Decision-Support Framework for Type-2 Fuzzy Multi-Choice Transportation Models

Abstract

The Multi-Choice Transportation Problem (MCTP) is an important extension of the classical transportation problem in which multiple transportation cost alternatives are available between each source and destination. In practical transportation systems, transportation costs, supplies and demands are often uncertain and cannot be represented accurately by crisp values. To address this issue, this study presents a Type-2 fuzzy framework for solving the MCTP under uncertain environments. The transportation costs, supplies and demands are represented as multi-choice interval Type-2 fuzzy numbers to capture the higher-order uncertainty. The Karnik-Mendel (KM) type-reduction algorithm is implemented to convert the Type-2 fuzzy parameters into the precise values using the defuzzification. The resulting crisp transportation problems are solved using Vogel’s Approximation Method (VAM) to obtain an initial basic feasible solution and apply the Modified Distribution (MODI) method to determine the optimal transportation plan. Further, the obtained optimal solutions are verified using the LINGO software. Numerical computations involving four transportation cost choices to demonstrates the working of the presented framework. The computational results show that the proposed approach efficiently handles uncertainty while producing reliable and optimal transportation plans. Furthermore, the comparative analysis identifies the transportation choice corresponding to the minimum transportation cost, thereby providing an effective decision-support framework for transportation planning under uncertainty.