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

The Multi-objective Solid Transportation Problem (MSTP) refers to a special class of vector-minimum linear programming problems, in which constraints are all equality type and the objectives, are conflicting in nature. A generalization of multi-objective solid transportation problem, in which the supply, demand and capacity constraints are not only equality type but also of inequality type is considered. All methods either generate a set of non-dominated solution or find a compromise solution. In this paper, fuzzy programming technique is applied to solve multi-objective solid transportation problem. Special type of non-linear membership functions - Hyperbolic and Exponential are used to represent objective function into fuzzy environment. It gives an optimal compromise solution. The obtained result has been compared with the solution obtained by using a linear membership function. The method is illustrated with a numerical example