.+. National Library of Canada Bibliothèque nationale du Canada Acquisitions and Bibliographic Services Branch Direction des acquisitions et des services bibliographiques 39S Wellington Street Ottawa. Ontario 395. nIe Wel1inglon Ottawa (Ontario) K1AON4 K1AON4 NOTICE AVIS The quality of this microform is heavily dependent upon the quality of the original thesis submitted for microfilming. Every effort has been made to ensure the highest quality of reproduction possible. La qualité de cette microforme dépend grar.dêment de la qualité de la thèse soumise au microfilmaqe. Nous avons tout fait pour assurer une Qualité supérieure de reproductioli. If pages are missing, contact the university which granted the degree. S'il manque des pages, veuillez communiquer avec l'université qui a conféré le grade. Sorne pages may have indistinct print especially if the original pages were typed with a poor typewriter ribbon or if the university sent us an inferior photocopy. La qualité d'impression de certaines pages peut laisser à· désirer, surtout si les pages originales ont été dactylographiées à l'aide d'un ruban usé ou si l'université nous a fait parvenir une photocopie de qualité inférieure. Reproduction in full or in part of this microform is governed by the Canadian Copyright Act, R.S.C. 1970, c. C-30, and subsequent amendments. La reproduction, même partielle, de cette m!croforme est soumise à la Loi canadienne sur le droit d'auteur, SRC 1970, c. C-30, et ses amendements subséquents. 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 .+. National Ubrary of Canada Bibliothèque nationale du Canada Acquisitions and Bibliographie Services Branch Direction des acquisitions et des services bibliographiques 395 Wellington Street Ottawa. Ontario K1A QN4 395. ruE Wellington Ottawa (volane) K1A QN4 Our f'k1 NOl'" r6/{jrttnCtJ THE AUTHOR HAS GRANTED AN IRREVOCABLE NON-EXCLUSIVE LICENCE ALLOWING THE NATIONAL LIBRARY OF CANADA TO REPRODUCE, LOAN, DISTRIBUTE OR SELL COPIES OF mS/HER THESIS BY ANY MEANS AND IN ANY FORM OR FORMAT, MAKING TmS THESIS AVAILABLE TO INTERESTED PERSONS. L'AUTEUR A ACCORDE UNE LICENCE IRREVOCABLE ET NON EXCLUSIVE PERMETTANT A LA BIBLIOTHEQUE NATIONALE DU CANADA DE REPRODUIRE, PRETER, DISTRIBUER OU VENDRE DES COPIES DE SA THESE DE QUELQUE MANIERE ET SOUS QUELQUE FORME QUE CE SOIT POUR METTRE DES EXEMPLAIRES DE CETTE THESE A LA DISPOSITION DES PERSONNE INTERESSEES. THE AUTHOR RETAINS OWNERSHIP OF THE COPYRIGHT IN mS/HER THESIS. NEITHER THE THESIS NOR SUBSTANTIAL EXTRACTS FROM IT MAY BE PRINTED OR OTHERWISE REPRODUCED WITHOUT HIS/HER PERMISSION. L'AUTEUR CONSERVE LA PROPRIETE DU DROIT D'AUTEUR QUI PROTEGE SA THESE. NI LA THESE NI DES EXTRAITS SUBSTANTIELS DE CELLE· CI NE DOIVENT ETRE IMPRIMES OU AUTREMENT REPRODUITS SANS SON AUTORISATION. ISBN 0-612-05661-9 Canad~ • • 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 • 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 • • 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 • 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 • • 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 • • 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 • 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 • • 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 • • 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 • • 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 • • 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 • • 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 • • 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 • 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 18 • 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 • 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 • 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 184 • • 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 185 • • 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 • • 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 • 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 • • 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 • • 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 • • 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. 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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. FI-Print screen and continue <EHTER>-Continue 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. FI-Print screen and continue <EHTER>-Continue • 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 FI-Print screen and continue 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. FI-Print screen and continue • 30001.948 <EH7ER>-Continue 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 FI-Print screen and continue <EHTER>-Continue 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 FI-Print screen and continue <EHTER>-Continue • 218 • CASH FLOU -- YEAR 8 (thou. $) Revenue eu coneentrate (USS1.05!lb Cu) : Au credits in eu cone (USS374.40!oz Ru): zn concentrate (USSO.64!lb Zn) Operating Costs Mine Mill Pernanent plant ctosure Jax Allowances , axable Inc:one Taxes Capital Expenditure Rnnual Sustaining Capital Mine 51633.042 24754.874 14934.085 11944.083 16698.695 11282.798 0.000 13.727 74.242 Mill Het Uorking capital COst Inflation: 5.4% Fl-Print screen and continue • 4621. 684 19029.866 5708.960 0.000 87.969 241.282 17613.340 Cash Flow Annual Rates E~change: 0.92 US$!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 Fl-Print screen and continue <EHTER>-Continue 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 F1-Print screen and continue • <EHTER>-Continue 220 • CASH FLOU -- YEAR 9 (thou. $) Revenue Cu concentrate (USSI.36/lb Cu) : Ru credits in Cu cone (US$351.45/02 Au): zn concentrate (USSO.71/lb Zn) 55244.341 28436.271 12556.942 14251.128 Operating COsts 15128.800 9912.982 0.000 Mine MiU Per"anent plant closure TaK AUowances TaMable Incane laMes Capital EKpenditure Annual Sustaining capital Mine 13.892 85.931 MiU Het UOrking capital Cost Inflation: 4.3r. FI-Print screen and continue • 3943.405 26259.155 7877.746 0.000 99.823 202.507 22022.483 Cash Flow Annual Rates -EKchange: 0.83 US$/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 FI-Print screen and continue ------------------- <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. FI-Print screen and continue <EHTER>-Continue • 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% Fl-Print screen and continue • 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. FI-Print screen and continue • 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 FI-Prlnt screen and continue <EHTER>-Continue 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$447.12/02 Ru): zn concentrate (USSO.31/lb Zn) Operating Costs Hine Hill Per~anent plant closure Ta.. Rllowances Taxable Incone TaMes Capital Ellpenditure Annual Sustaining capital Hine Hill Het Uorking capital 22293.934 18963.600 3191. 746 2447.342 16275.995 4662.799 0.000 IDD.466 18.804 81. 664 254.263 13465.766 Cost Inflation: 4.7% Fl-Print screen and continue • 25746.142 13325.513 12420.629 0.000 Cash Flow Annual Rates -Ellchange: 0.62 US$/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 FI-P~int sc~een 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 FI-Print screen and continue <EHTER>-Continue 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. FI-Print screen and continue • <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 ---------------------------------------------~------------------ FI-Print screen and continue <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