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A Hierarchical Preference Voting System for Mining Method Selection Problem / Wykorzystanie Systemu Głosowania Zakładający Hierarchię Preferencji Przy Wyborze Odpowiedniej Metody Wybierania

A Hierarchical Preference Voting System for Mining Method Selection Problem / Wykorzystanie... Arch. Min. Sci., Vol. 57 (2012), No 4, p. 1057­1070 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.2478/v10267-012-0070-x HAMIDREZA NOURALI*, SAEID NOURALI**, MOHAMMAD ATAEI***1, NARGES IMANIPOUR**** A HIERARCHICAL PREFERENCE VOTING SYSTEM FOR MINING METHOD SELECTION PROBLEM WYKORZYSTANIE SYSTEMU GLOSOWANIA ZAKLADAJCY HIERARCHI PREFERENCJI PRZY WYBORZE ODPOWIEDNIEJ METODY WYBIERANIA To apply decision making theory for Mining Method Selection (MMS) problem, researchers have faced two difficulties in recent years: (i) calculation of relative weight for each criterion, (ii) uncertainty in judgment for decision makers. In order to avoid these difficulties, we apply a Hierarchical Preference Voting System (HPVS) for MMS problem that uses a Data Envelopment Analysis (DEA) model to produce weights associated with each ranking place. The presented method solves the problem in two stages. In the first stage, weights of criteria are calculated and at the second stage, alternatives are ranked with respect to all criteria. A simple case study has also been presented to illustrate the competence of this method. The results show that this approach reduces some difficulties of previous methods and could be applied simply in group decision making with too many decision makers and criteria. Also, regarding to application of a mathematical model, subjectivity is reduced and outcomes are more reliable. Keywords: Mining Method Selection; Multi Attribute Decision Making; Preference Voting System; Data Envelopment Analysis Przy wykorzystywaniu teorii decyzyjnych do zagadnie zwizanych z wyborem wlaciwej metody wybierania, badacze na przestrzeni lat napotykali na dwie zasadnicze trudnoci: (i) obliczenie odpowiedniego wspólczynnika wagi dla poszczególnych kryteriów oraz (ii) niepewno osdów dokonywanych przez decydentów. W celu uniknicia tych trudnoci, zastosowalimy system glosowania zakladajcy hierarchi preferencji przy podejmowaniu decyzji odnonie wyboru metody wybierania. W tym celu wykorzystano model DEA (metoda obwiedni danych) dla wygenerowania wag zwizanych z poszczególnymi pozycjami w rankingu. Proponowana metoda zaklada rozwizanie problemu w dwóch etapach. W pierwszym etapie * FACULTY OF TECHNICAL & ENGINEERING, DEPARTMENT OF MINING ENGINEERING, ISLAMIC AZAD UNIVERSITY SOUTH TEHRAN BRANCH, TEHRAN, IRAN; E-mail: h.nourali@gmail.com ** FACULTY OF MANAGEMENT & ACCOUNTING, DEPARTMENT OF INDUSTRIAL MANAGEMENT, ISLAMIC AZAD UNIVERSITY SOUTH TEHRAN BRANCH, TEHRAN, IRAN; E-mail: st_s_nourali@azad.ac.ir *** DEPARTMENT OF MINING, GEOPHYSICS & PETROLEUM ENGINEERING, SHAHROOD UNIVERSITY OF TECHNOLOGY, SHAHROOD, IRAN; E-mail: ataei@shahroodut.ac.ir **** FACULTY OF ENTREPRENEURSHIP, TEHRAN UNIVERSITY, TEHRAN, IRAN; E-mail: nimanip@ut.ac.ir 1 Corresponding Author. Tel.:+98 9125732469, Fax: +98 2733395509 obliczane s wagi przyporzdkowane poszczególnym kryteriom, w etapie drugim przeprowadzany jest ranking rozwiza alternatywnych w odniesieniu do wszystkich kryteriów. Przedstawiono proste studium przypadku dla zilustrowania dzialania metody. Wyniki wskazuj, e zastosowane podejcie redukuje pewne niedogodnoci zwizane z poprzednio stosowanymi metodami i moe by z powodzeniem wykorzystane do podejmowania decyzji grupowych, w sytuacjach gdy mamy do czynienia z wieloma decydentami i wieloma kryteriami. Ponadto, zastosowanie modelu matematycznego pozwala na ograniczenie subiektywizmu w ocenie, dziki temu wyniki s bardziej wiarygodne. Slowa kluczowe: wybór metody wybierania, procesy decyzyjne, preferencyjny system glosowania, metoda obwiedni danych 1. Introduction Mining Method Selection (MMS) problem is one of the most critical and vital steps in designing an ore extraction system. The MMS problem has been widely studied in recent years. The approach to MMS problem can be classified into three divisions: qualitative methods such as Boshkov and Wright (1973), numerical ranking methods such as Nicholas (1993) and decision making methods. A comprehensive survey of literature on the first two groups can be found in Namin et al.(2009). Decision making methods have been widely used to solve MMS problem. Ataei et al. (2008b) used the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method with 13 criteria to develop a suitable mining method for Golbini.No.8 of Jajarm bauxite mine in Iran. Also, Ataei et al. (2008a) used AHP (Analytic Hierarchy Process) method to select mining method for the same mine. Namin et al. (2008) developed a Fuzzy TOPSIS based model for mining method selection problem. Moreover, Namin et al. (2009) used three MADM (Multi Attribute Decision Making) methods (AHP, TOPSIS and PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation)) to solve mining method selection problem. Jamshidi et al. (2009) used AHP approach to select optimum underground mining method. Mikaeil et al. (2009) developed a decision support system (DSS) using Fuzzy AHP and TOPSIS approaches to select the optimum underground mining method. In their DSS, Fuzzy AHP is used to determine the weight of each criterion by decision makers and then the methods are ranked via TOPSIS. Azadeh et al. (2010) modified the well-known MMS technique of Nicholas. They solved the MMS problem using Fuzzy AHP within 2 steps: in the first step mining alternatives were ranked according to technical and operational criteria while in the second step, the most profitable among them was selected based on economic criteria. Naghadehi et al. (2009) proposed application of Group Fuzzy AHP approach to select optimum underground mining method for Jajarm bauxite mine. Alpay and Yavuz (2009) used Yager's method and Fuzzy AHP approach to develop a computer program to select the best underground mining method. The process of solving MMS problem by decision making models can be divided into two stages: Stage 1: Determining relative weight associated with each criterion. Stage 2: Selecting the most suitable mining method with respect to all criteria. Considering the above mentioned literature, we realized that researchers have faced two difficulties in process of solving MMS problem: (i) calculation of relative weight associated with each criterion in the first stage, (ii) uncertainty in judgment for decision makers in both stages. According to previous studies, for the first stage, AHP had been a common approach to calculate weights of criteria. There are too many factors related to MMS problem such as geological and geotechnical properties, economic parameters and geographical factors; so it is very difficult to make pairwise comparisons in AHP. Moreover, the process of solving the problem is time-consuming and eventually may lead to unrealistic outcomes because of inconsistency in comparison matrix. Dealing with this difficulty, some researchers tried to reduce the dimensions of pairwise comparisons matrix. In this way, Naghadehi et al. (2009) selected the most important criteria among all criteria. It is obvious that in this approach, some criteria which are involved in MMS problem are eliminated. Also, some other researchers divided criteria into subgroups. (Azadeh et al., 2010; Alpay & Yavuz, 2009; Namin et al., 2009; Mikaeil et al., 2009). It is clear that this approach prevents comparison of individual criteria belonging to different subgroups and comparisons are limited among subgroups and members of each group. Furthermore, too computational effort remained a significant difficulty. Although AHP method has been widely used in the first step, some researchers developed a preference voting system to determine the weights of criteria (Ataei et al., 2008a, 2008b; Mohsen et al., 2009). In such systems the weight associated with each ranking place was predefined in a subjective way. The rest of approaches used linguistic terms to determine the weights of criteria (Namin et al., 2009). Such choices are also subjective. In this paper to calculate the weights of criteria, we applied a preference voting system (PVS). The main difference between this PVS with those which proposed in previous research, is in procedure of determining relative weight associated with each ranking place. This PVS uses a DEA model to determine the weights associated with ranking places which maximizes the lower bound of relative score of each candidate. This approach decreases the subjectivity in determining weights of ranking places and the results are more reliable. In addition, dealing with the second difficulty (i.e. uncertainty in judgment), researchers mainly used fuzzy approach which itself requires much computational effort. Since applying PVS leads to prioritizing criteria without the need to determine priority levels, uncertainty in judgment is reduced in more simple way than Fuzzy approach. Considering the 2nd stage, several decision making methods have been applied by researchers for MMS problem, such as AHP, TOPSIS and PROMETHEE. In this paper, to overcome the second difficulty (i.e. uncertainty in judgment), again we applied a PVS for alternatives according to each criterion. Then we aggregated all preferences with the weights that had been calculated in previous stage for each criterion. Finally, we computed an ultimate score for each alternative. Using these scores, we are able to rank alternatives and select the best one. In this approach decision makers only determine the priorities of alternatives with respect to each criterion. So, the subjectivity and uncertainty in judgment are decreased. Moreover, unlike previous methods, by means of this approach, we are able to use all criteria involved in MMS problem as a result of its less computational effort. Furthermore, this PVS enables us to perform a group decision making with many decision makers in a more simple way. The paper is organized as follows. In section 2 Preference Voting System (PVS) is introduced. In section 3 we applied a HPVS for mining method selection problem. In section 4 we investigated a case study and finally a conclusion has been made. 2. Preference Voting System In preference voting systems, each voter selects m candidates from among n candidates (n m) and ranks them from the most to the least preferred. Each candidate may receive some votes in different ranking places. The total score of each candidate is the weighted sum of the votes he/she receives in different places (Wang et al., 2007) that is defined as follow: (1) Let wj be the importance weight of j th ranking place (j = 1, ..., m) and vij be the vote of candidate i being ranked in the j th place. The structure of PVS is shown in Table 1. In this structure, the winner is the one with the highest total score. So, the key issue of the preference aggregation in a PVS is how to determine the weights associated with different ranking places (i.e. (wj)). TABLE 1 Structure of preference voting system p1 Candidates w1 candidate1 ... v11 ... Ranking Places pj ... pm Weights of ranking places ... wj ... wm Vote of each candidate in each ranking place ... v1j ... v1m ... Total Scores z1 = å j =1v1j wj ... candidatei ... vi1 ... vij ... vim ... j =1vij wj ... candidaten vn1 ... vnj ... vnm zn = å j =1vn j wj Broda-Kendall (BK) method (Cook & Kress, 1990) is a well-known approach to identify the weights. This approach assigns weights m, m ­ 1, m ­ 2, ..., 1 to m ranking places, from the highest ranking place to the lowest respectively. These weights are produced in a simple way, but their production process is quite subjective. To reduce subjectivity in generating weights, Cook and Kress (1990) proposed the application of Data Envelopment Analysis (DEA) in this problem, which considered candidates as Decision Making Units (DMUs). Their proposed model calculates weights for each candidate that maximizes its total score. Thereafter, the model is solved once for each candidate and the total score is computed. The candidate with the highest total score is considered as DEA efficient. This model is shown below: Maximize (2) Subject to å j=1vij wj £ 1 wj ­ wj +1 d(j, ) wm d(m,) j = 1, ..., m ­ 1 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. So 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: Maximize Subject to m m (3) å j=1vij wj £ 1 w1 2w2 ... mwm wm ³ e = 2 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 predetermine any parameters such as . These models are given as follows: Maximize Subject to (4) ³a å j=1 wj = 1 Model (4) determines weights for all candidates using a linear DEA model which maximizes the common lower bound of total scores (i.e. ). Also the sum of weights is equal to 1. Maximize Subject to (5) a £ j =1 vij wj £ 1 Model (5) determines weights in a same way, but the common upper bound of total scores are equal to 1. Also there is no constraint for sum of weights. Maximize Subject to (6) å j=1 wj2 = 1 Model (6) specifies weights for each candidate using a nonlinear DEA model which 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. Since, this study deals with too many candidates, we use model (4) to determine the weights associated with different ranking places due to its less computational effort. 3. Developing a HPVS for MMS problem We considered MMS problem to have a hierarchical structure, as shown in Figure 1. 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. Considering this structure, MMS problem is divided into 2 stages. (I) Ranking criteria and calculating their relative weights. (II) Ranking alternatives with respect to each criterion and selecting the most suitable alternative according to all criteria. Fig. 1. Hierarchical structure of problem 4. Ranking criteria and calculating their relative weights According to the reasons mentioned in section 1, we applied a preference voting system to calculate relative weight of each criterion. Applying Group decision making in methods which mentioned in literature, requires much computational effort, while PVS needs less calculations. The structure of PVS for criteria is shown in Table 2. TABLE 2 Structure of preference voting system for criteria Criteria Importance Levels ... ILk ... ILp Weights of importance levels ... wk ... wp w1 Vote of each criterion in each ranking place IL1 v11 ... v1k ... v1p ... Total Scores Weights C1 ... TC1 = å k =1v1k wk W1 ... Wj ... Wm Cj ... vj1 ... vjk ... vjp ... TCj = å k =1vjk wk Cm vm1 ... vmk ... vmp TCm = å k =1vmk wk To characterize the relative importance of each criterion, we defined a set of importance levels as ranking places: {IL1, ..., ILk, ..., ILp}, where IL1, ..., ILk, ..., ILp represent the importance from the most to the least and p is the number of importance levels. We asked decision makers from different domains to assess criteria in p importance levels. vjk s are the numbers of the decision makers who assess criterion j (Cj) in importance level ILk (k = 1, ..., p). Let wk be the weights associated with importance levels ILk (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: TCj = å k =1vjk wk ... ... (7) where TCj is the total score obtained by criterion j. Using these scores we are able to rank the criteria. After normalizing these scores, the weights associated with each criterion (Wj) could be calculated. 4.1. Ranking alternatives with respect to each criterion and selecting most suitable alternative associated with all criteria To deal with uncertainty of decisions on MMS problem, researchers mainly used Fuzzy theory. The fuzzy approach could be very helpful in situations dealing with uncertainty in decision making; however, as the number of decision makers rise, computational effort increases too. In this paper we applied a PVS to rank alternatives with respect to each criterion. Since, with the application of this approach, decision makers only need to determine the priority of alternatives (rather than amount of priority) according to each criterion, uncertainty in judgment will be decreased. Moreover, it simplifies group decision making with too many decision makers. The structure of this approach is shown in Table 3. TABLE 3 Structure of preference voting system for alternatives C1 Alternatives W1 ... Criteria Cj ... Cm Wm Ranking Places RPm1 ... RPmhm ... wmhm v1mhm ... Ultimate Scores Weights of each criterion ... Wj ... Ranking Places ... RPj1 ... RPj ... Ranking Places ... RP11 ... RP1h1 ... w11 ... w1h1 v11h1 ... Weights of each ranking place ... wj1 ... wj ... wm1 v1j1 ... v1j ... v1m1 ... Vote of each alternative in each ranking place A1 ... v111 ... UT1 = å j =1( å h =1v1jh wjh)Wj ... Ai ... vi11 ... vi1h1 ... vij1 ... vij ... vim1 ... vimhm ... UTi = å j =1( å h =1vijh wjh)Wj å j =1( å h =1vn jh wjh )Wj ... An vn11 ... vn1h1 ... vnj1 ... vnj ... vnm1 ... vnmhm UTn = To distinguish the priorities of alternatives with respect to each criterion, we define a set of ranking places: {RPj1, ..., RPj} (j = 1, ..., m) for each criterion, where RPj1, ..., RPj represent priority from the most to the least and is the number of ranking places for criterion j. By this definition, we can use different numbers of ranking places for different criteria to assess. Note that if two or more alternatives have no priority over each other, they can be assigned to a similar ranking place. To evaluate alternatives, we conduct a preference voting among decision makers who were selected from different functional areas. The priorities of alternatives over each other with respect to each criterion are characterized based on their utility. In other words, if a criterion represents benefit, then the alternative which has more benefit will be located in an upper ranking place. Likewise, if a criterion represents cost, then the alternative which has less cost, will be located in an upper ranking place. Using this approach, after voting, we are able to assume all criteria as benefit. Let vijh be the vote of alternative i () being ranked in the hth ranking place associated with j th criterion and wjh be the importance weight of hth ranking place with respect to j th criterion. As mentioned earlier we can calculate wjh by applying model (4). Then the total score of each alternative with respect to each criterion could be obtained just like equation (7). To aggregate preferences for all criteria we can exploit the following equation: UTi = å j =1(å =1 vijh wjh )Wj m h (8) where UTi is the ultimate score for alternative i. Finally the most suitable mining method is the one with the highest ultimate score. 5. Case Study In order to investigate the competence of this technique for MMS problem, we chose central mine of Tabas coal mine to conduct a case study. It is located in Parvadeh district in east of central Iran, west of the Yazd state, northwest of Lout Desert and southeast of Tabas city. It is in longitudes of 56°46'30" to 56°51'40" N and latitudes 33°02'15" to 33°59'48" E. The coal-bearing sediments are within the Iranian structural facies region from a part of the Shemshak Group, which is of Lower-Triassic to Mid-Jurassic era. Physical parameters such as deposit geometry (Ore body dip, thickness, volume and depth) rock mechanics characteristics have been shown in Table. 4. TABLE 4 Some information about Central Mine of Tabas Coal Mine Ore body Geomechanical data Hydrogeology Ore body dip Ore body thickness Ore body depth Ore body volume Mineable reserve Production rate Existence of strata gases Ore body RMR Hanging wall RMR Footwall RMR Hydrogeology conditions 12° 1.95 m 50 to 150 m 400000 m3 1.1 Million Tonnes 250000 Annual 5 to 15 m3/tonne 30 10 to 24 10 to 24 Dry Also some characteristics of primary non-coal lithology could be found in Table. 5. In this study, six feasible alternative methods (Traditional Longwall , Traditional Longwall with filling, Mechanized Longwall, Traditional Room & Pillar, Mechanized Room & Pillar and Shortwall), which obtained based on thoughts of experts, were evaluated with respect to 32 criteria. The list of criteria has been shown in Table. 6. Also 5 decision makers participated in decision making process. TABLE 5 Average of the results for three primary non-coal lithologies Lithology SG Porosity Comp. strength (MN/m2) Shear Strength (MN/m2) Slake% RQD Sandstone Siltstone Mudstone TABLE 6 Criteria for MMS problem Criteria Criteria Criteria C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 Ore body dip Ore body thickness Ore body depth Grade distribution Ore body volume Ore body uniformity Ore body RMR Hanging wall RMR Footwall RMR Hydrogeology conditions Climate of area C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 Production rate Recovery Development production Production per man shift Selectivity mining Flexibility (Ability of changing a mining method to another similar methods) Dilution Development rate (Rate of achieving to ore body since start of the project) Mineable reserve Existence of strata gases Ventilation C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 Technology availability Ability to mechanize and automate Labor availability Environmental aspects Surface subsidence Safety Occupational interests Capital costs Operating costs Reclamation/rehabilitation costs Based on previous section, at first stage we calculated weight of each criterion. We defined 4 importance levels: {Really Important, Quite Important, Not Very Important, Not Important}, where these importance levels represent the importance from the most to the least. It is clear that the votes in the last importance level (i.e. Not Important) should not influence the total score of each criterion. Because, from the perspective of decision makers, such criteria are known as not important criterion in decision making process. So, we considered the weight of this importance level equal to zero and applied model (4) based on 3 importance levels as ranking places to calculate the weights. Then we calculated score and normalized weight of each criterion according to previous section. The results could be found in Table. 7. TABLE 7 Preference voting for criteria related to their importance levels and weights obtained at the first stage of HPVS Weights of importance levels 0.273 0.182 0 Importance levels Really Quite Not very Not important important important important Vote of each criterion in each importance level 2 3 4 5 0.545 Criteria Total score for each criterion Normalized weight for each criterion C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 3 3 0 4 0 0 4 5 1 5 2 3 1 5 3 2 3 2 5 2 2 5 3 0 3 4 1 SUM In the second stage, we conducted a preference voting among decision makers about the priorities of alternatives over each other with respect to each criterion. Also, we applied model (4) to produce weights of ranking places. An example of this procedure for Surface subsidence criterion could be found in Table 8. Also, scores of each alternative with respect to each criterion are shown in Table. 9. Finally we calculated ultimate scores of alternatives and ranked them according to their scores. The result of the second stage has been shown in Table 10. According to Table 10, ,,Mechanized Longwall" was selected as the most suitable mining method from the perspective of all decision makers. TABLE 8 Preference voting for alternatives with respect to "Surface subsidence" criterion at the second stage of HPVS Weight of criterion 0.0323974 Ranking Places RP27­1 RP27­2 RP27­3 RP27­4 RP27­5 RP27­6 Score Weights of Ranking Places 0.444444 0.222222 0.148148 0.111111 0.074074 0 Vote of each alternative in each ranking place 1 2 1 1 0.0227982 4 1 1 1 1 4 3 2 1 4 1 1 1 0.0647948 0.0647948 0.0647948 0.0407967 0.0227982 TABLE 9 Alternatives Traditional Longwall Traditional Longwall with filling Mechanized Longwall Traditional Room& Pillar Mechanized Room & Pillar Shortwall Scores of alternatives with respect to criteria Alternatives Criteria 1 Traditional Longwall 2 Traditional Traditional Mechanized Mechanized Longwall Room& Room & Longwall with filling Pillar Pillar 3 4 5 6 Shortwall 7 Ore body dip Ore body thickness Ore body depth Grade distribution Ore body volume Ore body uniformity Ore body RMR Hanging wall RMR Footwall RMR Hydrogeology conditions Climate of area Production rate Recovery Development production Production per man shift Selectivity mining Flexibility (Ability of changing a mining method to another similar methods) Dilution Development rate (Rate of achieving to ore body since start of the project) Mineable reserve Existence of strata gases Ventilation Technology availability Ability to mechanize and automate Labor availability Environmental aspects Surface subsidence Safety Occupational interests Capital costs Operating costs Reclamation/rehabilitation costs TABLE 10 Scores for alternatives and ranking Alternatives Ultimate Score Ranking Traditional Longwall Traditional Longwall with filling Mechanized Longwall Traditional Room& Pillar Mechanized Room & Pillar Shortwall 6. Conclusion In this paper we applied a HPVS for mining method selection problem. This PVS uses a DEA model to produce weights associated with each ranking place. The process of solving the problem consists of two stages. At the first stage, criteria are ranked and relative weight according to each one is calculated. Then in the second stage, mining methods are ranked by their scores. A case study was also investigated to illustrate the competence of presented method. We showed that by application of HPVS for MMS problem, some difficulties related to the previous methods could be reduced. Also, regarding to application of a mathematical model, outcomes are more reliable. Moreover, this approach could be applied simply in group decision making with too many decision makers. It is expected that in the near future this method will be applied to various aspects of mining engineering. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archives of Mining Sciences de Gruyter

A Hierarchical Preference Voting System for Mining Method Selection Problem / Wykorzystanie Systemu Głosowania Zakładający Hierarchię Preferencji Przy Wyborze Odpowiedniej Metody Wybierania

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Arch. Min. Sci., Vol. 57 (2012), No 4, p. 1057­1070 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.2478/v10267-012-0070-x HAMIDREZA NOURALI*, SAEID NOURALI**, MOHAMMAD ATAEI***1, NARGES IMANIPOUR**** A HIERARCHICAL PREFERENCE VOTING SYSTEM FOR MINING METHOD SELECTION PROBLEM WYKORZYSTANIE SYSTEMU GLOSOWANIA ZAKLADAJCY HIERARCHI PREFERENCJI PRZY WYBORZE ODPOWIEDNIEJ METODY WYBIERANIA To apply decision making theory for Mining Method Selection (MMS) problem, researchers have faced two difficulties in recent years: (i) calculation of relative weight for each criterion, (ii) uncertainty in judgment for decision makers. In order to avoid these difficulties, we apply a Hierarchical Preference Voting System (HPVS) for MMS problem that uses a Data Envelopment Analysis (DEA) model to produce weights associated with each ranking place. The presented method solves the problem in two stages. In the first stage, weights of criteria are calculated and at the second stage, alternatives are ranked with respect to all criteria. A simple case study has also been presented to illustrate the competence of this method. The results show that this approach reduces some difficulties of previous methods and could be applied simply in group decision making with too many decision makers and criteria. Also, regarding to application of a mathematical model, subjectivity is reduced and outcomes are more reliable. Keywords: Mining Method Selection; Multi Attribute Decision Making; Preference Voting System; Data Envelopment Analysis Przy wykorzystywaniu teorii decyzyjnych do zagadnie zwizanych z wyborem wlaciwej metody wybierania, badacze na przestrzeni lat napotykali na dwie zasadnicze trudnoci: (i) obliczenie odpowiedniego wspólczynnika wagi dla poszczególnych kryteriów oraz (ii) niepewno osdów dokonywanych przez decydentów. W celu uniknicia tych trudnoci, zastosowalimy system glosowania zakladajcy hierarchi preferencji przy podejmowaniu decyzji odnonie wyboru metody wybierania. W tym celu wykorzystano model DEA (metoda obwiedni danych) dla wygenerowania wag zwizanych z poszczególnymi pozycjami w rankingu. Proponowana metoda zaklada rozwizanie problemu w dwóch etapach. W pierwszym etapie * FACULTY OF TECHNICAL & ENGINEERING, DEPARTMENT OF MINING ENGINEERING, ISLAMIC AZAD UNIVERSITY SOUTH TEHRAN BRANCH, TEHRAN, IRAN; E-mail: h.nourali@gmail.com ** FACULTY OF MANAGEMENT & ACCOUNTING, DEPARTMENT OF INDUSTRIAL MANAGEMENT, ISLAMIC AZAD UNIVERSITY SOUTH TEHRAN BRANCH, TEHRAN, IRAN; E-mail: st_s_nourali@azad.ac.ir *** DEPARTMENT OF MINING, GEOPHYSICS & PETROLEUM ENGINEERING, SHAHROOD UNIVERSITY OF TECHNOLOGY, SHAHROOD, IRAN; E-mail: ataei@shahroodut.ac.ir **** FACULTY OF ENTREPRENEURSHIP, TEHRAN UNIVERSITY, TEHRAN, IRAN; E-mail: nimanip@ut.ac.ir 1 Corresponding Author. Tel.:+98 9125732469, Fax: +98 2733395509 obliczane s wagi przyporzdkowane poszczególnym kryteriom, w etapie drugim przeprowadzany jest ranking rozwiza alternatywnych w odniesieniu do wszystkich kryteriów. Przedstawiono proste studium przypadku dla zilustrowania dzialania metody. Wyniki wskazuj, e zastosowane podejcie redukuje pewne niedogodnoci zwizane z poprzednio stosowanymi metodami i moe by z powodzeniem wykorzystane do podejmowania decyzji grupowych, w sytuacjach gdy mamy do czynienia z wieloma decydentami i wieloma kryteriami. Ponadto, zastosowanie modelu matematycznego pozwala na ograniczenie subiektywizmu w ocenie, dziki temu wyniki s bardziej wiarygodne. Slowa kluczowe: wybór metody wybierania, procesy decyzyjne, preferencyjny system glosowania, metoda obwiedni danych 1. Introduction Mining Method Selection (MMS) problem is one of the most critical and vital steps in designing an ore extraction system. The MMS problem has been widely studied in recent years. The approach to MMS problem can be classified into three divisions: qualitative methods such as Boshkov and Wright (1973), numerical ranking methods such as Nicholas (1993) and decision making methods. A comprehensive survey of literature on the first two groups can be found in Namin et al.(2009). Decision making methods have been widely used to solve MMS problem. Ataei et al. (2008b) used the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method with 13 criteria to develop a suitable mining method for Golbini.No.8 of Jajarm bauxite mine in Iran. Also, Ataei et al. (2008a) used AHP (Analytic Hierarchy Process) method to select mining method for the same mine. Namin et al. (2008) developed a Fuzzy TOPSIS based model for mining method selection problem. Moreover, Namin et al. (2009) used three MADM (Multi Attribute Decision Making) methods (AHP, TOPSIS and PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation)) to solve mining method selection problem. Jamshidi et al. (2009) used AHP approach to select optimum underground mining method. Mikaeil et al. (2009) developed a decision support system (DSS) using Fuzzy AHP and TOPSIS approaches to select the optimum underground mining method. In their DSS, Fuzzy AHP is used to determine the weight of each criterion by decision makers and then the methods are ranked via TOPSIS. Azadeh et al. (2010) modified the well-known MMS technique of Nicholas. They solved the MMS problem using Fuzzy AHP within 2 steps: in the first step mining alternatives were ranked according to technical and operational criteria while in the second step, the most profitable among them was selected based on economic criteria. Naghadehi et al. (2009) proposed application of Group Fuzzy AHP approach to select optimum underground mining method for Jajarm bauxite mine. Alpay and Yavuz (2009) used Yager's method and Fuzzy AHP approach to develop a computer program to select the best underground mining method. The process of solving MMS problem by decision making models can be divided into two stages: Stage 1: Determining relative weight associated with each criterion. Stage 2: Selecting the most suitable mining method with respect to all criteria. Considering the above mentioned literature, we realized that researchers have faced two difficulties in process of solving MMS problem: (i) calculation of relative weight associated with each criterion in the first stage, (ii) uncertainty in judgment for decision makers in both stages. According to previous studies, for the first stage, AHP had been a common approach to calculate weights of criteria. There are too many factors related to MMS problem such as geological and geotechnical properties, economic parameters and geographical factors; so it is very difficult to make pairwise comparisons in AHP. Moreover, the process of solving the problem is time-consuming and eventually may lead to unrealistic outcomes because of inconsistency in comparison matrix. Dealing with this difficulty, some researchers tried to reduce the dimensions of pairwise comparisons matrix. In this way, Naghadehi et al. (2009) selected the most important criteria among all criteria. It is obvious that in this approach, some criteria which are involved in MMS problem are eliminated. Also, some other researchers divided criteria into subgroups. (Azadeh et al., 2010; Alpay & Yavuz, 2009; Namin et al., 2009; Mikaeil et al., 2009). It is clear that this approach prevents comparison of individual criteria belonging to different subgroups and comparisons are limited among subgroups and members of each group. Furthermore, too computational effort remained a significant difficulty. Although AHP method has been widely used in the first step, some researchers developed a preference voting system to determine the weights of criteria (Ataei et al., 2008a, 2008b; Mohsen et al., 2009). In such systems the weight associated with each ranking place was predefined in a subjective way. The rest of approaches used linguistic terms to determine the weights of criteria (Namin et al., 2009). Such choices are also subjective. In this paper to calculate the weights of criteria, we applied a preference voting system (PVS). The main difference between this PVS with those which proposed in previous research, is in procedure of determining relative weight associated with each ranking place. This PVS uses a DEA model to determine the weights associated with ranking places which maximizes the lower bound of relative score of each candidate. This approach decreases the subjectivity in determining weights of ranking places and the results are more reliable. In addition, dealing with the second difficulty (i.e. uncertainty in judgment), researchers mainly used fuzzy approach which itself requires much computational effort. Since applying PVS leads to prioritizing criteria without the need to determine priority levels, uncertainty in judgment is reduced in more simple way than Fuzzy approach. Considering the 2nd stage, several decision making methods have been applied by researchers for MMS problem, such as AHP, TOPSIS and PROMETHEE. In this paper, to overcome the second difficulty (i.e. uncertainty in judgment), again we applied a PVS for alternatives according to each criterion. Then we aggregated all preferences with the weights that had been calculated in previous stage for each criterion. Finally, we computed an ultimate score for each alternative. Using these scores, we are able to rank alternatives and select the best one. In this approach decision makers only determine the priorities of alternatives with respect to each criterion. So, the subjectivity and uncertainty in judgment are decreased. Moreover, unlike previous methods, by means of this approach, we are able to use all criteria involved in MMS problem as a result of its less computational effort. Furthermore, this PVS enables us to perform a group decision making with many decision makers in a more simple way. The paper is organized as follows. In section 2 Preference Voting System (PVS) is introduced. In section 3 we applied a HPVS for mining method selection problem. In section 4 we investigated a case study and finally a conclusion has been made. 2. Preference Voting System In preference voting systems, each voter selects m candidates from among n candidates (n m) and ranks them from the most to the least preferred. Each candidate may receive some votes in different ranking places. The total score of each candidate is the weighted sum of the votes he/she receives in different places (Wang et al., 2007) that is defined as follow: (1) Let wj be the importance weight of j th ranking place (j = 1, ..., m) and vij be the vote of candidate i being ranked in the j th place. The structure of PVS is shown in Table 1. In this structure, the winner is the one with the highest total score. So, the key issue of the preference aggregation in a PVS is how to determine the weights associated with different ranking places (i.e. (wj)). TABLE 1 Structure of preference voting system p1 Candidates w1 candidate1 ... v11 ... Ranking Places pj ... pm Weights of ranking places ... wj ... wm Vote of each candidate in each ranking place ... v1j ... v1m ... Total Scores z1 = å j =1v1j wj ... candidatei ... vi1 ... vij ... vim ... j =1vij wj ... candidaten vn1 ... vnj ... vnm zn = å j =1vn j wj Broda-Kendall (BK) method (Cook & Kress, 1990) is a well-known approach to identify the weights. This approach assigns weights m, m ­ 1, m ­ 2, ..., 1 to m ranking places, from the highest ranking place to the lowest respectively. These weights are produced in a simple way, but their production process is quite subjective. To reduce subjectivity in generating weights, Cook and Kress (1990) proposed the application of Data Envelopment Analysis (DEA) in this problem, which considered candidates as Decision Making Units (DMUs). Their proposed model calculates weights for each candidate that maximizes its total score. Thereafter, the model is solved once for each candidate and the total score is computed. The candidate with the highest total score is considered as DEA efficient. This model is shown below: Maximize (2) Subject to å j=1vij wj £ 1 wj ­ wj +1 d(j, ) wm d(m,) j = 1, ..., m ­ 1 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. So 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: Maximize Subject to m m (3) å j=1vij wj £ 1 w1 2w2 ... mwm wm ³ e = 2 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 predetermine any parameters such as . These models are given as follows: Maximize Subject to (4) ³a å j=1 wj = 1 Model (4) determines weights for all candidates using a linear DEA model which maximizes the common lower bound of total scores (i.e. ). Also the sum of weights is equal to 1. Maximize Subject to (5) a £ j =1 vij wj £ 1 Model (5) determines weights in a same way, but the common upper bound of total scores are equal to 1. Also there is no constraint for sum of weights. Maximize Subject to (6) å j=1 wj2 = 1 Model (6) specifies weights for each candidate using a nonlinear DEA model which 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. Since, this study deals with too many candidates, we use model (4) to determine the weights associated with different ranking places due to its less computational effort. 3. Developing a HPVS for MMS problem We considered MMS problem to have a hierarchical structure, as shown in Figure 1. 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. Considering this structure, MMS problem is divided into 2 stages. (I) Ranking criteria and calculating their relative weights. (II) Ranking alternatives with respect to each criterion and selecting the most suitable alternative according to all criteria. Fig. 1. Hierarchical structure of problem 4. Ranking criteria and calculating their relative weights According to the reasons mentioned in section 1, we applied a preference voting system to calculate relative weight of each criterion. Applying Group decision making in methods which mentioned in literature, requires much computational effort, while PVS needs less calculations. The structure of PVS for criteria is shown in Table 2. TABLE 2 Structure of preference voting system for criteria Criteria Importance Levels ... ILk ... ILp Weights of importance levels ... wk ... wp w1 Vote of each criterion in each ranking place IL1 v11 ... v1k ... v1p ... Total Scores Weights C1 ... TC1 = å k =1v1k wk W1 ... Wj ... Wm Cj ... vj1 ... vjk ... vjp ... TCj = å k =1vjk wk Cm vm1 ... vmk ... vmp TCm = å k =1vmk wk To characterize the relative importance of each criterion, we defined a set of importance levels as ranking places: {IL1, ..., ILk, ..., ILp}, where IL1, ..., ILk, ..., ILp represent the importance from the most to the least and p is the number of importance levels. We asked decision makers from different domains to assess criteria in p importance levels. vjk s are the numbers of the decision makers who assess criterion j (Cj) in importance level ILk (k = 1, ..., p). Let wk be the weights associated with importance levels ILk (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: TCj = å k =1vjk wk ... ... (7) where TCj is the total score obtained by criterion j. Using these scores we are able to rank the criteria. After normalizing these scores, the weights associated with each criterion (Wj) could be calculated. 4.1. Ranking alternatives with respect to each criterion and selecting most suitable alternative associated with all criteria To deal with uncertainty of decisions on MMS problem, researchers mainly used Fuzzy theory. The fuzzy approach could be very helpful in situations dealing with uncertainty in decision making; however, as the number of decision makers rise, computational effort increases too. In this paper we applied a PVS to rank alternatives with respect to each criterion. Since, with the application of this approach, decision makers only need to determine the priority of alternatives (rather than amount of priority) according to each criterion, uncertainty in judgment will be decreased. Moreover, it simplifies group decision making with too many decision makers. The structure of this approach is shown in Table 3. TABLE 3 Structure of preference voting system for alternatives C1 Alternatives W1 ... Criteria Cj ... Cm Wm Ranking Places RPm1 ... RPmhm ... wmhm v1mhm ... Ultimate Scores Weights of each criterion ... Wj ... Ranking Places ... RPj1 ... RPj ... Ranking Places ... RP11 ... RP1h1 ... w11 ... w1h1 v11h1 ... Weights of each ranking place ... wj1 ... wj ... wm1 v1j1 ... v1j ... v1m1 ... Vote of each alternative in each ranking place A1 ... v111 ... UT1 = å j =1( å h =1v1jh wjh)Wj ... Ai ... vi11 ... vi1h1 ... vij1 ... vij ... vim1 ... vimhm ... UTi = å j =1( å h =1vijh wjh)Wj å j =1( å h =1vn jh wjh )Wj ... An vn11 ... vn1h1 ... vnj1 ... vnj ... vnm1 ... vnmhm UTn = To distinguish the priorities of alternatives with respect to each criterion, we define a set of ranking places: {RPj1, ..., RPj} (j = 1, ..., m) for each criterion, where RPj1, ..., RPj represent priority from the most to the least and is the number of ranking places for criterion j. By this definition, we can use different numbers of ranking places for different criteria to assess. Note that if two or more alternatives have no priority over each other, they can be assigned to a similar ranking place. To evaluate alternatives, we conduct a preference voting among decision makers who were selected from different functional areas. The priorities of alternatives over each other with respect to each criterion are characterized based on their utility. In other words, if a criterion represents benefit, then the alternative which has more benefit will be located in an upper ranking place. Likewise, if a criterion represents cost, then the alternative which has less cost, will be located in an upper ranking place. Using this approach, after voting, we are able to assume all criteria as benefit. Let vijh be the vote of alternative i () being ranked in the hth ranking place associated with j th criterion and wjh be the importance weight of hth ranking place with respect to j th criterion. As mentioned earlier we can calculate wjh by applying model (4). Then the total score of each alternative with respect to each criterion could be obtained just like equation (7). To aggregate preferences for all criteria we can exploit the following equation: UTi = å j =1(å =1 vijh wjh )Wj m h (8) where UTi is the ultimate score for alternative i. Finally the most suitable mining method is the one with the highest ultimate score. 5. Case Study In order to investigate the competence of this technique for MMS problem, we chose central mine of Tabas coal mine to conduct a case study. It is located in Parvadeh district in east of central Iran, west of the Yazd state, northwest of Lout Desert and southeast of Tabas city. It is in longitudes of 56°46'30" to 56°51'40" N and latitudes 33°02'15" to 33°59'48" E. The coal-bearing sediments are within the Iranian structural facies region from a part of the Shemshak Group, which is of Lower-Triassic to Mid-Jurassic era. Physical parameters such as deposit geometry (Ore body dip, thickness, volume and depth) rock mechanics characteristics have been shown in Table. 4. TABLE 4 Some information about Central Mine of Tabas Coal Mine Ore body Geomechanical data Hydrogeology Ore body dip Ore body thickness Ore body depth Ore body volume Mineable reserve Production rate Existence of strata gases Ore body RMR Hanging wall RMR Footwall RMR Hydrogeology conditions 12° 1.95 m 50 to 150 m 400000 m3 1.1 Million Tonnes 250000 Annual 5 to 15 m3/tonne 30 10 to 24 10 to 24 Dry Also some characteristics of primary non-coal lithology could be found in Table. 5. In this study, six feasible alternative methods (Traditional Longwall , Traditional Longwall with filling, Mechanized Longwall, Traditional Room & Pillar, Mechanized Room & Pillar and Shortwall), which obtained based on thoughts of experts, were evaluated with respect to 32 criteria. The list of criteria has been shown in Table. 6. Also 5 decision makers participated in decision making process. TABLE 5 Average of the results for three primary non-coal lithologies Lithology SG Porosity Comp. strength (MN/m2) Shear Strength (MN/m2) Slake% RQD Sandstone Siltstone Mudstone TABLE 6 Criteria for MMS problem Criteria Criteria Criteria C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 Ore body dip Ore body thickness Ore body depth Grade distribution Ore body volume Ore body uniformity Ore body RMR Hanging wall RMR Footwall RMR Hydrogeology conditions Climate of area C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 Production rate Recovery Development production Production per man shift Selectivity mining Flexibility (Ability of changing a mining method to another similar methods) Dilution Development rate (Rate of achieving to ore body since start of the project) Mineable reserve Existence of strata gases Ventilation C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 Technology availability Ability to mechanize and automate Labor availability Environmental aspects Surface subsidence Safety Occupational interests Capital costs Operating costs Reclamation/rehabilitation costs Based on previous section, at first stage we calculated weight of each criterion. We defined 4 importance levels: {Really Important, Quite Important, Not Very Important, Not Important}, where these importance levels represent the importance from the most to the least. It is clear that the votes in the last importance level (i.e. Not Important) should not influence the total score of each criterion. Because, from the perspective of decision makers, such criteria are known as not important criterion in decision making process. So, we considered the weight of this importance level equal to zero and applied model (4) based on 3 importance levels as ranking places to calculate the weights. Then we calculated score and normalized weight of each criterion according to previous section. The results could be found in Table. 7. TABLE 7 Preference voting for criteria related to their importance levels and weights obtained at the first stage of HPVS Weights of importance levels 0.273 0.182 0 Importance levels Really Quite Not very Not important important important important Vote of each criterion in each importance level 2 3 4 5 0.545 Criteria Total score for each criterion Normalized weight for each criterion C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 3 3 0 4 0 0 4 5 1 5 2 3 1 5 3 2 3 2 5 2 2 5 3 0 3 4 1 SUM In the second stage, we conducted a preference voting among decision makers about the priorities of alternatives over each other with respect to each criterion. Also, we applied model (4) to produce weights of ranking places. An example of this procedure for Surface subsidence criterion could be found in Table 8. Also, scores of each alternative with respect to each criterion are shown in Table. 9. Finally we calculated ultimate scores of alternatives and ranked them according to their scores. The result of the second stage has been shown in Table 10. According to Table 10, ,,Mechanized Longwall" was selected as the most suitable mining method from the perspective of all decision makers. TABLE 8 Preference voting for alternatives with respect to "Surface subsidence" criterion at the second stage of HPVS Weight of criterion 0.0323974 Ranking Places RP27­1 RP27­2 RP27­3 RP27­4 RP27­5 RP27­6 Score Weights of Ranking Places 0.444444 0.222222 0.148148 0.111111 0.074074 0 Vote of each alternative in each ranking place 1 2 1 1 0.0227982 4 1 1 1 1 4 3 2 1 4 1 1 1 0.0647948 0.0647948 0.0647948 0.0407967 0.0227982 TABLE 9 Alternatives Traditional Longwall Traditional Longwall with filling Mechanized Longwall Traditional Room& Pillar Mechanized Room & Pillar Shortwall Scores of alternatives with respect to criteria Alternatives Criteria 1 Traditional Longwall 2 Traditional Traditional Mechanized Mechanized Longwall Room& Room & Longwall with filling Pillar Pillar 3 4 5 6 Shortwall 7 Ore body dip Ore body thickness Ore body depth Grade distribution Ore body volume Ore body uniformity Ore body RMR Hanging wall RMR Footwall RMR Hydrogeology conditions Climate of area Production rate Recovery Development production Production per man shift Selectivity mining Flexibility (Ability of changing a mining method to another similar methods) Dilution Development rate (Rate of achieving to ore body since start of the project) Mineable reserve Existence of strata gases Ventilation Technology availability Ability to mechanize and automate Labor availability Environmental aspects Surface subsidence Safety Occupational interests Capital costs Operating costs Reclamation/rehabilitation costs TABLE 10 Scores for alternatives and ranking Alternatives Ultimate Score Ranking Traditional Longwall Traditional Longwall with filling Mechanized Longwall Traditional Room& Pillar Mechanized Room & Pillar Shortwall 6. Conclusion In this paper we applied a HPVS for mining method selection problem. This PVS uses a DEA model to produce weights associated with each ranking place. The process of solving the problem consists of two stages. At the first stage, criteria are ranked and relative weight according to each one is calculated. Then in the second stage, mining methods are ranked by their scores. A case study was also investigated to illustrate the competence of presented method. We showed that by application of HPVS for MMS problem, some difficulties related to the previous methods could be reduced. Also, regarding to application of a mathematical model, outcomes are more reliable. Moreover, this approach could be applied simply in group decision making with too many decision makers. It is expected that in the near future this method will be applied to various aspects of mining engineering.

Journal

Archives of Mining Sciencesde Gruyter

Published: Dec 1, 2012

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