Solution of a Multi-Objective and Multi-Index Real-Life Transportation Problem Using Different Fuzzy Membership Functions

Abstract

The paper presents the application of an exponential membership function to fuzzy programming technique for solving a multi-objective and multi-index real-life transportation problem. It focusses on the minimization of the transportation cost, deterioration rate and underused capacity of the transported raw materials like coal, iron ore, etc. from different sources to different destination sites at Durgapur Steel Plant, Durgapur, West Bengal, India, by different transportation modes like train, trucks, etc. A special type of non-linear (exponential) membership function is assigned to each objective function. Thus, the paper presents fuzzy programming approach with an exponential function to a real-life transportation problem and develops a non-dominated compromise solution. In addition, the interval-valued numbers used in supply and demand parameters represent the uncertainties in a real-life problems. The optimization models have a wide use in real-life multi-objective transportation problems. The use of fuzzy programming technique has been successfully concluded for the focussed transportation problem taking a linear and a hyperbolic membership function. But the numerical illustration shows that exponential membership function gives a better and comparable result for the problem.