State-variable modeling for healthcare planning and scheduling

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In 2017, the total health budget in Canada was $242 billion accounting for 11.5% of Canada's gross domestic product (GDP). Effective decision making in healthcare systems is very crucial and can result in significant savings. Multiple sources of uncertainty in healthcare systems is one of the main challenges to make effective decisions. From this perspective, it is essential to be able to solve stochastic optimization problems efficiently. This research program develops novel stochastic optimization models for decision making under uncertainty with applications in healthcare planning and scheduling problems. In this context, we will work on operating room planning and scheduling, outpatient appointment scheduling, and scheduling of production and delivery of radio-pharmaceutical by considering various uncertainty factors. Operating room planning and scheduling (ORPS) is one of the most important decision making problems in hospitals that accounts for more than 40% of their total annual budget. Outpatient appointment scheduling (OAS) is also another important instance of healthcare operations scheduling that is very critical for the efficient use of human medical resources such as physicians and equipment for diagnostic tests (e.g., CT-scan, MRI-scan, ultrasound). Available models in the literature can only solve very simplified stochastic versions of the ORPS and OAS problems. This research program proposes significantly more effective stochastic optimization models that are capable of solving considerably larger instances with an exponential number of stochastic scenarios. The proposed models will simultaneously address many uncertainty factors in these problems such as uncertainty in surgical durations and recovery times of patients in wards for ORPS and uncertainty in visit times, patients' arrival times, and the possibility of no-shows in OAS. We also consider scheduling in radio-pharmaceutical imaging that is an advance technology in diagnosing bone issues. It has a market of $3.5 billion that is predicted to increase to $5.26 billion by 2023. From a managerial viewpoint, optimal timing for production and delivery of radio-pharmaceuticals is very critical as they are expensive materials with very short life deteriorating in exponential rates. The state-of-the-art approaches are mainly deterministic models ignoring different sources of uncertainty. In this research direction, we will propose novel stochastic optimization models addressing various uncertainties such as stochastic-time-dependent travel times, uncertainty in imaging durations due to the change in the health's situations of patients because of the injection, and no-shows.