Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T09:50:25.968Z Has data issue: false hasContentIssue false
  • English
  • Français

STOCHASTIC BATCH SCHEDULING AND THE “SMALLEST VARIANCE FIRST” RULE

Published online by Cambridge University Press:  22 October 2007

Michael Pinedo
Michael Pinedo
Affiliation:
Stern School of Business New York University E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a single machine that can process multiple jobs in batch mode. We have n jobs and the processing time of job j is a random variable Xj with distribution Fj. Up to b jobs can be processed simultaneously by the machine. The jobs in a batch all have to start at the same time and the batch is completed when all jobs have finished their processing (i.e., at the maximum of the processing times of the jobs in that batch). We are interested in two objective functions, namely the minimization of the expected makespan and the minimization of the total expected completion time. We first show that under certain fairly general conditions, the minimization of the expected makespan is equivalent to specific deterministic combinatorial problems, namely the Weighted Matching problem and the Set Partitioning problem. We then consider the case when all jobs have the same mean processing time but different variances. We show that for certain special classes of processing time distributions the Smallest Variance First rule minimizes the expected makespan as well as the total expected completion time. In our conclusions we present various general rules that are suitable for the minimization of the expected makespan and the total expected completion time in batch scheduling.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 4 , October 2007 , pp. 579 - 595
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Brucker, P., Gladky, A., Hoogeveen, J.A., Kovalyov, M.Y., Potts, C.N., Tautenhahn, T., & Van De Velde, S.L. (1998). Scheduling a batching machine. Journal of Scheduling 1: 31–54.3.0.CO;2-R>CrossRefGoogle Scholar
2.Chandru, V., Lee, C.-Y., & Uzsoy, R. (1993). Minimizing total completion time on a batch processing machine with job families. Operations Research Letters 13: 61–65.Google Scholar
3.Hochbaum, D.S. & Landy, D. (1997). Scheduling semiconductor burn-in operations to minimize total flow time. Operations Research 45: 874–885.CrossRefGoogle Scholar
4.Koole, G. & Righter, R. (2001). A stochastic batching and scheduling problem. Probability in the Engineering and Informational Sciences 15: 465–479.CrossRefGoogle Scholar
5.Pinedo, M. (1982). Minimizing the expected makespan in stochastic flow shops. Operations Research 30: 148–162.CrossRefGoogle Scholar
6.Pinedo, M. & Weiss, G. (1987). The “largest variance first” policy in some stochastic scheduling problems. Operations Research 35: 884–891.Google Scholar
7.Pinedo, M. & Wie, S.-H. (1986). Inequalities for stochastic flow shops and job shops. Stochastic Models and Data Analysis 2: 61–69.Google Scholar
8.Potts, C.N. & Kovalyov, M.Y. (2000). Scheduling and batching: A review. European Journal of Operational Research 120: 228–249.CrossRefGoogle Scholar