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

Harish Guda, Milind Dawande, Ganesh Janakiraman, Kyung Sung Jung

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1194-1202
Number of pages9
JournalProduction and Operations Management
Volume25
Issue number7
DOIs
StatePublished - Jul 1 2016
Externally publishedYes

Keywords

  • appointment scheduling
  • convex order
  • smallest-variance-first rule
  • stochastic scheduling

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Management of Technology and Innovation

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