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Ruiwei Jiang(ruiweiumich.edu.) Abstract: We study a singleserver appointment scheduling problem with a fixed sequence of appointments, for which we must determine the arrival time for each appointment. We specifically examine two stochastic models. In the first model, we assume that all appointees show up at the scheduled arrival times yet their service durations are random. In the second model, we assume that appointees have random noshow behaviors and their service durations are random given that they show up at the appointments. In both models, we assume that the probability distribution of the uncertain parameters is unknown but can be partially observed via a set of historical data, which we view as independent samples drawn from the unknown distribution. In view of the distributional ambiguity, we propose a datadriven distributionally robust optimization (DRO) approach to determine an appointment schedule such that the worstcase (i.e., maximum) expectation of the system total cost is minimized. A key feature of this approach is that the optimal value and the set of optimal schedules thus obtained provably converge to those of the “true” model, i.e., the stochastic appointment scheduling model with regard to the true probability distribution of the uncertain parameters. While our DRO models are computationally intractable in general, we reformulate them to copositive programs, which are amenable to tractable semidefinite programming problems with highquality approximations. Furthermore, under some mild conditions, we recast these models as polynomialsized linear programs. Through an extensive numerical study, we demonstrate that our approach yields better outofsample performance than two stateoftheart methods. Keywords: Appointment scheduling; random noshows; distributionally robust optimization; ambiguity set; Wasserstein metric; copositive programming Category 1: Robust Optimization Category 2: Applications  OR and Management Sciences (Scheduling ) Category 3: Stochastic Programming Citation: Download: [PDF] Entry Submitted: 07/06/2019 Modify/Update this entry  
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