østanbul Üniv. Müh. Fak. Yerbilimleri Dergisi, C. 16, S. 2, SS, 1-11, Y.2003 1 A DECISION SUPPORT SYSTEM FOR OPTIMAL EQUIPMENT SELECTION IN OPEN PIT MINING: ANALYTICAL HIERARCHY PROCESS AÇIK OCAK MADENCø/ø öøNDE OPTøMUM EKøPMAN SEÇø0øø døN BøR KARAR DESTEK SøSTEMø : ANALø7øK HøYERARùø PROSESø Ataç BAùÇETøN Istanbul University, Mining Engineering Department, 34320, Istanbul, Turkey. ABSTRACT : This study has been directed to the research of an optimal loading-hauling system in an open pit mine. There are many factors that affect the equipment selection processes. These factors are both qualitative and quantitative according to structure of the selection. Decision-makers need a decision support system that evaluate the factors in a complex structure for optimal decision making. In this paper, Analytical Hierarchy Process (AHP) is used for equipment selection in open pit mining. For this purpose, this study involves with the selection of an optimal loading-hauling system from mine to a power station to be established in an open pit coal mine located Orhaneli, western part of Turkey. The optimum alternative has been found as shovel-in-pit crusher-belt conveyor, consequently. Keywords : Equipment selection, decision making, multiple attribute decision making, analytical hierarchy process ÖZ : Bu çalÕúma, açÕ k ocak madencili÷inde optimum yükleme-taúÕma sisteminin seçimine yöneliktir. Ekipman seçimi birçok etmene ba÷OÕ olarak yapÕ lmaktadÕ r. Bu seçimin yapÕ VÕ gere÷i, bu etmenler hem nicel hem de nitel özellikler taúÕ GÕ÷Õ görülmektedir. Karar vericinin; bu kararlarÕ QÕ sa÷OÕ klÕ bir biçimde verebilmesi için sözü edilen bu çok karmaúÕ k yapÕ da ve sayÕ da olan etmenleri irdeleyecek bir karar destek sistemine gerek duyarlar. Bu çalÕúmada, açÕ k ocak madencili÷i ekipman seçiminde bu karar destek sistemini olXúturmak için Analitik Hiyerarúi Prosesi (AHP) kullanÕ lmÕúWÕ r. Bu amaçla Türkiye Kömür øúletmeleri (TKø ) Orhaneli Linyitleri øúletmesi dekapaj kazÕ VÕ için yükleme-taúÕ ma sisteminin seçimi incelenmiú ve optimum çözüm elde edilmeye çalÕúÕ lmÕúWÕ r. ÇalÕúanÕ n sonucunda, ekskavatör-ocak içi kÕ UÕFÕ ve bant konveyör sistemi optimum sonuç olarak bulunmuútur. Anahtar Kelimeler : Ekipman seçimi, karar verme, çok kriterli karar verme, analitik hiyerarúi prosesi. INTRODUCTION Equipment selection is one of the most of their attributes. Usually MADM consists of a single important factor that affect open-pit design (pit slopes, goal, but this may be of two different type. The first is bench high, block sizes and geometries, ramp layout where the goal is to select an alternative from a set of as well as excavation sequences and open-pit layout) scored ones based on the values and importance of the and production planning. Further, equipment selection attributes of each alternative. The second type of goal also effects economic considerations in open-pit is to classify alternatives, using a kind of role model design, specifically overburden, waste rock and ore or similar cases. The use of past cases to deduce mining costs and cost escalation parameters as a answers or explanations is a recent field of research, function of plan location and depth. Mining costs are a termed Case-Based Reasoning. Both type of goals function of site conditions, operating scale and require information about the preferences among the equipment. The purpose of equipment selection is to instances of an attribute and the preferences across the select optimum equipment with minimum cost existing attributes. The assessment of these (Lizotte, 1988). We have used Analytical Hierarchy preferences is either provided directly by the decision Process (AHP) approach for the equipment selection maker or based on past choices. The geneal in final decision. formalisation is: Multiple attribute decision making (MADM) Let A1, A2, .....An be set of alternatives to be deals with the problem of choosing an alternative from assessed by criteria C1, C2, .....Cn . a set of alternatives which are characterised in terms 2 ATAÇ BAùÇETø N Let Rij be the numerical rating of alternative of the comparisons. Saaty proposed an eigenvector Ai for criteria Cj, i j. approach for the estimation of the weights from a Then the general decision function is: matrix of pairwise comparisons. The eigenvector D(A) =(Ri1o Ri2o Ri3o ....... Rijo) for j = 1, 2, approach is a theoretically and pratically proven .....,n and o represents the aggregation. method for estimating the weights. The eigenvector Further, the decision maker might express or also has an intuitive interpretation in that it is an define a ranking for the criteria as averaging of all possible ways of thinking about a importance/weights. There are many forms for given set of alternatives. After estimating the expressing these importance, but the most common weights, the decision-maker is also provided with a are: (a) utility preference functions; (b) the measure of the inconsistency of the given pairwise analytical hierarchy process and (c) a fuzzy version comparisons. It is important to note that the AHP of the classical linear weighted average. In this does not require decision-makers to be consistent paper, it is proposed developing the decision but, rather, provides a measure of inconsistency as support system that is possible to evaluate all well as a method to reduce this measure if it is parameters together and assess the weights of deemed to be too high. After generating a set of criteria and objectives for equipment selection weights for each alternative under any criterion, the problem. The Analytical Hierarchy Process is used overall priority of the alternatives is computed by to devolope the decision support system. The means of a linear, additive function (Munda, 1995, method measures relative “fuzziness” by tructuring Albayrak et al. 1997). the criteria and objectives of a system, hierarchical The method measures relative “fuzziness” in a multiple attribute framework (Riberio 1996). by structuring the criteria and objectives of a system, hierarchicaly in a multiple attribute THE ANALYTICAL HIERARCHY framework. In order to rate the alternatives Saaty PROCESS (1978a; 1978b) uses a hierarchical pair-wise This method has been developed by Saaty comparison between attributes and/or objectives [1980]. The AHP structures the decision problem in and then solves them with eigenvectors of the levels which correspond to one’s understanding of reciprocal matrices. Instead of presenting the the situation: goals, criteria, sub-criteria, and approach in mathematical form, an example is alternatives. By breaking the problem into levels, developed to facilitate understanding. The the decision-maker can focus on smaller sets of importance of this approach is mainly used to decisions. The AHP is based on 4 main axioms: calculate the criteria weights, since it has a non- 1) Given any two alternatives (or sub-criteria), fuzzy set nature. Consider the problem of selecting the decision-maker is able to provide a a site from the set íA, B, Cý to be located of a new pairwise comparison of these alternatives in-pit crusher in an open-pit mine, with the goal, G, under any criterion on a reciprocal ratio scale. of spending the minimum investment possible and 2) When comparing any two alternatives, the for criteria evaluation to be located near the pit and decision-maker never judges one to be plant, respectively C1 and C2. The analytical infinitely better than another under any hierarchy for this example is given in Figure 1. criterion. The judgement scale used is the one 3) One can formulate the decision problem as a proposed by Saaty (Saaty 1978a, 1978b): 1. Equally hierarchy. important, 3 weakly more important, 5 strongly 4) All criteria and alternatives which impact a more important, 7 demonstrably more important decision-problem are represented in the and 9-absolutely more important. In the hierarchy, hierarchy. the matrix of the upper nodes corresponds to level The above axioms describe the two basic zero (the comparison of criteria) while the other tasks in the AHP: formulating and solving problem correspond level one. The construction of the as a hierarchy, and eliciting judgements in the form square reciprocal matrices is performed by asking of pairwise comparisons. The alicitation of the decision maker to compare element i with priorities for a given set of alternatives under a element j, the value aij, with respect to a particular given criterion involves the completion of a nxn criteria or objective. The other values are assigned matrix, where n is the number of alternatives under as follows : (a) aji = 1/aij; (b) aii = 1. For the consideration. Since the comparisons are assumed example described, Saaty’s reciprocal matrices are: to be reciprocal, one needs to answer only n(n-1)/2 AÇIK OCAK MADENCø /ø öø NDE OPTø MUM EKø PMAN SEÇø 0ø ø dø N Bø R KARAR 3 DESTEK Sø STEMø : ANALø 7ø K Hø YERARùø PROSESø Select Site Level zero-Criteria Minimum Near Pit Near Ore Investment Dressing Plant Level one- Alternatives A B C A B C A B C Figure 1. The Hierarchy Structure of The Example ùekil 1. Örnek Problemin Hiyerarúik YapÕ VÕ Criteria Minimum Near Near Ore Comparison Investment Pit Dressing Plant G C1 C2 A B C A B C A B C G é1 1/ 7 1/ 7ù A é1 1/ 5 1/ 5ù A é1 3 3ù A é1 1 7ù ê ú 7 1 1 B ê ú B ê ú B ê ú C1 ê ú ê5 1 1 ú ê1/ 3 1 1ú ê1 1 5ú C2 ëê7 1 1 ûú C ëê5 1 1 ûú C ëê1/ 3 1 1ûú C ëê1/ 7 1/ 5 1ûú The values in the reciprocal matrices are given eigenvector corresponding to the maximum by the decision maker. For example, criteria C1 and C2 eigenvalue is a cardinal ratio scale for the elements are “demonstrably more important” (grade 7 on first compared.