The Siting of Emergency Service Facilities with Workload Capacities and Backup Service

By the very nature of the demand that they serve, emergency service systems require that timely service be readily available to those who need it. Yet, the distinct possibility exists that the closest facility will be occupied with another call for service, and when this primary responding unit is busy, a secondary or backup facility must be assigned. The need for backup service is most prevalent in heavily used systems, which are also prone to facility workloads that can be excessive if uncontrolled. The effective design of these systems should address the siting of both the primary responding facility and a designated backup unit, as well as reasonable workload limits on these facilities. In this paper, a model formulation for emergency service systems is presented where facility workload is controlled and backup service for some or all demand points is provided. The model is sufficiently general to allow it to be adapted to several problem settings and decision criteria. An effective solution procedure was developed using a Lagrangean relaxation of the original model formulation. Results of extensive computational experiments testing this solution procedure are discussed. Finally, a large-scale example using real world data was solved and a summary of results is presented to demonstrate the applicability of the model and the solution procedure.