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Flowshop scheduling with learning effect and job rejection

Abstract

We study scheduling problems on a proportionate flowshop. Three objective functions are considered: minimum makespan, minimum total completion time, and minimum total load. We consider a learning process; thus, the processing time of a job processed later in sequence is reduced. The scheduler has the option of job rejection; i.e., only a subset of the jobs are processed and the rejected jobs are penalized. An upper bound on the total permitted rejection cost is assumed. Since the single-machine versions of these problems were shown to be NP-hard, we focus on the introduction of pseudopolynomial dynamic programming algorithms, indicating that the problems are NP-hard in the ordinary sense. We provide an extensive numerical study verifying that the proposed solution algorithms are very efficient and instances containing up to 80 jobs are solved in no more than 5 ms.

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Acknowledgement

The second author was also supported by the Charles I. Rosen Chair of Management, and by The Recanati Fund of The School of Business Administration, The Hebrew University, Jerusalem, Israel.

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Correspondence to Baruch Mor.

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Mor, B., Mosheiov, G. & Shapira, D. Flowshop scheduling with learning effect and job rejection. J Sched 23, 631–641 (2020). https://doi.org/10.1007/s10951-019-00612-y

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  • DOI: https://doi.org/10.1007/s10951-019-00612-y

Keywords

  • Scheduling
  • Proportionate flowshop
  • Learning effect
  • Job rejection
  • Dynamic programming