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Minimize total tardiness and machine unavailability on single machine scheduling problem: bi-objective branch and bound algorithm

Author

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  • Asmaa Khoudi

    (University M’Hamed Bougara of Boumerdes)

  • Ali Berrichi

    (University M’Hamed Bougara of Boumerdes)

Abstract

The joint production scheduling and preventive maintenance problems have recently attracted researchers’ attention given their contribution, both the production and the maintenance functions and their integration, to the firms’ efficiency. In this paper, we deal with production scheduling and preventive maintenance (PM) planning on single machine problem. The aim is to find an appropriate sequencing of production jobs and a PM planning to minimize two objectives simultaneously: total tardiness of jobs and machine unavailability. We propose a bi-objective exact algorithm, that we called BOBB, based on bi-objective branch and bound method to find the efficient set. We introduced several properties and bound sets to enhance the performance of the proposed BOBB algorithm. Furthermore, we propose a hybrid method, that we called GA-BBB, based on genetic algorithm and binary branch and bound algorithm to compute an approximate efficient set to be used as an initial upper bound set in the BOBB algorithm. An experimental study was conducted to show the efficiency of the GA-BBB and the BOBB algorithms.

Suggested Citation

  • Asmaa Khoudi & Ali Berrichi, 2020. "Minimize total tardiness and machine unavailability on single machine scheduling problem: bi-objective branch and bound algorithm," Operational Research, Springer, vol. 20(3), pages 1763-1789, September.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:3:d:10.1007_s12351-018-0384-3
    DOI: 10.1007/s12351-018-0384-3
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    References listed on IDEAS

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    1. Fitouhi, Mohamed-Chahir & Nourelfath, Mustapha, 2012. "Integrating noncyclical preventive maintenance scheduling and production planning for a single machine," International Journal of Production Economics, Elsevier, vol. 136(2), pages 344-351.
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    3. Chen, Wen-Jinn, 2009. "Minimizing number of tardy jobs on a single machine subject to periodic maintenance," Omega, Elsevier, vol. 37(3), pages 591-599, June.
    4. Schaller, Jeffrey, 2009. "Note on Shim and Kim's lower bounds for scheduling on identical parallel machines to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 197(1), pages 422-426, August.
    5. Koulamas, Christos, 2010. "The single-machine total tardiness scheduling problem: Review and extensions," European Journal of Operational Research, Elsevier, vol. 202(1), pages 1-7, April.
    6. Kacem, Imed & Chu, Chengbin, 2008. "Efficient branch-and-bound algorithm for minimizing the weighted sum of completion times on a single machine with one availability constraint," International Journal of Production Economics, Elsevier, vol. 112(1), pages 138-150, March.
    7. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.
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    Cited by:

    1. Chung-Ho Su & Jen-Ya Wang, 2022. "A Branch-and-Bound Algorithm for Minimizing the Total Tardiness of Multiple Developers," Mathematics, MDPI, vol. 10(7), pages 1-24, April.

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