Nested-solution facility location models

Classical facility location models can generate solutions that do not maintain consistency in the set of utilized facilities as the number of utilized facilities is varied. We introduce the concept of nested facility locations, in which the solution utilizing p facilities is a subset of the solution utilizing q facilities, for all i ≤ p < q ≤ j , given some lower limit i and upper limit j on r , the number of facilities that will be utilized in the future. This approach is demonstrated with application to the p -median model, with computational testing showing these new models achieve reductions in both average regret and worst-case regret when r ≠ p facilities are actually utilized.