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Single-Machine Scheduling with Release Dates, Due Dates and Family Setup Times

Author

Listed:
  • J. M. J. Schutten

    (Faculty of Mechanical Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands)

  • S. L. van de Velde

    (Faculty of Mechanical Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands)

  • W. H. M. Zijm

    (Faculty of Mechanical Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands)

Abstract

We address the NP-hard problem of scheduling n independent jobs with release dates, due dates, and family setup times on a single machine to minimize the maximum lateness. This problem arises from the constant tug-of-war going on in manufacturing between efficient production and delivery performance, between maximizing machine utilization by batching similar jobs and maximizing customers' satisfaction by completing jobs before their due dates. We develop a branch-and-bound algorithm, and our computational results show that it solves almost all instances with up to about 40 jobs to optimality. The main algorithmic contribution is our lower bounding strategy to deal with family setup times. The key idea is to see a setup time as a setup job with a specific processing time, release date, due date, and precedence relations. We develop several sufficient conditions to derive setup jobs. We specify their parameters and precedence relations such that the optimal solution value of the modified problem obtained by ignoring the setup times, not the setup jobs, is no larger than the optimal solution value of the original problem. One lower bound for the modified problem proceeds by allowing preemption. Due to the agreeable precedence structure, the preemptive problem is solvable in O(n log n) time.

Suggested Citation

  • J. M. J. Schutten & S. L. van de Velde & W. H. M. Zijm, 1996. "Single-Machine Scheduling with Release Dates, Due Dates and Family Setup Times," Management Science, INFORMS, vol. 42(8), pages 1165-1174, August.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:8:p:1165-1174
    DOI: 10.1287/mnsc.42.8.1165
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    Citations

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    Cited by:

    1. Deck, Cary & Sheremeta, Roman M., 2019. "The tug-of-war in the laboratory," European Journal of Political Economy, Elsevier, vol. 60(C).
    2. Carsten Jordan & Andreas Drexl, 1998. "Discrete Lotsizing and Scheduling by Batch Sequencing," Management Science, INFORMS, vol. 44(5), pages 698-713, May.
    3. F Jin & J N D Gupta & S Song & C Wu, 2010. "Single machine scheduling with sequence-dependent family setups to minimize maximum lateness," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(7), pages 1181-1189, July.
    4. Luo, Xiaochuan & Chu, Chengbin, 2007. "A branch-and-bound algorithm of the single machine schedule with sequence-dependent setup times for minimizing maximum tardiness," European Journal of Operational Research, Elsevier, vol. 180(1), pages 68-81, July.
    5. Kenneth R. Baker, 1999. "Heuristic procedures for scheduling job families with setups and due dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(8), pages 978-991, December.
    6. Hoogeveen, J. A. & van de Velde, S. L., 2001. "Scheduling with target start times," European Journal of Operational Research, Elsevier, vol. 129(1), pages 87-94, February.
    7. Jordan, Carsten & Drexl, Andreas, 1997. "Discrete lotsizing and scheduling by batch sequencing," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 438, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    8. Marc R. Lambrecht & Philip L. Ivens & Nico J. Vandaele, 1998. "ACLIPS: A Capacity and Lead Time Integrated Procedure for Scheduling," Management Science, INFORMS, vol. 44(11-Part-1), pages 1548-1561, November.
    9. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    10. Allahverdi, Ali & Gupta, Jatinder N. D. & Aldowaisan, Tariq, 1999. "A review of scheduling research involving setup considerations," Omega, Elsevier, vol. 27(2), pages 219-239, April.

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