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Lagrangian relaxation algorithms for real-time hybrid flowshop scheduling with finite intermediate buffers

Author

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  • L Tang

    (Northeastern University)

  • H Xuan

    (Northeastern University)

Abstract

We investigate the problem of scheduling N jobs on parallel identical machines in J successive stages with finite buffer capacities between consecutive stages in a real-time environment. The objective is to find a schedule that minimizes the sum of weighted completion time of jobs. This problem has proven strongly NP-hard. In this paper, the scheduling problem is formulated as an integer programming model considering buffers as machines with zero processing time. Lagrangian relaxation algorithms are developed combined with a speed-up dynamic programming approach. The complication and time consumption of solving all the subproblems at each iteration in subgradient optimization motivate the development of the surrogate subgradient method, where only one subproblem is minimized at each iteration and an adaptive multiplier update scheme of Lagrangian multipliers is designed. Computational experiments with up to 100 jobs show that the designed surrogate subgradient algorithm provides a better performance as compared to the subgradient algorithm.

Suggested Citation

  • L Tang & H Xuan, 2006. "Lagrangian relaxation algorithms for real-time hybrid flowshop scheduling with finite intermediate buffers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(3), pages 316-324, March.
    • Handle: RePEc:pal:jorsoc:v:57:y:2006:i:3:d:10.1057_palgrave.jors.2602033
    DOI: 10.1057/palgrave.jors.2602033
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    Cited by:

    1. Lotte Berghman & Roel Leus & Frits Spieksma, 2014. "Optimal solutions for a dock assignment problem with trailer transportation," Annals of Operations Research, Springer, vol. 213(1), pages 3-25, February.
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    3. K-C Ying, 2009. "An iterated greedy heuristic for multistage hybrid flowshop scheduling problems with multiprocessor tasks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(6), pages 810-817, June.
    4. Berghman, Lotte & Leus, Roel, 2015. "Practical solutions for a dock assignment problem with trailer transportation," European Journal of Operational Research, Elsevier, vol. 246(3), pages 787-799.

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