FUZZY PROGRAMMING TECHNIQUE TO SOLVE MULTI-OBJECTIVE SOLID TRANSPORTATION PROBLEM WITH SOME NON-LINEAR MEMBERSHIP FUNCTIONS
Authors: Bodkhe S.G., Bajaj V.H., Dhaigude D.B.
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The Multi-objective Solid Transportation Problem (MSTP) refers to a special class of vectorminimum 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.