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Batching identical jobs

Author

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  • Philippe Baptiste

Abstract

We study the problems of scheduling jobs, with different release dates and equal processing times, on two types of batching machines. All jobs of the same batch start and are completed simultaneously. On a serial batching machine, the length of a batch equals the sum of the processing times of its jobs and, when a new batch starts, a constant setup time s occurs. On a parallel batching machine, there are at most b jobs per batch and the length of a batch is the largest processing time of its jobs. We show that in both environments, for a large class of so called “ordered” objective functions, the problems are polynomially solvable by dynamic programming. This allows us to derive that the problems where the objective is to minimize the weighted number of late jobs, or the weighted flow time, or the total tardiness, or the maximal tardiness are polynomial. In other words, we show that 1|p-batch,b>n, r i , p i =p|F and 1|s-batch, r i , p i =p|F, are polynomial for F∈{∑w i U i ,∑w i C i ,∑T i , T max }. The complexity status of these problems was unknown before. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Philippe Baptiste, 2000. "Batching identical jobs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(3), pages 355-367, December.
  • Handle: RePEc:spr:mathme:v:52:y:2000:i:3:p:355-367
    DOI: 10.1007/s001860000088
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    Cited by:

    1. Ozturk, Onur & Begen, Mehmet A. & Zaric, Gregory S., 2014. "A branch and bound based heuristic for makespan minimization of washing operations in hospital sterilization services," European Journal of Operational Research, Elsevier, vol. 239(1), pages 214-226.
    2. Chakhlevitch, Konstantin & Glass, Celia A. & Kellerer, Hans, 2011. "Batch machine production with perishability time windows and limited batch size," European Journal of Operational Research, Elsevier, vol. 210(1), pages 39-47, April.
    3. Christoph Hertrich & Christian Weiß & Heiner Ackermann & Sandy Heydrich & Sven O. Krumke, 2020. "Scheduling a proportionate flow shop of batching machines," Journal of Scheduling, Springer, vol. 23(5), pages 575-593, October.
    4. Yuan, J. J. & Yang, A. F. & Cheng, T. C. E., 2004. "A note on the single machine serial batching scheduling problem to minimize maximum lateness with identical processing times," European Journal of Operational Research, Elsevier, vol. 158(2), pages 525-528, October.
    5. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    6. Paul Schikora & Andrew Manikas & Michael Godfrey, 2015. "Determining Optimal Flow-Time Schedules For The Multiple-Product Batch-Flow Problem," International Journal of Management and Marketing Research, The Institute for Business and Finance Research, vol. 8(2), pages 19-35.
    7. Ridouard, Frédéric & Richard, Pascal & Martineau, Patrick, 2008. "On-line scheduling on a batch processing machine with unbounded batch size to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1327-1342, September.
    8. A. Beynaghi & F. Moztarzadeh & A. Shahmardan & R. Alizadeh & J. Salimi & M. Mozafari, 2019. "Makespan minimization for batching work and rework process on a single facility with an aging effect: a hybrid meta-heuristic algorithm for sustainable production management," Journal of Intelligent Manufacturing, Springer, vol. 30(1), pages 33-45, January.
    9. Deyun Wang & Olivier Grunder & Abdellah EL Moudni, 2014. "Using genetic algorithm for lot sizing and scheduling problem with arbitrary job volumes and distinct job due date considerations," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(8), pages 1694-1707, August.
    10. Tami Tamir, 2023. "Cost-sharing games in real-time scheduling systems," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 273-301, March.
    11. Passchyn, Ward & Coene, Sofie & Briskorn, Dirk & Hurink, Johann L. & Spieksma, Frits C.R. & Vanden Berghe, Greet, 2016. "The lockmaster’s problem," European Journal of Operational Research, Elsevier, vol. 251(2), pages 432-441.
    12. Onur Ozturk, 2020. "A bi-criteria optimization model for medical device sterilization," Annals of Operations Research, Springer, vol. 293(2), pages 809-831, October.
    13. Gur Mosheiov & Daniel Oron, 2023. "A note on batch scheduling on a two-machine flowshop with machine-dependent processing times," 4OR, Springer, vol. 21(3), pages 457-469, September.
    14. Jun-Qiang Wang & Guo-Qiang Fan & Zhixin Liu, 2020. "Mixed batch scheduling on identical machines," Journal of Scheduling, Springer, vol. 23(4), pages 487-496, August.
    15. Yuan, J.J. & Lin, Y.X. & Cheng, T.C.E. & Ng, C.T., 2007. "Single machine serial-batching scheduling problem with a common batch size to minimize total weighted completion time," International Journal of Production Economics, Elsevier, vol. 105(2), pages 402-406, February.

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