Selection of an Optimum Truck and
Shovel Fleet Based on Effective Flat
Haul and Capacity Constraint Modelling
S Campbell1 and P Hagan2
ABSTRACT
A study was undertaken using various methodologies to determine the optimum loading and
hauling configuration for different haul routes at Callide Mine, a coal mine located in central
Queensland. The study involved development of an effective flat haul model that was used to
estimate production rates in truck and shovel circuits that employ two excavators of differing
capacities then Queuing Theory to construct a capacity constraint model for scheduling purposes
to assist in truck allocation and finally a cost model to determine the most cost effective fleet
configuration.
The model was calibrated using haul road design and performance data of trucks and excavators
currently in use at the mine. The study examined the effects of cycle time for different truck and
excavator fleet configurations on production rate and costs.
The study found haulage cost was directly related to cycle time while production rate reduced
with cycle time. The study indicates the approach taken in combining a cost model with a capacity
constraint model offers a simple and effective method of scheduling an optimum number of trucks
in a haulage circuit.
INTRODUCTION
DESIGN OBJECTIVES
Optimum design of a truck and shovel fleet is an important
aspect in the design of the materials handling process at
any mining operation. The main design variables in the
process include number and capacity of the dig units and
trucks and the layout of the haulage circuit. Truck allocation
is important as it can result in higher costs and/or reduced
production output. During the planning phase of a mine,
scheduling an excavator and fleet of trucks can be difficult
when there isn’t detailed knowledge about the performance
of trucks in a proposed haulage circuit.
Callide Mine, a coal mine operated by Anglo American
located in central Queensland, has a homogeneous fleet
of trucks that service an excavator in a material handling
system removing overburden material. A combination
of data over a two-month period was gathered from field
measurements and the site-based equipment data recording
software were used in the study.
The purpose of this study was to investigate the various
approaches that could be used to estimate and compare the
performance of loading and hauling options in different
haulage circuits to derive an optimum fleet design. The
method was used to predict the performance of loaded
and unloaded haul truck for different haul road designs
having differing haulage lengths, grades of haul ramps
and position of corners and bends based on an effective
flat haul model leading to an estimation of the cycle time
for a particular haul route configuration. Once cycle time
was estimated then queuing theory was used to estimate
production rates and finally operating costs for the different
trucking configurations were estimated. The paper outlines
an approach based on first principles that can be applied
to similar types of mining operations where access to
commercially available software might not always be
possible or desirable.
Filtering of data based on statistical analysis was used to
discard unreliable data points from the data set. An effective
flat haul model was developed to calculate cycle times for
different haul truck configurations. Design graphs were used
to predict dig rates and cost of truck fleets.
Data was obtained for the following equipment that is
currently in use at the mine for prestrip overburden removal:
•
•
•
14 × Hitachi EH4500, 250 t capacity rear dump trucks
2 × Hitachi EX3600, 22 m3 bucket capacity hydraulic
excavators
1 × Hitachi EX5500, 27 m3 bucket capacity hydraulic
excavator.
METHODOLOGY
Effective flat haul
An effective flat haul (EFH) model was constructed based on
the speed that a haul truck will travel at in various haulage
scenarios. The scenarios considered included straight runs,
bends and corners as well as cases for loaded, unloaded
1. SAusIMM, Student, School of Mining Engineering, University of New South Wales, Sydney NSW 2052. Email: scotty9021@hotmail.com
2. FAusIMM, Lecturer, School of Mining Engineering, University of New South Wales, Sydney NSW 2052. Email: p.hagan@unsw.edu.au
EIGHTH AUSIMM OPEN PIT OPERATORS’ CONFERENCE / PERTH, WA, 18 - 19 SEPTEMBER 2012
19
S CAMPBELL AND P HAGAN
and operating on different grades. The results were used to
determine an EFH factor for the different scenarios.
Data from field time studies was collected for various trucks
and truck operators. This included recording truck speeds on
different grades, road configurations and times in each of
the phases in the haulage cycle as shown in Figure 1. Results
for the field measurements were calibrated against values
recorded in MinVu, the site equipment performance database,
to determine average times for load and dump.
FIG 1 - Phases of the shovel truck system (after Ercelebi and Bascetin, 2009).
Match factor
The productivity of a truck and shovel operation is mutually
dependent on the truck and shovel configuration in a fleet. If
one of these factors is altered than the overall production can
be enhanced or reduced from the optimum rate. Circuits are
affected by the occurrence of queuing, idling and bunching.
bunching in circuits is a major factor that isn’t accounted for
by the match factor. Also it does not account for production
targets or cost parameters hence additional methods need to
be considered.
Capacity constraints
The capacity constraint model is a useful theoretical approach
based on average load time and changing total cycle time
which was noted in some instances by Najor and Hagan
(2007) to result in a significant reduction in overall truck
productivity and material movement rate. They further
commented that by accounting for capacity constraints, mine
schedules could better reflect actual fleet capacity. It can be
used to determine the productivity of the circuit based on the
excavator and number of haul trucks.
The total haul cycle time was calculated by adding all four
phases in the haulage cycle as per the approach of Ercelebri
and Bascetin (2009). To simulate the haulage process required
appreciating an excavator had a limiting dig rate. Depending
on the haulage circuit, a point could be reached where the
addition of another truck will have no effect on increasing the
overall production output of the circuit. This behaviour has
been explained through the use of queuing theory proposed
by Ringwald (1987) whereby as more trucks are added to a
circuit, the utilisation of a truck at an excavator approaches
100 per cent. Queuing theory provides a probability factor for
queuing to occur and this when incorporated with the match
factor can result in more reliable fleet optimisation (Burt and
Caccetta, 2007).
Equations 2 and 3 from Carmichael (1987) were used to
predict the production rate of a circuit based on the number
of allocated trucks to an excavator:
-1
Pt = 1 - ;
(r) i E
/in= 0 (n n!
- 1) !
(2)
Match factor is a method of determining the optimum
number of trucks required to service a shovel. The
mathematical expression for match factor in relation to
homogeneous trucks is given in Equation 1:
P = μPtCt
Pt
= truck availability at excavator, per cent
Match factor = (number of haulers)/(number of loaders)
× (loader cycle time)/(hauler cycle time)
P
= production rate, bcm/h
n
= number of trucks allocated to a circuit
r
= loading time as a percentage of total cycle time
μ
= service rate of the excavator based on it not having
to wait for a truck (60/excavator loading time)
i
= integer from zero to n
Ct
= truck payload, bcm
(1)
Rai (2000) stated a match factor of one would mean that
shovel productivity is equal to truck productivity and that a
value of less than one would mean that a circuit is shovel-rich
leading to under-utilisation and idling of the shovel. If the
value is greater than one then the circuit is truck-rich resulting
in overloading the circuit with trucks reducing the efficiency
of the circuit through truck bunching of trucks. This makes it
important to attain a match factor as close to one as possible.
A deficiency of the match factor is that it does not compensate
for queuing, heterogeneous trucks and loaders nor explore
the consequences when the match factor is not equal to one.
Burt and Caccetta (2007) recognised that bunching of faster
trucks behind slower trucks is a common problem with many
truck fleets which is exacerbated in heterogeneous fleets of
differing truck size and performance the end result being an
increase in average cycle time. Bunching and queuing are two
variables that vary randomly being controlled by such factors
as operator experience, equipment quality, equipment age
and general maintenance.
Using a match factor is a simple method to test the
theoretical efficiency of a circuit when comparing the ratio
of trucks to shovels. Match factor can be usefully applied to
both homogeneous and heterogeneous circuits. Queuing and
20
(3)
where:
RESULTS
Load and dump times
Statistics on the dump time of the EH4500 haul trucks are
summarised in Table 1. The values shown were obtained
from the MinVu database based on a two-month sampling
TABLE 1
Average dump and loading times for the haul truck and hydraulic excavators.
Dump EH4500
Load EX3600
Load EX5500
Number of loads
8581
793
2023
Sample size
8581
793
2023
Mean load time
93 s (1.55 min)
242 s (4.03 min)
178 s (2.97 min)
Standard deviation
24 s (0.40 min)
40 s (0.66 min)
27 s (0.45 min)
EIGHTH AUSIMM OPEN PIT OPERATORS’ CONFERENCE / PERTH, WA, 18 - 19 SEPTEMBER 2012
SELECTION OF AN OPTIMUM TRUCK AND SHOVEL FLEET BASED ON EFFECTIVE FLAT HAUL AND CAPACITY CONSTRAINT MODELLING
period involving four dump locations. The mean dump time
of 93 seconds is in close alignment with actual times recorded
in field measurements having a mean of 82 seconds based on
one dump site. The dump time distribution for the trucks is
shown in Figure 2.
The loading times for the two hydraulic excavators EX3600
and EX5500 are also listed in Table 1 with mean loading times
for each of 242 seconds and 178 seconds with a difference
of 36 per cent. The loading time distributions for the two
excavators are shown in Figures 3 and 4 respectively. From
the field measurements it was noted there was a limit on how
quick a truck could dump and an excavator could load and
this was taken into account when filtering the dataset from
MinVu. Due to misreadings, outliers were eliminated such
that for example loading times by the EX5500 of less than
150 seconds and truck dump times of less than 50 seconds
were deemed too fast.
Effective flat haul model
When developing an EFH model, one critical factor that
needed to be established was the average speed a haul truck
could attain on different gradients and road conditions
(straight, bend or corner) as well as truck load condition
(loaded or unloaded). Different EFH factors were applied for
each scenario to derive an equivalent haulage distance. The
EFH factors used in the model for the loaded and unloaded
trucks are given in Table 2, while Table 3 shows the adjusted
truck speeds for different gradients and road conditions. The
factors are normalised against a truck travelling straight on
the flat at 60 k/h.
An actual haulage circuit at the mine was used to verify the
EFH values, the circuit shown in Figure 5. Values stated in
the circuit are the grades for a loaded truck travelling to the
dump point. The calculated values of EFH for the various road
conditions in the loaded and unloaded cycle of the circuit are
shown in Table 4.
TABLE 2
Effective flat haul factors used for loaded and unloaded EH4500 haul truck.
Gradient (%)
FIG 2 - Dump time distribution curve for the fleet of EH4500 haul trucks.
Straight
Bend
Corner
0-4
1.5/1.0
1.5/1.0
3.0/3.0
4-8
1.7/1.3
1.7/1.3
3.0/3.0
8 - 12
4.6/2.0
4.6/2.0
3.0/3.0
-(0 - 4)
1.5/1.0
1.5/1.0
3.0/3.0
-(4 - 8)
1.7/1.3
1.7/1.3
3.0/3.0
-(8 - 12)
3.0/1.7
3.0/2.4
3.0/3.0
Note: first value is loaded condition and second value is unloaded condition.
TABLE 3
Variation in maximum truck speed for different road conditions.
Gradient (%)
Straight (km/h)
Bend (km/h)
Corner (km/h)
Uphill loaded average speed
0-4
40
40
20
4-8
35
35
20
8 - 12
13
13
20
Downhill loaded maximum speed
FIG 3 - Load time distribution curve for the EX3600 excavator.
0-4
40
40
20
4-8
35
35
20
8 - 12
20
20
20
Uphill unloaded maximum speed
0-4
60
60
20
4-8
45
45
20
8 - 12
30
30
20
Downhill unloaded maximum speed
0-4
60
60
20
4-8
45
45
20
8 - 12
35
25
20
Sharp bend
FIG 4 - Load time distribution curve for the EX5500 excavator.
All
EIGHTH AUSIMM OPEN PIT OPERATORS’ CONFERENCE / PERTH, WA, 18 - 19 SEPTEMBER 2012
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21
S CAMPBELL AND P HAGAN
TABLE 5
Comparison of different phases in truck cycle times based on calculated
effective flat haul model and measured times.
Phase in truck cycle (min)
Load
FIG 5 - Haulage route showing varying grades.
TABLE 4
Variation in effective flat haul calculated values for haulage route under
different road conditions.
Straight uphill
Loaded haul
Straight downhill
Sharp bend
Grade (%)
Distance (m)
EFH (m)
0-4
942
1413
4-8
477
818
8 - 12
293
1352
0-4
996
1494
Sharp bend
Total
Total time (mins)
Total
Measured time
2.97
6.58
1.37
4.67
15.59
EFH model
2.97
6.38
1.55
4.13
15.03
reviewing the different EFH contributions to haulage cycle
time it can be seen that the graded ramps in particular the
steep eight to 12 per cent grade ramps despite their short
distance and to a lesser extent the corners and curves. The
impact that these had on the effective flat haul ranged from
a factor of two times through to 4.6 times longer duration.
The model showed for example that a loaded truck travelling
293 m up an eight to 12 per cent graded ramp was equivalent
to travelling 1.494 km on the flat at 60 km/h, which when
compared to the same loaded truck travelling on a four to
eight per cent ramp over nearly twice the distance of 477 m
had a much shorter EFH of 818 m at 60 m/h. This shows
that limiting the amount of steep ramps when designing
haul roads can have a much larger impact on cycle time than
making ramps steeper to shorten haul distances.
Using the EFH model approach can facilitate calculation of
the haulage cycle time in any circuit that can in turn be used to
determine the optimum number of trucks in a circuit servicing
an excavator. This will allow greater flexibility in knowing
when to use a certain excavator and how many trucks that are
required on that circuit to service the excavator.
4-8
445
763
80
240
All
150
300
3383
6380
Fleet match factor
6.38
A fleet match factor is a simple method of estimating the
number of trucks required in a circuit to minimise shovel idle
time and maximise truck utilisation. In order to account for
the variability observed in load times, calculation of the fleet
match factor was based on the summation of values stated
in Table 1 for average load time and one standard deviation
which is equivalent to 84 per cent of occurrences.
0-4
996
996
4-8
445
593
8 - 12
80
160
0-4
942
942
4-8
477
636
8 - 12
293
502
All
150
300
3383
4130
4.13
When load and dump times given in Table 1 are combined
with the travel time in Table 4, the total cycle time can be
determined. Table 5 contains the times for each phase in the
cycle as a well as the total cycle time, which in the case of
the EX5500 excavator was 15.03 minutes, which compares
favourably with the field time measurement of 15.59 minutes,
representing a difference of only 3.7 per cent. This difference
may be partly explained by the model not accounting for
truck acceleration times.
The results of the EFH model show that actual haul length
was not the only major contributor to cycle time. When
22
Return
8 - 12
Total time (mins)
Unloaded haul Straight downhill
Dump
Using the EFH model provides an approach to the
calculation of the haulage cycle time in any circuit that can
in turn be used to calculate the optimum number of trucks
in a circuit to service an excavator. This approach provides
some flexibility in knowing when to use a certain excavator
and how many trucks are required on that circuit to service
the excavator.
Total
Straight uphill
Haul
Two sets of results were determined for each excavator. The
first being the number of trucks to service an excavator for
various cycle times. The second being the fleet match factor.
Results for the EX5500 excavator are shown in Figures 6 and 7
with similar trends found for the EX3600. The fleet match
factor tended to stabilise around one for longer cycle times.
A deficiency in using the fleet match factor approach is that
it fails to account for a targeted mining rate as well as impact
on mining costs. While the fleet match factor may ultimately
reduce bunching and queuing it may not achieve a required
production rate. Where this is important then a further
approach is required.
Capacity constraint model
While the deterministic approach of the EFH model may
be useful in the first instance to determine optimum fleet
configuration, the variability inherent in the various phases
of loading and hauling process will often lead to significant
EIGHTH AUSIMM OPEN PIT OPERATORS’ CONFERENCE / PERTH, WA, 18 - 19 SEPTEMBER 2012
SELECTION OF AN OPTIMUM TRUCK AND SHOVEL FLEET BASED ON EFFECTIVE FLAT HAUL AND CAPACITY CONSTRAINT MODELLING
FIG 6 - Required number of trucks to service the EX5500 excavator for
various cycle times.
FIG 7 - Calculated fleet match factor for the EX5500 excavator.
FIG 8 - Capacity constraint model based on seven or fewer trucks servicing an
EX3600 excavator.
FIG 9 - Capacity constraint model based on eight or more trucks servicing an
EX3600 excavator.
underperformance of the haulage system. The capacity
constraint model is a stochastic approach that recognises the
random nature of elements in the process. It is based on a
probabilistic function that can be used to effectively allocate
trucks to a haulage circuit. Mine planners often aim to allocate
a sufficient number of trucks in a circuit to achieve a target
production rate. Using a combination of Equations 2 and 3, the
load times in Table 1 and assuming an average truck capacity
of 114 bcm, a capacity constraint model for different total
cycle times ranging from five to 40 minutes was generated.
The model showing the variation in the production rate
based on the EX3600 excavator in a circuit with varying truck
numbers and cycle times are given in Figures 8 and 9. For the
case of the EX5500 excavator, the capacity constraint model is
given in Figures 10 and 11.
The results show with shorter cycle times, fewer trucks are
required to achieve a target dig rate. A point will eventually be
reached when allocating tracks to a circuit that it will become
saturated with a ceiling reached in production rate. In the
case of the EX3600 and EX5500 the estimated maximum dig
rates are 1700 and 2300 bcm/h respectively, each requiring a
minimum of seven trucks for this haulage circuit with cycle
times of five minutes or less.
As one objective of mine planning is to achieve a target
dig rate, a combination of the EFH model and the capacity
constraint model provides a quick and simple method
to estimate the production rate in a circuit that is only in
the planning phase. For example, if the required dig rate
was 1600 bcm/h in a haulage circuit having a cycle time
FIG 10 - Capacity constraint model based on seven or fewer trucks servicing an
EX5500 excavator.
of 20 minutes then based on Figures 8 and 9, eight trucks
would be required to service an EX3600 excavator compared
to only six trucks for an EX5500 excavator. Alternatively if
only five trucks were available to service and excavator then
the maximum production rate that could be achieved for
the EX3600 and EX5500 would be approximately 1200 and
1400 bcm/h respectively which is equivalent to 67 per cent
and 59 per cent of the respective maximum potential capacity
in the circuit. Whereas if the excavators were over-trucked
having 14 trucks in a haulage circuit then the maximum
potential productivity of 1700 bcm/h for the EX3600 could
EIGHTH AUSIMM OPEN PIT OPERATORS’ CONFERENCE / PERTH, WA, 18 - 19 SEPTEMBER 2012
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S CAMPBELL AND P HAGAN
TABLE 6
A comparison of operating costs for various equipment types relative
to haul truck costs.
Equipment
FIG 11 - Capacity constraint model based on eight or more trucks servicing an
EX5500 excavator.
be sustained with truck cycle times less than 30 minutes but
the 2300 bcm/h productivity for the EX5500 could only be
sustained for truck cycle times less that 20 minutes.
Costing
While achieving an efficient high production circuit is
important in terms of equipment utilisation, cost is another
important factor that requires consideration. The costing
models for the EX3600 and EX5500 excavators shown in
Figures 12 and 13 respectively, are based on the relative
operating costs provided in Table 6. These models show
Cost factors
EX5500 excavator
50
EX3600 excavator
30
EH4500 haul truck
1
the variation in unit costs with haulage distance having
equivalent cycle times of ten, 20, 30 and 40 minutes based
on the number of trucks servicing an excavator. For the
shortest haulage route having a cycle time of ten minutes,
the optimum number of trucks to achieve the minimum unit
cost is approximately 3 - 4 trucks for the EX3600 excavator
whereas it is 5 - 6 trucks for the EX5500 excavator. This is
explained by more trucks being required with the larger
productive excavator to ensure it remains fully trucked up.
Beyond this optimum number, unit mining costs increase at
a greater rate with the EX3600 as more trucks are needed
to be added to the circuit compared to the larger excavator
EX5500 which is less sensitive to increases in truck numbers.
As haulage distance and hence cycle time increases, the
optimum number of trucks increases as does mining cost
though the difference narrows between the two excavators
as excavator cost becomes a less dominate cost factor.
While it is important to achieve a target production rate,
the most economical number of trucks allocated to a circuit
may not necessarily achieve a required production rate. When
combining the capacity constraint model and cost model an
overall comparison between the excavators can be made.
Figure 14 considers both excavators operating in the same
circuit having a 15-minute cycle time indicating the variation
in production and costing as additional trucks are added
to the circuit. The graph illustrates that the optimum truck
fleet size for the EX3600 excavator is four trucks achieving a
production rate of 1200 bcm/h. If a higher production rate is
required with the same size trucks but using the EX5500, the
optimum fleet size is seven trucks achieving a movement rate
of 2000 bcm/h, which is 60 per cent more material at the same
unit cost.
CONCLUSION
FIG 12 - The effect of truck fleet size on mining cost for different truck cycle
times servicing an EX3600 excavator.
It was possible to construct an effective flat haul model that
can provide a reasonable estimate of haulage cycle time for
FIG 13 - The effect of truck fleet size on mining cost for different truck cycle
times servicing an EX5500 excavator.
FIG 14 - A comparison of the performance of an EX3600 versus EX5500
excavator based on a 15-minute cycle time.
24
EIGHTH AUSIMM OPEN PIT OPERATORS’ CONFERENCE / PERTH, WA, 18 - 19 SEPTEMBER 2012
SELECTION OF AN OPTIMUM TRUCK AND SHOVEL FLEET BASED ON EFFECTIVE FLAT HAUL AND CAPACITY CONSTRAINT MODELLING
a given haul design scenario that correlated well with actual
cycle times. The EFH model was found to be useful in the
planning process as it indicated the sensitivity of changes in
ramp design (for example gradient versus length) on overall
cycle time.
A combination of the capacity constraint model and
costing model was found to provide a more effective
approach in allocating trucks to a circuit as it considered not
only cycle time but also production capacity. Keeping cycle
times short meant lower cost and higher productive circuits.
Fleet match factor was the least useful method in allocating
trucks to a circuit as it provided limiting information on the
performance of a circuit. Shovel idling and truck availability
are best used to gain the best utilisation out of the loader or
truck fleet.
When comparing the EX3600 and EX5500 excavators in
use at the Callide Mine on an identical circuit the smaller
EX3600 was more economic for smaller truck fleets size and
production rates but the eventual higher productivity of the
EX5500 would lower the cost of moving material achieving
much higher material movement rates. In the end a choice
has to be made between achieving higher production with
the EX5500 excavator or a lower cost with the EX3600
excavator in a given haulage circuit.
ACKNOWLEDGEMENTS
The authors wish to acknowledge Anglo American
Metallurgical Coal for allowing access to the data used in this
study and to conduct field measurements at the site. They
also acknowledge support given by staff at Callide Mine with
helping in organising the site visits and giving access to the
resources needed to generate this paper.
REFERENCES
Burt, C and Caccetta, L, 2007. Match factor for heterogeneous truck
and loader fleets, International Journal of Mining, 21(4):263-270.
Carmichael, D, 1987. Engineering Queues in Construction and Mining
(John Wiley and Sons: New York).
Ercelebi, S and Bascetin, A, 2009. Optimisation of shovel-truck system
for surface mining, The Journal of the Southern African Institute of
Mining and Metallurgy, 10(9):433-439.
Najor, J and Hagan, P, 2007. Improvements in truck and shovel
scheduling based on capacity constraint modelling, in Proceedings
Sixth Large Open Pit Mining Conference, pp 87-92 (The Australasian
Institute of Mining and Metallurgy: Melbourne).
Rai, P, 2000. Optimising shovel-truck combination, Coal International,
5(3):230-231.
Ringwald, R, 1987. Bunching theory applied to minimise cost,
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