The impact of directed choice on the design of preventive healthcare facility network under congestion

Preventive healthcare (PH) programs and services aim at reducing the likelihood and severity of potentially life-threatening illness by early detection and prevention. The effectiveness of these programs depends on the participation level and the accessibility of the users to the facilities providing the services. Factors that impact the accessibility include the number, type, and location of the facilities as well as the assignment of the clients to these facilities. In this paper, we study the impact of system-optimal (i.e., directed) choice on the design of the preventive healthcare facility network under congestion. We present a model that simultaneously determines the location and the size of the facilities as well as the allocation of clients to these facilities so as to minimize the weighted sum of the total travel time and the congestion associated with waiting and service delay at the facilities. The problem is set up as a network of spatially distributed M/G/1 queues and formulated as a nonlinear mixed integer program. Using simple transformation of the nonlinear objective function and piecewise linear approximation, we reformulate the problem as a linear model. We present a cutting plane algorithm based exact (oee--optimal) solution approach. We analyze the tradeoff between travel time and queuing time and its impact on the location and capacity of the facilities as well as the allocation of clients to these facilities under a directed choice policy. We present a case study that deals with locating mammography clinics in Montreal, Canada. The results show that incorporating congestion in the PH facility network design substantially reduces the total time spent by clients. The proposed model allows policy makers to direct clients to facilities in an equitable manner resulting in better accessibility.