Considering short-term and long-term uncertainties in location and capacity planning of public healthcare facilities

This paper addresses a real-world problem faced by the public healthcare sector. The problem consists of both the patients’ and service provider's requirements (i.e., accessibility vs. costs) for locating healthcare facilities, allocating service units to those facilities, and determining the facilities’ capacities. The main contribution of this study is capturing both short-term and long-term uncertainties at the modelling stage. The queuing theory is incorporated to consider stochastic demand and service time as a short-term uncertainty, as well as a service level measurement. The developed nonlinear model is then converted into a linear model after introducing a new set of decision variables and proving the properties of the service level constraints. We also demonstrate a way in which a linearized model can become more efficient by eliminating excessive binary variables when service level constraints are approximated using their properties. Additionally, long-term demographic variations are captured through robust optimization in order to create a robust model. To solve the problem under investigation, an evolutionary solution method is designed, and its performance is investigated under different settings. We apply this solution method to determine the location and capacity of healthcare facilities in one of the provinces of Iran. The results illustrate that the suggested network can significantly improve the performance measures compared to the existing network. Furthermore, the importance of robust solution in maintaining the desired service level is demonstrated through examining three levels of demographic variations.