Multi-objective multi-item solid transportation problem with fuzzy inequality constraints

Zimmermann (Int. J. Gen. Syst. 2: 209-215, 1976) first introduced the concept of fuzzy inequality in the field of linear programming problem (LPP). But this concept is hardly used in any real life applications of LPP. So, in this paper, a multi-objective multi-item solid transportation problem (MMSTP) with fuzzy inequality constraints is modeled. Representing different preferences of the decision maker for transportation, three different types of models are formulated and analyzed. Fuzzy inequality solid transportation problem is converted to parameter solid transportation problem by an appropriate choice of flexible index, and then the crisp solid transportation problem is solved by the algorithm (Cao in Optimal Models and Methods with Fuzzy Quantities, 2010) for decision values. Fuzzy interactive satisfied method (FISM), global criterion method (GCM) and convex combination method (CCM) are applied to derive optimal compromise solutions for MMSTP by using MatLab and Lingo-11.0. The models are illustrated with numerical examples and some sensitivity analysis is also presented.