Competitive facility location under attrition

In this paper we address the possibility that in a competitive facility location model, one of the existing competing facilities will go out of business. We find the best location for a new facility protecting against such a possibility. Four commonly used decision rules (optimistic, pessimistic, minimax regret, and expected value) are analyzed and optimally solved within a given relative accuracy. The results of extensive computational experiments are reported. Special upper bounds, that may be a basis for other optimization problems, are designed. They are much tighter than existing lower bounds. The number if iterations is reduced by a factor close to 5000, and consequently run times were improved by about the same factor. The largest instance of 10 existing competing facilities and 20,000 demand points was solved in less than one second by each of the four decision criteria. The idea of possible scenarios can be investigated by other models in future research.