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An asymptotically optimal algorithm for large-scale mixed job shop scheduling to minimize the makespan

Author

Listed:
  • Manzhan Gu

    (Shandong University
    Shanghai University of Finance and Economics)

  • Xiwen Lu

    (East China University of Science and Technology)

  • Jinwei Gu

    (Electrical & Information Engineering, Shandong University
    Shanghai University of Electric Power)

Abstract

This paper considers the large-scale mixed job shop scheduling problem with general number of jobs on each route. The problem includes ordinary machines, batch machines (with bounded or unbounded capacity), parallel machines, and machines with breakdowns. The objective is to find a schedule to minimize the makespan. For the problem, we define a virtual problem and a corresponding virtual schedule, based on which our algorithm TVSA is proposed. The performance analysis of the algorithm shows the gap between the obtained solution and the optimal solution is O(1), which indicates the algorithm is asymptotically optimal.

Suggested Citation

  • Manzhan Gu & Xiwen Lu & Jinwei Gu, 2017. "An asymptotically optimal algorithm for large-scale mixed job shop scheduling to minimize the makespan," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 473-495, February.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:2:d:10.1007_s10878-015-9974-7
    DOI: 10.1007/s10878-015-9974-7
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    References listed on IDEAS

    as
    1. Manzhan Gu & Xiwen Lu, 2011. "Asymptotical optimality of WSEPT for stochastic online scheduling on uniform machines," Annals of Operations Research, Springer, vol. 191(1), pages 97-113, November.
    2. J. G. Dai & Gideon Weiss, 2002. "A Fluid Heuristic for Minimizing Makespan in Job Shops," Operations Research, INFORMS, vol. 50(4), pages 692-707, August.
    3. Dimitris Bertsimas & David Gamarnik & Jay Sethuraman, 2003. "From Fluid Relaxations to Practical Algorithms for High-Multiplicity Job-Shop Scheduling: The Holding Cost Objective," Operations Research, INFORMS, vol. 51(5), pages 798-813, October.
    4. Mabel C. Chou & Hui Liu & Maurice Queyranne & David Simchi-Levi, 2006. "On the Asymptotic Optimality of a Simple On-Line Algorithm for the Stochastic Single-Machine Weighted Completion Time Problem and Its Extensions," Operations Research, INFORMS, vol. 54(3), pages 464-474, June.
    5. Penn, Michal & Raviv, Tal, 2009. "An algorithm for the maximum revenue jobshop problem," European Journal of Operational Research, Elsevier, vol. 193(2), pages 437-450, March.
    6. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    7. Lisa Fleischer & Jay Sethuraman, 2005. "Efficient Algorithms for Separated Continuous Linear Programs: The Multicommodity Flow Problem with Holding Costs and Extensions," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 916-938, November.
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