Probabilistic, maximal covering location-allocation models for congested systems

When dealing with the design of service networks, such as health and emergency medical services, banking or distributed ticket-selling services, the location of service centers has a strong influence on the congestion at each of them, and, consequently, on the quality of service. In this paper, several probabilistic maximal covering location-allocation models with constrained waiting time for queue length are presented to consider service congestion. The first model considers the location of a given number of single-server centers such that the maximum population is served within a standard distance, and nobody stands in line for longer than a given time or with more than a predetermined number of other users. Several maximal coverage models are then formulated with one or more servers per service center. A new heuristic is developed to solve the models and tested in a 30-node network.