Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach

Subject Areas : Mathematical Optimization

Kailash Lachhwani ¹ , Mahaveer Prasad Poonia ²

1 - Department of Mathematics, Government Engineering College, Bikaner 334004, India
2 - Department of Mechanical Engineering, Government Engineering College, Bikaner, 334004, India

Received: 2020-10-01 Accepted : 2020-10-01 Published : 2012-01-01

Keywords: Fuzzy Goal Programming, Membership function, Multilevel fractional programming, Tolerance values,

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.