Solution approaches for facility location of medical supplies for large-scale emergencies

In this paper, we propose models and solution approaches for determining the facility locations of medical supplies in response to large-scale emergencies. We address the demand uncertainty and medical supply insufficiency by providing each demand point with services from a multiple quantity of facilities that are located at different quality levels (distances). The problem is formulated as a maximal covering problem with multiple facility quantity-of-coverage and quality-of-coverage requirements. Three heuristics are developed to solve the location problem: a genetic algorithm heuristic, a locate-allocate heuristic, and a Lagrangean relaxation heuristic. We evaluate the performance of the model and the heuristics by using illustrative emergency examples. We show that the model provides an effective method to address uncertainties with little added cost in demand point coverage. We also show that the heuristics are able to generate good facility location solutions in an efficient manner. Moreover, we give suggestions on how to select the most appropriate heuristic to solve different location problem instances.