The impact of client choice on preventive healthcare facility network design

In contrast with sick people who need urgent medical attention, the clientele of preventive healthcare have a choice in whether to participate in the programs offered in their region. In order to maximize the total participation to a preventive care program, it is important to incorporate how potential clients choose the facilities to patronize. We study the impact of client choice behavior on the configuration of a preventive care facility network and the resulting level of participation. To this end, we present two alternative models: in the ‘probabilistic‐choice model’ a client may patronize each facility with a certain probability, which increases with the attractiveness of the available facilities. In contrast, the ‘optimal‐choice model’ stipulates that each client will go to the most attractive facility. In this paper, we assume that the proximity to a facility is the only attractiveness attribute considered by clients. To ensure the quality of care, we impose a bound on the mean waiting time as well as a minimum workload requirement at each open facility. Subject to a total capacity limit, the number of open facilities as well as the location and the capacity (number of servers) of each open facility is the main determinant of the configuration of a facility network. Both models are formulated as a mixed‐integer program. To solve the problems efficiently, we propose a probabilistic search algorithm and a genetic algorithm. Finally, we use the models to analyze the network of mammography centers in Montreal.