Abstract
The objective of this paper is to present a technique for order preference by similarity to ideal solution (TOPSIS) algorithm to linear fractional bi-level multi-objective decision-making problem. TOPSIS is used to yield most appropriate alternative from a finite set of alternatives based upon simultaneous shortest distance from positive ideal solution (PIS) and furthest distance from negative ideal solution (NIS). In the proposed approach, first, the PIS and NIS for both levels are determined and the membership functions of distance functions from PIS and NIS of both levels are formulated. Linearization technique is used in order to transform the non-linear membership functions into equivalent linear membership functions and then normalize them. A possible relaxation on decision for both levels is considered for avoiding decision deadlock. Then fuzzy goal programming models are developed to achieve compromise solution of the problem by minimizing the negative deviational variables. Distance function is used to identify the optimal compromise solution. The paper presents a hybrid model of TOPSIS and fuzzy goal programming. An illustrative numerical example is solved to clarify the proposed approach. Finally, to demonstrate the efficiency of the proposed approach, the obtained solution is compared with the solution derived from existing methods in the literature.
Highlights
Bi-level programming is recognized as a powerful mathematical apparatus for modeling decentralized decisions with two decision makers (DMs) in a large hierarchical organization
The objective of this paper is to present a technique for order preference by similarity to ideal solution (TOPSIS) algorithm to linear fractional bi-level multiobjective decision-making problem
Bi-level programming problems (BLPPs) have the following common features: the firstlevel decision maker (FLDM) or the leader and the second-level decision maker (SLDM) or the follower independently controls a set of decision variables; each DM tries to maximize his/her own interest, but the decision of each DM is affected by the action and reaction of the other DM; each DM should have an intention to cooperate each other in the decision-making situation
Summary
Bi-level programming is recognized as a powerful mathematical apparatus for modeling decentralized decisions with two decision makers (DMs) in a large hierarchical organization. Bi-level programming has been applied to model real-world problems regarding flow shop scheduling (Karlof and Wang 1996), bio-fuel production (Bard et al 2000), natural gas cash-out (Dempe et al 2005), logistics (Huijun et al 2008), pollution emission price (Wang et al 2011), etc. Lai (1996) introduced the concept of tolerance membership function of fuzzy set theory to multi-level programming problems (MLPPs) for satisfactory decisions. Shih et al (1996) extended Lai’s satisfactory solution concept and proposed a supervised search approach to MLPPs based on max–min aggregation operator. Shih and Lee (2000) further extended Lai’s Bi-level programming has been applied to model real-world problems regarding flow shop scheduling (Karlof and Wang 1996), bio-fuel production (Bard et al 2000), natural gas cash-out (Dempe et al 2005), logistics (Huijun et al 2008), pollution emission price (Wang et al 2011), etc. Lai (1996) introduced the concept of tolerance membership function of fuzzy set theory to multi-level programming problems (MLPPs) for satisfactory decisions. Shih et al (1996) extended Lai’s satisfactory solution concept and proposed a supervised search approach to MLPPs based on max–min aggregation operator. Shih and Lee (2000) further extended Lai’s
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