An Iterative Algorithm for a Capacitated Multi-Facility Weber Problem with Fuzzy Demands

A capacitated multi-facility Weber problem (CMFWP) is widely used in both theoretic and practical environments. The most studies in this field tackled the problem either by deterministic or probabilistic orientation. Nevertheless, in the real world, some parameters (e.g., demand) are usually imprecise (fuzzy) in nature. Thus, in this paper, we address the CMFWP with fuzzy demands. To solve this problem, the Jimenez method is considered as the defuzzification method, and an iterative approach including the Weiszfeld´s algorithm and linear programming (LP) are used to solve the resulting crisp problem efficiently. To assess the performance of the proposed heuristic method, the computational results are obtained using a data set taken from the literature. These results demonstrate that the new approach can provide encouraging results within the promising amount of computational time.