Prioritizing Patients: Stochastic Dynamic Programming for Surgery Scheduling and Mass Casualty Incident Triage

Abstract

The research presented in this dissertation contributes to the growing literature on applications of operations research models to problems in healthcare through the development and analysis of mathematical models for two fundamental problems facing nearly all hospitals: the single-day surgery scheduling problem and planning for triage in the event of a mass casualty incident. Both of these problems can be understood as sequential decision-making processes aimed at prioritizing between different classes of patients under significant uncertainty and are modeled using stochastic dynamic programming.

Our study of the single-day surgery scheduling problem represents the first model to capture the sequential nature of the operating room (OR) manager's decisions during the transition between the generality of cyclical block schedules (which allocate OR time to surgical specialties) and the specificity of schedules for a particular day (which assign individual patients to specific ORs). A case study of the scheduling system at the University of Maryland Medical Center highlights the importance of the decision to release unused blocks of OR time and use them to schedule cases from the surgical request queue (RQ). Our results indicate that high quality block release and RQ decisions can be made using threshold-based policies that preserve a specific amount of OR time for late-arriving demand from the specialties on the block schedule.

The development of mass casualty incident (MCI) response plans has become a priority for hospitals, and especially emergency departments and trauma centers, in recent years. Central to all MCI response plans is the triage process, which sorts casualties into different categories in order to facilitate the identification and prioritization of those who should receive immediate treatment. Our research relates MCI triage to the problem of scheduling impatient jobs in a clearing system and extends earlier research by incorporating the important trauma principle that patients' long-term (post-treatment) survival probabilities deteriorate the longer they wait for treatment. Our results indicate that the consideration of deteriorating survival probabilities during MCI triage decisions, in addition to previously studied patient characteristics and overall patient volume, increases the total number of expected survivors.