Abstract
In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, fuzzy goal programming approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.
Highlights
Hierarchical optimization or multilevel programming problems (MLPPs) have the following common characteristics: interactive decision making units exist within predominantly hierarchical structures; the execution of decision is sequential from higher level to lower level; each decisionmaking unit independently controls a set of decision variables and is interested in maximizing its own objective but is affected by the reaction of lower level decision makers (DMs)
The fuzzy goal programming (FGP) approach to multidecision-making problems was introduced by Mohamed (1997) which is extended by Pramanik and Roy (2007) to solve MLPPs
An effort has been made to solve the multilevel fractional programming problem based on the fuzzy set theory and goal programming approach
Summary
Hierarchical optimization or multilevel programming problems (MLPPs) have the following common characteristics: interactive decision making units exist within predominantly hierarchical structures; the execution of decision is sequential from higher level to lower level; each decisionmaking unit independently controls a set of decision variables and is interested in maximizing its own objective but is affected by the reaction of lower level decision makers (DMs). In the FMP techniques of Sinha (2003a,b), the last (lower) level is the most important, and the decision of the lowest level remains either unchanged or closest to individual best decisions, which leads to the paradox that the decision power of the lowest level DM dominates the higher level DM To overcome such difficulties, the fuzzy goal programming (FGP) approach to multidecision-making problems was introduced by Mohamed (1997) which is extended by Pramanik and Roy (2007) to solve MLPPs. Baky (2009) used fuzzy goal programming to solve decentralized bilevel multiobjective programming problems. Pal and Gupta (2009) studied a genetic algorithm to fuzzy goal programming formulation of fractional multiobjective decision-making problems
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