Solving a Fuzzy Capacitated Two-Index Transportation Problem

Abstract

The transportation problem is a fundamental model in operations research. It aims to minimize distribution costs while satisfying supply and demand constraints. The classical formulations of this problem rely on the assumption that all model parameters are perfectly known, which is rarely the case in real-world applications. In practice, unit transportation costs, availabilities, or demands are often subject to uncertainty or imprecision. To account for these aspects, the concepts of fuzzy logic, fuzzy sets, and fuzzy numbers have been introduced. These tools make it possible to formulate and analyze the two-index capacitated transportation problem in a fuzzy environment. The integration of fuzzy theory into transportation models provides a more realistic representation of decision-making situations and constitutes a particularly effective decision-support tool. In this dissertation, we focus on the study and resolution of a two-index capacitated transportation problem in a fuzzy context. To assess the performance of the proposed approach, we conducted a comparative numerical study with an advanced linear programming solver used as a benchmark. The obtained results are promising and confirm the effectiveness of our approach