Dynamically second-preferred p-center problem

This paper deals with the Dynamically Second-preferred p-center Problem (DSpP). In this problem, customers’ preferences and subsets of sites that each customer is willing to accept as service centers are taken into account. It is assumed that centers can fail and, thus, the decision maker is risk-averse and makes his decision taking into account not only the most favourite centers of the customers but also the worst case situation whenever they evaluate their preferred second opportunity. Specifically, the new problem aims at choosing at most p centers so that each demand point can visit at least two acceptable centers and the maximum sum of distances from any demand point to any of its preferred centers plus the distance from any of the preferred centers to any of the centers the user prefers once he is there is minimized. The problem is NP-hard as an extension of the p-next center problem. The paper presents three different mixed-integer linear programming formulations that are valid for the problem. Each formulation uses different space of variables giving rise to some strengthening using valid inequalities and variable fixing criteria that can be applied when valid upper bounds are available. Exact methods are limited so that a heuristic algorithm is also developed to provide good quality solution for large size instances. Finally, an extensive computational experience has been performed to assess the usefulness of the formulations to solve DSpP using standard MIP solvers.