A simulation-based risk management approach to locating facilities in open-pit mines under price and grade uncertainties

Accepted Manuscript

A simulation-based risk management approach to locating facilities in open-pit mines under price and grade uncertainties Morteza Paricheh , Morteza Osanloo PII: DOI: Reference:

S1569-190X(18)30142-4 https://doi.org/10.1016/j.simpat.2018.09.015 SIMPAT 1862

To appear in:

Simulation Modelling Practice and Theory

Received date: Revised date: Accepted date:

22 July 2018 22 September 2018 25 September 2018

Please cite this article as: Morteza Paricheh , Morteza Osanloo , A simulation-based risk management approach to locating facilities in open-pit mines under price and grade uncertainties, Simulation Modelling Practice and Theory (2018), doi: https://doi.org/10.1016/j.simpat.2018.09.015

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ACCEPTED MANUSCRIPT Highlights: Managing the risk of facility location in open pit mines by using simulation Considering price and grade uncertainties as the main hazardous elements Using the concept of probable pits to define the conceivable situations Probable pit advances are completely independent

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A simulation-based risk management approach to locating facilities in open-pit mines under price and grade uncertainties *

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Morteza Paricheh, Morteza Osanloo Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran

ABSTRACT

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Facility location is one main decision has to be taken at the primary stages of open pit mine design. The location mainly depends on ultimate pit limits and haulage costs. Undesired technical and economic conditions, such as rising fuel, tire and labor costs in line with extracting the ore from the deeper ground by open pit mining have forced mine designers more than ever to minimize the truck haulage distances by bringing the facilities closer to the pit. The ultimate pit limit is highly subject to the commodity market and geological uncertainties. An overestimation of the pit limit increases the haulage costs, while pit limit underestimation will impose relocation/rehandling cost or leaving tied up ore. Hence, this requires a risk management approach to evaluate different facility locations. In this paper, a generic quantitative simulation-based approach was developed to manage the risk associated with the facility locations in open-pit mining because of price and grade uncertainties. The methodology was described by using a hypothetical 2D geological block model. The concept of probable pits was used to calculate the probabilities of conceivable situations that exist. These probable pits define which part of the ground might be inside the pit limit with a specific probability of occurrence. To validate the methodology, it was applied in a real case study in Iran to evaluate the location of the existing primary crusher. The results showed that the existing crusher location involves the highest risk level. It must be placed about 300 m closer to the planned pit in order to mitigate the risk about 10 times. The robustness of the results was also shown using a sensitivity analysis in the presence of 20% increase or decrease in the parameters truck haulage and crusher relocation costs. The simulation-based approach provided here also would be a helpful tool to plan a more reliable pit limit at the outset of the project given to risk-taking or risk aversion of the mine designers.

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Keywords: simulation, facility location, risk management, open-pit mine, probable pits, price uncertainty, grade uncertainty

1. INTRODUCTION

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Facility location/equipment site selection is increasingly recognized to play a significant role in mine design, particularly in open-pit mines, where ultimate pit limit has a vital effect on the location of the facilities/equipment. The solution of the final pit limit problem is usually used to justify the point where the mining operation can progress economically and it is also a guide for the mine planners to locate the mine facilities. Since material handling cost is the largest single component (i.e., almost half) of the mining cost [1, 2], a well-designed location of the facilities plays a very important and critical role, affecting the expense of the total operation. Therefore, in addition to having a logical relationship, the facilities must be located as near as possible to the pit limit in order to minimize the transportation costs. This is the most popular strategy of the mine designers to be able to locate the facilities close to the pit. The Aitik copper mine (Sweden's largest open-pit copper mine) with a depth of 450 m is a 2

ACCEPTED MANUSCRIPT good example to illustrate this statement. The mine produces about 36 Mt of ore with a head grade of 0.22 % copper, annually [3]. Figure 1 shows an aerial photo of the mine and its industrial site placed in the pit rim. As it is shown in the figure, the mine site facilities have been placed exactly in the eastern rim of the pit.

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Corresponding author. E-mail address: [email protected] (M. Osanloo).

Figure 1. An aerial photo of the Aitik copper mine and its industrial site location (Photo by Lars deWall, 2013)

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Locating the facilities is usually done based on a predefined pit limit. This pit limit is strictly pursuing the commodity market and geological conditions. Hence, this embeds an uncertainty into the facility location problem. This is the need that this paper aims to address. Figure 2 shows both cross-sectional and plan views of an open pit with probable future expansions and multiple candidates of primary crusher location at the rim of each probable expansion. The question is: which location is the best for the entire life of the mine when considering price and grade uncertainties? An overestimation of the pit limit increases the haulage costs, whereas pit limit underestimation will impose relocation/rehandling cost or leaving tied up ore. The facilities would be placed far away from the gravity center of the pit when the pit is overestimated. Then, the haulage cost is increased when the pit limit is shortened during the period of falling commodity price. Inversely, if the pit limit is undersized, the facilities would be placed inside the regions where will be extracted in the period of the price increase. In this case, the facilities must be relocated or the mine owner should sacrifice the underneath ore materials. Therefore, there is a need for a risk management to evaluate different locations. The main question is that how close the facilities could be located to the open pit limit under uncertain conditions. The risk is the chance of price and grade fluctuations that will cause negative effects on overall costs in terms of facility relocation costs, material rehandling costs, and opportunity costs because of sacrificing the ore materials as well as increasing the haulage costs.

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Candidate primary crusher locations

Probable pit 3 Probable pit 2

Plant location

Probable pit 1

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Conveyor line

Figure 2. Schematic cross-sectional and plan views of an open pit and its probable future expansions as well as candidate primary crusher locations

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Literature review shows that the risk management in facility location problem has been, to some extent, well researched. The risk management has been investigated by using mathematical programming techniques in hazardous material transportation and location problems [4], facility location in disaster management [5], facility location problems under uncertainty [6] and combined supply chain management and facility location problems under uncertainty [7-9]. In some cases, the risk associated with facilities locations has been studied by multi-attribute decision-making models [10]. As shown, the risk management in facility location problems has been usually under the considerations in risky environments, critical situations and uncertain conditions.

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In the field of mining, the focus on primary crusher location problem has been more conducted on in-pit crushers [11-18] and the other studies related to mine’s facilities positioning dominantly belong to the processing plant, tailing dam and waste dump [19-28]. Despite the fact that mining operations are fraught with risk, uncertainties and vagueness, the risk associated with the mine’s facilities locations has never been managed. Considering these, there is a particular need for a sound approach to managing the risk of facility location. Risk analysis may be undertaken to various degrees of refinement depending upon the risk information and data available. The analysis may be qualitative, semi-quantitative or quantitative or a combination of these, depending on the circumstances [29]. This paper provides a new quantitative simulation-based risk management approach to determine the facility location because of the commodity price and grade uncertainties. The concept of probable pits was used for calculating the probabilities; also, facility’s relocation cost, material rehandling cost, sacrificing the locked ore and truck haulage cost increase are considered as the main consequences. Primary crusher, processing plant, and waste dump were counted as the main mine site’s facilities for which decision making related to their location has a strategic nature. In this study, the primary crusher as a representative of the other facilities is chosen to clarify the methodology. The term primary crusher refers to the in-ground crushers or rim-mounted first crushers that are located external to the pit at one place for the entire life of the mine and are not intended to relocate. In the next sections, firstly, the framework for the proposed method is explained by using a 2D block model step by step, then, the approach is applied in a real copper mine in Iran to evaluate the primary crusher location. 4

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2. PROPOSED RISK MANAGEMENT METHODOLOGY Risk is often expressed as the effect of uncertainty on the objectives. The effect is any deviation from the expected either positively or negatively. In other words, Risk Level (RL) is defined in terms of a combination of the Consequences (C) of an event and the associated Probabilities (P) of occurrence (Equation 1) [30, 31]. RL  P  C

(1)

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In this research, risk is the chance of price and grade fluctuations that will have negative effects on mine profitability. These negative effects are: increasing the haulage cost, facility relocation, material rehandling or sacrificing the tied up ore. Risk management is the coordinated activities to direct and control the risk. The main reason for conducting a risk management is to support decision-making; so that the system has the lowest vulnerability against the future unexpected events [29]. The risk management procedure proposed in this paper consists of five steps: (i) establishing the goal, (ii) risk identification, (iii) risk analysis, (iv) risk evaluation and (v) risk treatment associated with the facility location at the edge of open-pit mines. The main individual components of the proposed simulation-based risk management process are depicted in Figure 3. Suppose a geological block model of a copper deposit containing 210 blocks is given as in Figure 4. Block dimensions are assumed as 12.5 m 25 m in height and width, respectively. The perpendicular to the plane expansion of the model is assumed as 25 m. The rock density for both waste and ore materials is assumed to be equal to 2.43 tonnes per cubic meter. Besides, values of expected grade and estimation variance of the blocks have been known by using the available estimation techniques.

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Establishing the goal

Risk assessment

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Monitoring and review

Risk Identification What can happen? Sources of risks Price and grade uncertainties

Risk analysis Determine likelihood Determine consequence Estimate risk level Bow-tie diagram

Risk evaluation Determine critical risks Define treatment priorities Probable pits

Risk treatment Choosing the best position involving the lowest risk level

Figure 3. The key elements of the proposed risk management methodology

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2.1. Establish the analysis goals The first step of a risk management is to define the aims and objectives of the analysis. The objective of this risk analysis is to provide a well-organized decision-making tool based on risk management principles to locating the facilities in open pit mining. The main outcome of this risk management will be a prioritized list of alternative locations based on their risk levels.

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2.2. Risk assessment Risk assessment is the central and executive part of the risk management process, which purposes to establish a proactive safety strategy by investigating potential risks. In our research, risk assessment is a process of assessing the likelihood of causing or contributing to any change in the size of the pit; and the consequence of the pit size change on the facility location. In essence, risk assessment includes three steps: 1) risk identification, 2) risk analysis and 3) risk evaluation. That means, to assess a risk, potential sources of harm should be identified first and then the likelihoods and consequences should be estimated to analyze the risk. Thereafter, risk should be evaluated which means comparing the estimated risks (i.e., level of risk) against risk criteria (i.e., predetermined standards or target risk levels) to determine the significance of the risk [29, 32].

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2.2.1. Risk identification

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Once the goal and context of the risk management is properly established, the next step in a risk management process is to identify the hazards and the situations that have the potential to cause harm or losses, sometimes called ‘unwanted events’ [30]. In this paper, the commodity price and mineral grade uncertainties as the main hazardous elements of the mine design are evaluated. In fact, uncertainties of the commodity price and grade often cause a risk on the facility location. With the aim of identifying the price behavior, the historical data were gathered and assessed to be used in the risk analysis process. The 9550 daily price data from Jan 1980 to the end of Oct 2017 were collected [33]. Table 1 shows the descriptive statistics of the price data. Monte Carlo Simulation Technique (MCST) was applied in order to model the price volatilities. The MCST creates random numbers and links them with corresponding estimated variables by using specified statistical distributions. Thus, the main step is to generate a Cumulative Distribution Function (CDF) from subjective or historical data for the variable [34]. Figure 5 shows both histogram and CDF of the historical price data. In order to model the grade uncertainty, assuming a normal distribution 6

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for the grades, the MCST can also be applied based on the expected grades and the supposed estimation variances of the blocks. These expected and variances are the results of the estimation techniques. The techniques used for geostatistical conditional simulation provide a suitable tool for quantifying the grade variability in mineral deposits. These techniques use the expected value and estimation variance of the attributes in the blocks to generate a set of equally likely realizations of the ore body instead of a single estimated model. Based on these simulations, each single realization honors the actual data at the sampled locations. A conditional simulation is a kind of the Monte Carlo simulation approach, which considers three-dimensional spatial correlations [35]. In this 2D dummy model, a 10% deviation from the expected values of the grades shown in Figure 4 was considered as the estimation variance of each block. Maximum

Minimum

Std. deviation

Variance

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Table 1. Descriptive statistics of the data ($/kg cu)

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2.2.2. Risk analysis

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Figure 5. Copper price data, a) histogram of the price data, b) CDF of the price data

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Risk analysis includes analyzing the magnitude of the risk that may arise from the unwanted event/s. The objective of a risk analysis is to describe the risk that is to present an informative risk picture [29], and it can be illustrated in the form of a bow-tie diagram. A comprehensive examination of the hazards can be done as the overall evaluation of interactions between different parts of a single bow-tie diagram or consideration of a range of bow-tie diagrams together. The diagram clearly displays the links between the potential causes (i.e., hazards), preventative and mitigating controls and consequences of a major initiating event. Figure 6 shows the simplified bow-tie diagram resulted from our research on facility location because of price and grade uncertainties.

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Mitigating barriers

Preventive barriers

Facility relocation cost PU Topography, orebody shape, stripping ratio, type of mineral, grade distribution

Changing the size of the pit

locating the facility at the lowest risk position

Material rehandling cost Leaving tied up ore

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Figure 6. Bow-tie diagram for locating the primary crusher at the pit rim (notice that PU stands for price uncertainty and GU stands for grade uncertainty)

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The hazards and associated preventative controls are on the left-hand side of the bowtie flowing into the center "initiating event" and then flowing out to the mitigating controls and significant consequences. In the figure, the initiating event is any change in the size of the pit limit which is mainly followed by commodity price fluctuations and grade uncertainty. As it was mentioned earlier, facility relocation, material rehandling cost, leaving the tied up ore and increasing the haulage cost are the important consequences. Along the lines feeding into and out of the center are vertical ellipses that represent controls or barriers that either prevents the initiating event (in the left side) or the consequence (in the right side). Topography, ore-body shape, stripping ratio, type of mineral and grade distribution are the main barriers that control the effect of uncertainties on the pit limit while putting the facilities on a location involving the lowest risk is the only barrier that somehow mitigates the effect of the pit size change on the four consequences. Indeed, the preventative barriers are those factors which control the size and the shape of the pit limit. For instance, higher grades and bigger ore bodies usually create bigger pit limits. Probable pits generation

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2.2.2.1

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The Ultimate Pit Limit (UPL) defines a profitable excavation boundary of a given deposit beyond which the commodity value will not support the costs. It identifies which block should be left in the ground and which one should be mined. In other words, the optimum final pit limit will guarantee maximum value gained from a given input geological block model and a given set of economic conditions whilst satisfying the operational requirements of safe wall slopes [36]. With an increase in price and grade, the pit would expand in size assuming all other factors remain constant. The inverse is obviously also true. Therefore, the exact limits of the pit are not known even after mine closure. A closed open-pit mine might be opened again after a sharp increase in the commodity price. By knowing this fact, some probable UPLs can be constructed for a given deposit where each one realizes the possible future events with a distinct probability of occurrence. Figure 7 shows the proposed framework by which the probable UPLs can be generated during a simulation. The historical commodity price data and geological block model are identified previously in the first step. Afterward, the CDF is created by the historical commodity price data. Also, the expected grades and estimation variances correspond to each block are defined. Next, the price scenarios and geological realizations of the deposit are randomly generated by using MCST. The block economic values that are resulted from these scenarios would be applied in the subsequent ultimate pit limit determination process. The economic block model is created from the geological realization and takes into account production and processing costs as well as price scenario. If the metal content of a block is zero or not enough to extract, then block 8

ACCEPTED MANUSCRIPT value will be negative, thus, this block is considered a waste block otherwise it is considered an ore block. Each ore and waste block can take one of the two following values, respectively: BEVore = M 10g(r)y  p(r)  s   c p  co  BEVwaste  c w M

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generated in simulation r, M is block tonnage in tonne, y is recovery in percent, p(r) is commodity price scenario ($/kg cu) generated in simulation r, s is smelting and refining cost ($/ kg cu), cp is processing cost, co is considered as mining cost ($/tonne ore), cw is stripping cost ($/ tonne waste), and gc demonstrates the break-even cut-off grade and it can be calculated using Equation 4. co

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10y p(r) s

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Subsequently, the UPLs need to be identified subject to profit maximization through the set of Equations 5-13. Equation 5 is the objective function which maximizes the profit. Equations 6-8 define the slope requirements and the Equation 9 sets the binary condition for the variables.

max i

Figure 7. The proposed framework for estimating the probable pits

ci, j x i, j

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Later, the simulation continues and the second estimation of the parameters price and grade are generated by using MCST. Then, the new economic block model and UPL are generated. In this run, those blocks which were located inside the pit in the first run give a probability number of 2 out of N if they are placed inside again. Otherwise, the probability remains 1. Similarly, those blocks which were not located inside the UPL in the first run give the probability of 1 out of N if they are located inside in the second run, otherwise, the probability remains 0. Therefore, the probability can be calculated by: (11)

(12)

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Since each run provides a single estimate of the UPL; several replications are required to assure a reliable estimate of the probable pits. Hence, the process is repeated and the new results are added to the previous ones. The simulation would be repeated for a sufficient number of times (for example, 1000 times) until the probable pits are generated with no significant changes in their probabilities of occurrence. Actually, these probable pits are probable expansions of an open pit each of which has its own probability of occurrence. In other words, each part of the ground might be inside the pit limit with a distinct probability of occurrence. These pits start with the smallest expansion which gives the highest probability and go through the next expansions with lower probabilities of occurrences. 2.2.2.2

Calculating the probabilities

The framework containing the before-mentioned formulas (i.e., Equations 2-13) was coded in MATLAB. The technical and economic data presented in Table 2 were used for calculating the blocks economic values. The simulation was done one thousand times. The results of the simulation were illustrated in Figure 8 and Table 3. In this hypothetical 2D model, seven different pit advances were calculated via the proposed simulation-based method. The numbers inside the blocks demonstrate the likelihood of the pit occurrence. The number 1 means that the block was within the pit limit in all simulations. Actually, these blocks would 10

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Figure 8. The hypothetical probable pits (the numbers inside the blocks show the probability of pit occurrence)

Pit

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2.2.2.3

Table 3. The characteristics of the hypothetical probable pits Ore Waste No of ore Cum. Ore No of waste tonnage tonnage block (tonne) block (tonne) (tonne) 13 246797 246797 12 227813 3 56953 303750 8 151875 3 56953 360703 10 189844 1 18984 379688 6 113906 8 151875 531563 36 683438 1 18984 550547 9 170859 1 18984 569531 9 170859

Cum. Waste (tonne) 227813 379688 569531 683438 1366875 1537734 1708594

Calculating the risk levels

Up to now, the effects of price and grade uncertainties (i.e., hazards) on ultimate pit limit have been assessed and the probabilities of different outcomes have been calculated by 11

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using the proposed simulation-based methodology. It is commenced as a set of probable pits with unique likelihoods of occurrences. To explain how one can calculate the risk levels because of locating the facility at different probable pit rims, the term “effective probability” is to be defined first. It is worth noting that probable pits A and B are independent. As explained earlier, the probable pits are actually the probable pit advances. These probable pit advances do not overlap with each other. Each pit advance has its own blocks inside. In probability theory, events A and B are independent if ( | ) ( ) or ( | ) ( ). Similarly, ( | ) ) ( | ) ( ) ( ) ( ). Actually, two events are ( ). In other words, ( dependent if and only if having knowledge about one event changes our knowledge about the other one. In this case, suppose we know that the probable pit advance A has a 100 % probability of occurrence. In such a case, having knowledge about Pit A does not change our knowledge about Pit B. The probable pit B has its own blocks inside and Pit A has its own also. If Pit A has a probability of 100 %, we do not know how much chance exists for a block outside Pit A to be inside Pit B. Therefore, these pit advances are completely independent. Here, the effective probability is the probability that directly affects risk levels. Equation 14 shows how the effective probability can be calculated: n

Pi

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(14)

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Where, EPj is the effective probability that exists when a special situation j happens. This special situation is a chain of events which happens at the same time. For example, it may be the occurrence of the second pit and failures to the occurrence of the third and forth pits (see Figure 8). Pi is also regarded as the probability of an event. In this special situation, the probability of the second pit advance is 76% and the probabilities that the two other pit advances do not happen are 27.6% (100-72.4) and 64% (100-36), respectively. Therefore, the effective probability is equal to 0.134 ( ). Remember, n is the number of distinct events. In reality, the topography entails the facilities to be located in special parts/azimuths relative to the pit limits. Assuming that locating the crusher at the right half of these hypothetical pits is considered, if the crusher is placed at the rim of the first probable pit, then, it would be relocated if and only if the next pit advance happens. Actually, there is a 76% chance that the second pit advance occurs. This condition is governing the crusher location at the edge of other interior pits. For instance, there is also 35.6% chance that the crusher is relocated if it had already been placed at the rim of the third pit. Considering the location of the crusher at the right-hand side and the advance of Pit 4 to the left-hand side, the probability of Pit 4 is not used for calculating the probabilities. On the other hand, the haulage cost would be increased 25 meters (i.e., a block width) with the probability of 24% if the crusher had been placed on the rim of Pit 2. That is exactly the effective probability that the first pit occurs and the second pit does not occur simultaneously (i.e., ( )). In the same way, assuming that the crusher intended to be at the rim of the fifth pit, there exists only 7% chance that the crusher is relocated. Also, there are 0.354 ( ( ( ) ( ) ( ) )), 0.135 ( ( )) and 0.04 ( ( ) ) effective chances that the haulage lengths increase 75, 100 and 125 meters, respectively (please note that the right half of the pit is considered). It should be noted that the first pit is a benchmark for all scenarios and does not create any risk for locating the crusher because it will certainly happen. In other words, the facility location will not endure risk when there is just one definite pit. Now, the risk levels can be calculated using the Equation 15.

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RLm

Pm

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min RC / MRC, OC

EPj HCI j

(15)

j

CR IP T

Where, RLm is regarded as the risk level (in $) because of locating facility at the rim of the probable pit m, Pm+1 is the probability of the next (m+1) pit advance, RC is the relocation cost of the facility if the crusher and processing plant are considered, MRC is regarded as the material rehandling cost if the waste dump is considered, OC is the opportunity cost due to sacrificing the tied ore materials. HCIj is also the haulage cost increment due to special situation j. There are two options when the pit becomes larger. The facilities must be relocated or the underneath valuable materials must be left in the ground. With that, that option with the lowest cost contributes to risk level calculations. There are m-1 special situations/conceivable conditions for haulage cost increment. Considering the fact that occurrence of pit m+1 without the occurrence of the previous pit m is meaningless, for either candidate pit rim, there are m-1 conceivable conditions. Table 4 shows a general form of these conceivable conditions. Numbers inside each set refer to the probable pits. The set {2'∩1} means that the second probable pit does not occur and the first probable pit occurs, simultaneously. The other sets can be interpreted by the same way.

Conceivable conditions (j)

M

}{ {2'∩1} {3'∩2∩1},{3'∩2'∩1} {4'∩3∩2∩1},{4'∩3'∩2∩1},{4'∩3'∩2'∩1} {5'∩4∩3∩2∩1},{5'∩4'∩3∩2∩1},{5'∩4'∩3'∩2∩1},{5'∩4'∩3'∩2'∩1}, . . .

{n'∩(n-1)∩(n-2)∩…∩1},{n'∩(n-1)'∩(n-2)∩…∩1},{n'∩(n-1)'∩(n-2)'∩…∩1},…,{n'∩(n-1)'∩(n-2)'∩…2'∩1},

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Pit rim 1 2 3 4 5 . . . n

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Table 4. Possible conceivable conditions associated with locating facility at the rim of either pit

OHCI j

Oj

Dj

PT

In the case of primary crusher and processing plant, the haulage cost increment for either j can be calculated by using Equation 16. (16)

AC

CE

Where Oj is the tonnage of ore materials inside the biggest pit in special situation j and Dj is regarded as the unit haulage cost from the candidate pit rim to the rim of the biggest pit in special situation j. In addition, in the case of waste dump location: WHCI j

Wj

(17)

Dj

Where Wj is considered as the waste materials inside the biggest pit in special situation j and Dj is the unit haulage cost from the candidate pit rim to the biggest pit in special situation j. For instance, if the third pit rim is considered, in the first special situation (i.e., {3'∩2∩1}), the biggest pit is the second pit and in the second special situation (i.e., {3'∩2'∩1}), the biggest pit is the first one. The risk levels associated with locating the crusher at different five hypothetical pit rims (i.e., at the right half of Figure 8) were examined based on the above methodology. The results of the risk level calculation for the fifth pit rim are shown in Equation 18. The computational results of the risk levels for other probable pits are depicted in Figure 9. The 13

ACCEPTED MANUSCRIPT parameters relocation cost and unit haulage cost are assumed as $1,000,000 and $0.05 per tonne per 100 meters, respectively. RL5 (1

RC P6 P5 ) (1

(1

P5 )

P3 ) (1

P2 )

P3

P2

P1

P1

O3

O1 125

75

0.05 100

0.05 100

(1

P5 ) (1

P3 )

P2

P1

O 2 100

0.05 100

(18)

71799 $

2.2.3. Risk evaluation

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The purpose of a risk evaluation is to make decisions, based on the outcomes of risk analysis, about which risks need treatment and what the treatment priorities are. The process is performed by comparing the level of risk against predetermined standards, target risk levels or other criteria. The output of a risk evaluation is a prioritized list of risks for further actions [29]. The risk should be reduced to a level that is as low as reasonably practicable. In the case which is concerned here, the levels of risk raised from locating the facility at different probable pit rims are prioritized. Then, because of the lack of any predetermined acceptable risk level in this regard, the probable pit rim with the lowest practicable risk level is selected as the best option. As shown in Figure 9, the rim of the sixth probable pit advance involves the lowest possible risk level. It means that locating the crusher at the rim of the sixth pit would make the mine plan less vulnerable whatever the values of uncertain parameters are. 800000

600000 500000 400000

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Risk level ($)

700000

300000 200000 100000

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0

1

2

3 Alternative pit rim

5

6

PT

Figure 9. Risk levels associated with alternative pit rims

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2.3. Risk Treatment As it is depicted in Figure 3, the risk assessment is followed by risk treatment wherein the measures to avoid, reduce, optimize and transfer risk are processed. How one chooses to treat risk will depend on which type of strategy the organization has in place for the risk management [29, 30]. Low and accepted risks should be monitored and periodically reviewed to ensure they remain acceptable. The risk associated with the facility location can be minimized by putting the facility on a location with the lowest risk level. In other words, a proactive policy in the preliminary design process must be taken before locating the facility. In the second level of treatment, relocating the facility during the mine life needs a costbenefit analysis.

3. VALIDATION The proposed approach was applied in the Sungun Copper Mine (SCM) of Iran to evaluate the location of the existing primary crusher. SCM is the second largest open pit mine in Iran. It is located in the northwest part of the country in Varzaghan city. The 14

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geological reserve was discovered to be 806 million tonnes with an average grade of 0.67% cu. The mine is now in operation with a planned annual production of 14 million tonnes. The primary crusher has been located in the south part of the pit at a distance of about 300 meters relative to the planned pit. The main waste dump is also in the northwest of the pit. Trucks usually dump the waste materials on the same levels as extraction levels. Figure 10 shows a plan view of the pit and the main site facilities.

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Figure 10. A plan view of SCM and its industrial site

AC

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The question is that how reliable the location of the existing crusher is and what is the safest and the lowest risk position for locating the primary crusher since the pit limit drastically pursues the commodity market and geological uncertainties. To this end, 50 geological realizations of the deposit were built by using Sequential Gaussian Simulation Technique. These realizations were individually combined with a price scenario created by using the CDF of the price data (Figure 5). The technical and economic data brought in Table 5 and Table 6 were used to define the economic block model and then to optimize the pit limit.

Table 5. Technical and economic data of SCM

Parameter type Economic

Parameter Mining

Value Unit cost 1.5 $/tonne rock 15

ACCEPTED MANUSCRIPT (waste) Mining cost (ore) Processing cost Selling cost Mining dilution Mining recovery Processing recovery Rock density

$/tonne ore $/tonne ore $/tonne cu

8 95 85

% % %

2.43

Tonnes/cubic meter

CR IP T

Technical

1.68 5.08 400

Table 6. Ultimate pit wall slopes

Pit wall slope (degree) 38 38 30 30 36 38

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Azimuth (degree) 0 90 180 235 275 315

The resulted economic block models were used in the subsequent UPL determination processes. Indeed, 50 distinct UPLs were obtained by using commercially available software each of which represents a possible UPL. Table 7 shows a summary of the geological realizations, price scenarios and UPLs.

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Table 7. Geological simulations, price scenarios and probable pit limits

Ore tonnage (tonne) 47,795,990

Pit characteristics Waste tonnage Mine life (year) (tonne) 89,053,468 3.4

516,140,977

1,023,198,040

36.9

2

741,659,490

1,575,443,300

53

2.1

1,531,081,691

52.3

2.1

62,187,203

2.3

1.92

989,082,784

35.5

2

36,686,088

1.3

1.97

41,278,427 . . . 497,995,729

79,089,923 . . . 988,447,129

2.9 . . . 35.6

1.9 . . . 2

51,267,775

96,203,349

3.7

1.88

Price scenario ($/kg cu)

1

1916

2

2698

3

6228

4

5376

5

1736

32,410,970

6

2625

497,100,241

1569

18,599,611

1805 . . . 2641 1943

PT

AC

8 . . . 49

CE

7

50

ED

Geological simulations

732,465,217

Stripping ratio 1.86

These UPLs were combined based on what was explained earlier (i.e., in sub-section 2.4.1) to extract the probable pits. In order to combine these pits, a code in MATLAB was written to count the number of times that each block is placed inside the pit limit. For instance, a block which is placed inside the pit in all 50 UPLs has a 100% probability of occurrence and the block which is determined to be inside the pit in just 25 pits out of 50 pits has a 50% probability. In this case, nine different probable pit advances were generated 16

ACCEPTED MANUSCRIPT (Figure 11). The main characteristics of these probable pit advances have been illustrated in Table 8. The lines A-A' and B-B' in Figure 10 represent the exact locations of the crosssections shown in Figure 11-a and Figure 11-b, respectively. 5500

5250

5000

4750

4500

4250

4000

9500

9000

8500

8000

7500

2250

2250

E

N

2000

2000

2000

2000

4500

c)

9000

8500

4000

8000

4500

7500

7000

9500

9000

8500

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8000

5500

5000

d)

9500

4500

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5000

7500

5250

5500

5000

7000

9500

9000

8500

8000

7500

7000

9500

9000

8500

8000

7500

7000

5500

5000

4000

N

5500

N

Probability (%) [0-7] [8-23] [24-35] [36-47] [48-53] [54-59] [60-79] [80-85] [86-100]

b)

1500

5500

5000

4750

4500

9500

9000

8500

8000

7500

a)

1500

4250

1750

4000

1750

96 82 70 56 50 42 28 16 4

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1 2 3 4 5 6 7 8 9

Cum waste tonnage (tonne) 45,206,086 60,822,908 89,043,228 189,172,505 427,263,696 1,021,287,678 1,575,059,933 1,640,944,162 1,700,719,626

ED

Probability (%)

Table 8. The characteristics of the probable pits of SCM Cum ore No of No of ore Ore tonnage Waste tonnage tonnage waste block (tonne) (tonne) (tonne) block 1,915 22,126,089 22,126,089 2,505 45,206,086 753 9,043,397 31,169,486 781 15,616,822 1,302 16,655,258 47,824,744 1,399 28,220,320 3,965 47,917,003 95,741,747 5,040 100,129,277 9,703 129,878,960 225,620,707 10,957 238,091,191 20,118 287,441,775 513,062,482 29,113 594,023,982 15,789 228,409,447 741,471,929 28,113 553,772,255 628 8,672,524 750,144,453 3,598 65,884,229 312 4,260,881 754,405,334 3,293 59,775,464

PT

Pit

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Figure 11. Cross-sectional and plan views of the probable pits of SCM, a) Y=4966, b) X=8975, c) Z=2050, d) Z=1850

CE

AC

5500

4500

4000

3500

5000

As stated earlier, we are going to evaluate the location of the existing primary crusher. The crusher is now in operation on the coordinates of x=9192, y=3926 and z=1987. To this end, a cross-section of the probable pits in which the crusher is also seen (i.e., x=9192) was chosen. Figure 12 shows the cross-section. The exact location of this cross-section has been shown in Figure 10 by using line C-C'. In this case, the block dimensions are the same as those of the 2D hypothetical model. However, the smaller blocks were used in order to truly model the ore-body shape and topography. N

2000

2000 0m

100 m

200 m

300 m

Existing primary crusher location

Probability (%) [0-7] [8-23] [24-35] [36-47] [48-53] [54-59] [60-79] [80-85] [86-100]

17

5500

5000

4500

4000

3500

Figure 12. A cross-sectional view of the probable pits and the primary crusher location in SCM 1500

1500

ACCEPTED MANUSCRIPT

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As shown in Figure 12, the rims of probable pits 4-7 are four alternatives on which the crusher can be located. Now, the crusher site is even about 120 meters far away from the biggest possible pit advance (i.e., Pit 7). Besides, in this section, the probable pit advance 4 wholly represents the planned final pit limit in the current production plan of the SCM. Also, the ramping system exits from the pit in the coordinate of x=9255 and y=4310. Therefore, putting the crusher inside the pit advance 4 is meaningless. In such a case, the first four probable pits are supposed to happen definitely. Considering the relocation cost and haulage cost defined in the section before, the risk levels for different pit rims and also the Existing Location (EL) of the crusher are calculated. Figure 13 shows the risk levels for different candidate crusher locations. As it can be seen from the graph, the pit rim 4 which somehow represents the rim of the planned pit involves the lowest risk level whereas the existing crusher location embeds the highest risk into the project. This is because of the extra haulage cost which should be paid during the mine life. 6000000 5000000

3000000 2000000 1000000 0 4

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Risk level ($)

4000000

5

6

7

EL

M

Candidate locations

4. DISCUSSION

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Figure 13. Risk levels of crusher location at different pit rim of SCM

AC

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PT

In the previous section, the risk levels associated with the crusher location were calculated for each probable pit rim with constant parameters. However, these parameters may deviate when the operation starts. Therefore, the critical parameters should be identified and their influences on the risk levels should be measured by using sensitivity analysis. The two parameters relocation cost and unit haulage cost per 100 meters were examined to evaluate different outcomes of ranking the candidate crusher locations. Figure 14 shows the prioritizations in the presence of 20% variation for each parameter when the other parameter is constant. As shown in the figure, the prioritization does not change, no matter what the parameters are. However, the risk levels for the outer candidate locations (i.e., Pit 7 and the existing crusher location) are intensively changing by changes in the parameter unit haulage cost. Whereas, the risk levels for the interior pits change slightly when the relocation cost changes.

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ACCEPTED MANUSCRIPT 7000000 6000000

Risk level ($)

5000000

pit rim 4 pit rim 5

4000000

pit rim 6

3000000

pit rim 7 2000000 EL 1000000 0 Base case

RC+20

RC-20 Scenario

HC+20

HC-20

CR IP T

Figure 14. Sensitivity analysis of relocation cost and unit haulage cost on ranking of the candidate crusher locations, RC+/-20 means 20% increase/decrease in relocation cost, HC+/-20 means 20% increase/decrease in unit haulage cost

75%

175% 200%

CE

100%

150%

% of change in parameter value

50%

125%

Relocation cost

Relocation cost

PT

25%

AC

% of change in parameter value

Unit haulage cost/100 m

ED

M

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To understand the dependence of the risk levels of each pit rim on the parameters, the sensitivity analysis was computed separately for each probable pit rim. The computational results are illustrated in Figure 15. The results describe the fact that the risk raised from crusher location is completely pursuing the relocation cost for Pit 4 with a high likelihood of occurrence, while the risk value is completely varied by the unit haulage cost for Pit 7 and also the existing crusher location. In the case of the middle pits (i.e., Pits 5 and 6), the risk levels are sensitive to both parameters. From the pits with higher probabilities toward the pits with lower probabilities, the dependence of the risk levels on the relocation cost decreases while the dependence of the risk levels on the unit haulage cost increases. This fact makes sense and reveals that how reliable the methodology is. Suppose that the planned pit limit is underestimated and the facility is placed very close to the pit, therefore, frequent relocations of the facility and then periodic relocation costs will be unavoidable. Inversely, if the pit is overestimated, it is very likely that trucks go through long unnecessary routes; while they could have smaller cycle times.

0%

50%

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25% 50% 75% 100% 125% 150% 175% 200%

0%

% of change in risk level

Unit haulage cost/100 m

50%

100%

150%

% of change in risk level

(a)

(b)

19

200%

ACCEPTED MANUSCRIPT Unit haulage cost/100 m

Relocation cost

% of change in parameter value

% of change in parameter value

Relocation cost

25% 50% 75% 100% 125% 150% 175% 200%

0%

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100%

150%

200%

125% 150% 175% 200%

0%

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50% 75% 100% 125% 150% 175% 200%

150%

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% of change in risk level

(e)

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% of change in parameter value

Unit haulage cost/100 m

100%

75% 100%

(d)

25%

50%

50%

CR IP T

(c)

0%

25%

% of change in risk level

% of change in risk level

Relocation cost

Unit haulage cost/100 m

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Figure 15. Sensitivity analysis of relocation cost and unit haulage cost for each candidate point separately, a) pit rim 4, b) pit rim 5, c) pit rim 6, d) pit rim 7, e) existing crusher location

AC

CE

PT

ED

In the hypothetical example, it was shown that the outermost pit was suggested as the best location and in the real case the innermost one had the lowest possible risk level, while both parameters unit haulage cost and relocation cost are the same for both cases. In order to clarify this contradiction, let’s back to Table 3 and Table 8 where the main characteristics of the probable pit advances in both cases were tabled. The second part of the risk level (Equation 15) defines the risk of truck haulage cost increases, which can be calculated by using Equations 16 and 17. This part of the risk is a function of the amount of ore/waste materials inside the pit. As shown in Table 3, the amounts of ore materials inside the pit advances are on the order of a few dozens of thousands to hundreds of thousands of tonnes while in Table 8, the ore tonnages are on the order of millions and hundreds of millions of tonnes. Since the relocation cost was assumed one million dollars, it would be logical that the outermost pit has the lowest risk level in the 2D model. Anyway, the hypothetical case was mainly presented in order to describe the methodology. The simulation-based idea defined in this paper mainly comes from the basic principles of the probability theory. For instance, in tossing a coin, in either toss, it will come up a head or a tail. Therefore, there is a probability of one that either of these two will happen. A probability of zero means that an event is impossible. In UPL determination process, a block would be inside the pit or outside. You cannot get both inside and outside at the same time. When tossing a coin for a large number of times, the probability can be calculated by counting the number of tosses which match the probability that you want and then divide it by the total number of throws. In our case, simulation helps us generate these throws. The

20

ACCEPTED MANUSCRIPT higher the number of simulation is done, the more accurate amount of the probability would be obtained. The methodology proposed here for calculating the probable pit advances could even be used during the first phase of mine design when the final pit limit is planned. Depending on the risk aversion/taking of the mine designer, one of the interior or outer pits can be chosen as the planned pit limit. In such a situation, the risk of the planned pit occurrence has been already accepted by the mine designer. The exit point of the ramping system from the pit is defined in the wall of the planned pit. Subsequently, the rim of this planned pit would be used as a benchmark during the truck haulage cost evaluation.

Probable pit 3

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It is worth noting that in some cases, the probable pits do not advance in a special part of the pit. Indeed, they all reach the largest possible final pit limit. Figure 16 schematically illustrates this scenario. The topography, ore-body shape, depth of the ore-body, type of mineral and grade distribution may avoid probable pits in a special part of the pit (see point A in Figure 16). In these cases, the facility would not endure any risk because of price and grade uncertainties if it is located on the point A.

Probable pit 2

A

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Probable pit 1

AC

Figure 16. Both plan and cross-sectional views of those pit limits which do not advance in a special part.

5. CONCLUSION The most popular assumption in conventional open pit mine planning is that metal price is fixed and it does not change during the life of mine and is known with certainty. Looking at the past history of metal price, obviously, this assumption is far from reality. We do not have reliable tools to consider sudden jumps and drop-offs of prices in our long-term plans. Another factor which overshadows the open pit mine planning is the grade uncertainty. The grades are mainly estimated by using the available techniques. The term estimation means that the exact values of the grades are not known until the materials are extracted from the earth. Assuming that these variables will not change throughout the life of mine, mine planning will result in either over- or under-valuation of mining blocks or, subsequently, the 21

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ACKNOWLEDGMENTS

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pit limits. In both cases, deviations from scheduled plan and sub-optimized project value are likely outcomes. The tonnages of mineable reserves, the production scale of the operation, and size and location of the surface facilities, such as ore stockpiles, waste dumps, processing plant and primary crusher are established based on the preliminary pit area and its expected future expansions. These facilities are likely to be positioned in the pit rim exactly due to the haulage cost limitations, even though; their locations are restricted to topographical circumstances. In this paper, a quantitative simulation-based risk management approach was proposed to help decision maker to overcome the risk raised from locating the facilities at the pit rim because of price and grade uncertainties. A widespread risk picture was prepared to identify the main elements of the problem. The methodology was explained by using a 2D copper example step by step first. Afterward, to validate the proposed methodology, it was applied in a real copper mine in Iran to explore, from the perspective of risk, how reliable the existing location of the primary crusher is. Furthermore, the robustness of the design parameters was evaluated through a sensitivity analysis to determine the relative importance of the selected parameters. The results show that, according to the given parameters, the existing location of the crusher imposes ten times higher risk to the project compared to that location involving the lowest risk level. It should be placed 300 m closer to the planned pit. Besides, the present simulation-based approach would help the mine designers to plan the pit limit based on their risk-taking or risk aversion levels. Our computational results indicate that regarding the relocation cost/rehandling cost and unit haulage cost, one of the interior, middle or outer probable pits can be selected to locate the facilities. As a future research direction, uncertain pit wall slopes can be considered in line with price and grade uncertainties.

Darling, P. (2011), SME Mining Engineering Handbook, Third edition, Published by Society for Mining, Metallurgy, and Exploration, pp. 941-956. ISBN: 978-0-87335264-2.

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[2]

Czaplicki, J. (2009), Shovel-truck Systems, CRC Press/Balkema, Leiden, pp. 1–9. ISBN: 9780415481359.

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[1]

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6. References

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The authors are pleased to show their gratitude to two anonymous reviewers for their insightful comments on the paper, as these comments led us to a significant improvement of the work.

[3]

Beyglou, A., Johansson, D., and Schunnesson, H. (2017). Target fragmentation for efficient loading and crushing-the Aitik case, J. South Afr. Inst. Min. Metall. 117(11), 1053-1062. http://dx.doi.org/10.17159/2411-9717/2017/v117n11a10.

[4]

List, G. F., Mirchandani, P. B., Turnquist, M. A., and Zografos, K. G. (1991). Modeling and analysis for hazardous materials transportation: Risk analysis, routing/scheduling and facility location. Transp. Sci. 25(2). 100-114. https://doi.org/10.1287/trsc.25.2.100.

22

ACCEPTED MANUSCRIPT Akgün, I., Gümüsbuga, F., and Tansel, B. (2015). Risk based facility location by using fault tree analysis in disaster management. Omega, 52, 168-179. https://doi.org/10.1016/j.omega.2014.04.003.

[6]

Wagner, M. R., Bhadury, J., and Peng, S. (2009). Risk management in uncapacitated facility location models with random demands. Comput. Oper. Res. 36(4), 1002-1011. https://doi.org/10.1016/j.cor.2007.12.008.

[7]

Goh, M., Lim, J. Y., and Meng, F. (2007). A stochastic model for risk management in global supply chain networks. Eur. J. Oper. Res. 182(1), 164-173. https://doi.org/10.1016/j.ejor.2006.08.028.

[8]

Prakash, S., Soni, G., and Rathore, A. P. S. (2015). A grey based approach for assessment of risk associated with facility location in global supply chain. Grey Syst: Theory. Appl. 5(3), 419-436. DOI 10.1108/GS-12-2014-0059.

[9]

Bilir, C., Ekici, S. O., and Ulengin, F. (2017). An integrated multi-objective supply chain network and competitive facility location model. Comput. Ind. Eng. 108, 136148. https://doi.org/10.1016/j.cie.2017.04.020.

[10]

Farahani, R. Z., SteadieSeifi, M., and Asgari, N. (2010). Multiple criteria facility location problems: A survey. Appl. Math. Modell. 34(7), 1689-1709. https://doi.org/10.1016/j.apm.2009.10.005.

[11]

Sturgul, J. R. (1987), How to determine the optimum location of in-pit movable crushers, Int. J. Min. Geol. Eng. 5.2, pp. 143-148. https://doi.org/10.1007/BF01560872.

[12]

Konak, D. (2007), Selection of the optimum in-pit crusher location for an aggregate producer, J. South Afr. Inst. Min. Metall. 107.3, pp. 161-166.

[13]

Rahmanpour, M., Osanloo, M., Adibee N., and Akbarpour Shirazi, M. (2014), An approach to locate an in pit crusher in open pit mines, Int. J. Eng-Trans. C: Aspects. 27.9, pp.1475.

AN US

M

ED

PT

CE

Paricheh, M., Osanloo, M., and Rahmanpour, M. (2016), A heuristic approach for in-pit crusher and conveyor system’s time and location problem in large open-pit mining, Int. J. Min. Reclam. Environ. pp. 1-21.

AC

[14]

CR IP T

[5]

[15]

Yarmuch, J., Epstein, R., Cancino R., and Carlos Peña, J. (2016), Evaluating crusher system location in an open pit mine using Markov chains, Int. J. Min. Reclam. Environ. 31.1, pp. 24-37.

[16]

Paricheh, M., Osanloo, M. (2016), Determination of the optimum in-pit crusher location in open-pit mining under production and operating cost uncertainties, 6th International Conference on Computer Applications in the Minerals Industries, Istanbul, Turkey, 5-7 October 2016.

23

ACCEPTED MANUSCRIPT Paricheh, M., Osanloo, M., and Rahmanpour, M., (2017). In-pit crusher location as a dynamic location problem. J. South Afr. Inst. Min. Metall. 117(6): p. 599-607

[18]

Abbaspour, H., Drebenstedt, C., Paricheh, M., and Ritter, R. (2018). Optimum Location and Relocation Plan of Semi-mobile In-pit Crushing and Conveying Systems in Open-pit Mines by Transportation Problem. Int. J. Min. Reclam. Environ. p. 1-21.

[19]

Roumpos, C., Partsinevelos, P., Agioutantis, Z., Makantasis, K., and Vlachou, A. (2014). The optimal location of the distribution point of the belt conveyor system in continuous surface mining operations. Simulat. Model. Pract. Theory. 47, 19-27.

[20]

Kennedy, B. A. (1990), Surface mining, SME, 2nd edition. Society for Mining, Metallurgy, and Exploration, Inc. (SME), Shaffer Parkway, Littleton, Colorado, USA 80127. Electronic edition published 2009.

[21]

Ataei, M. (2005), Multi-criteria selection for an alumina-cement plant location in East Azerbaijan province of Iran, J. South Afr. Inst. Min. Metall., 105.7, pp. 507-514.

[22]

Osanloo, M., Ataei, M. (2003), Factors affecting the selection of site for arrangement of pit rock-dumps, J. Min. Sci.39.2, pp. 148-153.

[23]

Kumral, M. (2004), Optimal location of a mine facility by genetic algorithms, Min. Technol. 113.2, pp. 83-88.

[24]

Hekmat, A., Osanloo M., and Akbarpour Shirazi, M. (2008), New approach for selection of waste dump sites in open pit mines, Min. Technol. 117.1, pp. 24-31.

[25]

Karimi Nasab, S., Azadehn H., and Mollaei Fard, M. R. (2007), Technical factors for selecting optimum heap leach pad sites, Eng. Min. J. 208.7, pp. 54.

[26]

Safari, M., Ataei, M., Khalokakaie, R., and Karamozian, M. (2010), Mineral processing plant location using the analytic hierarchy process—a case study: the Sangan iron ore mine (phase 1), Int. J. Min. Sci. Technol. 20.5, pp. 691-695.

AN US

M

ED

PT

CE

Fazeli, M., Osanloo, M. (2014), Mine Facility Location Selection in Open-Pit Mines Based on a New Multistep-Procedure, Mine Planning and Equipment Selection Springer International Publishing, pp. 1347-1360.

AC

[27]

CR IP T

[17]

[28]

Kumral, M., Dimitrakopoulos, R. (2008), Selection of waste dump sites using a tabu search algorithm, J. South Afr. Inst. Min. Metall. 108.1, pp. 9-13.

[29]

Aven, T. (2008), Risk analysis: assessing uncertainties beyond expected values and probabilities, John Wiley & Sons Ltd, Chichester, UKT.

[30]

ISO Guide, (2009), Risk management—vocabulary, International Organization for Standardization, 1st edition, p. 73.

24

ACCEPTED MANUSCRIPT Barnes, M. (2009), Risk assessment workbook for mines, Metalliferous, extractive and opal mines, and quarries, Mine Safety Operations, p. 64, [IGA-019 (TRIM: OUT09/16488)].

[32]

Joy, J. (2004), Occupational safety risk management in Australian mining, Occup Med, 54, pp. 311–315.

[33]

https://www.lme.com, visited on October 2017.

[34]

Law, A. M., Kelton, W. D., and Kelton, W. D. (1991). Simulation modeling and analysis (Vol. 2). New York: McGraw-Hill.

[35]

Journel AG, Huijbregts C. (1978). Mining geostatistics. London: Academic Press.

[36]

Marcotte, D., & Caron, J. (2013). Ultimate open pit stochastic optimization. Comput. Geosci. 51, 238-246.

AC

CE

PT

ED

M

AN US

CR IP T

[31]

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