In this study, the discrete p-center problem with the presence of multilevel capacities and fixed (opening) cost of a facility under a limited budget is investigated. A mathematical model of the problem is produced, where we seek the location of open facilities, their corresponding capacities, and the allocation of the customers to the open facilities in order to minimise the maximum distance between customers and their assigned facilities. | Yugoslav Journal of Operations Research 28 (2018), Number 4, 453–473 DOI: THE CAPACITATED SINGLE-SOURCE P-CENTER PROBLEM IN THE PRESENCE OF FIXED COST AND MULTILEVEL CAPACITIES USING VNS AND AGGREGATION TECHNIQUE Chandra A. IRAWAN Nottingham University Business School China Trent Building Room 250, 199 Taikang East Road Ningbo 315100, China Kusmaningrum SOEMADI Jurusan Teknik Industri Institut Teknologi Nasional, Jl. PKH. Mustafa no 23, Bandung 40134 kusmaningrum@ Received: January 2017 / Accepted: July 2018 Abstract: In this study, the discrete p-center problem with the presence of multilevel capacities and fixed (opening) cost of a facility under a limited budget is investigated. A mathematical model of the problem is produced, where we seek the location of open facilities, their corresponding capacities, and the allocation of the customers to the open facilities in order to minimise the maximum distance between customers and their assigned facilities. Two matheuristic approaches are also proposed to deal with larger instances. The first approach is a hybridisation of a clustering-based technique, an exact method, while the second one is based on Variable Neighbourhood Search (VNS). Computational experiments show that the proposed methods produce interesting and competitive results on newly and randomly generated datasets. Keywords: Capacitated p-center Problem, Mathematical Model, Matheuristic, VNS. MSC: 90B85, 90C26. 454 . Irawan and K. Soemadi / the capacitated p-center problem using VNS 1. INTRODUCTION The discrete p-center problem deals with finding the location of p facilities among M potential sites and assigning customers to these facilities in order to minimise the maximum distance between customers and their nearest facility. This problem is also known as the minimax location problem where the minimax criterion aims to minimise the adverse effects of worst-case .
