题目：Risk-Sensitive Appointment Scheduling: A Data-Driven Approach
报告人：庞湛（Purdue Krannert School Supply Chanin & Operations）
摘要: We study an appointment scheduling problem with uncertain service times for a risk-sensitive health care service provider. We first perform discrete convex analysis for the model in which the provider minimizes the overtime risk subject to multi-class tolerance levels for waiting time risk under the downside risk measure of conditional value-at-risk (CVaR). We show that for a single-class system the model has some discrete convex structure (e.g., L-natural-convexity), which enables us to design efficient algorithms. As for the multi-class setting, we show that the problem in sample average approximation (SAA) formulation can be transformed into a mixed integer linear program (MILP). We then distributional ambiguity, we employ Wasserstein distance to describe the ambiguity set which enables us to utilize the service time data directly. We then reformulate the problem with ambiguity as a data-driven distributional robust optimization (DRO) model which has tractable reformulations which allows us to show that the discrete convexity structure is preserved under the worst-case in the ambiguity set, adding new insights into the optimal appointment scheduling problem.