Two-MILP models for scheduling elective surgeries within a private healthcare facility.

This paper deals with an Integrated Elective Surgery-Scheduling Problem (IESSP) that arises in a privately operated healthcare facility. It aims to optimize the resource utilization of the entire surgery process including pre-operative, per-operative and post-operative activities. Moreover, it addresses a specific feature of private facilities where surgeons are independent service providers and may conduct their surgeries in different private healthcare facilities. Thus, the problem requires the assignment of surgery patients to hospital beds, operating rooms and recovery beds as well as their sequencing over a 1-day period while taking into account surgeons' availability constraints. We present two Mixed Integer Linear Programs (MILP) that model the IESSP as a three-stage hybrid flow-shop scheduling problem with recirculation, resource synchronization, dedicated machines, and blocking constraints. To assess the empirical performance of the proposed models, we conducted experiments on real-world data of a Tunisian private clinic: Clinique Ennasr and on randomly generated instances. Two criteria were minimised: the patients' average length of stay and the number of patients' overnight stays. The computational results show that the proposed models can solve instances with up to 44 surgical cases in a reasonable CPU time using a general-purpose MILP solver.