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Final Research Porposal

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TABLE OF CONTENTS CHAPTER I...................................................... 2 1. INTRODUCTION................................................ 2 1.1. BACKGROUND............................................... 2 1.2. INTRODUCTION............................................. 4 1.3. STATEMENT................................................ 5 1.4. AIMS..................................................... 5 1.5. OBJECTIVES............................................... 5 1.6. QUESTION................................................. 6 1.7. DELIMITATIONS............................................ 6 1.8. DEFINITIONS OF TERMS.....................................6 CHAPTER II..................................................... 7 2. LITERATURE REVIEW........................................... 7 2.1. THEORETICAL LITERATURE...................................8 SECTION 2.1 – Dispatch system...............................8 SECTION 2.2 –The application of dispatching systems.........9 SECTION 2.3 – Linear programming...........................11 SECTION 2.4 – Dynamic program..............................13 2.2. CONCEPTUAL FRAMEWORK....................................14 CHAPTER III – METHODOLOGY.....................................15 3. INTRODUCTION..............................................15 1
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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.

BIBLIOGRAPHY1. Alarie S. and Gamache M., 2002. "Overview of 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 2. 43-49.

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