Fuzzy Programming Technique for Solving Uncertain Multi-objective, Multi-item Solid Transportation Problem with Linear Membership Function

Abstract

The simple transportation problem (TP) is extended to the solid transportation problem (STP) by taking into consideration the mode of transportation as the third dimension along with the two dimensions of sources and destinations. A multi-objective, multi-item STP (MMISTP) with uncertain variables is known as uncertain MMISTP. Using the basic theory of uncertainty and the expected values of the uncertain parameters, the uncertain programming model is firstly converted into its deterministic form. By using the fuzzy programming technique, the transformed deterministic model is then solved using LINGO software to derive the optimal compromise solution of the problem. Finally, numerical examples are illustrated at the end to show the application of the uncertain programming model, and the obtained results are compared with results of other developed approaches.