TABLE OF CONTENTSCHAPTER
I21.INTRODUCTION21.1.BACKGROUND21.2.INTRODUCTION41.3.STATEMENT51.4.AIMS51.5.OBJECTIVES51.6.QUESTION61.7.DELIMITATIONS61.8.DEFINITIONS
OF TERMS6CHAPTER II72.LITERATURE REVIEW72.1.THEORETICAL
LITERATURE8SECTION 2.1 Dispatch system8SECTION 2.2 The application
of dispatching systems9SECTION 2.3 Linear programming11SECTION 2.4
Dynamic program132.2.CONCEPTUAL FRAMEWORK14CHAPTER III
METHODOLOGY153.INTRODUCTION153.1.RESEARCH DESIGN163.2.POPULATION
AND SAMPLING163.3.DATA COLLECTION16CHAPTER IV DATA
PRESENTATION164.INTRODUCTION164.1.DATA PRESENTATION164.2.ANALYSIS
AND INTERPRETATION194.2.1.SIMULATION OF MINING BEHAVIOUR USING LP
SOLVER20CHAPTER
V215.CONCLUSION215.1.RECOMMENDATION22BIBLIOGRAPHY22
CHAPTER I1. INTRODUCTIONThis is a brief introduction to the
chapter I where will intend to present of the topic and integrate
the readers into the field of the productivity.This chapter is
divided into eight parts namely background; introduction;
statements; aims and objectives; research question; delimitation of
the research and definition of terms.
1.1. BACKGROUND
Mining companies carry out their activities either by
underground mode or open cast mode. In open-cast mining the loading
activities occur as follows: trucks goes to the front of mine and
then discharge the material in discharge points. These discharge
points can be sterile piles, piles of homogenization. In addition,
this ore must meet certain conditions in order to the beneficiation
occurs, i.e., the contents of each control variable should be
between the upper and lower limits established for each one of
them.
To provide ore of same quality for the beneficiation process it
is needed to mix ore of different qualities of various parts of the
mine or of different mines in order to ensure the uniformity of
ore, which is important from an operational standpoint, since
changes are usually accompanied by an increase in the total cost of
operation (Manangement mining operation- subject note).
Open pit mines use two criteria for the allocation of trucks:
static and dynamic allocation. In static allocation, the trucks are
secured to a loading point and an unloading point, i.e. its
movement only occurs between these two points for a certain period
of time. The dynamic allocation, each loading and/or unloading, the
truck is directed to a specific point, according to previously
established criteria.
Historically, according to Kolonja et al., The open pit mines
operated with each truck allocated to a given loading equipment,
but with monitoring and controlling via computer. The strategy used
was to dispatch the trucks to the loading equipment which would
contribute more to production targets in the short term plans.
Static allocation is still the method most used in mining for
not presenting the requirement to use an automatic allocation.
However, this method provides lower productivity due to queues of
trucks and the idleness of the load equipment. This type of
allocation is generally applied to small and medium-sized
mines.
The use of dynamic allocation requires the use of a dispatch
system. According Knights and Bonates the term dispatch refers to
the dynamic allocation of trucks to load equipment. This system
uses pre-established criteria for its operation. Among these
criteria can cite, among others, maximizing equipment utilization,
with the objective to increase productivity and meet the quality
needs of the treatment works.
The activity of transport of material is one of the most
important aspects in the operation of open pit mines (Alarie and
Gamache). Moreover, according to Maran and Topuz transport systems
in these mines involve large amounts of capital and resources. The
purpose of the transportation problem is to move the material
removed from the mine to the plant so that the cost is minimized,
since that associated cost influences the choice of where removing
ore (Gershon).
In mining, allocation of trucks is an important and complex
process and an optimal allocation can result in significant
savings. It is recognized that the operation of trucks and loading
equipment contributes significantly to the cost of the operation as
a whole.
Therefore, it is necessary a deep study about dispatch which is
applied at Vale Company because an optimal dispatch system can
reduce the cost of capital and operation, reducing the required
fleet of trucks and increased production with the use of the same
fleet.
1.2. INTRODUCTION
This topic is relevant because the standards of dispatching
trucks are very low. The main objective of production planning in
an open pit mine, is to determine what would be the rhythm of
production on every front, providing the client with a suitable
product. This problem is known in literature as the problem of
mixing or blending.
In real cases of the mining industry, it is necessary to
consider a number of other issues that are usually not addressed in
the literature together. Separately optimize the problem without
addressing these issues can lead to conflicts that prevent the
implementation of solutions. One of these questions relates to
meeting the goals addressed by Chanda and Dagdelen, whether it is
production or quality policy. Meeting the production targets is
important, since a higher than required production can cause
problems such as lack of adequate space for storage and additional
handling costs, since a lower output causes a reduction in the rate
of use of the equipment of the mine and beneficiation plant, and
contractual penalties for failure to supply the product. Another
aspect of great importance is related to the meeting of the goals,
now considering the quality specifications of the mixture, is
connected, in the case of the processing plant, the control of
fluctuations should be minimal, making the process more efficient,
or even previously determined so that the appropriate action to
adjust the processing plant are taken.
The work in question has all necessary methodologies for both
dispatch policies in order to improve the standards at Vales
company, and this research is divided into five chapters where the
first chapter refers to the introduction where the objectives are
exposed, defining the terms used during the research and other
relevant aspects. The second chapter refers to the literature
review which the theories about the dispatch according to their
policy will be established and there will be a brief description
about the reality that is being applied. In the third chapter
refers to the methodologies applied for doing this research. The
results of what is practiced and the confrontation of the theory
and the reality will be presented in the fourth chapter. Finally
the fifth chapter will give the conclusions and
recommendations.
1.3. STATEMENT An efficient truck-and shovel system reduces
hauling, operating, and maintenance costs, while meeting production
targets and providing a steady and reliable feed of material.
(Torkamani 2013).
1.4. AIMS To find out if dispatch system is being applied
correctly at Vale company.
1.5. OBJECTIVES Design a better policy of truck dispatch at
Vales Company; Introduce the use of discrete-event simulation in
Vales company to achieve the main goal of productivity at low cost;
Introduce another standpoint, which would increase the production
using the same fleet;
1.6. QUESTIONIs Vale Company applying the correct procediments
of dispatching trucks?
1.7. DELIMITATIONSI am not going to do a full research involving
all workers of trucks and shovels because there is not enough
resources.
1.8. DEFINITIONS OF TERMS
Front of Mine - are points of mine where by the ore and sterile
are being removed, and loaded by loading equipment.
Discharge points It is where the ore and sterile are being
discharged.Sterile piles - Are materials that is not used by the
process;
Piles of homogenization - when it is carried a quantity of ore
higher than the plant can benefit or when it is necessary to "mix"
the ores before starting the processing.
Client Can be either an external customer or internal customer,
an internal customer is beneficiation plant.
VRDC Vale do Rio Doce Company
CHAPTER II2. LITERATURE REVIEWThis chapter will be presented in
a succinct way, a literature review of the main techniques
referenced throughout this work. This section will be divided into
two main title, the theoretical literature and a conceptual
framework. In theoretical literature will be all about the theories
concerning dispatch and will be shown a brief review of dispatch
systems in section (2.1) within the theories, in section (2.2) will
described the application of dispatching systems, section (2.3)
will be about linear programming and at last will be addressed
dynamic programming as section (2.4). In conceptual framework will
be presented what is the real concept about the topic and it will
describe the concepts of this two main approaches of dispatch
trucks which is Linear Programming and dynamic programming in a
practical manner.
2.1. THEORETICAL LITERATURESECTION 2.1 Dispatch systemThe
transport system utilizing trucks at large mines is so complex that
quantitative results are difficult to obtain analytically by theory
of queues once the simulation is probably the only practical method
for predicting the performance of the transport system under
computer control dispatch (Tu method, and Hucka).
According Munirathinam and Yingling, at large mines is more
advisable the representation of transport systems models of
stochastic network rather than models of queues theory.
According Kolonja et al. the dispatching strategies and systems
are complex and generally can be analyzed only by simulation.
However, it is common to produce the best dispatch system is only
slightly better than the strategy less effective clearance
compared.
According Alarie and Gamache, truck dispatching problems do not
occur only in the mineral industry. They are present in any
industry that manages a fleet of vehicles or a group of people,
such as transportation industries, taxi and package delivery.
However, applied to mining presents simplicity than that found in
other industries. Among these simplities, these same authors cite
that mines are closed systems, the points of loading and unloading
remain the same distance for a long period of time, the distances
are small compared with the duration of the shift and the frequency
of each demand point is high.
Maran and Topuz claimed that the computer simulation can be used
as a way of testing and assessment of allocation of trucks and
problems of dispatch, especially when analytical methods are not
appropriate. Furthermore, Kolonja according et al. and White et al.
says that in most cases, computer simulation is the most applicable
and effective method of comparing dispatch systems.
Turner states that the simulation results refer to improvement
in the availability and utilization as well as the efficiency of
the system, and make it possible to analyze a transaction before it
has been installed and configured.
According Srajer et al., the efficient operation of trucks and
load equipment in mines depends on the proper allocation of trucks
to load equipment and the discharge points. Because of breakage of
equipment, changes in conditions excavation, truck capacity,
characteristics of the mixture, often the relocation of trucks is
required to maintain the operation efficient.
Furthermore, according to Alarie and Gamache, the efficiency of
a transport fleet depends on its size and distance transported.
When trucks are not sufficient, the load equipment will have
substantial unproductive periods and when there are many trucks the
size of the queue for loading installations increases. When the
fleet is too large, the queue of truck will appear, but as the
system is closed and the demand is known, the events can be
provided in a future next to confiability which can be used to
reduce such the queue (Alarie and Gamache).
According Munirathinam and Yingling, in dispatch systems with
restricted allocation, allocation decisions are made in real time
optimizing the production rate by minimizing the waiting time. As
systems driven by planning, these formulations consider the
allocation of the truck together with allocating other trucks which
will be made in near future. However, operational constraints, such
as the need of the mixture of ore, are embedded in formulation
allocation and restrict each allocation decision. The weaknesses of
this type of method are strict obedience operational restrictions,
which could be relaxed in the short term to increase productivity
and no explanation of the stochastic nature the cycle time of the
elements in the allocation model. This author cites the procedure
developed by Hauck, as an example of application of this type of
system order.
SECTION 2.2 The application of dispatching systemsTu and Hucka
developed a model to simulate a truck in open pit mine using a
computerized system of dispatch. The developed model can be used to
study the impact of the dispatch system on productivity of trucks
and loading equipment, to test dispatching policies that improve
the performance of trucking as a tool to stimulate the production
of the transport system and to reveal bottlenecks. This model can
also be used to simulate the static and dynamic allocation with
multiple shipping options. The result obtained from the model
system showed that the order generated savings 2 to 3% of the total
fleet of trucks.
Pinto and Merschmann proposed a model that considers the problem
of mixing and allocation of charging equipment, ration sterile/ore
minimum and dynamic allocation trucks. This model is not linear, so
there is no guarantee that the solution obtained is optimal.
White et al. propose a model that minimizes the number of trucks
needed through related restrictions related on the continuity of
use of material through the points of load and unloading and
production capacities of the load points.
White et al. propose a model that minimizes the number of trucks
needed through related restrictions related on the continuity of
use of material through the points of load and unloading and
production capacities of the load points.Turner reports a virtual
mine operation managed in real time by a system of dispatch system.
This simulation was performed in order to determine combinations of
truck / loading equipment suitable for the proposed operation the
mine.
Nogueira developed a model for simulating the truck / equipment
system load in order to assess the best combination of cargo truck
/ equipment to determine the capacity of the mine and analyze the
impact of admission one more load equipment in mine production Cau
of VRDC (Vale do Rio Doce company). This study found that the truck
dispatching in mines open pits mines tends to increase production
and smooth the irregularities in the queues within the system.
Pereira studied the effect of dynamic dispatch in productivity,
comparing with the conventional method of using fixed allocation
order. This study was done in Conceio mine at VRDC, before the
introduction of dispatch system.
Costa et al. proposed a model of linear goal programming applied
to the problem of mining production, with the aim of determining
the rate of extraction of each front considering allocating loading
and transport equipment in order to provide adequate ore to the
plant. In this work, it was used a static allocation of trucks and
can concluded that it is possible to achieve the required goals and
optimize transport and loading operations, with a slight reduction
in productivity.
Costa et al. presented a model of linear goal programming with
the goal of increasing the productivity of transport facilities.
The allocation of these equipment to the fronts, this case is made
dynamically at the end of the cycle of charge and discharge. The
model of linear goal programming was used in this work to be
considered more appropriate to the reality of mining, because it's
goal is to make the solution great, be as close as possible to the
goal production and quality.
Hauck (quoted by Munirathinam and Yingling) used dynamic
programming to develop a procedure for order in real time in the
open pit. The goal was to maximize total production by minimizing
the lost productive time stops due to the load equipment. This
model includes several restrictions operational restrictions such
as the mixture of ore processing capacity of the plant and state of
the ore stockpiles. He showed that globally optimal decisions can
be resolved quickly with dynamic programming when the problems are
small scale.
SECTION 2.3 Linear programmingLinear programming comprises
programming models where the variables are continuous and all
expressions have a linear behavior.
A linear programming model reduces to a real set of equations or
mathematical expressions, where every decision taken is associated
with a decision variable system. A numerical function of the
decision variables, objective function, expresses the measure
sought. This function can be the type to maximize or minimize.
Resource limitations, requirements or conditions are expressed by
means of equations and inequalities, restrictions on the values of
the variables.
After the formulation of the model, this should be reduced to
the standard form with the intention of obtaining the optimal
solution. The equations (2.1) to (2.4) show a linear programming
model in standard form. Equation (2.1) represents the objective
function to be minimized. The equations (2.2), (2.3) and (2.4) are
the restrictions of the linear programming problem. The
non-negativity constraint is expressed in (2.4) and ensures that
the decision variable not present any negative value.
(2.1)(2.2) (2.3) (2.4)Where:i = activity to be realized = cost
of the activity ij = restriction = the available quantity of
resource j = the quantity of resource j in activity i = level of
the operation of activity i (decision variable)n = number of
activitiesm = number of resourceWith the model in standard form, we
use algorithms to yield numerical solutions for these models.
According to Wagner, there are different methods for solving linear
programming problems, but the Simplex algorithm is the most
widespread. This method is a matrix procedure that seeks the
optimal solution of the model at the vertices of the polytope
formed by the feasible solutions of the problem.
An integer programming problem is a linear programming problem
with additional constraint that the values of all the input
variables are integers (Bronson). When at least one of these input
variables admits values that do not are integers this problem is
called mixed integer programming. For the resolution of this
problem are usually applied algorithms based on Branch-and-bound or
branching and limit.
Costa states that most of the real problems of integer
programming is combinatorial complexity and, therefore, can only be
solved efficiently by an accurate technique such as
branch-and-bound, if they are small.
SECTION 2.4 Dynamic programThe dynamic programming is applied to
problems where decisions are made in stages, i.e. is used,
according to Bronson, to optimize multistage decision processes.
Furthermore, it is employed usually in smaller scale problems
(Wagner).
According to Bertsekas, a key aspect of this type of problem is
that decisions can not be seen in isolation, it is necessary to
balance the desire for low cost at present and prevent the
possibility of high cost in the future. Thus, at each stage a
decision is selected since it minimizes the cost in the current
stage, and take the best expected cost in future stages.Dynamic
programming is based on the principle of optimality of Bellman.
This principle says:
An optimal policy has the property whereby, despite the
decisions taken to assume a particular state at a certain stage,
the remaining decisions from this state must be an optimal policy.
Thus, we start from the last stage of a process of n stages and
determine the best policy to leave that state and complete the
process, assuming that all stages have been completed earlier.
Moves, then, throughout the process, the last for the first stage.
At each (n) stage determines the best policy to leave each state
(u) and complete the process, assuming all previous stages have
been completed and using the results already obtained for the next
stage (Bronson).
Factors relating to the last (n) stage, are computed directly
and others are obtained recursively, i.e., as the base of the stage
immediately later.
Mutmansky states that when a decision-making problem can be
formulated with a series of individual decisions are interrelated,
then the problem can be solved by dynamic programming.
2.2. CONCEPTUAL FRAMEWORK
The productive process of ore extraction can be resumed in two
main phase: extraction and processing. The extraction phase,
involves basically, in extracting the ore beneath the earth. Then
this ore is transported by trucks, sometimes by conveyors which
takes it to the processing plant. The processing phase consist in
crushers, sieving and gridding, chemical treatments within others
process linked to ore separation based in phisico-chemical
characteristic.
Generally, mines are divided into various mining fronts. Each
front, normally has a different content of ore. The ore leaving the
mine, with the target to treatment plant, is called Run of Mine
(ROM). Of course, the content of the Run of Mine (ROM) ore is the
result of combination of the levels of the various fronts that make
up, i.e. the content of the ROM ore and the weighted average of the
levels of the mine fronts that provide ore for this ROM.
For example, if the ROM is being formed from the extraction of
two fronts, the ore content of a particular variable of the front
is 20% and other front is 24%, and their fronts and contribute 60%
and 40%, respectively, of the ore from the ROM, the contents of the
ore R.O.M., will be 21.6%, as calculated below:
The content of each variable R.O.M. must be between the lower
and upper limits stipulated by the processing plant for that
variable. To ensure service quality of this specification, trucks
are sent to fronts more or less content according to the time of
need ROM
This policy of dispatching trucks for mining fronts due to the
guarantee of that level of mix is called quality policy. Its aim,
is to ensure that the contents of the ROM variables are within the
limits and also reduce the variance of each variable of feeding the
ROM.
CHAPTER III METHODOLOGY
3. INTRODUCTION
In this chapter it will be presented the population of the
production area, the sampling and methodologies which helped to
gather data at Vales company.
3.1. RESEARCH DESIGN
In order to study the present problem, it was necessary to
select the ideal people to study with in which for its selection
observed the rule of sampling so that this study becomes a
representative, thus the collection of data was by observation and
questionnaire. The questioner was directed to the managers and the
drivers were observed in two shifts of 26th October.
3.2. POPULATION AND SAMPLING
At a production section there was a population of 70 workers, 20
shovels drivers, 50 trucks drivers and 7 productions manager in
both shifts. According to the sampling rules, it will be choose 10%
of all areas shovels drivers, trucks drivers and managers
section.
SEXNATIONALITY EDUCATION LEVELAGEWORK EXPERIENCEPOPULATION
Shift
MFNFPRSETE21-2426-29+301-34-7+8ND
7068213507262915383023030
3.3. DATA COLLECTION
The selected method is observation and observation the reasons
of choosing those method is that: Observation will help discovering
the obstacles, which makes the selected dispatch being or not being
able to meet the productivity rhythm, and questionnaire will help
discovering the reasons of choosing the current dispatch, so with
these two ways it will be possible to propose a good way approach
of dispatch which will meet the middle term of obstacles found by
the drivers and the obstacles found by the manager. CHAPTER IV DATA
PRESENTATION
4. INTRODUCTIONIn this chapter will be presented the data and
further analysis
4.1. DATA PRESENTATIONPREAMBLE
I am Bic de Sousa, student of Mining Engineering at ISPT and I
am carrying out a research to find out if Vale Company is following
the correct procedures for dispatching trucks in order to increase
productivity. The research in question is for the partial
fulfilment of the degree requirement of the course which I am
doing. I am collecting this information just for academic purpose.
All information is to be treated as confidential.
QUESTIONNAIREAnswer the following questions with X to the best
answer, and with clarity to the questions where there is no
limitation.
1. Does the applied dispatch meet the goals of productivity at
Vale?[ ] Yes [ ] No [X] Sometimes
2. What are the inconvenient that makes this dispatch not being
able to meet the goals in terms of productivity? Drivers
shortages
3. What are the mechanism that Vale adopts to reverse this
inconvenient? Awareness of their shortages and their impacts to our
production
4. What are the ways in which Vale adopts to explain the impacts
of the drivers in a dispatch method? We create an ideal forum in
which we talk to them
5. Are the number of fleet trucks enough for increasing the
productivity of Vale? [X] Yes[ ] No[ ] Sometimes
6. What are the lessons learnt in previous dispatch?We have
learnt that in order to dispatch model works it is needed that all
workers have to be trained and become a part of the company.
7. Does the productions manager use time cycle to dynamise the
unproductive times?[X] Yes[ ] No[ ] Sometimes
8. Does the unexpectedness of failures of trucks, shovels, and
crushers and repairing processes are scheduled in the present model
of dispatch?[X] Yes [ ] No[ ] Sometimes
OBSERVATION SHEETTONNAGE OF THE AVAILABLE MATERIAL IN EACH
FRONTMining areasShovel 1Shovel 2
Available material in front of each shovel
(ton)111,000130,000
Table 1. Available material in front of each shovel in mining
area.
LOADING TIME FOR TRUCKS (seconds)Types of trucksShovel 1Shovel
2
Truck A250250
Truck B300300
Truck C373277
Truck D232315
Table 2. Loading time for trucks (seconds)
UNLOADING TIME FOR TRUCKS (seconds)Type of truckCrusherWaste
dump 1Waste dump 2
Truck A12010590
Truck B145122110
Truck C133118123
Truck D155125135
Table 3. Unloading time for trucks (seconds)
NUMBER AND CAPACITY OF TRUCKSType of truckNumber of each
truckCapacity of each truck
Truck A8200
Truck B16250
Table 4. Number and capacity of trucks
4.2. ANALYSIS AND INTERPRETATION
Thus, from the observation sheet clearly it can be seen that
there are limited amount of material in front of each shovel in
these two mining areas at the beginning of the shift. However,
there is no restriction for capacity of crusher and waste dumps in
this case.Concerning to the table of loading and unloading time,
there is no possibility of mobility between two unloading areas or
two loading areas. Also, trucks from the two mining areas which are
located in the ore area are only allowed to travel to the crusher
and the loaded truck from the waste area can travel either to the
waste dump #1 or waste dump #2.
4.2.1. SIMULATION OF MINING BEHAVIOUR USING LP SOLVERFor a shift
of 12 hours is presented in the following tables. The tonnage of
extracted ore and waste is presented in Table 4.9. According to
this table, the tonnage of the ore extracted and transported to the
crusher is 74,400 tons per shift using the 8 trucks type A and 16
trucks type B during the 12 hours shift. Also, the tonnage of the
waste is 34,400 ton per shift which is about 32 percent of the
total extracted material.
Amount of extracted material (ton)LP Optimal result
Ore74,400
Waste34,400
Table 5: Tonnage of extracted ore and waste per shiftThe LP
model also determines the number of trips between mining areas and
dumping sites. In the following tables, first, the numbers of empty
trucks that have been sent from the unloading areas to the mining
areas and then, the number of full trucks from mining areas to the
dumping sites will be presented. Table 4.10 shows the number of
empty trucks form each of the unloading areas to the mining areas
for type A trucks.
Truck Type A Empty
ToFromShovel 1 Shovel 2 Total number
Waste dump 1Waste dump 2Crusher0 120 00 0
17200
Total number 0 12172
Table 6: Number of empty trucks type A in the LP solutionAs it
can be seen in this table, the total number of trips of truck type
A is 172 in one shift. According to this table no empty truck has
been sent to shovels 1 and no full truck of type A has been sent to
the waste dump #2.Table 7 presents similar information for type B
trucks.
Truck Type A Empty
ToFromShovel 1 Shovel 2 Total number
Waste dump 1Waste dump 2Crusher0 01 0 58 77
00135
Total number 58 77135
Table 7: Number of empty trucks of type B in the LP
solutionAccording to the above table, the total number of trips for
truck type B is 135 in one shift.
CHAPTER V
5. CONCLUSION
From the relation of the trends observed on the questionnaire
and the observation sheet, it is concluded that the Vales managers
dont have a clear politics of dispatching trucks because it would
be recommended to use the LP solver which maximize the number of
trucks that is sent to the ore areas while considering the blending
constrains as explained in simulation above.
5.1. RECOMMENDATION Use LP Solver; A sensitivity study of input
parameter to understand how the system reacts to the different
scenarios; A time study with probability analysis to determine the
cycle time more accurately.
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Solution Strategies Used in Truck Dispatching Systems for Open Pit
Mines", International Journal of Surface Mining, Reclamation and
Environment 16, 59-76.
2. Chanda, and Dagdelen, K. et. al., 1995. "Optimal blending of
mine production using goal programming and interactive graphics
systems". International Journal of Surface Mining. Reclamation and
Environment 9. 203-208.
3. Gershon, M., 1982. "A linear programming approach to mine
scheduling optimization", Proceedings of the 17th Application of
computers and operations research in the mineral industry,
483-493.
4. Kolonja, B., Kalasky, D. R. and Mutmansky, J. M., 1993.
"Optimization of dispatching criteria for open pit truck haulage
system design using multiple comparisons with the best and common
random numbers". Proceedings of the 1993 Winter Simulation
Conference. 393-401.
5. Knights, P. F. Bonates, and. J. L., 1999. "Applications of
discrete mine simulation modeling in South America", International
Journal of Surface Mining, Reclamation and Environment 13,
69-72.
6. Maran, J. e Topuz, E., 1988."Simulation of truck haulage
systems in surface mines". International Journal of Surface Mining
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