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A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines

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  • Tanaka, Shunji
  • Araki, Mituhiko

Abstract

The purpose of this paper is to propose a new branch-and-bound algorithm for a class of scheduling problems to minimize total tardiness on identical parallel machines. In this algorithm, the Lagrangian relaxation technique is applied to obtain a tight lower bound. In addition, the job dominance conditions for the single machine total tardiness problem are utilized for both restricting branches and improving the lower bound. As will be shown by computational experiments, instances with up to 25 jobs and with any number of machines are optimally solved by the proposed algorithm.

Suggested Citation

  • Tanaka, Shunji & Araki, Mituhiko, 2008. "A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines," International Journal of Production Economics, Elsevier, vol. 113(1), pages 446-458, May.
    • Handle: RePEc:eee:proeco:v:113:y:2008:i:1:p:446-458
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    References listed on IDEAS

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    1. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    2. Koulamas, C., 1997. "Polynomially solvable total tardiness problems: Review and extensions," Omega, Elsevier, vol. 25(2), pages 235-239, April.
    3. Azizoglu, Meral & Kirca, Omer, 1998. "Tardiness minimization on parallel machines," International Journal of Production Economics, Elsevier, vol. 55(2), pages 163-168, July.
    4. Hamilton Emmons, 1969. "One-Machine Sequencing to Minimize Certain Functions of Job Tardiness," Operations Research, INFORMS, vol. 17(4), pages 701-715, August.
    5. Christos Koulamas, 1994. "The Total Tardiness Problem: Review and Extensions," Operations Research, INFORMS, vol. 42(6), pages 1025-1041, December.
    6. Yalaoui, Farouk & Chu, Chengbin, 2002. "Parallel machine scheduling to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 76(3), pages 265-279, April.
    7. Pascal Babu & Laurent Peridy & Eric Pinson, 2004. "A Branch and Bound Algorithm to Minimize Total Weighted Tardiness on a Single Processor," Annals of Operations Research, Springer, vol. 129(1), pages 33-46, July.
    8. James G. Root, 1965. "Scheduling with Deadlines and Loss Functions on k Parallel Machines," Management Science, INFORMS, vol. 11(3), pages 460-475, January.
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    Cited by:

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    2. Wong, W.K. & Guo, Z.X. & Leung, S.Y.S, 2014. "Intelligent multi-objective decision-making model with RFID technology for production planning," International Journal of Production Economics, Elsevier, vol. 147(PC), pages 647-658.
    3. 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.
    4. Halil Şen & Kerem Bülbül, 2015. "A Strong Preemptive Relaxation for Weighted Tardiness and Earliness/Tardiness Problems on Unrelated Parallel Machines," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 135-150, February.
    5. Arthur Kramer & Anand Subramanian, 2019. "A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems," Journal of Scheduling, Springer, vol. 22(1), pages 21-57, February.
    6. Mensendiek, Arne & Gupta, Jatinder N.D. & Herrmann, Jan, 2015. "Scheduling identical parallel machines with fixed delivery dates to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 243(2), pages 514-522.
    7. Teobaldo Bulhões & Ruslan Sadykov & Anand Subramanian & Eduardo Uchoa, 2020. "On the exact solution of a large class of parallel machine scheduling problems," Journal of Scheduling, Springer, vol. 23(4), pages 411-429, August.

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