Who to See Next? Guiding Physicians with Time-dependent Patient Selection Policies Under Shift Work

Patient selection in healthcare settings with walk-in patients is often a decision at a physician's discretion. In some overcrowded environments such as Emergency Departments (EDs), how patients are selected and prioritized can significantly impact operational performance as well as clinical outcomes. We propose a time-dependent policy to guide ED physicians in deciding who to serve next, considering that they often have new patients waiting for an initial assessment, returning patients waiting for a reassessment, and might have to hand off their patients to a different physician at the end of their shift. To gain insights, we formulate a transient optimal control problem and demonstrate that a time-threshold-type policy is optimal. For special cases, we derive prioritization rules between patient classes that can be seen as extensions of the cµ-rule when there are returning patients as well as a penalty cost for patient hand-offs. For more general settings, insights are obtained into when to prioritize certain patient classes as well as how this prioritization can switch during the physician's shift. Simulation analyses calibrated with detailed hospital data under realistic ED features such as multiple physicians and time-varying arrival rates indicate that our proposed policy can improve ED operational performance measures. In particular, our results show that, if the insights from our analysis are implemented, ED throughput can significantly increase, and the wait time, length of stay, number of patient hand-offs, and number of patients who leave without being seen by a physician can decrease compared to both the current practice and various other potential selection policies.