A Huff-like location model with quality adjustment and/or closing of existing facilities

The problem of an expanding chain in a given area is considered. It may locate a new facility, vary the quality of its existing facilities, close some of them, or a combination of all these possibilities, whatever is the best to maximize its profit, given a budget for the expansion. A new competitive location and design model is proposed that allows all these possibilities. The resulting model is a difficult to solve MINLP problem. A branch-and-bound method based on interval analysis is proposed to cope with it. The method can solve medium-size problems in a reasonable amount of CPU time. An ad-hoc heuristic and a hybrid method that usually find a near-optimal solution in a fraction of time of the exact method are also proposed. Some computational studies are presented to show the performance of the algorithms.