Integer Programming Approaches for Appointment Scheduling with Random No-Shows and Service Durations

• 成果类型: Article
• 署名作者: Jiang, Ruiwei; Shen, Siqian; Zhang, Yiling
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1656
• 发表日期: 2017
• 页码: 1638-1656
• 关键词: health-care; optimization; overbooking; ARRIVALS; demand; server; MODEL

摘要

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.