Multi-period capacity planning for maternity facilities in a perinatal network: A queuing and optimization approach

This paper presents a methodology for determining bed capacity of maternity facilities in a perinatal network while considering the interaction among the facilities and long-term demand demographics. Maternity facilities, consisting of obstetrics units, basic and intensive care neonatal units, are heavily stochastic systems where capacity requirements cannot be set deterministically. Therefore, in this paper queuing theory is utilized to obtain a performance measure (the refused admission probability) which sets an analytical relationship between capacity and the required service level for each service unit in each maternity facility. This performance measure is embedded into a multi-period mixed-integer optimization model for determining the necessary capacity decisions in each time-period for each maternity facility in the network. The model takes into account demand demographics while minimizing the total cost of capacity decisions and refused admissions. The model is then applied to a real-world perinatal network in Hauts-de-Seine in Paris, France.