Effective and Efficient Heuristic Approaches for Solving the Capacitated P-Median Clustering Problem

Abstract

The Capacitated Clustering Problem (CCP) involves the definition of capacity-constrained weighted individuals' sets such that the maximum similarity with respect to the cluster center value is granted among points belonging to the same cluster. The individuals' weights are represented by their demand, all the demands belonging to the same cluster have to be covered. This work concerns the application of the CCP problem where the center of a given cluster is a particular individual of the cluster. We focused on the Capacitated p-Median (CpMP) variant of the problem proposed by Mulvay and Beck, where the number of clusters is given. Specifically, we propose its mathematical programming formulation and, being this problem NP hard, a two-phase polynomial heuristic algorithm: the first phase consists in generating the desired number of clusters without any constraint on their capacity (different variations are provided); the second one aims to capacitate the former clusters to respect capacity limits.