Integer Programming Approaches for Appointment Scheduling with Random No-Shows and Service Durations
研究在预约失约和服务时长随机且分布信息模糊时，如何用分布鲁棒优化模型最小化等待、空闲和加班惩罚成本，并给出整数规划求解方法。
We consider a single-server scheduling problem given a fixed sequence of appointment arrivals with random no-shows and service durations. The probability distribution of the uncertain parameters is assumed to be ambiguous, and only the support and first moments are known. We formulate a class of distributionally robust (DR) optimization models that incorporate the worst-case expectation/conditional value-at-risk penalty cost of appointment waiting, server idleness, and overtime into the objective or constraints. Our models flexibly adapt to different prior beliefs of no-show uncertainty. We obtain exact mixed-integer nonlinear programming reformulations and derive valid inequalities to strengthen the reformulations that are solved by decomposition algorithms. In particular, we derive convex hulls for special cases of no-show beliefs, yielding polynomial-sized linear programming models for the least and the most conservative supports of no-shows. We test various instances to demonstrate the computational efficacy of our approaches and to compare the results of various DR models given perfect or ambiguous distributional information. The e-companion is available at https://doi.org/10.1287/opre.2017.1656 .