The stratified p-center problem

TL;DR

This paper introduces the Stratified p-Center Problem, an extension of the p-center problem that accounts for demand stratification and multiple service types at sites, with formulations and heuristics for solution.

Contribution

It develops new formulations, inequalities, and preprocessing techniques for the Stratified p-Center Problem and applies a heuristic based on Sample Average Approximation for probabilistic cases.

Findings

New formulations and inequalities improve problem-solving efficiency.

Heuristic based on SAA effectively addresses probabilistic p-center scenarios.

Application demonstrates practical utility in complex service location problems.

Abstract

This work presents an extension of the p-center problem. In this new model, called Stratified p-Center Problem (SpCP), the demand is concentrated in a set of sites and the population of these sites is divided into different strata depending on the kind of service that they require. The aim is to locate p centers to cover the different types of services demanded minimizing the weighted average of the largest distances associated with each of the different strata. In addition, it is considered that more than one stratum can be present at each site. Different formulations, valid inequalities and preprocessings are developed and compared for this problem. An application of this model is presented in order to implement a heuristic approach based on the Sample Average Approximation method (SAA) for solving the probabilistic p-center problem in an efficient way.