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Single machine scheduling with batch set-up times to minimize maximum lateness

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  • A.M.A. Hariri
  • C.N. Potts

Abstract

This paper considers a problem of scheduling N jobs on a single machine to minimize the maximum lateness. A partitioning of the jobs into F families is given. A set-up time is required at the start of each batch, where a batch is a largest set of contiguously scheduled jobs from the same family. We propose a single-batch heuristic in which all jobs of a family form a batch, and a double-batch heuristic in which each family is partitioned into at most two batches according to the due dates of its jobs. Both heuristics require O(N log N) time. It is shown that the single-batch heuristic has a worst-case performance ratio of 2 -1/F, whereas a composite heuristic which selects the better of the schedules generated by the single- and double-batch heuristics has a worst-case performance ratio of 5/3 for arbitrary F. Lower bounds are derived and are incorporated in a branch and bound algorithm. This algorithm uses a procedure to reduce the size of the problem, and employs a branching rule which forces pairs of jobs to lie in the same batch or in different batches. Computational tests show that the algorithm is effective in solving problems with up to 50 jobs. Copyright Kluwer Academic Publishers 1997

Suggested Citation

  • A.M.A. Hariri & C.N. Potts, 1997. "Single machine scheduling with batch set-up times to minimize maximum lateness," Annals of Operations Research, Springer, vol. 70(0), pages 75-92, April.
    • Handle: RePEc:spr:annopr:v:70:y:1997:i:0:p:75-92:10.1023/a:1018903027868
    DOI: 10.1023/A:1018903027868
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    Citations

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    Cited by:

    1. Hinder, Oliver & Mason, Andrew J., 2017. "A novel integer programing formulation for scheduling with family setup times on a single machine to minimize maximum lateness," European Journal of Operational Research, Elsevier, vol. 262(2), pages 411-423.
    2. Steinhofel, K. & Albrecht, A. & Wong, C. K., 1999. "Two simulated annealing-based heuristics for the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 118(3), pages 524-548, November.
    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. 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.
    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. 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.
    7. Schaller, Jeffrey, 2007. "Scheduling on a single machine with family setups to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 105(2), pages 329-344, February.
    8. Baker, Kenneth R. & Magazine, Michael J., 2000. "Minimizing maximum lateness with job families," European Journal of Operational Research, Elsevier, vol. 127(1), pages 126-139, November.
    9. Guruprasad Pundoor & Zhi‐Long Chen, 2005. "Scheduling a production–distribution system to optimize the tradeoff between delivery tardiness and distribution cost," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 571-589, September.

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