Optimal Policy for a Stochastic Scheduling Problem with Applications to Surgical Scheduling

• 成果类型: Article
• 署名作者: Guda, Harish; Dawande, Milind; Janakiraman, Ganesh; Jung, Kyung Sung
• 署名单位: University of Texas System; University of Texas Dallas; State University System of Florida; University of Florida
• 刊物名称: PRODUCTION AND OPERATIONS MANAGEMENT
• ISSN/ISSBN: 1059-1478
• DOI: 10.1111/poms.12538
• 发表日期: 2016
• 页码: 1194-1202
• 关键词: stochastic scheduling; Appointment Scheduling; smallest-variance-first rule; Convex Order

摘要

We consider the stochastic, single-machine earliness/tardiness problem (SET), with the sequence of processing of the jobs and their due-dates as decisions and the objective of minimizing the sum of the expected earliness and tardiness costs over all the jobs. In a recent paper, Baker () shows the optimality of the Shortest-Variance-First (SVF) rule under the following two assumptions: (a) The processing duration of each job follows a normal distribution. (b) The earliness and tardiness cost parameters are the same for all the jobs. In this study, we consider problem SET under assumption (b). We generalize Baker's result by establishing the optimality of the SVF rule for more general distributions of the processing durations and a more general objective function. Specifically, we show that the SVF rule is optimal under the assumption of dilation ordering of the processing durations. Since convex ordering implies dilation ordering (under finite means), the SVF sequence is also optimal under convex ordering of the processing durations. We also study the effect of variability of the processing durations of the jobs on the optimal cost. An application of problem SET in surgical scheduling is discussed.