Ambulance routing for disaster response with patient groups

We consider a routing problem for ambulances in a disaster response scenario, in which a large number of injured people require medical aid at the same time. The ambulances are used to carry medical personnel and patients. We distinguish two groups of patients: slightly injured people who can be assisted directly in the field, and seriously injured people who have to be brought to hospitals. Since ambulances represent a scarce resource in disaster situations, their efficient usage is of the utmost importance. Two mathematical formulations are proposed to obtain route plans that minimize the latest service completion time among the people waiting for help. Since disaster response calls for high-quality solutions within seconds, we also propose a large neighborhood search metaheuristic. This solution approach can be applied at high frequency to cope with the dynamics and uncertainties in a disaster situation. Our experiments show that the metaheuristic produces high quality solutions for a large number of test instances within very short response time. Hence, it fulfills the criteria for applicability in a disaster situation. Within the experiments, we also analyzed the effect of various structural parameters of a problem, like the number of ambulances, hospitals, and the type of patients, on both running time of the heuristic and quality of the solutions. This information can additionally be used to determine the required fleet size and hospital capacities in a disaster situation.