the drill i ng was fo 11 owed by
extraction.
If a selected block is more northerly than the existing
northern 1i mit of the deve1opment dri ft,
requlred.
then addit i ona1 dri ft i ng 1s
The drift is extended the entire distance between the current
northern llmit of the development drift and the northern boundary of the
selected block.
Stope
selection
follows
the
specification
sublevel on whlch mining is to occur.
•
of
the
level
and
A stope comprises up to five
mining units which may be extracted in different years, or in the same
year
either through a single stope selection, grouping ~he units
21
as
a
•
•
S
N
Jf11
........
Shaft
Most-northerly
drilling site
Block selected for
drilling and/or extraction
r--
Development drift
•
Additional drifting
required
L...
Northern Iimit of
development drifting
Figure 4: Block Sequencing on a Sublevel Requiring Advancement of the Development Drift
•
block, or by repeating the selection procedure up to five times. The
block of one or more mining units to be mined from a stope is delimited
by the coordinates of its northern, southern, western and eastern
boundaries at its base.
The eastings delimiting a stope are specified only for the base of
the first sublevel of a new stope, and must be the same as or within the
easti ngs of the boundari es sel ected for the development drift.
The
width of a stope, set upon commencement of extraction on the first
sublevel, remains unchanged when mining takes pl ace on the second and
third sublevels above.
The western and eastern boundaries of blocks
bei ng mi ned from these upper subl eve1sare automat i cally set accordi ng
to the boundaries of the stope on the first sublevel, with an adjustment
reflecting the forty-five degree dip of the stope (figure 5).
Thi s
reduces the number of decisions which would otherwise have to be made,
and ensures that the fall of material from upper sublevels to the base
of the stope is not impeded.
Although the width of a single stope
cannot be changed once i t has been set, stope wi dth can be vari ed from
stope to stope.
In the selection of the northern and southern boundaries of a
block to be extracted, cons iderat i on must be gi ven to the property
boundaries, the maximum length of a stope, the minimum length of a rib
pillar and the condition that mining advances northwards. For mining on
upper sublevels there is an additional constraint imposed by the mining
technique with regards to the correct positioning of a sel ected block
relative to the stope boundaries on the sublevel below. The northern
and southern boundaries of the selected block must be the same as or
within the corresponding boundaries of the stope on the sublevel below.
In other words, mining on an upper sublevel cannot ex tend beyond the
stope limits on a lower sublevel. Mining must be at least as advanced
on a lower subl eve1 as on an upper subl eve1 (fi gure 6) so as to permit
the free fall of blasted material to the base of the stope.
•
Blocks mined from the second or third sublevels of a stope must be
contiguous. Assuming that some extraction has already taken place on an
23
•
w
E
Sill pillar
r
-......------.....
-
75m
- - - - -
Sublevel3
235 mE
SOm
Sublevel2
r------------ ------------ ----'1'
230 mE
255 mE
20 m
Sublevel 1
250 mE
275 mE
Figure 5: Cross-Section Through a Stope Showing the
Relative Positions of the Western and Eastern
Stope Boundaries at the Base of Each Sublevel
•
24
•
s
N
Siii pillar
----------~--,-----------------
Sublevel3
______ ,....__..1-
L..----, _ _ _ _ _ _ _ _ _ _ _ _ _
Stope
------
Sublevel2
----------~------.------
Sublevel1
(mined out)
Direction of advance - . .
Figure 6: Horizontal Projection of Sublevels in a St ope
on to a Longitudinal Section Showing Mining to
be More Advanced on the Lower Sublevel$
•
25
•
upper sublevel of a stope, the southern boundary of the selected block
must be the same as the northern boundary of the stope on the particular
sublevel. If the block is the first to be mined from an upper sublevel
of the stope, its southern boundary must be at least as far north as the
southern boundary of the stope on the sublevel below.
The northings selected for a block on the first sublevel determine
"Ihether mining is to be started in a new primary stope or in a new
secondary stope, or continued in an existing stope. Secondary stoping
takes place in the rib pillars separating primary stopes. One secondary
stope can be mined in each of the se pillars. A secondary stope may also
be developed in the southern wall of the most southerly primary stope.
If the southern boundary of the selected block is at least twentyfive metres north of the most northerly stope, th en mining is taking
place in a new primary stope. If the selected block is contiguous with
the most northerly primary or secondary stope, then that stope is being
extended.
Once mlnlng units have been selected on the first sublevel of a
new stope, operations in a more southerly stope of the same type are
assumed to have been completed; further mining on the level is carried
out in the new stope or in a more northerly stope. In other words, the
most northerly primary stope is the active primary stope; the same holds
true for secondary stopes. If mining takes place in the pillar south of
the most northerly primary stope, extraction in the rJrimary stope is
assumed to have been completed, and primary stoping ma}' be resumed in a
new stope.
It is assumed that backfilling of a primary stope is carried out
immediately following the termination of
particular stope. It is also assumed that
enough to allow extraction in a secondary
year in which mining of the adjacent primary
•
mining operations in the
the curing period is short
stope to begin in the sam,~
stope or stopes has ended .
Validation of the coordinates of the boundaries of a selected
26
•
block also requires a comparison of the maximum amount of material which
could become available from mining the block with the amount which can
be mined given the remaining mine capacity. The mine capacity remaining
at any point during a year is calculated as the maximum overcapacity
production level less the capacity util ized for mining and exploratory
drilling activities.
Drilling which does not lead to immediate extraction is considered
to be exploratory. A unit of exploratory drill ing is assumed to be
equivalent to two-thirds of a unit of mining, that is, each unit of
exploratory drill i ng reduces the rema ini ng mi ne capaci ty by two-thi rds
of a unit.
If the amount of materiai which is available from mlnlng a
selected block is more than can be extracted given the remaining mine
capacity, the boundaries of the block must be modified so as to reduce
its size.
Providing that the coordinates delimiting a block are
acceptable, estimates of the grade of copper, zinc and gold in each in
situ mining unit are generated on the basis of blasthole sample data.
These estimates of grade may be used by the player to support decisions
concerning the selection of mining units for extraction. On the basis
of the grade estimates, the user may decide to extract some or all of
the mining units delimited by the specified coordinates, or to leave the
block in the ground.
•
Stope boundari es can be modifi ed from those previ ously sel ected
prior to extraction.
Any material which is in a block under
consideration, and which is external to any others selected in the
current stope speci fi cat ion, has to be dri 11 ed for purpose of grade
estimation and blasting.
Reselection of previously drilled, but
unextracted, mat~rial from a separate stope specification results in
redrilling and the production of new estimates. This occurs even if the
sel ect ion i s repeated in the same year. If more than one set of grade
estimates is produced for a given mining unit, it is the most recent set
which is used in any subsequent computations. The amount of material
which lias been drilled is cumulated throughout the year .
27
•
A block of material which has been drilled may be extracted
without further modification to its boundaries, or may be left in place.
At the end of a year, the total amount of material drilled is compared
ta the amount of material which was targeted for extraction during the
year. Any drilling in excess of that required for current production is
considered to be exploratory drilling.
In order to ensure that the actual amount of material mined does
not exceed the limit of overcapacity, several assumptions are made with
regards to the levels of mine recovery and dilution" and the tonnage
factor to be appl ied to mined material.
In estimating the amount of
m~terial which could be mined for any given block specification, it is
assumed that there is full recovery and that dilution is at a maximum.
The maximum rate of dil utton i s set at t\~enty per cent.
The tonnage
factor for massive sulphides, 0.263 cubic metres per tonne, i5 used in
estimating the amount of material available l'rom mining because a block
of maximum !limensions could lie entirely within the boundaries of the
deposit.
For any mlnlng unit specification, the adual amount of material
mined during a particular year is a function of the average annual rates
of dil uti on and mi ne recovery; these rates are generated l'rom mostli kely val ues of fi fteen percent for dil uti on and ni nety-three percent
for mine recovery, and are unknown to the user until mining operations
have been completed for the year.
The amount of material which is
extracted l'rom the mine is also a function of the composition of the
selected mining units. The amount of material to be mined is increased
by dilution.
Depending upon where the stope walls are located, the
additional material associated with dilution may be mineralized or
•
, The term 'dilution' refers here to external dilution, that is,
material lying adjacent to, but beyond, the boundaries of the selected
in situ mining unit(s), and which is mined along with the targeted
material.
The diluting material derives l'rom the hangingwall and
footwall.
28
•
barren, and therefore, does not necessarily reduce the mined grade. The
cumulative amount of mined material, updated after each stope selection,
is the basis for calculating the remaining mine capacity.
The difference between the assumed and actual rates of mine
recovery and dilution may lead to a situation in which there appear to
be conflicting messages. If the underground mine is operating at a rate
which is close to the limit of overcapacity, it may appear, for example,
that only one additional mining unit can be accommodated by the
remaining capacity. Once extraction of the unit has been completed and
the actual rates of mine recovery and dilution have been applied instead
of the assumed maximum rates, further extraction may be possible.
Mining activities for a given year have been completed if at least
one of the following conditions is met:
I} all levels have been mined out between the northern and southern
limits to mining as determined by the northern property boundary
and the shaft site, respectively. A level is regarded as mined
out if neither primary nor secondary stoping can take place.
Primary stoping has been completed if the third sublevel of the
northernmost stope has a} advanced to the northern boundary, or b}
the maximum allowable stope length, and the distance from the
northern stope boundary north to the property boundary is
insufficient to accommodate a rib pillar and a new stope of
minimum length. Secondary stoping has been terminated if the
third sublevel of the secondary stope in the most northerly pillar
has a} advanced to the northern boundary of the pillar, or b} the
maximum allowable stope length.
2} there is insufficient mine capacity remaining for the extraction
of the smallest available mining unit.
3} the user decides to terminate mining activities.
•
Should a decision be taken to continue mining, it may be necessary
to reselect the level and sublevel. The specified parameters must meet
certain criteria for acceptability.
Mining can take place on the
29
•
selected level providing that all of the following are true:
1) the level exists, that is, the level number lies between 1 and the
number of levels.
2) the 1evel is not mined out, and· at 1east one mining unit is
currently available for extraction.
3) the minimum mineable increment on the 1evel is acceptable in terms
of the remaining mine capacity.
On an acceptable level, mining can take place on a selected
sublevel if two conditions are met:
1) the sublevel exists, that is, the sublevel number lies between one
and the number of sublevels on the particular level. All levels
have three sublevels with the possible exception of Level 1.
2) extraction has not been suspended on the selected sublevel of both
primary and secondary stopes. Extraction cannot proceed on
Sublevel ·1 of a primary stope if mining has advanced to the
northern property boundary, or if the stope. has the maximum
allowable length and the distance from the northern stope boundary
north to the property bOllndary is insufficient to accommodate a
rib pillar and new stope of minimum length. Extraction cannot
proceed on Sublevel 1 of a secondary stcpe if mining has advanced
to the northern pillar boundary, or if the stope has the maximum
allowable length.
On the second and third sublevels of either a primary or a
secondary stope, extraction is suspended if the northern boundary
of the northernmost stope is in vertical continuity with the
corresponding stope boundary of the sublevel below. This arises
from the rule that mining must advance northwards and be more
advanced on a lower sublevel than on a higher one .
•
30
•
2.3 Open-Pit Operation
The arder of removal of ore and waste is set by the user within
certai n constrai nts. These constrai nts are intended to increase the
level of t'ealism in the simulation of open-pit operations. The minimum
mining width of twenty metres applies to mining on a new level, and has
been preset based on a consideration of normal operating practice. The
maximum pit slope angle is forty-five degrees, and mining units are
cubic blocks with a height equal to the bench heigilt, that is, ten
metres.
Mining takes place in a pit which is approximately square or
This pit shape, while uncommon in practice,
rect.angular in plan.
reduces the compl exity in the speci ficat ion of pit increments by the
There are four
user, and simplifies the software development.
boundaries, each referring to a side of the pit. A boundary may be
straight over its entire length or divided into segments which parallel
the north-south or east-west axes. As shown in figure 7, each boundary
is defined by three coordinates which del imit the outermost section of
the pit along the boundary:
northern boundary
southern boundary
western boundary
eastern boundary
northern, western
southern, western
western, northern
eastern, northern
and
and
and
and
eastern éoordinùtes
eastern coordinates
southern coordinates
southern coordinates
The northern boundary, for example, is considered to be straight
if its western coordinate is the same as that of the western boundary,
and its eastern coordinate is the same as that of the eastern boundary.
Similar criteria must be met for other boundaries to be considered
straight. On the pit level outlined in figure 7, the northern and
western boundaries are straight. A side of the pit may be segmented
into as many as three parallel sections, depending upon the selection of
pit increments.
•
The limits of the open-pit are extended in two ways.
31
A block of
•
Northern boundary
Western
Eastern
boundary
bo undary
-
1
1
1
SE
Southern boundary
LEGEND
AB
•
Boundary Coordinats
Figure 7: Boundaries of the Open-Pit and their Delimiting
Coordinates
32
•
one or more mlmng units may be removed from a straight boundary, thus
extending the pit limit, or part thereof, in a direction perpendicular
to the sel ected boundary. Thi s process i s therefore referred to as
perpendi cul ar extensi on, and i s il ~ ustrated in fi gure Sa with reference
to the eastern pit boundary.
At least one block of mining units may be removed from a boundary
which is not straight. Along the selected boundary, the outer limit of
the pit, as defined by its coordinate, for example, the eastern
coordinate of the eastern boundary, remains unchanged after the pit
extension.
The block or blocks removed paraI leI the selected pit
boundary. This type of extension, termed parallel extension, is shown
in figure Sb for the eastern pit boundary.
To produce a perpendicular extension, the coordinates delimiting
the block to be mined must be specified. If the extension takes pl ace
along a section of the eastern boundary, as in figure Sa, the eastern
pit limit is extended by ten metres, the length of a mining unit.
Following such a perpendicular extension, the boundary is no longer
straight and can be extended further through a paraI leI extension.
If a perpendicular extension affects the entire length of a
boundary, the pit limit can be extended, in one specification, by
several rows of units, that is, for distances which are multiples of ten
The distance by which the pit limit can be extended is,
metres.
however, constrained by the maximum pi'. slope angle or, on the first
level, by the property boundaries.
•
If underground mine construction is being carried out during openpit operations, perpendicular pit extension on the first level is also
constrained by the location of the shaft. If the shaft site northing
lies between the outermost pit limits on the northern and southern
boundaries of the pit, the shaft is assumed to be sited to the east or
the west of the pit and, therefore, the eastern and western pit
baundaries cannat bath be extended ta their carrespanding praperty
The alternative case is that in which the shaft is
baundaries.
33
•
al
N
t
••,.
1
Ex isting pit limits
Black ta be
extracted
rt:JWI
~.
ifJP41if:
-..
b)
Directi on of extension
N
t
Existing pit limits
1t
l
•
Direction
of
e xtension
Black ta be extracted
Figure 8: a) Perpendicular Extension b) Parallel Extension
of the Open-Pit Along the Eastern Boundary
34
•
originally sited to the north or south of the open-pit. If the eastern
and western pit boundaries are subsequently extended to the property
boundaries, the northern or southern pit limit can be extended towards,
but not as far as, the shaft.
To effect a parallel extension, the user specifies the coordinates
which will defi ne the boundary after the pit increment. As shown in
figure 9, the block delimited must include all of the mining units which
have previously been extracted from the boundary being extended.
Drilling is simulated for only those units remaining in situ.
Given the bench height of ten metres, the maintenance of a pit
slope angle of forty-five degrees or less requires that the minimum
horizontal distance between the· corresponding boundaries on two
consecutive levels of the pit be ten metres. If the boundaries are not
straight and parallel extension is under consideration, it is the
position of the inner segment of the boundary on the upper level
rel ative to the position of the outer segment of the boundary on the
lower level which is relevant.
In a parallel extension southwards along the eastern boundary, for
example, the block being removed cannot extend further south than the
southern limit of the pit on the southern boundary. This ensures that
the plan of the pit on each level is approximately square or
rectangular.
Val idation of the coordinates bounding a block selected in th~
open-pit is similar to that performed for blocks in the underground
mine. The maximum amount of material which could become available from
mining the block is compared with the amount which can be mined given
the remaining capacity. It may be necessary to modify the boundaries of
the block so that mining of the incremental material is possible given
the remaining capacity.
•
Providing that the coordinates delimiting the block are
acceptable, estimates of the grade of copper, zinc and gold in each in
35
•
N
Previously extracted
mining units
t
1••
Existing pit Iimits
1!
1) irection
of
extension
Mining units to
be extracted
LEGEND
•
Block delimited for
parallel extension
Figure 9: Block Specification for Parallel Extension of
the Open-Pit Along the Eastern Boundary
•
36
•
situ mlnlng unit are generated on the basis of blasthole sample data.
On the basis of the grade estimates for the selected mining units, the
user may decide to extract some or all of the mining units delimited by
the specified coordinates, or to leave the entire block of units in the
ground.
Block boundaries can be modified prior to extraction.
Any
material which is in the block under consideration, and which is
external to any other blocks selected in the current block
specification, has to be drilled for purpose of grade estimation and
possibly also production.
Reselection of previously drilled, but
unextracted, materi al from a previ ous block specifi cat ion results in
redrilling of the material and the generation of new estimates.
Redrill ing occurs even if the selection is repeated in the same year.
If more than one. set of grade estimates is produced for a given mining
unit, it is the most recent set which is used in any subsequent
The amount of material which has been drilled is
computations.
cumul ated throughout the year. The amount of exploratory dri 11 ing -drill ing which does not lead to immediate extraction -- is determined.
Each unit of exploratory drill ing reduces the mining capacity by twothirds of a unit.
The calculation of the amount of material mined in a given year is
based on the assumption of full recovery and no dilution. In estimating
the amount of material associated with a proposed pit increment, it i 5
assumed that mineralized material constitutes the maximum volume
possible. This ensures that the actual amount of material mined during
a year does not exceed the limit of overcapacity production. A drawback
of this assumption is that the estimate of the amount of material to be
mined is higher than the actual amount associated with any pit increment
in which the volume of mineralized material is lower than the maximum
volume. The assumption is unlikely to affect block selection unless the
mine is operating at a rate close to the limit of overcapacity.
•
Mining activities in the open-pit have been completed for a given
year if at least one of the following conditions ~s met:
37
•
1) all levels have been mined out: On the first level, the pit
cannot be extended further than the four property boundaries. On
a lower level, a lack of accessible mining units at a particular
point in time does not necessarily render the level unavailable
for future mining; subsequent removal of material from the level
above may make extraction possible. A lower level is mined out if
there is no material available for extraction from it or from any
of the levels above.
2) there is insufficient mine capacity remaining for the smallest
allowable pit increment from a technical standpoint.
3) the user decides ta terminate mining activities.
Should a decision be taken ta continue mining, it may be necessary
or desirable to select a pit level and boundary which differ from those
last specified. The selected parameters have ta meet certain criteria
for acceptability.
Mining can take place on the selected level
providing that all of the following conditions are satisfied:
1) the level exists, that is, mining operations have already
commenced on the level, or mining is to begin on a new level. A
new level is considered to be acceptable if it is the first level
in the pit or if the level number is the next in sequence after
the number of the deepest level in the pit.
2) the level is not mined out and material is currently available for
removal. In other words, mining must be possible on at least one
of the four boundaries on the selected level.
3) the minimum tonnage to be mined on the level is acceptable in
terms of the remaining mine capacity.
On an acceptable level, a boundary can be selected fur mining
operations if two conditions are met:
•
1) the boundary exists, that is, the northern, southern, western or
eastern boundary is selected.
2) a parallel or perpendicular extension can take plac~ along the
38
•
•
boundary.
Any boundary is acceptable for the first cut on Level
1. On a level on which sorne extraction has taken place, at least
one unit must be available for mining on the specified boundary.
If mining is to take place on a new level below Level l, the
acceptability of the chosen boundary is depe~dent upon the
configuration of the pit on the level above. It must allow access
on the selected level to at least two mlnlng units lying adjacent
to each other such that, as a whole, they parallel the specified
boundary. The minimum number of mining units which must be
accessible is higher for a new level in order to meet the
requirement of a minimum mining width .
39
•
2.4 Preproduction Period
The length of the preproduction period of the underground mine or
mill is a function of the installed capacity:
pp = O. 84Qo.22
where:
pp
is the preproduction period (rounded to the nearest whole
number of years)
Q is the installed annual capacity of the underground mine or
mill ('000 tonnes)
A plant comprlslng an underground mine and a mill with an
installed annual capacity of 300 000 tonnes requires three years of
The longest preproduction period which can be
preproduction work.
expected for an underground mine or mill of maximum allowable installed
capacity is four years. The preproduction period for an open-pit mine
designed within the range of permissible installed capacities is two
years.
If there is a difference between the preproduction period
determined on the basis of the mine design and that calculated for the
mill, the preproduction period is. taken as the longer of the two
periods.
The t ime needed to compl ete a capaci ty expansi on program for an
underground mi ne or mi 11 i s a funct i on of the difference between the
preproduction period required for the mine or mill of the former
installed capacity and that required for a new installation of the
expanded capacity:
EP
=
1.15 X (0.84QxO.22 - 0.84Qo.22)
where:
EP is the period required for expansion (rounded to the nearest
positive whole number of years)
•
Q is the former installed annual capacity of the underground
mine or mill ('000 tonnes)
40
•
Qx is the expanded annual capacity of the underground mine or the
mi 11 (' 000 tonnes)
The
difference
in
the
lengths
of
the
preproduction
period
associ ated with the two capaci t i es i s mult i pl i ed by a factor whi ch i s
greater than one.
This reflects the inefficiencies arising
in
the
selection and irstallation of additional equipment as a separate project
following the initial capacity installation. Expansion of the installed
capacity of an open-pit mine requires one year.
The commencement of preproduction work can be delayed for a period
of up to fifteen years, thus providing the user with sorne flexibility in
timing the start-up of operations.
As is mentioned in section 2.6,
metal priees display cyclical behaviour.
Provided that the player is
able to match project start-up correctly with cycle position, the mining
firm may be able to benefit from a delay in the start of production.
For example, if the start of production is timed ta coincide with a
period of priee recovery, the firm has the potential to increase early
cash inflows and thus impl"OVe project economics.
In making a decision
with respect to project postponement, the pl ayer should bear in mind
that
inflation
opera~;r',1
•
during
a
period
of delay
costs (sections 2.5 and 2.7) .
41
will
affect
capital
and
•
2.5 Capital Costs
The capital cutlay required ta set up a mine and mill has a fixed
cast component and a vari abl e cost component rel ated to the 1evel of
i nsta11 ed capacity. The general form of the funct ions whi ch rel ate
capital costs to the installed capacity of the mine or mill is:
cc
=
a + bQc
where:
CC is the capital cost of the mine or mill ($'000)
Q is the installed annual capacity ('000 tonnes)
a, band c are constants
The values of the constants in the hypothetical capital cost
functions used in the Game are given in table 2. The capital costs
generated by the functions are close to 1990 levels.
Capital costs may al so ari se in connect ion wi th funct ions other
than mi ni ng and mill i ng. It i s assumed that other capital costs, such
as those associated with the provision of access and power, are included
in the capital costs of the mine and mill. The total capital cost is:
CCtotal
=
CC mine + CC mill
The capital cost of an underground mine developed while the openpit is in operation is seventy percent of the value obtained using the
capital cast function. This is because some of the costs of providing
infrastructure and general plant services would already have been
incurred at the time of development of the open-pit mine.
•
The capital cast of an expansion program is the difference between
the capital cast of the mine or mi" of the former capacity and the
capital cost associated with a new installation of the expanded
capacity, multiplied by an adjusting factor. The factor has a value of
1.15, and results in an upward adjustment to the difference in capital
42
Table 2: Constants in the Capital Cost
Functions for the Mine and Mill
•
Capital
Cost
Function
Constant
Value
a
b
c
3226.3109
233.31596
0.7662613
Open-pit min!!
a
b
c
475.40588
132.44452
0.6088922
Mill
a
b
c
5767.6280
229.9.1615
0.7093054
Underground
mi~e
costs. This reflects the fact that additional capacity is l ikely to
cost more if it is put in place after completion of the plant.
Calculation of the cost of shaft sinking is based on the following
relationship' and an assumption of competent host rock conditions:
SOCC
=
307252SAo. 25 + 1259. 223S0'·'SAo. 25
where:
SOCC is the capital cost of the shaft ($)
SA is the cross-sectional area of the shaft (square metres)
SO is the shaft depth (metres)
The cross-sectional area of the shaft is calculated as follow:;:
SA
•
=
1.682Qo.4
, The capital cost relationships presented here are based on those
generated by Mackenzie (1987) and O'Hara (1987) .
43
•
where:
Q is the installed annual capacity ('000 tonnes)
The cost of shaft deepening is the difference in the capital costs
of shaft sinking to the original depth and to the proposed- depth.
multiplied by a factor of 1.15. The use of this adjustment factor
results in a higher unit cost for an increase in shaft depth after
completion of the initial shaft sinking. A shaft deepening project can
be completed in one year.
The amount of working capital which must be available at the end
of a year is the estimated working capital requirement of the following
year. Working capital is typically calculated as a proportion of the
operating costs to be incurred during a year:
wc = 0.25
(Expected annual operating costs)
where:
WC is the working capital investment ($)
The annual operating costs referred to are those expected to be
incurred for operation at the installed capacity, or for maintaining a
mine or mill which is temporarily closed. The values of the installed
capacity and operating cost variables may change from year to year and,
therefore, the working capital requirements can also be expected to
vary. The working capital recovered each year is the amount which was
i nvested at the end of the previ ous year. The net effect on cash flow
in any given year is the difference between the amount invested and the
amount recovered; this is referred to as the net working capital.
The annual sustaining capital required for the mine is a function
of the installed mine capacity:
open-pit mine
ASC mfne
underground mine - - ASC mfne
•
where:
44
= 0.2638Q
=
+ 132.124
223. 39Qo.6791
•
ASC.
is the annual sustaining capital for the mine ($)
mlne
Q is the installed annual mine capacity ('OÙO tonnes)
The annual sustaining capital needed for the mill is calculated as
follows:
ASC mill
=
0.01 (1/4.5) CC mill
where:
ASC mill is the annual sustaining capital for the mill ($'000)
The susta ini ng capi ta1 costs are adjusted if the operati on i s
expanded. If an installation has been shut down, no sustaining capital
is required for the period of closure. In anticipation of permanent
closure, no expenditure of sustaining capital takes place in the final
year of operation.
The values generated by the capital cost functions are the mostlikely costs.
Uncertainty concerning the exact level of capital
exptlnditure required for the project is reflected by incorporating a
random factor in the generation of capital costs, excluding working
capital.
The capital expenditure associated with the initial
installation and expansion of mining and milling capacity is spread
evenly, in constant dollar terms, over the construction period.
Capital costs are fully responsive to inflation which has a mostlikely value of 4.70 percent.
Inflation also influences the
requirements for working capital. The amount of working capital which
must be available at the end of a year is based on the expectation that
inflatioli will occur at the most-likely rate in the following year.
Therefore, the working capital investment reflects the actual annual
cost inflation rates up to the current year, and a rate of 4.70 percent
for the following year .
•
45
•
2.6 Metal Priee
The average annual priees of eopper, zinc and gold are generated
in current U.S. dollars. Each priee is that at which the supply and
demand for the particular metal are balanced throughout the year.
The historical behaviour of metal priees can be described in terms
of a trend, cyel i cali ty and a randof11 component. These features have
been incorporated into the pricing model in order to depict the type of
behaviour exhibited by priees on the free market.
In the Game, the
pri ees of mi neral commodit i es are affected by two cycl es of di fferi ng
lengths.
A new series of priees is generated for each run of the Game. The
positions of the peaks and troughs of the pric~ cycles can be expected
to change from one run to the next .
•
46
•
2.7 Operating Costs
Each mine or mill which could be installed for the exploitation of
the deposit has a different minimum average operating cost for full
capacity operat ions; a seri es of these costs defi nes the i ntermedi aterun average operating cost curve.
Thi~ arrangement,
in which the
intermediate-run cost curve is the locus of short-run cost minima, is
used for modelling purposes only.
A different short-run average
operating cost curve is associated with each installation.
The relationship between the intermediate- and short-run average
operating cost curves for the mine and for the mill are shown in figure
10. The intermediate-run average cost curve for the mine and the shortrun average cost curves for the mine and mill are generated using
functions of the general form:
oc = aQ2
- bQ + c + d / Q
where:
OC ois the average operating cost
intermediate-run average operating
underground or open-pit mine, or
operating cost (SROC) associated with
Q is the annual
($/tonne),
i.e. the
cost (IROC) of the
the short-run average
the mine or mill
rate ('DaO tonnes)
product~on
a, b, c and d are constants
The intermediate-run average operatir.g cost curve for the mill is
generated using a function of the form:
IROC
=
a + bQ-c
where:
IROC is the intermediate-run average operating cost ($/tonne)
Q is the annual production rate ('000 tonnes)
a, b, and c are constants
•
The cost functions which have been developed yield values which
47
•
a)
~
~
Cii
o
C,)
Cl
c:
~
Q)
C-
o
Annual Production Rate (t)
b)
IROC
Annual Production Rate (t)
•
Figure 10: Intermediate-Run Unit Operating Cost Curve as
the Locus of Short-Run Unit Operating Cost
Minima for the a) Mine b) Mill
48
•
are close to 1990 operating cost levels, but are purely hypothetical.
The values generated using the IROC and SROC functions for the
underground mine and the SROC function for the mi11 reach their minima
at an annual production rate of 300 000 tonnes. The minima generated
using the IROC and SROC functions for the open-pit mine occur when the
annual production rate is 3.3 million tonnes. The IROC function for the
mill does not yield a minimum value, but rather ~ series of decreasing
val ues as the i nsta11 ed annual capacity i ncreases. Th~ val ues of the
constants in the IROC and SROC functions for the underground and openpit mines and the mill are given in table 3.
An
installed
operating
processed
underground mine/mi11 pl ant operating at a rate equal to the
annual capacity of 300 000 tonnes is expected to incur
costs of $20.15' per tonne mined, and $18.00 per tonne
through the mill:
IROC mine = SROC mine = 20.15
IROC mill
=
SROC mill
=
18.00
If the plant operates at eighty percent of its installed capacity, the
short-run operating costs would rise to $21.56 per tonne mined dnd
$19.26 per tonne milled.
Assumi ng that the form of the short-run average operat i ng cost
curve i s constant regardl ess of its pos iti on on the i ntermedi ate-run
cost curve, the SRGC function can be used to determine the premium which
must be added to the intermediate-run operating cost for any size of
installation.
The minimum short-run operating cost is achieved by
operating at a rate which is equal to the installed capacity of the mine
or the mill. The actual production rate is expressed as a proportion of
this short-run cost-minimizing rate. Since the SROC function is valid
only for an installed annual capacity of 300 000 tonnes, the proportion
•
, Unless otherwise indicated, monetary values are in Canadian
dollars.
49
•
Table 3: Constants in the Intermediate-Run and Short-Run
Average Operating Cost Functions for the Mine and Mill
Operating Cost Function
Insta11 at ion
Constant
IROC
Underground mine
a
b
c
d
2.1279619 x 10- 4
0.1165666
32.634990
1000.0000
Open-pit mine
a
b
c
d
1.2453014 x 10- 7 1. 6710645
7.5761974 X 10-4 1. 0392662
2.3318907
2.7997892
700.00000
693.00000
Mill
a
b
c
d
2.0002226
164.48033
0.4085363
1
•
SROC'
2.8693481
0.1670942
39.934133
906.00000
10- 4
X
X
10- 7
10- 3
2.5624317 x 10-4
0.1447459
35.661884
810.00000
For an installed annual capacity of 300 000 tonnes
for the underground mine and mill, and 3.3 million
tonnes for the open-pit mine
50
X
•
obtained above is multiplied by 300 000 ta arrive at an adjusted
The premi um i s the difference between the values
product i on rate.
deri ved from the SROC funct i on with Q equa l ta 300, and with Q based on
the adjusted production rate.
For example, if the installed annual capacity of the underground
mine is 250000 tonnes, the intermediate-run average operating cast is
$21.62 per tonne mined. If the mine produces 275 000 tonnes in a given
year, the adjusted production rate ta be used in the SROC function is
calculated as follows:
Adjusted rate = (275/250) 300 000
= 330 000
The short-run operating cast function yields a value of 20.44 when
Q is based on this adjusted production rate. The addition of a premium
of $0.29 (SROC,Q.330) - SROC,Q.300») ta the intermediate-run cast results in
a short-run operating cast of $21.91 per tonne mined.
The underground operating cast functions are val id when hoisting
takes place from a depth of 170 metres. Given that unit hoisting costs
increase by 0.33 cents per metre, the unit operating costs increase with
the shaft depth as follows:
oc = value
from functions + [0.0033 (shaft depth - 170)]
The open-pit cast functions are valid for mining operations on the
first level. Unit haulage costs increase by two cents per bench, and
the weighted average incn,ase in unit operating costs with depth is
based on the proportion (p) of material mined from each level:
I~crease
•
in OC = ~ {p [0.02 (level number - Il])
The cast of drill ing is $4 per cubic metre. Drifting costs are
$72 per cubi c metre. The ma i ntenance cast for the mi ne or mi 11 i s the
cast of upkeep of the installation on a stand-by basis. These costs are
i ncurred in the event of a temporary cl osure. The annua l maintenance
51
•
costs are S100 000 for the underground mine and S70 000 each for the
open-pit mine and the mill. If drifting and/or exploratory drilling are
carried out without any extraction of material. the costs of these
activities are added to the maintenance costs to produce the total
annual mine 'operating' cost.
The cost of permanent closure is incurred in the fina~ year of the
project. At this time, the dismantling, reclamation and severance costs
associated with permanent closure of the mine/mi" plant exceed the
proceeds from the sale of assets by the amount of two million dollars.
The costs of drifting, drilling and plant closure, and the values
The
generated using the cost functions are the most-likely costs.
actual operating costs incurred by the mining firm are characterized by
uncertainty. They are also influenced by the economic cycles mentioned
in sect i on 2.6; however, a l ag of a few years can be expected between
the peaks in priee cycles and those in cost cycles. Operating costs are
responsive to inflation; the most-likely cost inflation rat~ is 4.70
percent .
•
52
•
2.8 Estimated Value of an Extracted Mining Unit
The material mined as a single mining unit is assigned an average
doll ar value per tonne. The est imate of val ue i s a funct i on of the
estimates of the grade of copper, zinc and gold in the unit, the priees
of the three metals, the net smelter return and the mill recovery rate
for each metal. The estimated average value per tonne of material in a
mining unit is the estimated total revenue to be derived from the sale
of its constituent metals divided by the number of tonnes of material
extracted as the single unit:
Estimated Average Value per Tonne =
(Revenue copper + Revenue Zinc + Revenue GOld ) / Tonnes mined
The estimated revenue generated by each metal is a product of the
estimates of four variables:
RevenueMetal
=
Metal content x N5R x MR x Metal price
where:
Metal content refers to the mass of metal (tonnes of copper and
zinc, or grams of gold)
N5R is the net smelter return
MR is the rate of mill recovery
Metal price is in current dollars per unit of mass of the metal
•
In the open-pit operation, it is assumed that there is full
Therefore, a mining unit selected for
recovery and no dilution.
extraction is removed in its entirety. The situation differs in the
underground mi ne in that the materi al sel ected for extraction may be
augmented by dilution and/or reduced by incomplete mine recovery. For
the purpose of estimating the average value of the mined material, it
assumed that any dil uti ng materi al i s unmi nera1i zed. The meta1 content
is therefore determined on the basis of the estimated grades and the
amount of material comprising the undiluted mining unit .
53
•
The net smelter return at the smelter is the proportion of the
value of the metal in the concentrate which is received by the mine .
The value of the metal in the concentrate is determined using a
generalized net smelter relationship:
NSV
= (CG p
-
UD) / 100 (PR / 100) (P - RC) - [TC B + e(P - PB)] + CR - PN
where:
NSV is the net smelter value per tonne of concentrate
CG p is the concentrate grade of the product, e.g., percent zinc
UD is the unit deduction
PR is the proportion of the metal content paid for (percent)
P - RC is the settlement metal price less the refining charge
TC B is the base treatment charge
P - ,PB is the settlement price less the smelter contract base
pnce
e is the treatment charge adjustment factor
CR refers to credits for by-products (S/tonne 'of concentrate)
PN refers to penalties for deleterious elements
concentrate)
(S/tonne of
The credits for by-products are calculated as follows:
CR
= (CG B - UD) (PR / 100) (P - RC)
where:
CG B is the concentrate grade of the
grams/tonne)
by-product
(e.g.,
The concentrate grade of by-product gold is calculated in two
steps. The mass of the concentrate of the product, that i s, copper,
which is produced in a given period of time is determined as a function
of the grade of the ore processed through the mill:
•
54
•
where:
CV p is the mass of the concentrate
GRp is the grade of the ore, i.e., percent copper
MR p is the mill recovery of the product
ORE is the amount of ore (tonnes) processed during the given
period of time
The concentrate grade of by-product gold is the mass of gold in
the copper concentrate divided by the mass of the concentrate:
where:
GR B is the grade of the by-product in the ore (grams/tonne)
MR B is the mill recovery of the by-product
The net smelter return at the minesite is the net smelter value,
including any penalties, but excluding by-product credits, less the
transportation costs from the mill to the smelter, divided by the value
of the metal in the concentrate:
NSR
= (NSV - TR) / [(CG p
/
100) Pl
where:
TR is cost of transporting the concentrate from the mill to the
smelter (S/tonne)
The contract between the smelter and the mlnlng firm is the basis
for calculating the net smelter return associated with each metal. The
details of the smelter schedules for copper, zinc and gold are given in
table 4. Neither of the two concentrates contain deleterious elements
and no penalty is imposed for their moi sture content.
•
The copper concentrate is transported ninety kilometres by truck,
and the zinc concentrate 580 kilometres by rail, to the nearest
55
•
Table 4. Smelter C~ntract Terms for a Copper Concentrate
with By-Product Gold and a Zinc Concentrate
Smelter Contract Term
Copper
Zinc
Gold
25.5%
52%
CG a
Unit deduction
1.0
0.15(CG)
1.0
Proportion of content
paid for
99%
85%
95%
Concentrate grade
Refining charge
S150/t
SO . 18/g
Base treatment charge
S80/t
S180/t
Smelter contract base
price
S2000/t
S1l50/t
0.025
(P>=2000)
0.01
(P<2000)
0.1
(P>=1l50)
0.05
(P<1l50)
Treatment charge
adjustment factor
•
Metal
56
•
smelters. Freight charges arlslng from truck and rail haulage are $0.14
Freight charges are
and $0.04 per tonne-kilometre, respectively .
assumed to be fixed by long-term contract.
The net smelter return is a function of the metal priee. At the
stage at which a decision is required concerning the destination of an
extracted mining unit, the average annual metal priees are not yet known
with certainty. The user is responsible for providing the estimates of
copper, zinc and gold priees, in U.S. dollars, along with an estimate of
the annual average exchange rate between the U.S. dollar and the
Canadian dollar. These inputs are used to estimate the net smelter
return and the revenue to be generated by each metal in a mining unit.
The mill recovery of copper, zinc and gold is discussed in the
section on milling parameters (section 2.10).
Following the simulation of mlnlng activities, decisions
concerning the allocation of mined material amongst the waste dump,
stockpiles and mill are based on the estimated value and/or grade of the
material in each mining unit .
•
57
•
2.9 Stocl<pil es
Four stockpiles can be created at the minesite. The tonnage of
material in each stockpile is monitored, but no upper limit is placed on
the size of stockpiles. The material in each stockpile is thoroughly
mixèd such that homogeneity of grade is achieved.
Thus, there is an
estimated average grade and a true average grade which apply throughout
each stockpil e.
The calculation of the estimated grades of copper, zinc and gold
in a stockpil e i s based on the est imated grades of the constituent
mining units. The true grades of the mining units are the basis for
determining the true average grades in the stockpile. The total weight
of metal, estimated or true, derived from the constituent units is
divided by the number of tonnes of material in the stockpile in order to
arrive at an average grade.
The transfer of stockpiled material to the mill requires the
specification of the number of the stockpile, from 1 to 4, which is to
suppl y the mi 11 feed.
The user i s provided with i nformat i on on the
tonnage and estimated average grades of copper, zinc and gold in the
stockpile. The tonnage of material which is to be transferred to the
mill feed is then specified.
For tonnage verification, values are rounded to the nearest whole
number of tonnes.
Providing that the amount of material selected for
transfer does not exceed the size of the stockpile, or the remaining
mill capacity, transfer of the material is simulated and the size of the
stockpile reduced accordingly. It is possible to select 0 tonnes from a
stockpile; this feature a110ws the user to reverse a decision to mi11
stockpil ed materi al before i t i s transferred from the stockpil e. The
process of selecting stockpiled material for mill feed can bs repeated
as long as there is remaining mill capacity and at least one stockpile
exists.
•
Subsequent
to
underground
58
or
open-pit
mining
operations,
•
stockpiling decisions also determine the immediate destinatio~, of the
mined units which are regarded as ore. All of the material which has
been extracted from an underground mi ne i s handl ed as if it were ore,
that is, the material which is not allocated tO a stockpile is sent to
the mill for processing in the current year. Of the material mined from
an open-pit, the amount of mineralized material to be considered as
waste, and dumped along with unmineralized mined material, is determined
by a combination of the cut-off grade and cut-off value specified by the
user. A mining unit is dumped if its estimated grade or value falls
below any one of the selected cut-offs. Any remaining material from the
open-pit is considered to be ore and must be assigned to one or more of
the stockpiles or to the mill.
Mining units are chosen for stockpil ing on the basis of their
estimated grade and/or value per tonne. Following the selection of a
stockpile, cut-off grades and/or values are applied in order to
distinguish the mining units which are to be stored from those which
will constitute the direct mill feed.
A grade or value range is
delimited by an upper and lower cut-off. If the user selects only a
value range, those mining units having estimated values which are
greater than or equal to the lower limit and less than the upper limit
of a specified value range are sent to the designated stockpile
regardl ess of thei r grade. 1f the user al so selects grade ranges, the
units are stockpiled providing that their estimated grades of copper,
zinc and gold fall within the selected grade ranges. In other words, in
order to be stockpiled, a mining unit must meet all of the grade and
value criteria which have been set. If no grade or value ranges are
specified after the selection of the stockpile number, then no material
is stockpiled.
•
After a value range and/or grade ranges for copper, zinc or gold
have been specified, the user is informed of the amount of material, if
any, by. which the selected stockpile has been augmented. An update of
the quantity of unallocated mined material is also provided; the
stockpil i ng procedure can be repeated until thi s quanti ty, rounded to
the nearest whole number, has been reduced to zero .
59
•
2.10 Hilling Parameters
The mi 11 recei ves feed of a uniform grade throughout the year.
The sel ect i on of mi ni ng units and stockpi l ed materi al for mill feed i s
based on estimates of grades, and establishes the annual production rate
at the mill. It is, however, the true milled grades which determine the
net smelter return of gold, as described in section 2.d, and the mostl ikely mill recoveries of copper and zinc. The true grades are the
average grades of the materi al arri vi ng at the mil l from a11 sources,
that is, directly from the mine, and from the stockpiles.
For concentrates of constant grade produced in a mill of a given
design, the mill recoveries of copper and zinc from copper-zinc ore vary
with the ore grade according to Q'Hara's (1987) formulae:
MR Copper -- 1 - 0.16 (GRCopper )"0.8
)"0.6
MR zinc = 1 - 0.45 (GR.
Zinc
where:
MRcopper i s the mi 11 recovery of copper
GR capper is the grade of copper in the ore (percent)
MRzinc i s the mi 11 recovery of zi nc
GRzinc is the grade of zinc in the ore (percent)
A single typical recovery rate of 0.60 (Mackenzie, 1987) is used
for gold in a copper-zinc mill.
•
Uncertainty in the level of mill recovery for each metal is
incorporated in the generat i on of the actual mi 11 recovery rate. The
mi 11 recovery of copper i s requi red for the cal cul at ion of the net
smelter return of gold. The net smelter return for each metal at the
minesite is calculated fo11owing the simulation of mining and milling
operations for the year. At this time, the average price for each metal
during the year is available as an input in the net smelter
relationship .
60
•
2.11 Cash Flow and Financial Performance
The cash flow associated with the mlnlng project is calculated on
an annual basis. The cash flow components are revenue, operating costs,
capital expenditures and taxes.
Revenue is generated by the sale of copper and zinc concentrates.
The annual revenue ascribable to each metal in the concentrates is a
function of the average grade and amount of ore which is processed
during a year, the average annual price of the metal, the level of mill
recovery and the net smelter return:
REV
=
GR p x ORE x P x MR x NSR
where:
REVp is the annual revenue from the product (metal)
zinc or gold ($)
copper,
GRp is the grade of the product in the milled ore (percent/IOO
copper or zinc; grams/tonne gold)
ORE is the tonnage of ore milled
P is the metal price ($/tonne copper or zinc; $/gram gold)
MR is the mill recovery
NSR is the net smelter return
Metal prices are expressed in U.S. dollars, and revenue is
converted from U. S. to Canad i an currency on the bas i s of the annual
exchange rate. The most-l ikely exchange rate throughout the project
life is 0.86 U.S. dollars per Canadian dollar.
The exchange rate
prevailing each year is generated on the basis of this most-likely
value, and incorporates a random component.
•
The annual operating costs are related to the type of activities
which have been carried out in the mine and mill during the year. If no
extraction occurred, mine operating costs may or may not be incurred.
If the mine has been closed on a permanent basis either by management
61
•
decision, or because no extraction is pos~ible given the constraints of
the mining method, no mine-related costs are incurred. The mine can no
longer be operated and, therefore, need not be maintained in a state of
readiness for resumption of mining activities.
If extraction was
technically possible, but no extraction took place, t~e operating costs
for the mine comprise the co st of maintaining it on a stand-by basis and
thè expenses asscciated with drifting and exploratory drilling, if these
have beèn carried out. If material has been extracted from the mine,
the operating costs are determined by multiplying the unit mine
operating costs by the number of tonnes mined, and adding the costs
which may have been incurred for d~ifting and exploratory drilling.
The annua1 operat i ng costs of the mi 11 are i ts maintenance costs
while temporarily closed, or the product of the unit mill operating
costs and the number of tonnes mi 11 ed duri ng the year. At the end of
the project life, the net costs of permanent plant closure are added to
any costs directly related to operations or the maintenance of
installations closed on what was originally a temporary basis.
Tax allowances are determined by applying a fixed depreciation
r~te to a declining-balance pool of mine and mill plant assets 1 •
The
pool of depreciable as sets is generated by capital expenditure
associated with the initial 'installation, and any subsequent expansion,
of mi n: and mi 11 capacity, deepeni ng of the shaft in an underground
mine, and the replacement of worn-out or obsolete machinery and
equipmRnt. In order to determine the depreciation allowance, a rate of
fifteerJ percent is applied to thd balance remaining in the pool at yearend, including aIl capital expenditures on fixed assets during the year.
Depreciation allowances are claimed as soon as they are available,
that is, from the first year of the preproduction period. The company
is assumed to be integrated and to have enough other sources of
•
1 For tax purposes, aIl plant assets are assumed to be in the same
deprec i ab1e poo1.
62
•
operating profits to allow it to benefit from a flow-through form of tax
allowances. Thus, any excess allowances related to the mineral project
are absc~bed.
Corporate income taxes are based on a simple profit taxation
model. Taxes are thirty percent of the taxable income, and are payable
in full each year. Tax credi ts whi ch ari se beyond the end of the
project life due to undepreciated book balances are ignored. The aftertax cash flow is the operating profit less the tax payments and capital
expenditures, including the annual sustaining capital and the net
working capital.
As no profits are generated while preproduction
activities are being carried out, the cash flows during this period
reflect the capital expenditures for the initial installation of mine
and mill capacity, the tax credits arising from the depreciation of
plant assets starting in the year of their acquisition, and the
investment of working capital prior to the start of production.
The financial performance of the mineral project is measured using
discounted cash flow techniques. The current dollar cash flows of the
project are first deflated using a series of general inflation rates
from the start of the preproduct i on peri od to the end of the project
1i fe. The most-l i kely general i nfl at ion rate throughout the project
1i fe i s 6.40 percent. The genera1 i nflat ion rate in effect each year
incorporates a random factor. The direction and degree of change in the
general inflation rate from year to year is the same as for the cost
inflation rate.
Based on the project's constant dollar cash flow distribution, the
rate of return i s determi ned and the net present val ue computed for
discount rates of five, ten, fifteen, twenty and twenty-five percent.
The success, or failure, of the mineral project can be measured in terms
of these criteria .
•
63
•
3. THE MINE MANAGER AT WORK
3.1 The Sequence of Decisions
3.1.1 Overview
The sequence of decisions for mine deve10pment and production is
displayed in flow chart format in figure Il. At the development stage,
the player decides which method, underground or open-pit, will be used
to mine the ore reserves. Although not indicated in the diagram, a
decision must be made concerning the length of delay, if any, in the
start-up of the preproduction activities. These activities lead to the
installation of the annual mining and milling capacities which are
selected by the p1ayer.
If an open-pit mine is deve10ped and operated, a decision may
made to convert to underground mining operations.
Shou1d such
decision be télken, the installed underground mining capacity must
selected, and conversion of the mining method wou1d be due to occur
the end of the underground mine construction period.
be
a
be
at
The deve10pment of underground mining faci1ities, whether for
conversion from open-pit operations or as the sole means of extracting
the ore reserves, requires specification of the shaft site northing and
the depth to which the shaft is to be sunk. Further decision-making
takes place during the operating 1ife of the underground mine.
•
The decisions which are required for mine and mil1 production are
dependent upon the choice of mining method and installed mining and
mi1ling capacities. Decisions concerning grade control and the 1eve1 of
utilization of mine capacity are made indirect1y through selection of
the b10cks to be extracted in a particular year. The leve1 of mill
capacity utilization is determined by the amount of ore assigned to the
mi1l from the stockpiles and by grade- and/or value-range selection with
respect to the mining units extracted in a given year .
64
START
•
Development
Stage -,
Select mining method
Select installed
mining and
milling capacities
Production
T
F
Open-pit mine
Stage -,
Select shaf:
sequencing
Select installed
depth and site
underground
mining capacity
Underground mine
T
sequencing
_i
Financial
Evaluation
•
Figure Il: The Sequence of Decisions for Mine Development
and Production -- An Overview
65
•
Upon completion of mlnlng and milling operations, the plant i5
closed on a permanent basis.
the final step in the Game.
The financial evaluation of the project is
Figure 12 shows elements of a generalized mlnlng system with both
open-pit and underground oper.:t ions, such as might be produced from a
similar sequence of decisions.
The open-pit mine is divided into leve15
from which ore and waste are extracted. A crown pillar lies between the
open-pi t and the underground mi ne worki ngs.
There are three l eve 15
separated by si11 pi11ars in the underground mine; Level 1 is composed
of two sublevels, élnd Levels 2 and 3 have three sublevels each.
takes place in stopes wh; ch are separated by ri bpi 11 ars,
material is hoisted to the surface from the deepest level .
•
66
Mining
and mi ned
•
Open-Pit Mine
Level 1
,
\~Î~~~~2C±~Mining
unit,
...;
in waste
,,
,
,
Underground Mine \
\
LEVEL 1
\
,
Hangingwall
sm pillar _......1~~~;;::::::
-~~:~~::::~~:~~~~
_
Sublevel 2 ~~:~~;~~~~~~~~~Mining
unit
Sublevel'S
LEVEL2
==========~S~u~b~le~ve~I~1;;;~~~~~~~5~~;:\
Development\
1~
drift
\
\
\
\
\
Footwall
LEVELS
Limil of ore
Haulage level
•
Figure 12: Elements of a Mining System -- Open-Pit and Underground Mine
67
•
3.1.2 Open-Pit Operation
The sequence of decisions made during the open-pit mine life is
shown in figure 13.
Upon completion of mine and mill installation,
production can begin.
The player may, however, decide to delay the
start of operations. This is not reflected in figure 13 in which it is
assumed that production begins immediately after the preproduction
period. As shown, mining sites in the open-pit are to be specified in
terms of the level and boundary on which they are located. The player
must select the appropriate block limits according to whether the first
cut is being made on the level, or a parallel or perpendicular pit
extension is being carried out. Providing that there are mineable ore
reserves remaining and that mine production has not reached the limit of
overcapacity, the player has the option of selecting more material for
extraction; otherwise, no further specification of mining sites is
possible.
When the player has completed the selection of mlnlng units for
extraction in the current year, the stockpiling decisions which are made
control the flow of mined material into and out of the stockpiles.
Stockpiled material, if it exists, may be selected for processing as a
supplement to or substitute for direct mill feed.
At this stage,
decisions must also be made concerning the allocation of mined material
to the mill, stockpiles and dump.
Thus, the mill ing and stockpil ing
decisions are interlinked.
The user should not plan future open-pit production in certain
situations. If the project l Ife has been extended for forty-five years
beyond the end of the preproduct i on peri od, the plant i s cl osed on a
permanent basi s.
Open-pi t operati ons cease if the open-pit cannot be
extended at depth or wi dened on any l evel, or if a dec i sion has been
taken to change the mining method, and underground development work has
been completed.
In the latter case, mine sequencing can begin
underground the following year.
•
Providing that open-pit mine production is possible, the user can
68
•
START
Selectlevelkboundary
and bloc Iimits
T
F
T 1-ooiI
--:....J
Select stockpiled material
for milling and allocate
mined materialto mill
L _..;a_n_dJ_o_r_st'r:0:;ck~p=i1e=s==~-I Select stockpiled
material for milling
F
Consider nex! year's mine and mill activities,
change of mining method. and expansion or
permanent closure of mine and mill
F
F
Increment year
Increment year
RETURN
•
Figure 13: The Sequence of Decisions During the Open-Pit Mine Life
69
•
opt to mine and mill.
If mill feed is available from one or more
stockpiles, the mill can be operated while the mine is closed. If no
operations are planned for either of the installations, the player must
indicate whether the closure of the mine at the end of the current year
15 expected to be temporary, or is permanent. If the mine is closing
temporarily, then mill closure must also be temporary, and both
facilities are maintained on stand-by.
If the mine is closed on a
permanent basis, the player must indicate whether or not the plant
closure is permanent.
At the end of each year of the open-pit life, the player has the
opt i on of start ing underground mi ne construction duri ng the foll owi ng
year if 1) the plant is not closing permanently, 2) at least one of the
pit boundaries has not been extended to a property boundary, 3) a shaft
can be sunk to a depth which allows at least one level containing at
least one sublevel to be developed, and 4) a decision has not already
been made to convert from open-pi t to underground operations.
The
second condition ensures that the mine shaft can be sited on the
property.
The player is also given the OPpo\"tunity to initiate an
expansion program for the mine or mill, providing that there is no
expansion of the'installation already underway, and the maximum feasible
size would not be exceeded.
In the case of an open-pit operation,
provision of the option to begin a mine expansion program is contingent
upon the fact that no underground mine development work is taking place
or due to start the following year.
If the plant is closing permanently, no further decisions are to
be made, otherwise decision making continues the following year.
If
open-pit mining is to take place, the player repeats the process of
decision making, beginning with the selection of one or more mining
sites. If at the end of the previous year, the player took the decision
to carry out milling operations without mining, stockpiled material can
be selected as mill feed; if no material is actually dispatched from the
stockpiles, the mill is closed for the year .
•
70
•
3.1.3 Underground Operation
The sequence of decisions made during the underground mine life is
shown in figure 14.
Production underground can begin when mine
development work has been completed.
The sequence of decisions
displayed in the figure is based on the assumption that although the
player has the option of delaying the start-up of mine operations, the
decision is taken to start mining activities during the year following
the complet i on of mi ne devel opment. As shown, an underground mi ni ng
site is selected by specifying the level and sublevel on which mining is
to take place.
When the first mining site is being selected on a
particular level, the eastern and western l imits of the development
drift at the base of the level must also be specified.
The player
chooses the coordinates which delimit a block in a stope and thus
determines whether primary or secondary stoping i s to take pl ace, and
which mining units may be extracted. If the reserves of the mine are
not exhausted and the overcapacity limit of the mine has not been
reached, further mine production is possible.
The selection of material for extraction has been completed when
no further extraction from the mine is possible, there is no remaining
mine capacity or the player elects not to continue mining in the current
year. The player can select any previously stockpiled material to feed
the mill, and must allocate material which has been mined in the current
year amongst the stockpiles and mill.
If the underground mine cannot be extended on any of the existing
levels and no stockpiles exist, the underground mine and the mill are
closed permanently. Providing that there are ore reserves available for
extraction, or there is at least one stockpile of mined material, t~e
player selects the course of action in the following year -- mining and
milling, temporary shut-down of the mine and/or the mill, permanent mine
closure, or no operations consequent to a decision to close the entire
plant on a permanent basis at the end of the current year.
•
Unl ess the pl ant has been closed permanently, deci sion maki ng
71
START
•
Select level,_ sublevel
and blocl\ Iimits
T
F
T.I:4
....:...J
Select stockpiled material
for milling and allocate
mined material to mill
and/or stockpiles
F
Select stockpiled
material for milling
T
T
Consider next year's mine and mill aclivilies
change of mining method. and expansion or
permanent closure of mine and mill
F
F
Increment year
Increment year
RETURN
•
Figure 14: The Sequence of Decisions During the Underground Mine Life
72
•
continues the following year.
If the underground mine is to be in
operation, the process is repeated beginning with the selection of
mining units at one or more sites.
A decision to mill without
concurrent mine production requires that at least one stockpile be
sel ected as the source of mill feed; however, it i s possi bl e to l eave
the stockpiled material intact, and the mill, therefore, remains closed
for the year.
At the end of each year, the player is given the opportunity to
initiate an expansion program for the mine or mill, providing that there
is no expansion of the installation already underway, and the maximum
feasible size would not be exceeded. The option of deepening the shaft
is given at the end of each year beginning the year after completion of
underground mi ne construction. A positive outcome to deci si on maki ng
concerning shaft deepening or the expansion of installed capacity
results in implementation commencing the year after the decision is
taken .
•
73
•
3.2 Rules of the Game
The development and operation of a mine and mill plant are
simulated according to the series of decisions made by the player,
provided that the rules of the game are respected. The rules are set
according to the scope and degree of detail of the model upon which the
Game is based.
The rules govern the behaviour of the player in
assigning values to the decision variables, and adherence to the rules
ensures that only feasible decisions are made. Most of the operational
rules pertain to the constraints of the mining method.
The rul es are li sted accord ing to the type of act ivity to wh ich
they apply.
3.2.1 Development and Expansion
•
1) an open-pit or underground mine is to be developed; should an
open-pit mine be selected initially, the development of an
underground mine for conversion of operations may subsequently be
possible;
2) the installed annual capacities of the mine and mill must fall
within a range of feasible values -- 75 000 to 675 000 tonnes for
the underground mine and mill, and 227 000 to Il 340 000 tonnes
for the open-pit mine;
3) a period of delay in the start-up of preproduction activities can
be specified, but must not exceed fifteen years;
4) the shaft must be sited between 0 mN and 32 760 mN; if the
selected northing is not a multiple of five, the value is
automatically rounded to the nearest multiple;
5) the shaft depth in an underground mine must be at least 170
metres, no more than 495 metres, and a multiple of five metres; a
value which is not a multiple of five is automatically rounded to
the nearest multiple;
6) if conversion from open-pit to underground mining is planned, the
shaft must be deep enough to provide access to at least one
sublevel beneath a crown pillar at the base of the pit;
74
•
•
7) increments to the shaft depth must be multiples of seventy-five
metres;
8) an expansion of the underground mine or mill must increase the
installed annual capacity by a minimum of 75 000 tonnes;
g) an expansion of the open-pit mine must increase the installed
annual capacity by at least 227 000 tonnes;
la) underground mine construction work can be initiated while open-pit
operations are taking place, providing that at least one of the
pit boundaries has not been extended to the corresponding property
boundary, and the shaft can be sunk deep enough to allow the
development of at least one sublevel below a crown pillar at the
base of the pit .
75
•
•
3.2.2 Open-Pit Hining
1) open-pit mining must be carried out within the limits of
overcapacity associated with the existing mine design; in any
given year, the mine may be temporarily closed, or operated at a
rate of up to twenty percent over the stated capacity.
2) the four boundaries of the pit must be parallel to the north-south
and east-west axes, and can be segmented;
3) the levels of the open-pit are to be developed in sequence of
depth;
4) the pit slope angle cannot exceed forty-five degrees;
5) a mining site is to be specified in terms of the level and
boundary on which it is located;
6) a minimum mining width of twenty metres is required;
7) exploratory drilling andl.or extraction can be carried out on
several benches in a single year providing that technical and
capacity constraints are met;
8) the open-pit can be expanded in two ways: a) parallel extension
along a segmented boundary, and b) perpendicular extension of a
straight boundary;
9) mining units are cubic blocks which have a height equal to the
bench height, that is, ten metres;
10) block selection for lateral pit expansion or pit deepening cannot
lead to fragmentation of mining units, that is, mining units
cannot be subdivided into smaller blocks.
11) blocks selected for mining mllst lie within the property
boundaries, in other words, the coordinates delimiting blocks of
one or more mining units must lie between 0 mN and 32 765 mN, and
between 0 mE and 32 765 mE; northings and eastings which are not
multiples of five are automatically rounded to the nearest
multiple .
76
•
•
3.2.3 Underground Hining
1) underground mining must be carried out within the limits of
overcapacity associated with the existing mine design; in any
given year, the mine may be temporarily closed, or operated at a
rate of up to twenty percent over the stated capacity;
2) the maximum depth of mining is dictated by the shaft depth; the
deepest level at which mining car. take place is twenty metres
above the base of the shaft;
3) mining can take place within a vertical interval determined by the
depth of the open-pit, if one exists, the thickness of the crown
pillar, and the depth of the shaft (refer to rule 2);
4) the deposit is to be accessed from drifts on levels at seventyfive-metre intervals, and on sublevels at twenty-metre intervals
of depth;
5) the deposit is to be mined in one cut from the hangingwall to the
footwall;
6) a mlnlng site is to be specified in terms of the level and
sublevel on which it is located;
7) the western and eastern boundaries of the development drift on the
first sublevel of a new level are to be specified prior to stope
selection, and must be no more than twenty-five metres apart;
providing that no extraction has taken place, the development
drift may be relocated once such that the drifts are at least five
metres apart;
8) mining units are selected by specifying the coordinates which
delimit the base of the block containing them;
g) exploratory drilling and/or extraction can take place at several
sites in a single year providing that technical and capacity
constraints are met;
10) mine sequencing must respect the constraints imposed by the use of
sublevel stoping as the mining technique;
Il) rib pillars have a minimum length of twenty-five metres and extend
the full height of the stope; the crown pillar and the sill pillar
between two levels should be at least fifteen metres in vertical
thickness;
77
•
•
12) mlnlng which takes place in a pillar between primary stopes or in
the southern wall of the most southerly primary stope is to be
considered secondary stoping;
13) primary and secondary stopes must be located at least as far north
as the shaft site;
14) primary and secondary stoping must advance northwards;
15) mining unit selection in a new stope on a level where there exists
a more southerly stope of the same type, that is, primary or
secondary, signifies that mining activities in the more southerly
stope have been completed;
16) mining in the pillar adjacent to the most northerly primary stope
signifies that mining in that primary stope has been terminated,
and further primary stoping on the level will have to take place
in a new stope;
17) extraction can begin in a secondary stope once mining and
backfilling of the adjacent primary stope(s) have been completed;
18) stopes dip forty-five degrees to the east;
19) stopes .must be no more than sixtY metres in vertical height, and
no more than twenty-five metres in width and length; stope width
may vary from stope to stope but must be uniform within a single
stope;
20) mining units have a length of five metres, a height equal to the
sublevel interval of twenty metres, and a width equal to or less
than that of the development drift;
21) the minimum advance in any stope is five metres;
22) blocks selected for mining must lie within the property
boundaries, in other words, the coordinates selected to delimit
blocks of mining units must lie between 0 mN and 32 765 mN, and
between 0 mE and 32 765 mE; northings and eastings which are not
multiples of five are automatically rounded to the nearest
multiple .
78
•
•
3.2.4 Stockpi1ing and Hi11ing
1) up to four stockpi1es of mined materia1 can be created at the
minesite;
2) a stockpi1e can be augmented in any year in which materia1
considered to be minera1ized has been extracted from the mine;
3) the allocation of mined materia1 to the stockpi1es, mill or dump
is by mining unit, and is based on the estimated grade and/or
average value per tonne of material extracted as a unit;
4) all of the material mined underground must be stockpiled or milled
in the year in which it is extracted;
5) material from an open-pit is dumped, stockpiled or milled in the
year of extraction;
6) mill feed is to be obtained directly from the mine and/or from
stockpiles;
7) milling is to be carried out within the limits of overcapacity
associated with the existing mill design; in any given year, the
mill may be temporarily closed, or operated at a rate of up to
twenty percent over the stated capacity .
79
•
•
3.2.5 Permanent Closure
1) the open-pit or underground mine is closed when the mineable ore
reserves have been fully depleted;
2) if conversion to underground mining is planned, the open-pit mine
is closed at the time origin~lly scheduled for the start of
underground operations;
3) the mill is closed if there is no stockpiled material when the
underground mine closes, that is, the entire plant is shut down;
4) the mine/mill plant is closed when the project life has been
extended for forty-five years beyond the end of the preproduction
period .
80
•
3.3 Getting Started (at Last)
The Mine Manager is a standalone application which requires an
IBM-compatible personal computer using the DOS operating system, version
3.0 or higher. The Mine Manager game package consists of a single 5.25
inch 1.2 Mb or 3.5 inch 1.44 Mb floppy disk and a user's manual. The
diskette contains program and data files, some of which have been
compressed using the archive creation shareware PKPAK, version 3.61, by
PKWARE, Inc. The Mine Manager was written in Turbo Pascal, version 6.0.
The Game is to be run on an IBM XT-, AT- or PS/2-compatible having
a floppy di sk dri ve, but not necessarily a hard di sk. The software
The program supports most
requi res 640 K of random access memory.
standard video modes, for example, Hercules monochrome, and IBM-CGA,
-EGA and -VGA.
If the Game is to be run from a hard disk, installation is
required.
Prior to the installation, there must be at least 600 K
available on the selected drive. This ensures that sufficient space is
available for decompression of individual data files as needed. Hard
disk users have the option of decompressing all of the data files at the
start of the Game. Complete decompression avoids subsequent delays when
data must be accessed. At least 5 Mb must be available on the selected
drive if complete decompression is to be performed.
No installation package has been designed for the Mine Manager
because the installation procedure is simple. It is advisable that the
user create a di rectory on the hard dri ve to whi ch a11 fil es from the
program diskette should be .copied; only Game files should exist in this
directory.
The program directory is created using the DOS make directory (md)
command:
•
> md [directory name]
81
•
The directory is then changed to the newly-created one using the
DOS change directory (cd) command:
> cd [directory name]
The DOS copy command i s used to ccpy fil es from the program
diskette in the floppy disk drive to the new directory on the hard
drive:
> copy [floppy disk drivel:*.*
The Game directory should contain twenty files: two .EXE files,
including the main executable file for the Gamej one .OVR file; and
seventeen data fil es havi ng .DAT or .ARC extens ions. The PKUNPAK. EXE
file is part of the shareware package developed by PKWARE, rnc., and is
used to decompress data files during the operation of the Game. All of
the data fi l es whi ch have been compressed are del eted pri or to normal
termination of the Game.
If the Game is stopped prematurely, for
example, by using Ctrl<Break>, decompressed data files with names
beginning with 'level' may remain nn the drive in use, and should be
deleted before any subsequent runs of the Game.
The Mine Manager must be run from the directory containing all of
the files listed above. To start the Game, the user types 'mg' at the
DOS prompt .
•
1
82
•
REFERENCES
Mackenzie, B.W., 1987, 'Economie Guidelines for Exploration Planning',
Mineral Project Evaluation Techniques and Applications Seminar
Notes, McGill University.
O'Hara, T.A., 1987, 'Quick Guides to Mine Operating Costs and Revenue',
paper presented at the 89th Annual General Meeting of CIM,
Toronto, May .
•
1
83