Benders decomposition approach to solve the capacitated facility location problem

TL;DR

This paper applies Benders Decomposition and its variants to efficiently solve the NP-hard capacitated facility location problem, demonstrating improved performance of the L-shaped method over classic approaches.

Contribution

It introduces a hybrid Pareto-L-shaped method and compares various Benders Decomposition techniques for capacitated facility location problems.

Findings

L-shaped decomposition outperforms other algorithms in speed and iteration count.

Classic Benders Decomposition converges slowly on large-scale problems.

Hybrid Pareto-L-shaped method offers promising performance improvements.

Abstract

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.