Data-Driven Distributionally Robust Appointment Scheduling

Monday, January 28, 2019 - 1:25pm - 2:25pm
Lind 305
Guanglin Xu (University of Minnesota, Twin Cities)
Stochastic decision making is an important approach to solve problems arising in many contexts including clinical appointment scheduling applications. A fundamental assumption of using such an approach is that the probability distribution of the stochastic parameters is completely known to the decision maker. However, it is challenging or even impossible to fully estimate the underlying distribution in many real-life situations. In the context of appointment scheduling, it is common that there is insufficient data. For example, in the application of operating room management, there are not enough samples for approximately 50 percent of surgeries performed on any given day across the United States. This ambiguity in the probability distribution introduces significant modeling challenges. To address this issue, we introduce a data-driven distributionally robust framework in which a decision maker seeks a schedule that minimizes the worst-case expected waiting, idleness, and overtime costs. Importantly, the expectations are taken with respect to distributions from a so-called ambiguity set that is constructed by using historical data. We establish a finite-sample performance guarantee and asymptotic consistency of the data-driven distributionally robust approach, and develop scalable solution methods for solving the resulting decision-making problems. We showcase the effectiveness of our technical approach and solution methods via numerical experiments.