• MULTIOBJECTIVE FRACTIONAL TRANSPORTATION PROBLEM IN FUZZY ENVORONMENT

Abstract

The fractional programming is a generalization of linear programming where the objective function is a ratio of two linear functions. Similarly, in fractional transportation problem the objective is to optimize the ratio of two cost functions or damage functions or demand functions. As the ratio of two functions is considered, the fractional programming models become more suitable for real life problems. Keeping in view the complexities associated with real life transportation problem like vagueness and uncertainty involved with the parameters. The implementation of fuzzy techniques can be very useful. Therefore, in this article a Fully Fuzzy Multi-objective Fractional Transportation Problem (FFMOFTP) is considered. All the coefficients of the parameters, demands and supplies are considered as fuzzy numbers. The purpose of using fuzzy numbers is to deal with the uncertainties and vagueness associated with the parameters. Two cases are considered, one with triangular and other with trapezoidal fuzzy numbers. The fuzzy problem is converted into crisp form by two ranking methods; Yager’s ranking method and Maleki ranking method respectively. The converted crisp problem is linearized by using Taylors series. Finally the compromise solution of the converted problem is obtained using fuzzy goal programming technique. The aim of this paper is not only to provide a method for solving FFMOFTP but also to evaluate the efficiency of the two ranking methods under the same circumstances. Two numerical problems for each case are also solved at the end to demonstrate the efficiency of the proposed approach.