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Batch scheduling with controllable setup and processing times to minimize total completion time

Author

Listed:
  • C T Daniel Ng

    (The Hong Kong Polytechnic University, Hung Hom)

  • T C E Cheng

    (The Hong Kong Polytechnic University, Hung Hom)

  • M Y Kovalyov

    (Belarus State University)

Abstract

We study a problem of scheduling n jobs on a single machine in batches. A batch is a set of jobs processed contiguously and completed together when the processing of all jobs in the batch is finished. Processing of a batch requires a machine setup time dependent on the position of this batch in the batch sequence. Setup times and job processing times are continuously controllable, that is, they are real-valued variables within their lower and upper bounds. A deviation of a setup time or job processing time from its upper bound is called a compression. The problem is to find a job sequence, its partition into batches, and the values for setup times and job processing times such that (a) total job completion time is minimized, subject to an upper bound on total weighted setup time and job processing time compression, or (b) a linear combination of total job completion time, total setup time compression, and total job processing time compression is minimized. Properties of optimal solutions are established. If the lower and upper bounds on job processing times can be similarly ordered or the job sequence is fixed, then O(n 3 log n) and O(n 5) time algorithms are developed to solve cases (a) and (b), respectively. If all job processing times are fixed or all setup times are fixed, then more efficient algorithms can be devised to solve the problems.

Suggested Citation

  • C T Daniel Ng & T C E Cheng & M Y Kovalyov, 2003. "Batch scheduling with controllable setup and processing times to minimize total completion time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(5), pages 499-506, May.
    • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:5:d:10.1057_palgrave.jors.2601537
    DOI: 10.1057/palgrave.jors.2601537
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    References listed on IDEAS

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    1. 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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    7. Cheng, T. C. Edwin & Janiak, Adam & Kovalyov, Mikhail Y., 2001. "Single machine batch scheduling with resource dependent setup and processing times," European Journal of Operational Research, Elsevier, vol. 135(1), pages 177-183, November.
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    Cited by:

    1. Gurel, Sinan & Akturk, M. Selim, 2007. "Considering manufacturing cost and scheduling performance on a CNC turning machine," European Journal of Operational Research, Elsevier, vol. 177(1), pages 325-343, February.
    2. 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.
    3. 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.
    4. Evgeny Gurevsky & Sergey Kovalev & Mikhail Y. Kovalyov, 2021. "Min-max controllable risk problems," 4OR, Springer, vol. 19(1), pages 93-101, March.
    5. Zhi-Long Chen & Nicholas G. Hall, 2007. "Supply Chain Scheduling: Conflict and Cooperation in Assembly Systems," Operations Research, INFORMS, vol. 55(6), pages 1072-1089, December.

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