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Fuzzy Goal Programming Method for Solving Multi-Objective Transportation Problems

The multi-objective transportation problem refers to a special class of vector minimum linear programming problem, in which constraints are of inequality type and all the objectives are non-commensurable and conflict with each other. A common problem encountered in solving such multi-objective problems is that to identify a compromise solution among a large number of non-dominated solutions, the decision maker has to develop a utility function for meeting the desired goal. In this paper, fuzzy membership functions are considered and deviation goals also taken for each objective function. Fuzzy max-min operator is implemented to show the effectiveness of the proposed methodology. LINGO software package is used to solve constrained optimization problem. To illustrate the proposed method, two numerical examples are solved and the results have been compared with interactive, fuzzy and deviation criterion approaches.