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Heuristics for the single machine weighted sum of completion times scheduling problem with periodic maintenance

Author

Listed:
  • Hanane Krim

    (Polytechnic University of Hauts-de-France)

  • Rachid Benmansour

    (Polytechnic University of Hauts-de-France
    INSEA)

  • David Duvivier

    (Polytechnic University of Hauts-de-France)

  • Daoud Aït-Kadi

    (University of Laval)

  • Said Hanafi

    (Polytechnic University of Hauts-de-France)

Abstract

This paper tackles the single machine scheduling problem with periodic preventive maintenance in order to minimize the weighted sum of completion times. This criterion is certainly less studied than the makespan but it remains nonetheless interesting on the theoretical and practical levels. Indeed, the weights can quantify the holding cost per unit of time of the products to transform. Thus, this criterion can represent the global holding cost. This problem is proved to be NP-hard and a mixed integer linear programming formulation is proposed to solve small size instances of the problem. To solve large instances, we proposed three properties for this problem which generalize already existing works. These properties have been of great use in designing efficient heuristics capable of solving instances with up to 1000 jobs. To evaluate the performances of the proposed heuristics, lower bounds based on special cases of the problem are provided. Computational experiments show that the average percentage error of the best heuristic is less than 10%.

Suggested Citation

  • Hanane Krim & Rachid Benmansour & David Duvivier & Daoud Aït-Kadi & Said Hanafi, 2020. "Heuristics for the single machine weighted sum of completion times scheduling problem with periodic maintenance," Computational Optimization and Applications, Springer, vol. 75(1), pages 291-320, January.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:1:d:10.1007_s10589-019-00142-5
    DOI: 10.1007/s10589-019-00142-5
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    References listed on IDEAS

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    1. Guoqing Wang & Hongyi Sun & Chengbin Chu, 2005. "Preemptive Scheduling with Availability Constraints to Minimize Total Weighted Completion Times," Annals of Operations Research, Springer, vol. 133(1), pages 183-192, January.
    2. Roux, O. & Duvivier, D. & Quesnel, G. & Ramat, E., 2013. "Optimization of preventive maintenance through a combined maintenance-production simulation model," International Journal of Production Economics, Elsevier, vol. 143(1), pages 3-12.
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    6. Kacem, Imed & Chu, Chengbin, 2008. "Worst-case analysis of the WSPT and MWSPT rules for single machine scheduling with one planned setup period," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1080-1089, June.
    7. Li, Guo & Liu, Mengqi & Sethi, Suresh P. & Xu, Dehua, 2017. "Parallel-machine scheduling with machine-dependent maintenance periodic recycles," International Journal of Production Economics, Elsevier, vol. 186(C), pages 1-7.
    8. Sadfi, Cherif & Penz, Bernard & Rapine, Christophe & Blazewicz, Jacek & Formanowicz, Piotr, 2005. "An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints," European Journal of Operational Research, Elsevier, vol. 161(1), pages 3-10, February.
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    Cited by:

    1. Abdelhak Elidrissi & Rachid Benmansour & Nicolas Zufferey & Mohammed Benbrahim & David Duvivier, 2024. "Minimization of maximum lateness on parallel machines with a single server and job release dates," 4OR, Springer, vol. 22(3), pages 351-385, September.

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