Benders decomposition approach to solve the capacitated facility location problem

Facility Location (FL) problems as one of the most important problems in operations research aim to determine the location of a set of facilities in a way that the total costs, including costs of opening facilities and transportation costs, are minimized. This study addresses an FL problem in which the capacity of each facility is limited. Because this problem is in the category of np-hard problems, we use the Benders Decomposition (BD) approach to efficiently solve the FL problem. In this paper, we implement the classic BD algorithm and some accelerating BD methods such as Pareto-optimality cut and L-shaped decomposition methods. Furthermore, we propose and implement the hybrid Pareto-L-shaped (PL) method, and evaluate the performance of the implemented algorithms. The results show that the L-shaped decomposition outperforms the other algorithms in terms of time and the number of iteration, while the classic BD converges slowly especially on large scales.