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Lot-sizing scheduling with batch setup times

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Abstract

This paper is concerned with scheduling independent jobs on m parallel machines in such a way that the makespan is minimized. Each job j is allowed to split arbitrarily into several parts, which can be individually processed on any machine at any time. However, a setup for uninterrupted s j time units is required before any split part of job j can be processed on any machine. The problem is strongly NP-hard if the number m of machines is variable and weakly NP-hard otherwise. We give a polynomial-time \(\frac{5}{3}\)-approximation algorithm for the former case and a fully polynomial-time approximation scheme for the latter.

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Author information

Authors and Affiliations

  1. Warwick Business School, University of Warwick, Coventry, CV4 7AL, UK

    Bo Chen

  2. Department of Management Science and Engineering, School of Engineering, Stanford University, Stanford, CA, 94305, USA

    Yinyu Ye

  3. Department of Information, Operations, and Management Sciences, Stern School of Business, New York University, NY, 10012-1126, USA

    Jiawei Zhang

Authors
  1. Bo Chen
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  2. Yinyu Ye
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  3. Jiawei Zhang
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Corresponding author

Correspondence to Bo Chen.

Additional information

AMS Subject Classifications: 68M20 · 90B35 · 90C59

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Chen, B., Ye, Y. & Zhang, J. Lot-sizing scheduling with batch setup times. J Sched 9, 299–310 (2006). https://doi.org/10.1007/s10951-006-8265-7

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  • DOI: https://doi.org/10.1007/s10951-006-8265-7

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