Abstract

We consider the capacitated p-median problem (CPMP) in which a set of n customers must be partitioned into p disjoint clusters so that the total dissimilarity within each cluster is minimized and constraints on maximum cluster capacities are met. The dissimilarity of a cluster is computed as the sum of the dissimilarities existing between each entity of the cluster and the median associated to such cluster. In this paper we present an exact algorithm for solving the CPMP based on a set partitioning formulation of the problem. A valid lower bound to the optimal solution cost is obtained by combining two different heuristic methods for solving the dual of the LP-relaxation of the exact formulation. Computational tests on problems proposed in the literature and on new sets of test problems show the effectiveness of the proposed algorithm.

Scope and purpose

A basic location problem consists of locating a number of facilities or depots to supply a set of customers. The objective is to minimize the cost of locating the facilities and assigning the customers to them. This problem has been extensively studied in the literature and is commonly referred to as the plant location problem, or facility location problem. When each potential facility has a constraint on the maximum demand that it can supply and the number of facilities to locate is specified, the problem is known as the Capacitated p-median problem (CPMP). The purpose of this paper is to present a new exact algorithm for the CPMP and evaluate its computational performance on a set of test problems taken from the literature and on a new set of test problems.

Author Keywords: Capacitated p-median; Facility location; Set partitioning problem; Dual heuristic solution

Article Outline

1. Introduction

2. Mathematical formulations of the CPMP

2.1. Variable reduction of problem SP

3. A heuristic procedure for solving problem DSP

3.1. Procedure H¹

3.2. Procedure H²

3.2.1. The computation of U_i, iN

4. Generation of the set

5. Methods for solving the CPMP

5.1. The EHP procedure

5.2. Branch and bound method BB

5.3. Dealing with real-world constraints

6. Computational results

7. Conclusions

References