Operating Room Scheduling and Integrated Block Assignments under Emergency Arrivals

Operating rooms provide crucial health services and generate significant hospital revenue. It is challenging to use operating rooms efficiently due to uncertainty in surgery durations and emergency patient arrivals. In this dissertation, we propose an operating room scheduling model that integrates the tactical decisions of assigning operating rooms to departments and the operational decisions of scheduling both planned and emergency patients. Our goal is to minimize the expected undertime of the operating rooms while ensuring that the probability of overtime is sufficiently small. We model the operating room scheduling problem as a threestage decision problem and formulate it as a two-stage stochastic mixed-integer program. We then present two generalized value function reformulations that convert the model to a pure binary program. We propose a novel dynamic program to calculate the value functions. We show that our approach gives optimal scheduling policies in a reasonable amount of time. We present numerical studies using operational data from a major hospital that demonstrate the value of the integration of block assignments and considering emergency surgery arrivals. Furthermore, we investigate the properties of generalized value functions and provide reformulations for stochastic mixed-integer programming and multi-follower bilevel mixed-integer programming problems. We finally present the exact set of objectives that make a given solution uniquely optimal through inverse optimization