Transportation Problem of Multi-objective Multi-item Solid Using Fuzzy Environment

Abstract

The transportation issue pertains to the reservation of fully loaded vehicles, which may include light commercial vehicles, medium-duty trucks, and heavy-duty trucks, among others. The transportation costs are incurred irrespective of whether the vehicle's capacity is fully utilized. Moreover, instead of transporting a single item, it may be essential to transfer various types of items from multiple sources to different destinations utilizing a variety of conveyances. The optimal transportation approach can be affected by several factors, such as the volume and weight of each product unit, as well as the insufficient availability of a sufficient number of specific vehicle types. This paper introduces a formulation of a multi-objective, multi-item solid transportation problem that considers all these factors. The problem is characterized by transportation cost and time parameters that are treated as fuzzy variables. By utilizing the credibility theory of fuzzy variables, a chance-constraint programming model is created and subsequently transformed into its deterministic equivalent. Lastly, a numerical example is included to illustrate the problem.