Fuzzy programming technique to solve multi-objective transportation problems with some non-linear membership functions

Abstract

The Multi-objective transportation problem refers to a special class of vector-minimum linear programming problems in which the constraints are of equality type and all the objectives are non-commensurable and conflict with each other. All the methods either generate a set of non-dominated solutions or find a compromise solution. In this paper, we use a special type of non-linear (hyperbolic and exponential) membership functions to solve the multi-objective transportation problem. It gives an optimal compromise solution. The obtained result has been compared with the solution obtained by using a linear membership function. To illustrate the methodology a numerical example is presented.