A Multi-objective Hierarchical Location-allocation Model for the Healthcare Network Design Considering a Referral System

This paper presents a multi-objective and multi-service location-allocation model with capacity planning to design a healthcare facilities network through considering a referral system. Therefore, a mixed integer nonlinear programming (MINLP) model containing two objective functions is proposed. The first objective function is  relates to minimization of total opening cost, minimization of total set up cost of different types of services and minimization of total traveled distance by patients to reach each facility. The second objective function in the model aims to minimize maximum normalized workload between opened facilities in each level. Specifying location of different facilities, allocating patients zones to family physician centers, establishing an optimal flow between different levels in the network and determining the optimal capacity for different specialized and super specialty facilities are main strategic and tactical decisions in the proposed model. In order to solve the proposed model and arrive at Pareto solutions, a primary nonlinear integer program is transformed to linearize the model and then, an augmented -constraint method is applied on numerical examples. Finally, the results obtained by sensitivity analysis on the main parameters are reported to show that the presented model can be used to design a multi-level healthcare facility network.