Minisum and Minimax Location Models for Helicopter Emergency Medical Service Systems

This paper presents minisum and minimax location problems for helicopter emergency medical service (HEMS) systems. Given demand points (origins) and hospitals (destinations), the locations of rendezvous points and helicopter stations are selected to minimize the total demand-weighted transport time (minisum objective) and the maximum transport time (minimax objective) to a hospital. Rendezvous points are required for a helicopter to meet with an ambulance. In minimizing these objectives, each demand is allocated to either an already-available ground ambulance or a newly-introduced helicopter. We provide 0-1 integer formulations of the minisum and minimax problems, and develop a variable reduction procedure that reduces the size of the problem. Some optimal solutions of the proposed models tested for an idealized square city are analyzed. We also apply the models to the case study of Japan using geographical and population data, and the locations of the actual emergency medical centers. The proposed variable reduction procedure is shown to be effective for both examples. Results show that the proposed problems tend to focus on low-accessibility locations and that accessibility to a hospital is greatly improved.