Multi Objective Multi Item Fuzzy Transportation Problem with Congestion Charge

Abstract

In the present scenario supply, demand and transportation cost per unit of the commodity in multi objective transportation problem for multi items may be rarely specified precisely due to uncertain conditions. Vehicular emission generates harmful air pollutants in urban areas which leads to severe health hazardous. In this paper, a multi objective profit transportation problem for multi items has been framed and solved in fuzzy environment, it emphasizes on fuzzy methodology to solve transportation problem to minimize the travel time and maximize the profit by reducing emission charge during traffic congestion. Unit transportation cost, environmental protection cost, transportation time and congestion charge during peak time and non peak time, loading and unloading time, total supply and demand, selling and purchasing prices are all considered as triangular type-2 fuzzy numbers. Then the multi objective profit transportation problem has been transformed into single objective transportation problem by applying Fuzzy Goal programming Technique (FGPT) and Weighted Fuzzy Goal Programming Technique (WFGPT) and the corresponding model is solved using Generalized Reduced Gradient (GRG) method LINGO-(18.0). Numerical illustration has been given to show the efficiency of the proposed model.