  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.
