Fix-and-Relax-Coordination for a multi-period location-allocation problem under uncertainty

A multi-period discrete facility location problem is introduced for a risk neutral strategy with uncertainty in the costs and some of the requirements along the planning horizon. A compact 0-1 formulation for the Deterministic Equivalent Model of the problem under two alternative strategies for the location decisions is presented. Furthermore, a new algorithmic matheuristic, Fix-and-Relax-Coordination, is introduced. This solution scheme is based on a specialization of the Branch-and-Fix Coordination methodology, which exploits the Nonanticipativity Constraints and uses the Twin Node Family concept. The results of an extensive computational experience allow to compare the alternative modeling strategies and assess the effectiveness of the proposed approach versus the plain use of a state-of-the-art MIP solver.