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A note: approximation algorithms for batch scheduling on shops with job rejection

Author

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  • Gur Mosheiov

    (The Hebrew University
    Lev Academic Center)

  • Assaf Sarig

    (The Hebrew University)

Abstract

The most popular and cited model of batch scheduling was introduced and solved almost four decades ago. This pioneering model assumed a single machine, serial batching of unit-time jobs and batch-independent setup times. In the current note, we extend this setting by (i) allowing job-rejection, and (ii) considering flowshop and openshop. The objective function contains two cost components: sum of job completion times and total rejection cost. We introduce approximation algorithms for these problems, which are based on solving to optimality the relaxed versions (allowing non-integer batches) in the first stage, followed by rounding procedures to create integer batches. The results of our numerical tests verify that these efficient approximation algorithms produce very close-to-optimal schedules.

Suggested Citation

  • Gur Mosheiov & Assaf Sarig, 2025. "A note: approximation algorithms for batch scheduling on shops with job rejection," Operational Research, Springer, vol. 25(2), pages 1-14, June.
    • Handle: RePEc:spr:operea:v:25:y:2025:i:2:d:10.1007_s12351-025-00921-5
    DOI: 10.1007/s12351-025-00921-5
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    References listed on IDEAS

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    1. Shabtay, Dvir, 2014. "The single machine serial batch scheduling problem with rejection to minimize total completion time and total rejection cost," European Journal of Operational Research, Elsevier, vol. 233(1), pages 64-74.
    2. Gur Mosheiov & Vitaly A. Strusevich, 2017. "Determining optimal sizes of bounded batches with rejection via quadratic min‐cost flow," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 217-224, April.
    3. Juan Zou & Cuixia Miao, 2016. "The single machine serial batch scheduling problems with rejection," Operational Research, Springer, vol. 16(2), pages 211-221, July.
    4. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
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