Appraising production targets through agent-based Petri net simulation of material handling systems in open pit mines

Accepted Manuscript

Appraising production targets through agent-based Petri net simulation of material handling systems in open pit mines Burak Ozdemir , Mustafa Kumral PII: DOI: Reference:

S1569-190X(18)30092-3 10.1016/j.simpat.2018.06.008 SIMPAT 1825

To appear in:

Simulation Modelling Practice and Theory

Received date: Revised date: Accepted date:

22 March 2018 26 June 2018 29 June 2018

Please cite this article as: Burak Ozdemir , Mustafa Kumral , Appraising production targets through agent-based Petri net simulation of material handling systems in open pit mines, Simulation Modelling Practice and Theory (2018), doi: 10.1016/j.simpat.2018.06.008

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Highlights 

Uncertainty management in mining engineering

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Agent-based Petri net simulation for materials handling systems in open-pit mining operation Control of production rates, head grade and fuel consumption

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Appraising production targets through agent-based Petri net simulation of material handling systems in open pit mines Burak Ozdemir and Mustafa Kumral* Department of Mining and Materials Engineering, McGill University, Montreal, Canada

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*Corresponding Author: Mustafa Kumral, Department of Mining and Materials Engineering, McGill University, 3450 University Street, Montreal, Quebec H3A 0E8, Canada. e-mail: [email protected]

Abstract

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In a mining operation, significant differences between production targets in the planning stage and actual production quantities are a common issue. These differences can be related to heterogeneity of quality of ore within orebody, availability, and reliability of mining equipment,

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design-related problems of mining activities, and external factors. One way to understand the

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feasibility of targeted production rates is to simulate the activities. In this paper, an agentbased Petri net simulation model is proposed to check whether production targets are feasible,

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and the extent to control head grade in mineral processing. The model evaluates different realizations under the uncertain operation environment. Moreover, the fuel consumption of

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haul trucks is tracked in the proposed model. A case study was carried out to evaluate the

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proposed approach in an open pit mine. The research outcomes showed that this approach could assist in capacity installation, mineral processing design, and fuel tracking in mining operations.

Keywords: Petri nets; agent-based simulation; operator effect; capacity installation; grade control; fuel tracking

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1. Introduction In mining operations, technical uncertainty emerges due to the heterogenous distributions of ore quality within the mineral deposit. Therefore, control of ore grade fed into mineral

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processing is a difficult task, and may cause high liberation and concentration costs. If the head grade is out of the range imposed by the processing design, the recovery and throughput will also decrease [1]. The grade consistency in orebody can be, to some extent, managed through mine planning. Since mine plan is achieved by material handling system including loading,

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hauling and dumping cycles, the fulfillment of mine planning targets depends upon the performance of material handling.

Mine production plans should be carefully made and reviewed. In most cases, the primary

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objective of mine planning is to maximize the value of the final mining product considering sale price, variable costs and fixed costs for different alternatives [2]. The value of the final product

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can be maximized by controlling the quality and quantity of the mined material. A mine

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production plan can be made by using different optimization methods with a variety of commercial software. For example, production scheduling, mine block sequencing, and

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production rate determination problem for drilling, blasting and excavating operations can be

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optimized by using a mixed integer programming [3], linear programming [4] or combined dynamic programming and heuristics [5]. Most of the mine planning methods are based on deterministic models. As such, they are not robust, and cannot react to deviations from the plans due to uncertainties in the material handling. For example, the number of available equipment or cycle time of the trucks are

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considered constant in the planning. However, the number of available equipment may change during the operation due to the unexpected failures. Similarly, the cycle time of the trucks may vary depending on road condition, weather or operators’ driving competency. Because of these uncertainties, the conditions constantly change during the operation. This causes a deviation

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from the mine plan. Hence, the production targets cannot be achieved in actual operation. For example, the deterministic mine planning methods use constant cycle time for the trucks; however, the cycle time can vary during the operation due to the reasons mentioned above.

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Similarly, the number of equipment and loading time of the shovels are assumed as constant. The variations of these variables in actual operation accumulate and create deviation from the plan.

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The success of the mine plans, to a certain extent, depends on the performance of material handling systems as well as their reliability, availability and maintainability. The material

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handling systems may include the combination of various mining equipment such as trucks, shovels, in-pit crushing and conveying system. The compliance/matching of the equipment

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enhances the total performance of the system. It may fluctuate during the operation due to the

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uncertainties in the dynamic working environment such as loading time, cycle time of trucks, grade, payload, etc. These uncertainties cannot be eliminated from the system. However, their

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effects on the performance of the equipment may be foreseen by simulation techniques which provides a way to quantify qualitative and quantitative production risks. Simulations can be performed to quantify effects of the stochastic elements within a mining environment [6]. Since mining systems consist of operations (tasks or activities) which have a discrete sequence of time-ordered events such as loading, hauling, dumping, etc., it has a non4

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Markovian property where the events are dependent not only on the present state but also the previous states. Hence, the events in mining system can be modeled by dynamic discrete-event simulation (DES). DES is a method for modeling the behavior of a dynamic system to portray process performance opportunities. It has a broad application in finance, manufacturing and

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healthcare industries. DES assumes no changes in the system between consecutive events in a given period [7]. The simulation directly jumps in time from one event to the next. The technique helps to quantify the risks associated with uncertainties and unexpected events by

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creating multiple realizations. DES is also used as an experimental tool to support decomposition and modularity of complex adaptive systems [8]. More information about discrete-event simulation can be found at Jerry [9].

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In mining literature, DES was used to model for the complex internal traffic behavior of the haulage network to support real-time fleet management in the internal transport system in a

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surface mine and solve dispatching and routing problem [10]. Also, Blouin, Guay and Rudie [11] applied discrete-event theory to help decision-making process of truck dispatching in an oilsand

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excavation process. It was used to compare the current procedures and other applicable

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techniques to find the suitable solution for the problem. In another application, the methodology is combined with Program Evaluation Review Technique (PERT) to assist short-

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term mine planning and equipment allocation by evaluating different alternatives and optimizing the pre-production period in block cave mines [12]. Moreover, Torkamani and Askari-Nasab [13] developed a DES model to analyze the behavior of a stochastic materialshandling and haulage system in open-pit mines by considering the uncertainties associated with the truck-shovel operation. These uncertainties include the tonnage, loading time of the 5

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shovels, cycle time of the trucks, mean time between failures and mean time to repair. In addition, DES is used as a tool for maintenance analysis of mining equipment to analyze the effect of equipment failures on production [14]. To improve the accuracy of the results, agentbased simulation models are preferred. As an example, Jabri and Zayed [15] proposed an agent-

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based modeling and simulation method which consider the interaction of agents and environment for earthmoving operations. Since the model considers the static and dynamic attributes of the agents, it provides an accurate estimation of the duration of the activities.

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The previous research mainly addressed equipment allocation, mine traffic, production, cycle times and maintenance times. However, the other possible outcomes (e.g., ore grade and fuel consumption) are also important. This gap was filled in the research. In other words, the grades

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of ore to be produced for a given period were simulated as well as ore quantities. Total fuel consumption for a given period was also simulated. Furthermore, in the input parameters,

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driver habits affecting truck cycle time and reliability also quantified by using historical data. Combining all these contributions requires a powerful simulation modeling tool such as Petri

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nets which is a mathematical and graphical representation of a system. It is used to model

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material and/or information flow networks to detect any bottlenecks and inconsistencies in the system. Also, the efficiency and practicability of the system can be examined by this technique

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[16].

Petri net methodology is used in different industries such as manufacturing, management, communication, programming, transportation [17]. It also started to be used in the mining industry. Petri net simulation model was used to model material handling systems in surface coal mines and support equipment scheduling [18]. Also, Konyukh and Davidenko [19] modeled 6

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mine wide conveyor net and conveyor-locomotive transport for a longwall mine by using Petri nets. Coordination problem of a cutting and supporting, designing, and dispatching of combined transport systems are solved. Moreover, the profitability of the robotics-based

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mining system was evaluated by Petri net simulation model [20]. This paper proposes a novel agent-based Petri net framework to evaluate the performance of material handling systems in open pit mines. The proposed approach generates possible realizations by considering the human effect on the cycle time and reliability of haul trucks to

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estimate ore attributes, the quality and quantity of ore, the quantity of waste, and fuel consumption of the fleet for a given shift. The proposed model measures if the production targets (e.g., grade and quantity requirements of mineral processing plant) are attainable. The

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research outcomes assist to decide if short-term mine plans need revision; if fuel consumption of fleet in a shift is acceptable; and if there are bottlenecks in the mine system. In a sense, the

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proposed approach can be seen as a risk quantification tool for technical uncertainties. Multiple simulations generate probable realizations regarding production qualities and quantities, and

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consumed fuel quantity for a given period. When a distribution is fitted to these realizations,

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the distribution parameters or percentiles provide opportunity to assess risks. If the risk is not acceptable, mine management can consider (a) additional training programs for operators, (b)

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conducting road maintenance, (c) implementing more detailed equipment maintenance programs. Thus, cycle and loading times can be more consistent, and equipment reliabilities can increase. These actions assist to improve the productivity of operation.

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2. Methodology Petri nets consist of two kinds of nodes as places for conditions and transitions for events. Tokens exist in the places, and they move between places when the transitions are

*

number of places and m is the total number of transitions, places,

*

*

+ is a finite set of transitions, + is weight function and M0:

*

+. Let n is the total

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initiated/fired. The structure of Petri net is defined as

(

+ is a finite set of

) (

) is a set of arcs, W:

+ is the initial marking [21].

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To solve complex problems, Petri net has many variations such as colored, stochastic, timed, queuing, etc. Colored Petri net is the one of the widely used high-level Petri net which can model the dynamic behavior of a system and information flow [22]. This method enables

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tokens to transfer complex data information [23]. Since the tokens carry attributes of the objects, colored Petri net is preferred for systems including communication processes. When a

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time delay exists before firing a transition in the Petri net, it is named as timed Petri net [24]. If

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these times are randomly selected from a probability distribution, it is called as stochastic Petri net [25]. On the other hand, queuing Petri net is used to model the queuing networks [26]. In

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this paper, a high-level Petri net modeling technique is used by coupling colored, timed and

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stochastic Petri nets. 2.1. Mine model

A case study was conducted to an open pit iron ore mine in Canada which has three pits, three waste dumps, two in-pit crusher stations and one ex-pit crusher. The mine produces iron ore pellets and concentrate. The mining process includes drilling, blasting, loading, hauling and

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primary crushing activities. Material handling is achieved by the conventional truck-shovel method and in-pit crushing and conveying (IPCC) systems. The mining equipment including shovels, trucks, crushers, conveyors is modeled as the resource. There are six 250-tonne capacity trucks, twenty-three 350-tonne capacity trucks, five 27 m3 bucket capacity shovel and

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two 25 m3 bucket capacity shovel in the mine. Due to the dynamic work environment, the variables of the material handling system (such as loading time, hauling time, payload, etc.) are uncertain. In the model, a distribution was selected for each variable based on historical data

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instead of using a single deterministic variable.

The layout of the mine is illustrated in Figure 1. The ore extracted in the Pit 1 is hauled by trucks to Crusher 1 which is fixed primary crusher located near the secondary crusher. The ore in the

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Pit 2 and Pit 3 is hauled by haul trucks to Crusher Station 2 and Crusher Station 3, respectively. The ore is crushed by the fixed in-pit crushers in these stations and transported to the

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secondary crusher by conveyor belts. The Crusher 1 and in-pit crushers reduce the material size from about 1.2 m to 35 cm and conveyed to secondary crusher. The mine is modeled until the

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secondary crushing. Since the simulation results are recorded before the material is carried by

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conveyor belts, the operation of conveyor belts does not have an impact on the simulation results. However, the stoppage of the conveyor belt causes the stoppage of the production.

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Moreover, there are three waste dumps in the mine. The waste material extracted in all pits is carried by haul trucks to these waste dumps depending on waste characteristics, the availability of dumping spots in the dumps and distance from the waste shovel.

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Figure 1: Layout of the mine

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2.2. Petri net framework of loading and hauling operation The Petri net framework of the loading and hauling cycle in the open pit mine is represented in

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Figure 2. P1 is the place which contains required fuel to operate haul trucks. Tokens in P1 represent the fuel. P2 is a material place which has tokens representing the quantity of ore or waste material while the tokens in P5 represent the haul trucks. T1 is the transition for loading cycle. Since material, fuel, truck, and shovel are necessary for loading, the required number of tokens should be available in places P1, P2 and P5 to fire transition T1. The time spent on the 10

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transition T1 is different each time with respect to Petri net model which makes the model be stochastic [27]. The details of T1 will be described later. When T1 is fired, some tokens will be removed from P1 and P2, and some tokens will be added to P3 where haul truck is loaded and ready for hauling. The number of removed tokens in P 2 and added to P3 are randomly

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generated from a probability distribution fitted to the previous observations in certain limits. The number of tokens removed from P1 depends on the conditions and the virtual age of haul truck. If the virtual age of the truck is high, it consumes more fuel. T 2 includes the hauling and

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dumping process. At the end of the cycle, the material in the truck transferred to P4 which is the final place for the ore material. On the other hand, the token appeared in P 5 after firing transition T2 represents haul truck which travels back to shovel to haul the remaining of the material. The same flowchart is used for the haulage of waste material. In that case, P 4

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represents the waste dump instead of crusher as final place.

Figure 2: Petri net framework of loading and hauling operation to the crusher

The weight of the arc from place place

is denoted as

to transition

is denoted as

and from transition

to

. If there is no arc between transition and place, the weight of arc is

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zero. To fire a transition, each of the input places must have enough tokens. The matrix representation of the Petri net framework is given as follows.

[ ,

Given initial marking

]

- which represents places having tokens in, the

̅)

[ ]

[ ] ,

([

]

)

(2) [

]

- is the firing vector which initiates T1 and T2. In the final state, some tokens

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where ̅

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final marking M can be obtained as follows.

(

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(1)

in the P1 and P2 are removed at the end of the transitions while some tokens are added to P 4.

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The tokens which represent trucks moves back to P 5. However, since the maintenance activity

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of the trucks is considered in T2, the time needed for T2 varies depending on the maintenance requirement of the trucks.

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The transitions are modeled through dynamic discrete-event systems. The detailed model of T1

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is given in Figure 3. Truck comes to shovel station and waits in the queue if there is any. After truck approaches to the shovel by maneuvering, shovel loads the truck. A random number is generated from the probability distribution fitted to historical data for the spot time and loading time. In doing so, the uncertainties in the time of these operations are incorporated in the model. The loading time of the shovels has an impact on the truck queues and the cycle

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time of the trucks. Hence, it affects the simulation results related to the queue times. Also, material attributes such as grade, tonnage, destination are assigned. During the operation, the material amount hauled in each cycle varies depending on material and specifications seasonal effects. The looseness and particle size of the material, and weather conditions affect the

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bucket fill factor of the trucks. Moreover, some of the material stick on the bucket of the trucks in humid areas which is called as carry-back problem. This decreases the bucket capacity. The material amount hauled in each cycle is decided based on a probability distribution fitted to the

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historical data. Randomly generated tonnages consider both the fill factor and the carry-backs. Once material attributes are assigned, the truck departs for its destination which can be one of the ex-pit crusher, in-pit crushers or waste dumps depending on its specifications and

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destination availability.

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Figure 3: The discrete-event system model of loading

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The detailed discrete-event system model of T2 which represent dumping hauled material to

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the crusher is given in Figure 4. Truck comes to the crusher and seizes a dumping spot. It approaches to the hopper by maneuvering and dumps its load into the hopper. The dumping

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and maneuvering times are generated from a probability distribution formed based on the historical time data. If the crusher is not working when the truck arrives at the crusher station, the truck dumps its load to crusher stockpile. The quality and quantity attributes of the material are recorded at this point. Once the dumping cycle is completed, the dumping spot is released. If it is the end of the shift, the truck moves to pit stop for shift change. If not, it comes to 14

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another decision block which decides whether truck needs maintenance. This decision is made based on the reliability model. Reliability of trucks drops in time; however, its magnitude changes depending on the truck’s condition and operator. These factors are considered in the model. More details about the reliability calculations and factors affecting reliability can be

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found at [28]. If the reliability of the truck decreases below the minimum allowable reliability which is 40% in this operation, it means that truck needs maintenance, and it is directed to truck shop. Otherwise, it is dispatched to a shovel to complete another cycle. The travel time is

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condition, traffic, operator factor, etc.

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generated from a fitted distribution to consider the uncertainty in cycle time caused by road

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Figure 4: The discrete-event system model of dumping cycle to Crusher 1

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2.3. Petri net framework of the material haulage from stations to the crusher The ore comes to the station is first crushed by the in-pit crusher and hauled by conveyors to the mineral processing plant. The Petri net framework of the material hauling from stations to the processing plant is given in Figure 5. P4 is the station and tokens in P4 represent the ore

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material in the crusher's hopper. The material flows to the crusher and is broken in T3. The crusher is modeled as resource in P8. The tokens must be available in P4 and P8 to start T3. After T3 is fired, the tokens are removed from P4 and P8, and the tokens are added to P6 which means

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that ore is being crushed. When the material is crushed, T4 is initiated, and the material is passed through to the conveyor belt. After completion of T4, the material tokens are transferred to P7 which represent the secondary crusher. The crusher token moves back to its

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repeated during the operation.

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initial place (P8) which indicates the crusher is available. This Petri net material flow scheme is

Figure 5: Petri net framework of the material hauling from stations to secondary crusher

The matrix representation of the Petri net framework of the material movement from stations to the processing plant is given as follows.

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[

,

- which represents places having tokens in, the final

marking M can be obtained as follows.

where ̅

,

̅)

[

]

([

]

[ ])

[ ]

(4)

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(

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Given initial marking

(3)

]

- is the firing vector which initiates T3 and T4. In the final state, the tokens in

the P4 is removed in the final stage while tokens are added to P 7. Since the crusher is available

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after the material is crushed, the tokens appear in P8.

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The detailed discrete-event system model of T3 and T4 is illustrated in Figure 6. When a truck

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arrives at the in-pit crusher station, the truck seizes a dumping spot and approaches to the hopper of the in-pit crusher by maneuvering. Before the trucks dump the material into the

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hopper of the crusher, the material attributes (such as the amount and quality of the ore) are recorded. These material attributes are used in the calculation of total tonnage and average

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grade of a destination. Then, maneuvering and dumping times are generated from a probability distribution formed by historical events. Once dumping process is completed, the truck goes to its next destination depending on the current time and its reliability. The material is crushed and conveyed to the mineral processing plant. This cycle is continuously repeated during the mining operation. 18

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Figure 6: The discrete-event system model of material movement from stations to the corresponding secondary crusher

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The simulation framework is applied to verify the feasibility of mine plan and production targets for a given period. In the model, uncertain variables were defined as distributions based on historical field data. Since the mining activities are dynamic, these distributions should be updated during the operation. For example, a distribution is selected for the cycle time of the

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trucks. As the time goes, the distribution parameters change by the effect of weather or road conditions. Furthermore, the model is specific to a mine site. Since the mine characteristics are different in each operation, the model should be updated before it is applied to another site.

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2.4. Fuel Consumption

The factors affecting fuel consumption of haul trucks are truck payload, empty travel time, empty idle time, loading time, loaded travel time, loaded idle time [29]. Moreover, seasonal

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weather variations affect the fuel consumption [30]. The haul trucks consume more fuel in winter season than the rest of the year. Furthermore, the mechanical condition of the

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equipment has a substantial impact on fuel consumption. This mechanical condition can be

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quantified as virtual age [31]. 2.4.1. Virtual Age

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Virtual age is related to the utilization of the equipment and the quality of the previous

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maintenance activity. Similar to the real age of the equipment, it is a function of time. The equipment deteriorates as its age increases and the fuel consumption of the equipment increases as the equipment deteriorates. Since the utilizations and the maintenance quality of each equipment is different, virtual age is used instead of real age as an indicator of the condition of the equipment. Since the fuel consumption and virtual age of the truck have a positive correlation, lower virtual age is preferable. 20

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Assuming t1, t2, …, tn are the time between the consecutive failures and x1, x2, …, xn are the duration of the corresponding repairs, the virtual age after the nth repair is calculated by the following equation [32]. )

(5)

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(

where q is the action effectiveness (1 – RF), vn-1 is the virtual age before the nth repair and

is

the time of nth repair. RF is restoration factor which indicates the quality of the maintenance activity [33]. It will be between 0 and 1 for the mining equipment depending on how the repair

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affects the equipment’s degradation. If RF = 0, there is no recovery on the system and the system is in as bad as old after the repair. On the other hand, RF = 1 indicates the perfect repair on the system and the system is recovered to as good as new condition after the repair.

(

)

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( |

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The cumulative distribution function (cdf) of the nth failure is obtained by Eq. 6 [34]. ) (

,

( )

)

-

,

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,

(

(6)

) -

-

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where λ and β are shape and scale factor, respectively. Then, the conditional probability

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distribution function (pdf) is given in Eq. 7 [35]. ( |

) (

( |

) )

,

,(

)

--

(7)

where ti > ti-1. When there is a reasonably enough data available, the shape, scale and virtual age parameters are estimated by Maximum Likelihood Estimation (MLE) method as shown in Eq. 8 [36]. 21

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(

)

)

[(

∑[(

)

] ]

(

)∑

(

)

(8)

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where T is the stop time of the observation. Since there is no closed form mathematical solution for this equation, Gauss-Newton method [37] is used to solve the equation and estimate the parameters. The derivatives of the log-likelihood function (Eq. 8) should be zero for the optimal results. The results are checked in each iteration to determine whether the

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current step reduces the log-likelihood function. If it does not reduce, the search is repeated until it reaches an acceptable solution. More information about virtual age can be found at Mettas and Zhao [35] and Finkelstein [38].

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2.4.2. Regression Analysis

Once the virtual age of each truck is calculated, the fuel consumption is predicted by Least

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Square Regression (LSR) model. The method reveals the relationship between the dependent

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variable and independent variables. The general regression formula is given in Eq. 9 [39]. (9)

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where Y is the dependent variable, X is the independent variable, β is the coefficient of each is the error. In the simulation framework, fuel consumption is the

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independent variable and

dependent variable while season, truck payload, empty travel time, empty idle time, loading time, loaded travel time, loaded idle time and virtual age are the independent variables. Rsquare value is used to determine how well the regression equation fit to the actual data. If the error term ( ) is zero, it indicates that the regression model explains all the variability in the

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data. The regression formula is used in the simulation framework to decide the number of tokens removed from the place P1.

3. Results and Discussion

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Dynamic images of materials handling systems are created in simulation model such that system bottlenecks are identified, and the associated risks are assessed. First of all, the activities used in the model were selected as loading trucks, transporting materials to ore crusher or waste destinations, disposing material to the destination and maneuvering, and

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returning the assigned loader. The details of the haulage system are provided in Figure 1. For each activity, a probability distribution is fitted based on historical information. The samples are drawn from these distributions. Depending on random generations, production quantities and

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qualities, and fuel consumption is computed. In addition to this, effect of driver habit on truck

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performance is quantified such that more realistic distribution for truck cycle time is fitted. The Petri net framework of the agent-based material handling system was modeled in Arena©

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[40] simulation software. The operator effect on truck and shovel performance was quantified

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for the distributions fitted to cycle times and equipment reliability. The operators are created as an entity. The operator attributes are assigned as a coefficient to each haul truck operator

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working in the mine. Since the performance of each operator is different, the travel time and the reliability drop vary in each cycle and operator. The scores are calculated based on a machine learning technique proposed by Ozdemir and Kumral [41]. In this research, the operator scores are generated randomly from the probability distribution.

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The proposed model was validated by conducting a case study on a Canadian iron ore operation. To protect the confidential information of the company, the other parameters such as activity times, the reliability of the equipment, fuel consumption, production plan and actual production used in the simulation model are scaled based on the actual data. The results

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showed that actual productions and simulation outcomes comply each other. At the beginning of the simulation, the created operator entities seize corresponding to equipment and utilize them until the end of the shift. At the end of the shift, the operator entities release their

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equipment to allow operator entities in the next shift seize it. This cycle is repeated until the end of the simulation. During this period, the attributes and variables are recorded. Once the model is completed as described, the simulation framework was executed for a certain week of the operation. The simulation results were compared with the plan and actual production. If

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the number of simulations increase, the compliance of simulations with actual production can

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further be improved. The selected distributions and their parameters are also significant on the

accuracy.

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performance of simulation. The improvement on these aspects has extra potential to increase

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3.1. Estimation of the Amount of the Hauled Material The simulation model considers weekly production such that realizations of production

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quantities, ore grades, and fuel consumptions are yielded. Each simulation takes a few seconds. To assess the risks associated with the uncertainties, 100 equally probable realizations were generated. Effects of uncertainties on production rates are investigated. As a result of these simulations, the histograms of the hauled material amounts to each destination in the specified period are shown in Figure 7. 24

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Figure 7: The histograms of the hauled material amounts to each destination

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The details of the histogram result on a daily basis for each destination are given in Table 1. The

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amount of the hauled material to Crusher 1 will be between 25.4 k tonnes and 88.5 k tonnes with an average of 61.9 k tonnes on Day 1. Similarly, the amounts hauled material in Day 1 to

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Station 2 and Station 3 are expected in a range of 5.0-18.0 k tonnes and 8.3-41.0 k tonnes, respectively. Furthermore, 49.7 k tonnes waste material is expected to be hauled in Day 1. The

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results for the other days can be found in the table. In some days, the estimated output range is wide due to the selected distribution for uncertain events such as the equipment failures and changing road conditions, etc. The reason for minimum output might be the failure of some of the equipment or longer cycle time of the haul trucks because of the road conditions in one realization. On the other hand, the roads might be stable, and there might be no equipment 25

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failure in another realization. In this case, the estimated output will be high. If the standard deviations of the selected distributions of the mining events are smaller, the estimated output range will be smaller.

Minimum (k tonnes)

Maximum (k tonnes)

Average (k tonnes)

1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7

25.4 43.3 13.8 32.6 10.7 27.4 11.3 5.0 8.6 6.9 5.8 5.4 6.3 6.9 8.3 18.7 17.1 18.5 15.1 17.8 17.7 26.7 24.4 21.5 26.9 23.7 7.5 5.6

88.5 89.1 67.7 83.3 69.1 79.7 66.1 18.0 28.8 22.0 21.3 23.8 22.0 21.5 41.0 42.5 38.7 42.8 44.3 44.2 42.9 65.3 57.1 64.1 66.3 51.9 33.7 31.8

61.9 64.8 40.1 53.7 35.5 52.6 37.3 12.9 16.2 13.7 13.9 13.9 14.5 14.3 26.9 29.3 28.1 29.3 29.3 31.0 30.2 49.7 43.1 42.5 47.1 38.5 20.4 20.1

Crusher 1

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Station 3

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Station 2

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Waste Dumps

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Day

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Destination

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Table 1: The details of the material movement to each destination

Since the mine model was developed based on actual field data, the comparison among planned, estimated and actual production becomes meaningful. Figure 8 shows a benchmark of the production amounts of planned, proposed framework and actual in the week of the 26

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operation. Since the proposed method considers the uncertainties in the operation, it can quantify probable deviations from the plan. Also, by comparing actual production with the simulation results, the performance of simulation is benchmarked. For example, the material movement to Crusher 1 was planned as 383 k tonnes for the week in the mine plan. However,

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this planned production could not be achieved in the operation due to the unexpected events during the operation. The planned amount was 12.3% higher than the actual material movement. On the other hand, since the framework estimates the uncertainties, the proposed

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framework estimates the material movement to Crusher 1 as 346 k tonnes which is 1.5% higher than the actual production. As seen from Figure 8, the estimation of the material amount

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hauled to other destinations was also closer to the actual production.

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Figure 8: Benchmarking of planned, proposed framework and the actual production amounts

3.2. Estimation of the Grade of the Hauled Material

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The grade distribution histograms of the material hauled to Crusher 1 is shown in Figure 9 on

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daily basis. Since iron and aluminum oxide percentages are important in the mineral processing of iron, they are analyzed in the model. However, other quality measurements (such as water content, rock characteristics, SiO2 or CaCO3 content, etc.) can be added to analysis depending on the mine specifications. The daily variations in the grade are noticed in the figures. Moreover, the histograms for other ore destinations are also obtained from the model.

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Figure 9: Daily grade distribution histograms of the material hauled to Crusher 1

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The details of the simulation results regarding the ore quality hauled to Crusher 1 is given in

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Table 2. From the table, the iron grade in Day 1 is between 36.47% and 55.64% with the average of 46.58% while the aluminum oxide grade in Day 1 is in a range from 0.17% to 0.27%

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with an average of 0.23%. The quality values of the other days can be found in the table.

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Table 2: The details of the quality of the material hauled to Crusher 1

1 2 3 4 5 6 7

Fe Grade (%) Min Max Avg. 36.47 55.64 46.58 42.48 59.91 49.71 39.69 65.70 56.63 52.05 68.07 60.88 47.13 69.35 61.44 47.08 65.20 57.46 45.14 67.45 54.83

Al2O3 Grade (%) Min Max Avg. 0.17 0.27 0.23 0.17 0.28 0.24 0.17 0.27 0.23 0.17 0.29 0.24 0.17 0.28 0.23 0.10 0.25 0.17 0.19 0.29 0.25

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Day

Figure 10 represent a comparison among grades obtained from the simulation, planned grades

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and actual grades in Crusher 1. As seen from this figure, the simulation results are fairly close to actual grades for both iron and aluminum oxide. The grade information can be used in stockpile management and mineral processing control. Similar observations were made for the other

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destinations. Therefore, it is concluded that the simulation results are compatible with the

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actual production rates.

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Figure 10: Benchmarking of simulation results and the actual ore grades

3.3. Bottlenecks of the operation

In addition to material quality and quantity estimations, the proposed framework provides information about the equipment utilization. Table 3 denotes the utilization of the equipment during the operation. The bottlenecks of the operation can be revealed by this information. For 31

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example, the utilization of Shovel 2, Shovel 4, Truck 4, Truck 6, Truck 12 and Truck 13 is low in the simulation results. Since the opportunity cost of mining equipment is high, the reasons behind this should be investigated, and their utilization should be maximized. Furthermore, the

is 0% because it is in maintenance during that week.

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Utilization 0% 52% 78% 43% 70% 83% 87% 81% 75% 80% 55% 77% 50% 79% 71% 82% 76% 83%

Equipment Truck 12 Truck 13 Truck 14 Truck 15 Truck 16 Truck 17 Truck 18 Truck 19 Truck 20 Truck 21 Truck 22 Truck 23 Truck 24 Truck 25 Truck 26 Truck 27 Truck 28 Truck 29

Utilization 48% 37% 87% 76% 77% 80% 82% 76% 78% 88% 93% 75% 69% 74% 74% 76% 71% 92%

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Equipment Shovel 1 Shovel 2 Shovel 3 Shovel 4 Shovel 5 Shovel 6 Shovel 7 Truck 1 Truck 2 Truck 3 Truck 4 Truck 5 Truck 6 Truck 7 Truck 8 Truck 9 Truck 10 Truck 11

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Table 3: Equipment utilization

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maintenance schedule of the equipment is considered in the model. The utilization of Shovel 1

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Truck queues are observed due to the discrete-events in the mining system such as loading, hauling, dumping and empty traveling, etc. Waiting times of the trucks in these queues were also analyzed to determine the bottlenecks of the operation. They are treated probabilistically; hence, the uncertainties in the mining operation are included in the model while calculating bottlenecks. Moreover, the cycle time and reliability of the equipment are affected by the habit of the haul truck operators. The human effect on the cycle time and reliability of the equipment 32

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was incorporated into the model by using historical data regarding drivers. Considering operator attributes (such as competency and driving habits) in the model improves the accuracy of the results.

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Average queueing times for the trucks on each queue were also obtained from the proposed framework. As seen from Table 4, the maximum queueing times for the trucks were observed for Shovel 6 and Shovel 7. Therefore, they are the bottlenecks of the operation and their performances should be analyzed in detail. To increase the efficiency of the system, these

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queueing times should be minimized. If the trucks spend too much time in the queue, some of the trucks may be parked to reduce the queueing times. Table 4: Average waiting time in the queue

Average Queueing Time (minutes) 4.2 6.1 5.8 3.6 7.8 8.2 5.4 2.8 3.6

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Shovel 1 Shovel 2 Shovel 3 Shovel 4 Shovel 5 Shovel 6 Shovel 7 Crusher 1 Station 2 Station 3

3.4. Estimation of Virtual Age and Fuel Consumption

The action effectiveness of each truck is obtained by Reliasoft © [42] software by using the historical reliability data of each truck. Then, the virtual age of the haul trucks is calculated. The results are given in Table 5. The action effectiveness value and virtual age values are low. This 33

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indicates that the quality of the repair is sufficient. These values should be updated after each repair. Table 5: Restoration factor and virtual age of the haul trucks

PT CE AC

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Virtual Age (hr) 3,860 3,903 2,088 2,699 978 1,481 15,787 18,697 10,684 9,974 14,223 11,715 11,732 3,040 3,286 1,760 13,245 8,113 10,721 12,784 7,787 8,040 697 11,932 11,154 9,797 9,991 9,147 5,412

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Action Effectiveness, q 0.1101 0.1113 0.0596 0.0770 0.0108 0.0422 0.4504 0.5334 0.3047 0.2846 0.4057 0.3342 0.3347 0.0867 0.0938 0.0050 0.3778 0.2313 0.3058 0.3646 0.2222 0.2294 0.0265 0.4537 0.4240 0.3725 0.3799 0.5214 0.3088

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

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Actual haul truck data is analyzed by linear regression technique to estimate fuel consumption per each cycle. The field data was retrieved from dispatching system of the mine and includes

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fuel consumption rate, time, payload, empty travel time, empty idle time, loading time, loaded travel time and loaded idle time. In addition to these variables, virtual age is calculated as it was mentioned above. The details of the dependent and independent variables are given in Table 6. The findings are consistent with the previous literature [29]. Furthermore, fuel consumption

operation.

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rate and virtual age of the haul trucks should be updated after each condition change in the

Table 6: The details of the dependent and independent variables

12.171

Standard Deviation

Coefficient of Variation

22.754

17.205

1.763

0.102

349.960 16.995 7.996 4.000 21.991 5.000

302.312 11.379 5.300 2.835 15.051 2.982

20.495 3.151 1.290 0.553 3.490 1.084

0.068 0.277 0.243 0.195 0.232 0.363

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228.025 5.002 3.000 1.502 8.000 1.000

Mean

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Dependent Variable Fuel Consumption (l/cycle) Independent Variables Payload (tonne) Empty Travel Time (min) Empty Idle Time (min) Loading Time (min) Loaded Travel Time (min) Loaded Idle Time (min)

Maximum

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Minimum

Variables

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Fuel consumption formula is found as given in Eq. 10 by regression where the R-square value of

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the fit is 90.7%. The unexplained part of the equation could be caused by factors such as human factor, road conditions, engine load, etc. )

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(

(10)

where FC is fuel consumption, PL is payload (tonne), ETT is empty travel time (min), EIT is empty idle time (min), LT is loading time (min), LTT is loaded travel time (min), LIT is loaded idle time 35

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(min), and VA is the virtual age of the truck (hr). W is the binary variable which represents the winter season. If the current season is winter, W=1. Otherwise, W=0. The coefficient values also show that the truck consumes more fuel when it is loaded. This fuel consumption equation is

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also dynamic which should be updated during the operation to obtain accurate results. The total fuel consumption of each truck during the week is calculated by the values produced in the simulation. The results of simulation and actual fuel consumption are given in Table 7. The difference between the estimated and the actual fuel consumption for all the trucks in the

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week of operation is 4,963 liters. Given that the fuel tank capacity of the trucks is 4,542 liters, the difference is not significant. Actual fuel consumption depends on the working hours of the trucks. Besides, the utilization of the truck in the given period affects the fuel consumption. If

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than the others as expected.

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the utilization of a truck is low because of maintenance activity, its fuel consumption will be less

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Table 7: Benchmarking of estimated and actual fuel consumption of haul trucks

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Actual Fuel Consumption (l) 8,421 8,717 12,112 5,008 5,272 6,507 15,185 12,292 15,941 11,338 5,134 7,125 4,952 8,519 6,909 8,767 13,158 15,984 12,670 15,828 11,898 8,600 14,212 14,841 10,548 13,353 11,788 8,873 13,318 307,270

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Total

Estimated Total Fuel Consumption (l) 9,247 10,927 10,125 6,319 4,742 6,761 12,328 12,596 13,304 12,751 5,426 7,214 6,891 10,152 6,623 11,458 11,908 13,235 12,425 13,326 13,132 11,116 13,129 12,442 9,659 14,494 12,979 6,602 10,996 302,307

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4. Conclusion In this paper, an agent-based Petri net framework is demonstrated for dynamic discrete-event systems in open pit mines to evaluate the performance of material handling system and the

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feasibility of the mine plan by considering the uncertainties in the mining operation. The original contribution of this paper rests on incorporating grade and fuel track into the simulation model. As shown in the case study, deviation from grade targets and fuel consumption associated with equipment unreliability can be detected from simulation results.

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Furthermore, the effect of truck operators on vehicle was quantified by tracking reliability drops for a given period. Given that the success of simulation depends on fitting distributions, the quantification of operator habit will enhance the quality of the simulation.

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The agent-based model provides a range of probable realizations regarding some outcomes (i.e., ore- waste quantities, ore grade and fuel consumption) in such a way as to assess risks in a

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given period. The success of such a simulation is highly dependent on the correctness of fitting

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distribution to uncertain duration events of material handling system. In this scope, driving habits of the operators are incorporated into the simulation procedure. Overall, the proposed,

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the framework helps engineers to have a better understanding of materials handling system in

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an open pit mining operation. Hence, production targets are controlled. The framework also provides useful information about the feasibility of the plan by evaluating different realizations. In realizations, the production is calculated based on the number of available equipment during the specified time and the number of available equipment is estimated based on historical reliability data. The utilizations of the equipment and queueing times are considered as indicators of the system efficiency and the maintenance schedule of the mining equipment can 38

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be arranged in the light of this information. For example, if queueing time for trucks are high, some of the trucks can be parked or sent to the maintenance. This decreases the equipment waiting times and increases the efficiency of the material handling system.

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Moreover, the model helps to define the bottlenecks of the operation. The system performance can be furthered significantly by improving these bottlenecks. Additionally, the factors affecting fuel consumption were investigated. A dynamic fuel consumption equation was obtained to calculate the required amount of fuel for the haul trucks for a certain period. The effect of

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equipment's virtual age and the season were incorporated into the equation. When this equation was used in the model, it gives an estimate of the total fuel consumption during the operation. This helps companies to manage their fuel reserves.

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The proposed approach can be applied to construction and earthmoving operations as well as other surface or underground mining operations extracting different minerals. The simulation

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time can also be lengthen as needed. The model will be extended to the simulation of mineral

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processing operations in the future in such a way as to help mine – mill reconciliation.

5. Acknowledgments

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This work is supported by Natural Sciences and Engineering Research Council of Canada (NSERC) and Iron Ore Company of Canada (IOC) for funding this research (ID: NSERC CRDPJ 500016 - 16).

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