Feature-based Scheduling and Dynamic Learning with a Large Backlog

Abstract

Motivated by mass emergencies such as pandemics and earthquakes that result in a large number of patients requiring critical services, we study a feature-based scheduling problem with N patients waiting to be served by a decision maker. The decision maker knows each patient's features and waiting cost, but does not know how the expected service time depends on the patient features. After a patient is served, the decision maker observes the realized service time and determines which patient to serve next. We prove that the decision maker's expected regret, i.e., the difference between the expected total waiting cost of the decision maker and that of a clairvoyant who knows the patients' expected service times, is at least of order N^{3/2}. We then design a learn-then-commit policy and an uncertainty ellipsoid policy to dynamically learn the expected service times, and prove that the expected regrets of these two policies are of order N^{5/3} log^{1/2} N and N^{3/2} log^{3/2} N , respectively. Finally, we conduct simulation experiments and a case study based on real-world data from Duke University Hospital to demonstrate the practical value of our policies relative to commonly used approaches.

Keywords: feature-based scheduling, data-driven prioritization, dynamic learning, service time uncertainty