Fuzzy Efficient Interactive Goal Programming Approach for Multi-objective Transportation Problems

Abstract

Multi-objective transportation problem (MOTP) is a special case of vector minimization linear optimization problem with equality constraints and the objectives are conflicting in nature. Due to the conflicting nature of objectives, no method is available to find single optimal solution for MOTP. All the methods can find only the compromise solution. This paper presents an efficient method for solving MOTP to find fuzzy efficient and compromise solution using the qualities of three well known approaches i.e. (i) fuzzy programming, (ii) goal programming, (iii) interactive programming. In this approach, fuzzy goals are decided by the decision maker (DM) for each objectives and membership functions are constructed for each objective. Then the method is developed using fuzzy set theory and the best quality of the developed method is that the decision maker is focussed only in the part of evaluation of the solution at each step using the acceptable terms and conditions. The present method is the extension of Waeil and Lee (Omega 34:158–166, 2006). To measure the efficiency of the method, some distance metric functions are used and it is verified by two numerical examples. The results are compared with previous reported work for the same numerical problems.