A OPEN PIT MINING AÇIK OCAK MADENCİLİĞİ

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Table 1- Structure of preference voting system Candidates Candidiate 1 ... Ranking Places P 1 … P j … P m Weights of ranking places w … w j … w m 1 Vote of each candidate in each ranking place v 1 1 … … v 1j … v 1m … … … … Total Scores z m w 1 1 j j v j … 2 w m Nm( m 1) Where N is the number of voters. Wang et al. (2007) proposed three models to produce the weights, without the need to These models are given as follows: Maximize (4) Subject to m zi j vijw 1 j i 1,..., n Candidiate i v i1 … v ij … v im 1 z i m v w j 1 ij j w 1 2w 2 ... mwm 0 ... Candidiate n … v n 1 … … … … … v nj … v nm … The candidate with the highest total score is considered as DEA efficient. This model is shown below: Maximize z i m j 1 m j vijw 1 j (2) Subject to v 1 i 1,..., n w ij j w w d( j, ) j 1,..., m 1 j j 1 w m d( m, ) Where d (. ) is referred to as a discrimination intensity function. This model led to reduction of subjectivity, however often more than one DEA efficient is derived from calculations. Therefore, Cook and Kress (1990) suggested maximizing the gap between the weights so that only one candidate is considered to be DEA efficient. Green et al. (1996) utilized cross-efficiency evaluation in DEA to select only one winner candidate. Noguchi et al. (2002) used the same technique, but they suggested a strong ordering constraint for weights, which is shown below: m Maximize z v w (3) i j 1 j 1 ij m Subject to v 1 i 1,..., n w ij j w 1 2w 2 ... mw m j z n m v j 1 nj w j m j 1 w 1 j Model (4) determines weights for all candidates using a linear DEA model, which maximizes the common lower bound of total weights is equal to 1. Maximize (5 j 1 ij m Subject to z v w 1 i 1,..., n i w 1 2w 2 ... mwm 0 Model (5) determines weights in a same way, but the common upper bound of total scores are equal to 1. In addition, there is no constraint for sum of weights. m Maximize z v w (6) i j 1 ij Subject to w w ... mw 0 1 2 2 m m w 2 j 1 j 1 Model (6) specifies weights for each candidate using a nonlinear DEA model that maximizes the total score of it. This model should be solved for each candidate and candidate obtaining the highest total score could be considered as the winner. In this study, model (4) is used to determine the weights associated with different ranking places due to its less computational effort. j j ) 134
23 rd 6 THE HIERARCHICAL PREFERENCE VOTING SYSTEM Proper haulage system can be considered a hierarchical structure, then it can be called hierarchical preference voting system (HPVS) (Figure 5). The figure includes objective of the problem in the upper level, m criteria in the intermediate level and n decision alternatives in the lower level. Criteria Table 2- Structure of preference voting system for criteria IL 1 w 1 C 1 v 11 … … Importance Levels IL … IL p … k Weights of importance levels … w k … w p Vote of each criterion in each ranking place … v 1 k … p … … … Total Scores v TC p 1 v w k 1 1 k k … … Weights W 1 1 … p C j v j1 … v jk … v jp TC j v w W k 1 jk k j … … … … … … … … Figure 5- Hierarchical structure of problem 7 RANKING CRITERIA AND CALCULATING THEIR RELATIVE WEIGHTS The preference voting system was used to calculate relative weight of each criterion. Applying group decision making in methods that mentioned in literature, requires much computational effort, while PVS needs less calculations. The structure of PVS for criteria is shown in Table 2. To characterize the relative importance of each criterion, a set of importance levels were defined as ranking places: {IL 1 , ..., IL k , ..., IL p }, where IL 1 , ..., IL k , ..., IL p represent the importance from the most to the least and p is the number of importance levels. The decision makers were asked, from different domains to assess criteria in p importance levels. v jk s are the numbers of the decision makers who assess criterion j (C j ) in importance level IL k (k = 1, ..., p). Let w k be the weights associated with importance levels IL k (k = 1, ..., p). Using model (4) we calculated weights for each importance level. The total score of each criterion could be obtained by following equation: p TC j vmk w 1 k (7) k p C m v m1 … v mk … v mp TCm k vmk w 1 k W m Where TC j is the total score obtained by criterion j. Using these scores, it is possible to rank the criteria. After normalizing these scores, the weights associated with each criterion (W j ) could be calculated. 8 CASE STUDY In this study, the selection of proper haulage system of Sarcheshmeh copper mine in Iran was done by PVS method. Sarcheshmeh is a large open pit copper mine in the Kerman Province of Iran, the Sarcheshmeh Copper Complex is located 65 km southwest of Kerman and 50 km south of Rafsanjan. Production units of Sarcheshmeh Copper Complex involves the mine itself, concentrator, smelter, refinery, foundries and leaching. The deposit is known as a typical porphyry copper deposit with respect to alteration types, mineralization style, ore grade and size, tectonic setting, and igneous rock features (Waterman & Hamilton, 1975). In the development plan of Sarcheshmeh copper mine, the mine depth will reaches to 837.5 meter at 2062.5 level. Average haulage distance will reach to 4.5 km, by increasing the depth of the mine. To select the suitable haulage system for Sarcheshmeh copper mine, among the possible methods, three methods were identified as the most appropriate methods. These methods are truck & shovel, combination of truck-shovel & in-pit crusher and shovel & mobile in-pit crusher. 135
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Chapter - A OPEN PIT MINING
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A OPEN PIT MINING AÇIK OCAK MADENCİLİĞİ

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