Selecting hierarchical facilities in a service-operations environment

This paper presents and solves a hierarchical model for the location of service facilities and further looks at the operational issues associated with managing such facilities. By the very nature of the demand they serve, service systems require that timely service be readily available to those who need it. We argue that the location–allocation of such facilities often involves several layers of service. When all of a facility's resources are needed to meet each demand for service, and demand cannot be queued, the need for a backup unit may be required. Effective siting decisions must address both the need for a backup response facility for each demand point and a reasonable limit on each facility's workload. The paper develops an integer linear programming model for locating facilities offering several layers of service. A Lagrangian relaxation methodology coupled with a heuristic is employed. Results of extensive computational experiments are presented to demonstrate the viability of the approach.