A two-stage flow shop scheduling with a critical machine and batch availability

Enrique Gerstl*, Gur Mosheiov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We study a two-stage flowshop, where each job is processed on the first (critical) machine, and then continues to one of two second-stage (dedicated) machines. We assume identical (but machine-dependent) job processing times. Jobs are processed on the critical machine in batches, and a setup time is required when starting a new batch. The setting assumes batch-availability, i.e., jobs become available for the second stage only when their entire batch is completed on the critical machine. We consider three objective functions: minimum makespan, minimum total load, and minimum weighted flow-time. Polynomial time dynamic programming algorithms are introduced, which are numerically shown to be able to solve problems of medium size in reasonable time. A heuristic for makespan minimization is presented and shown numerically to be both accurate and efficient.

Original languageAmerican English
Pages (from-to)39-56
Number of pages18
JournalFoundations of Computing and Decision Sciences
Issue number1
StatePublished - 1 Oct 2012

Bibliographical note

Funding Information:
Acknowledgement: This paper was supported in part by The Recanati Fund and The Charles Rosen Chair of Management, The School of Business Administration, The Hebrew University, Jerusalem, Israel. We would like to thank Professor Michail Kovalyov for providing us a very relevant reference to this paper.


  • Batch scheduling
  • Critical machine
  • Dynamic programming
  • Flowshop
  • Flowtime
  • Heuristics
  • Makespan
  • Total load


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