Sustainable facility location-allocation problem under uncertainty

This paper addresses a sustainable facility location-allocation problem under uncertain environment with considering economic and sustainable dimensions simultaneously. We establish three types of belief degree constrained mathematical models to investigate the problem under the optimistic value criterion, the pessimistic value criterion, and the Hurwicz criterion. The corresponding crisp determinants of the models are derived, and several properties of the models are also discussed. The theoretical analysis demonstrates that the optimal objective values of the models crucially depend on the predetermined confidence level given by decision makers. What's more, the total cost of the problem in the belief degree constrained Hurwicz criterion model decreases as Hurwicz coefficient becomes larger. To evaluate the performance of our novel models, several numerical examples are conducted. The numerical results are obtained by using the standard optimization software LINGO.