Multi-choice multi-objective capacitated transportation problem — A case study of uncertain demand and supply

Abstract

In this paper, we study a special class of transportation problem with capacitated restrictions. The formulated multi-objective capacitated transportation problem (MOCTP) has some of the objective functions are linear and fractional; these objectives are conflicting in nature. This problem defined in an uncertain environment where the uncertainty in input information presented by the multi-choices and trapezoidal fuzzy numbers. The multi-choice in input information dealt with the binary numbers and transformed it into the equivalent deterministic form by the suitable method. While the other pattern of uncertainty in input information defined by the trapezoidal fuzzy numbers and handled by ranking function approach to get the crisp value. Due to the presence of the uncertainties, and the conflicting objective functions, we cannot directly solve the formulated multi-choice MOCTP. So, therefore, we solve the formulated MOCTP in two phases. In the first stage, we transform the uncertain MOCTP into the deterministic form by using the suitable solution procedure of multi-choice and fuzzy numbers respectively. In the second stage, we have suggested a goal programming solution procedure to linearise the fractional objective function and then solve the resultant MOCTP for the compromise solution. A case study has also done to illustrate the stepwise solution procedure.