FORMULATIONS FOR THE ROBUST CAPACITATED P-MEDIAN PROBLEM

The  Robust Capacitated p-Median Problem (RCPMP) addressed in this article consists of selecting exactly p facilities from a set of n candidate facilities to serve as medians, and allocating the remaining facilities to minimize the transportation cost and the fixed installation cost of the medians, while respecting the facilities’ service capacity limits and accounting for uncertainties in the objective function and/or constraints. This article presents two formulations for the RCPMP. The first considers uncertainty in facility opening costs, and the second considers uncertainties in both opening costs and customer demand. The models were implemented in CPLEX Solver and applied to instances from the literature. The results show that the approach considering uncertainties in both customer demand and facility opening costs has characteristics closer to the real-world problem than approaches that treat these parametric uncertainties in isolation.