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Scheduling Open Shops with Unit Execution Times to Minimize Functions of Due Dates

Author

Listed:
  • C. Y. Liu

    (National Sun Yat-Sen University, Kao Hsiung, Taiwan, Republic of China)

  • R. L. Bulfin

    (Auburn University, Auburn, Alabama)

Abstract

We examine the problem of scheduling n jobs, each of which must be processed by m machines. If the order in which a given job is processed on the machines is not fixed, the system is called an open shop. This situation might occur in testing components of an electronic system or doing repair work on an automobile. The computational difficulty of solving most open shop problems is known, with the majority being NP-hard. The computational difficulty of a few special cases is unknown, most notably when the jobs have identical processing time and the measure of performance is a function of job due dates. We reduce this uncertainty by developing polynomial algorithms to minimize the total tardiness and the number of tardy jobs in an open shop with identical processing time jobs.

Suggested Citation

  • C. Y. Liu & R. L. Bulfin, 1988. "Scheduling Open Shops with Unit Execution Times to Minimize Functions of Due Dates," Operations Research, INFORMS, vol. 36(4), pages 553-559, August.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:4:p:553-559
    DOI: 10.1287/opre.36.4.553
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    Cited by:

    1. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    2. Hans Kellerer & Thomas Tautenhahn & Gerhard Woeginger, 1995. "Note: Open‐shop scheduling with release dates to minimize maximum lateness," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 141-145, February.
    3. Baptiste, Philippe, 2003. "On minimizing the weighted number of late jobs in unit execution time open-shops," European Journal of Operational Research, Elsevier, vol. 149(2), pages 344-354, September.
    4. Christos Koulamas & George J. Kyparisis, 1998. "Open shop scheduling to minimize the number of late jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(5), pages 525-532, August.
    5. Ramudhin, Amar & Marier, Philippe, 1996. "The generalized Shifting Bottleneck Procedure," European Journal of Operational Research, Elsevier, vol. 93(1), pages 34-48, August.
    6. Timkovsky, Vadim G., 2003. "Identical parallel machines vs. unit-time shops and preemptions vs. chains in scheduling complexity," European Journal of Operational Research, Elsevier, vol. 149(2), pages 355-376, September.
    7. Lushchakova, Irene N., 2006. "Two machine preemptive scheduling problem with release dates, equal processing times and precedence constraints," European Journal of Operational Research, Elsevier, vol. 171(1), pages 107-122, May.
    8. Matta, Marie E. & Elmaghraby, Salah E., 2010. "Polynomial time algorithms for two special classes of the proportionate multiprocessor open shop," European Journal of Operational Research, Elsevier, vol. 201(3), pages 720-728, March.
    9. Burak Cankaya & Ezra Wari & Berna Eren Tokgoz, 2019. "Practical approaches to chemical tanker scheduling in ports: a case study on the Port of Houston," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 21(4), pages 559-575, December.

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    Keywords

    production/scheduling: open shop;

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