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Makespan minimization in single-machine scheduling with step-deterioration of processing times

Author

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  • A A K Jeng

    (National Chi Nan University)

  • B M T Lin

    (National Chi Nan University)

Abstract

This paper considers a single-machine scheduling problem of minimizing the maximum completion time for a set of independent jobs. The processing time of a job is a non-linear step function of its starting time and due date. The problem is already known to be 𝒩𝒫-hard in the literature. In this paper, we first show this problem to be 𝒩𝒫-hard in the ordinary sense by proposing a pseudo-polynomial time dynamic programming algorithm. Then, we develop two dominance rules and a lower bound to design a branch-and-bound algorithm for deriving optimal solutions. Numerical results indicate that the proposed properties can effectively reduce the time required for exploring the solution space.

Suggested Citation

  • A A K Jeng & B M T Lin, 2004. "Makespan minimization in single-machine scheduling with step-deterioration of processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 247-256, March.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:3:d:10.1057_palgrave.jors.2601693
    DOI: 10.1057/palgrave.jors.2601693
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    References listed on IDEAS

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    3. Cheng, T. C. E. & Ding, Q., 2001. "Single machine scheduling with step-deteriorating processing times," European Journal of Operational Research, Elsevier, vol. 134(3), pages 623-630, November.
    4. Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
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    6. B Alidaee & N K Womer, 1999. "Scheduling with time dependent processing times: Review and extensions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 711-720, July.
    7. Hsu, Y. S. & Lin, B. M. T., 2003. "Minimization of maximum lateness under linear deterioration," Omega, Elsevier, vol. 31(6), pages 459-469, December.
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    Cited by:

    1. Baoyu Liao & Qingru Song & Jun Pei & Shanlin Yang & Panos M. Pardalos, 2020. "Parallel-machine group scheduling with inclusive processing set restrictions, outsourcing option and serial-batching under the effect of step-deterioration," Journal of Global Optimization, Springer, vol. 78(4), pages 717-742, December.
    2. Lalla-Ruiz, Eduardo & Voß, Stefan, 2016. "Modeling the Parallel Machine Scheduling Problem with Step Deteriorating Jobs," European Journal of Operational Research, Elsevier, vol. 255(1), pages 21-33.

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