Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach
محورهای موضوعی : Mathematical OptimizationKailash 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
کلید واژه: Fuzzy Goal Programming, Membership function, Multilevel fractional programming, Tolerance values,
چکیده مقاله :
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.
