Implementation of new and classical set covering based algorithms for solving the absolute p-center problem

Abstract

The p-center problem is a model of locating p facilities on a network in order to minimize the maximum coverage distance between each vertex and its closest facility. The main application areas of p-center problem are emergency service locations such as fire and police stations, hospitals and ambulance services. If the p facilities can be located anywhere on a network including vertices and interior points of edges, the resulting problem is referred to as the absolute p-center problem and if they are restricted to vertex locations, it is referred to as the vertex-restricted problem. The absolute p-center problem is considerably more complicated to solve than the vertex-restricted version. In the literature, most of the computational analysis and new algorithm developments are performed through the vertex restricted case of the p-center problem. The absolute p-center problem has received much less attention in the literature. In this thesis, our focus is on the absolute p-center problem based on an algorithm for the p-center problem proposed by Tansel (2009). Our work is the first one to solve large instances up to 900 vertices on the absolute p-center problem. The algorithm focuses on solving the p-center problem with a finite series of minimum set covering problems, but the set covering problems used in the algorithm are constructed differently compared to the ones traditionally used in the literature. The proposed algorithm is applicable for both absolute and vertex-restricted p-center problems with weighted and unweighted cases.