Facility Location Selection using PROMETHEE II Method

Transcription

1 Proceedings of e 200 International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh, January 9 0, 200 Facility Location Selection using PROMETHEE II Meod Viay Manikrao Aawale Department of Mechanical Engineering, Government Polytechnic Amravati , India Shankar Chakraborty Department of Production Engineering, Jadavpur University Kolkata , India Abstract Selecting a location for a new organization or expansion of an existing facility is of vital importance to a decision maker. The cost associated wi acquiring e land and facility construction makes e facility location a long-term investment decision. The best location is at which results in higher economic benefits rough increased productivity and good distribution network. Selecting e proper facility location from a given set of alternatives is a difficult task, as many potential qualitative and quantitative criteria are to be considered. This paper solves a real time facility location selection problem using PROMETHEE II (preference ranking organization meod for enrichment evaluation meod which is an effective multi-criteria decision-making (MCDM tool often applied to deal wi complex problems in e manufacturing environment. Keywords: Facility location, Multi-criteria decision-making, PROMETHEE. Introduction Facility location decisions are observed to be of immense importance in long-term planning for e manufacturing organizations. High costs related to property acquisition and facility construction make e facility location selection a long-term investment decision. The location selection decision may be required due to various reasons, like change in production capacity, addition or deletion of product line, change in distribution cost or change in customer demand. Wrong selection of location may result in inadequate qualified work force, unavailability of raw materials, insufficient transportation facility, increased operating expenses or even disastrous effect on e organization due to political and societal interference. Thus, e decision maker must select e location for a facility at will not only perform well, but also it will be flexible enough to accommodate e necessary future changes. Various important qualitative and quantitative criteria, such as availability of resources for production, investment cost, nearness of oer facilities etc. are usually considered while selecting a facility location for a specific industrial application. The success or failure of a manufacturing organization largely depends on e consideration of ose criteria as ey directly influence e organizational performance. Selection of a proper location involves consideration of multiple feasible alternatives. It is also observed at e selection procedure involves several obectives and it is often necessary to make compromise among e possible conflicting criteria. For ese reasons, multi-criteria decisionmaking (MCDM is found to be an effective approach to solve e location selection problems. In is paper, e preference ranking organization meod for enrichment evaluation (PROMETHEE II is employed to obtain e best choice from a finite set of alternative facility locations. While applying e PROMETHEE II meod to solve a real time facility location selection problem [], it is observed at is meod proves its applicability and potentiality to solve such types of decision-making problems wi multiple conflicting criteria and alternatives. 2. Literature Review Past researchers have already applied different techniques to solve facility location selection problems. But most of ose techniques use complex maematical formulations, while ignoring qualitative information regarding criteria values. Randhawa and West [2] proposed a solution approach to facility location selection problems while integrating analytical and multi-criteria decision-making models. Houshyar and White [3] developed a maematical model and heuristics approach at assigns N machines to N equal-sized locations on a given site such at e total adacency flow between e machines is maximized. The proposed model is based on a 0- integer programming formulation which may produce an optimal, but infeasible solution, followed by e heuristic which begins wi e 0- integer solution and generates a feasible solution. Owen and Daskin [4] provided an overview of e

2 Viay Manikrao Aawale, Shankar Chakraborty meodologies at have been developed for solving facility location selection problems. Chu [5] presented a fuzzy TOPSIS (technique for order preference by similarity to ideal solution meod-based approach for e plant location selection problems. The ratings and weights assigned by e decision makers are first normalized into a comparable scale. The membership function of each normalized rating of each alternative location for each criterion is en developed. A closeness coefficient is proposed to determine e ranking order of e alternatives. Klose and Drexl [6] reviewed in details e contributions to e current state-of-e-art related to continuous location models, network location models, mixed-integer programming models and eir applications to location selection decision. Yong [7] proposed a new fuzzy TOPSIS meod which deals wi e selection of plant location decision-making problems in linguistic environment, where e ratings of various alternative locations under different criteria and eir relative weights are assessed in linguistic terms represented by fuzzy numbers. Farahani and Asgari [8] presented a TOPSIS meodology to find e supportive centers wi e minimum number and maximum quality of locations in military logistic systems. Önüt and Soner [9] employed a fuzzy TOPSIS based meodology to solve e solid waste transshipment site selection problem, where e criteria weights are estimated using analytic hierarchy process (AHP. Amiri et al. [0] applied TOPSIS meod along wi heuristics based on fuzzy goal programming to select e best location. The facility location selection problem is solved in ree stages, i.e. (a finding e least number of distribution centers, (b locating em in e best possible location, and (c finding e minimum cost of locating e facilities. Alough e facility location selection problems have already been solved using different MCDM techniques, is paper makes a maiden attempt to implement anoer appropriate MCDM approach, i.e. PROMETHEE II meod to tackle is complex location selection decision-making problem. 3. PROMETHEE Meod Preference function based outranking meod is a special type of MCDM tool at can provide a ranking ordering of e decision options. The PROMETHEE (preference ranking organization meod for enrichment evaluation meod was developed by Brans and Vincke in 985 []. The PROMETHEE I meod can provide e partial ordering of e decision alternatives, whereas, PROMETHEE II meod can derive e full ranking of e alternatives. In is paper, e PROMETHEE II meod is employed to obtain e full ranking of e alternative locations for a given industrial application. The procedural steps as involved in PROMETHEE II meod are enlisted as below [, 2]: Step : Normalize e decision matrix using e following equation: R = X min(x max(x min(x (i =,2,..., n : =,2,..., m ( i i i i i where X i is e performance measure of i alternative wi respect to criterion. For non-beneficial criteria, Eqn. ( can be rewritten as follows: R = max(x X max(x min(x (2 i i i i i Step 2: Calculate e evaluative differences of i alternative wi respect to oer alternatives. This step involves e calculation of differences in criteria values between different alternatives pair-wise. Step 3: Calculate e preference function, P (i,. There are mainly six types of generalized preference functions as proposed by Brans and Mareschal [2, 3]. But ese preference functions require e definition of some preferential parameters, such as e preference and indifference resholds. However, in real time applications, it may be difficult for e decision maker to specify which specific form of preference function is suitable for each criterion and also to determine e parameters involved. To avoid is problem, e following simplified preference function is adopted here: P (i, = 0 if R i R (3 P (i, = (R i R if R i > R (4 Step 4: Calculate e aggregated preference function taking into account e criteria weights. m Aggregated preference function, = m π (i, = w x P (i, w (5 = where w is e relative importance (weight of criterion. Step 5: Determine e leaving and entering outranking flows as follows:

3 Viay Manikrao Aawale, Shankar Chakraborty Leaving (or positive flow for i alternative, φ + (i = π(i, n n = n Entering (or negative flow for i alternative, φ - (i = π(,i n = (i (i where n is e number of alternatives. Here, each alternative faces (n number of oer alternatives. The leaving flow expresses how much an alternative dominates e oer alternatives, while e entering flow denotes how much an alternative is dominated by e oer alternatives. Based on ese outranking flows, e PROMETHEE I meod can provide a partial preorder of e alternatives, whereas, e PROMETHEE II meod can give e complete preorder by using a net flow, ough it loses much information of preference relations. Step 6: Calculate e net outranking flow for each alternative. ϕ (i = ϕ + (i ϕ (i (8 Step 7: Determine e ranking of all e considered alternatives depending on e values of ϕ(i. The higher value of ϕ(i, e better is e alternative. Thus, e best alternative is e one having e highest ϕ (i value. The PROMETHEE meod is an interactive multi-criteria decision-making approach designed to handle quantitative as well as qualitative criteria wi discrete alternatives. In is meod, pair-wise comparison of e alternatives is performed to compute a preference function for each criterion. Based on is preference function, a preference index for alternative i over is determined. This preference index is e measure to support e hypoesis at alternative i is preferred to. The PROMETHEE meod has significant advantages over e oer MCDM approaches, e.g. multi-attribute utility eory (MAUT and AHP. The PROMETHEE meod can classify e alternatives which are difficult to be compared because of a trade-off relation of evaluation standards as noncomparable alternatives. It is quite different from AHP in at ere is no need to perform a pair-wise comparison again when comparative alternatives are added or deleted. 4. Illustrative Example Rao [] employed e graph eory and matrix approach (GTMA for selection of e best facility location for a given industrial application. The same example is considered here to demonstrate e applicability and effectiveness of PROMETHEE II meod as a MCDM tool. This example takes into account eight facility location selection criteria and ree alternative facility locations. The obective and subective information regarding different location selection criteria are given in Table. All ese criteria, except e cost of labor, are expressed subectively in linguistic terms. The obective values for ese criteria are assigned from an -point scale, as given in Table 2. The fuzzy udgments average (A, above average (AA, high (H and very high (VH, shown in Table, are considered equivalent to good, very good etc. wi respect to different criteria. The eight selection criteria as considered here to affect e location selection decision are closeness of market (CM, closeness to raw material (CR, land transportation (LT, air transportation (AT, cost of labor (CLR (in rupees/worker, availability of labor (AL, community education (E and business climate (BC. Among ese criteria, only CLR is a non-beneficial attribute and e remaining are e beneficial attributes. Table Information for facility location alternatives [] P H VH H AA 250 H AA VH P2 VH H H VH 265 AA H VH P3 A H VH AA 255 AA VH H At first, e information for various facility location alternatives wi respect to different criteria, as shown in Table, are converted to crisp scores using e -point scale, as given in Table 2. The transformed obective data, as given in Table 3, are en normalized using Eqn. ( or (2 and are given in Table 4. Rao [] determined e criteria weights for e considered criteria as w CM = 0.267, w CR = 0.267, w LT = , w AT = 0.057, w CLR = , w AL = , w E = and w BC = using AHP meod and e same criteria weights are used here for PROMETHEE II meod-based analysis. (6 (7

4 Viay Manikrao Aawale, Shankar Chakraborty Table 2 -point fuzzy scale Linguistic term Crisp score Exceptionally low Extremely low 0.35 Very low Low Below average 0.40 Average Above average High Very high Extremely high Exceptionally high Table 3 Obective data for facility location selection problem P P P Table 4 Normalized decision matrix P P P Now, e preference functions are calculated for all e pairs of alternatives, using Eqns. (3 and (4, and are given in Table 5. Table 6 exhibits e aggregated preference function values for all e paired alternatives, as calculated using Eqn. (5. The leaving and e entering flows for different location alternatives are now computed using Eqns. (6 and (7 respectively, and are shown in Table 7. Table 5 Preference functions for all e pairs of alternatives Location pair CM CR LT AT CLR AL E BC (P,P (P,P (P2,P (P2,P (P3,P (P3,P Table 6 Aggregated preference function Location P P2 P3 P P P Table 7 Leaving and entering flows for different locations Location Leaving flow Entering flow P P P

5 Viay Manikrao Aawale, Shankar Chakraborty Table 8 Net outranking flow values for different location alternatives Location Net outranking flow Rank P P P The net outranking flow values for different alternative locations and eir relative rankings are given in Table 8. Now, e alternative locations are arranged in descending order according to eir net outranking flow values. The best choice of location for e given industrial application is location 2, which exactly matches wi e observations as derived by Rao [] while solving is problem using graph eory and matrix approach. This proves e applicability and potentiality of e PROMETHEE II meod for solving complex decision-making problems in e manufacturing domain. 5. Conclusions Location selection decision has long-term implications because changing e locations of e existing facilities may be quite expensive. It is erefore important to select e most appropriate location for a given industrial application which will minimize e cost over an extended time period. The problem of facility location selection is a strategic issue and has significant impact on e performance of e manufacturing organizations. The present study explores e use of PROMETHEE II meod in solving a location selection problem and e results obtained can be valuable to e decision maker in framing e location selection strategies. It is also observed at is MCDM approach is a viable tool in solving e location selection decision problems. It allows e decision maker to rank e candidate alternatives more efficiently and easily. The cited real time industrial example demonstrates e computational process of e PROMETHEE II meod and e same can also be applied to oer strategic decision-making problems. 6. References. Rao R.V., 2007, Decision Making in e Manufacturing Environment using Graph Theory and Fuzzy Multiple Attribute Decision Making Meods, Springer-Verlag, London. 2. Randhawa S.U., and West T.M., 995, An integrated approach to facility location problem, Computers and Industrial Engineering, 29, Houshyar A., and White B., 997, Comparison of solution procedure to e facility location problem, Computers and Industrial Engineering, 32, Owen S.H., and Daskin M.S., 998, Strategic facility location: A review, European Journal of Operational Research,, Chu T.-C., 2002, Selecting plant location via a fuzzy TOPSIS approach, International Journal of Advanced Manufacturing Technology, 20, Klose A., and Drexl A., 2005, Facility location models for distribution system design, European Journal of Operational Research, 62, Yong D., 2006, Plant location selection based on fuzzy TOPSIS, International Journal of Advanced Manufacturing Technology, 28, Farahani R.Z., and Asgari N., 2007, Combination of MCDM and covering techniques in a hierarchical model for facility location: A case study, European Journal of Operational Research, 76, Önüt S., and Soner S., 2008, Transshipment site selection using e AHP and TOPSIS approaches under fuzzy environment, Waste Management, 28, Amiri M., Kazemi A., Sadaghiani J.S., Yaghoubi A., and Mashatzadegan H., 2009, Developing and solving a new model for e location problems: Fuzzy-goal programming approach, Journal of Applied Sciences, 9, Doumpos M., and Zopounidis, C., 2004, A multi-criteria classification approach based on pair-wise comparison, European Journal of Operational Research, 58, Hakowicz S., and Higgins, A., 2008, A comparison of multiple criteria analysis techniques for water resource management, European Journal of Operational Research, 84, Seo Y-J., Jeong H-Y., and Song Y-J., 2005, Best Web service selection based on e decision making between QoS criteria of service, L.T. Yang et al. (Eds., Springer-Verlag Berlin,