A bilevel model for preventive healthcare facility network design with congestion

Preventive healthcare aims at reducing the likelihood and severity of potentially life-threatening illnesses by protection and early detection. The level of participation in preventive healthcare programs is a critical determinant in terms of their effectiveness and efficiency. This article presents a methodology for designing a network of preventive healthcare facilities so as to improve its accessibility to potential clients and thus maximize participation in preventive healthcare programs. The problem is formulated as a mathematical program with equilibrium constraints; i.e., a bilevel non-linear optimization model. The lower level problem which determines the allocation of clients to facilities is formulated as a variational inequality; the upper level is a facility location and capacity allocation problem. The developed solution approach is based on the location–allocation framework. The variational inequality is formulated as a convex optimization problem, which can be solved by the gradient projection method; a Tabu search procedure is developed to solve the upper level problem. Computational experiments show that large-sized instances can be solved in a reasonable time. The model is used to analyze an illustrative case, a network of mammography centers in Montreal, and a number of interesting results and managerial insights are discussed, especially about capacity pooling.