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In this study, the discrete p -centre 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 the model seeks 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 facility. Two matheuristic approaches are also proposed to deal with larger instances. The first approach is a hybridisation of a clustering-based technique and 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 dataset.

The capacitated single-source p-center problem in the presence of fixed cost and multilevel capacities using VNS and aggregation technique