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Branch and bound algorithms for single-machinescheduling with batch set-up times to minimizetotal weighted completion time

Author

Listed:
  • H.A.J. Crauwels
  • A.M.A. Hariri
  • C.N. Potts
  • L.N. Van Wassenhove

Abstract

This paper presents several branch and bound algorithms for a single-machine scheduling problem with batching. Jobs are partitioned into families, and a set-up time is necessary when there is a switch from processing jobs of one family to jobs of another family. The objective is to minimize the total weighted completion time. A lower bound based on Lagrangian relaxation of the machine capacity constraint is derived. Also, a multiplier adjustment method to find values of the multipliers is proposed. Computational experience with instances having up to 50 jobs shows that the lower bounds are effective in restricting the search. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • H.A.J. Crauwels & A.M.A. Hariri & C.N. Potts & L.N. Van Wassenhove, 1998. "Branch and bound algorithms for single-machinescheduling with batch set-up times to minimizetotal weighted completion time," Annals of Operations Research, Springer, vol. 83(0), pages 59-76, October.
    • Handle: RePEc:spr:annopr:v:83:y:1998:i:0:p:59-76:10.1023/a:1018920416308
    DOI: 10.1023/A:1018920416308
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    Cited by:

    1. Lingye Tan & Tiong Lee Kong & Ziyang Zhang & Ahmed Sayed M. Metwally & Shubham Sharma & Kanta Prasad Sharma & Sayed M. Eldin & Dominik Zimon, 2023. "Scheduling and Controlling Production in an Internet of Things Environment for Industry 4.0: An Analysis and Systematic Review of Scientific Metrological Data," Sustainability, MDPI, vol. 15(9), pages 1-37, May.
    2. Mazdeh, Mohammad Mahdavi & Sarhadi, Mansoor & Hindi, Khalil S., 2007. "A branch-and-bound algorithm for single-machine scheduling with batch delivery minimizing flow times and delivery costs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 74-86, November.
    3. Hinder, Oliver & Mason, Andrew J., 2017. "A novel integer programing formulation for scheduling with family setup times on a single machine to minimize maximum lateness," European Journal of Operational Research, Elsevier, vol. 262(2), pages 411-423.
    4. S Karabatı & C Akkan, 2006. "Minimizing sum of completion times on a single machine with sequence-dependent family setup times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(3), pages 271-280, March.
    5. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    6. Kramer, Arthur & Iori, Manuel & Lacomme, Philippe, 2021. "Mathematical formulations for scheduling jobs on identical parallel machines with family setup times and total weighted completion time minimization," European Journal of Operational Research, Elsevier, vol. 289(3), pages 825-840.

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