The discrete p-center location problem with upgrading

Abstract

In this paper, different upgrading strategies are investigated in the context of the p-center problem. The possibility of upgrading a set of connections to different centers is considered as well as the possibility of upgrading entire centers, i.e., all connections made to them. Two variants for these perspectives are ana- lyzed: in the first, there is a limit on the number of connections or centers that can be upgraded; in the second, an existing budget is assumed for the same purpose. Different mixed-integer linear programming models are introduced for those problems as well as data-driven lower and upper bounds. In most cases, an optimal solution can be obtained within an acceptable computing time using an off-the-shelf solver. Nevertheless, this is not the case for one particular family of problems. This motivated the development of a math-heuristic seeking high-quality feasible solutions in that specific case. Extensive computational experiments are reported highlighting the relevance of upgrading connections or centers in the context of the p-center problem.