A Model for Solving Uncertain Multi-Objective Solid Transportation Problem

A Model for Solving Uncertain MOSTP

Abstract

Solid transportation problem (STP) extends the classic transportation model into three dimensions by incorporating sources, destinations, and different modes of transport, known as conveyances. This paper addresses the Uncertain Multi-objective Solid Transportation Problem (UMOSTP), a complex variant where the goal is to simultaneously minimize total transportation cost and time under conditions of uncertainty. Fuzzy cost coefficients are used here to represent the ambiguity introduced by variables such as route availability and fluctuating fuel prices. Using the $\alpha$-cut method, we first translate these fuzzy costs into precise numerical values. We then use a Modified Vogels Approximation Method (MVAM) to identify a basic feasible initial solution that satisfies all supply, demand, and conveyance constraints while optimising cost and time. There is a comparison with the conventional Vogels Approximation Method (VAM). A numerical example illustrating the efficacy of the suggested model reveals that MVAM offers a more practical and efficient solution for the UMOSTP.