Profit Maximizing Distributed Service System Design with Congestion and Elastic Demand

In this paper we develop a service network design model that explicitly takes into account the elasticity of customer demand with respect to travel distance and congestion delays. The model incorporates a feedback loop between customer demand and congestion at the facilities. The problem is to determine the number of facilities, their locations, their service capacity, and the assignment of customers to facilities so as to maximize the overall profit of the system. Two versions of the problem are presented. In one, each facility is modeled as an M/M/1 queuing system where the service rate is a decision variable; in the other one, the facility is modeled as an M/M/k queuing model where the service rate is given, but the number k is a decision variable. An exact algorithm and heuristics are developed and tested via computational experiments. Although our model is of the “directed choice” type where the assignment of customers to facilities is controlled by the decision maker, computational results show that in the vast majority of cases the customers are assigned to the utility-maximizing facility, indicating that there is no conflict between the customers' and decision makers' goals. A case study of locating preventive medicine clinics in Toronto, Ontario, illustrates the model.