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A Fluid Heuristic for Minimizing Makespan in Job Shops

Author

Listed:
  • J. G. Dai

    (School of Industrial and Systems Engineering and School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, 30332-0205)

  • Gideon Weiss

    (Department of Statistics, Haifa University, Mount Carmel, Haifa 31905, Israel)

Abstract

We describe a simple online heuristic for scheduling job shops. We assume there is a fixed set of routes for the jobs, and many jobs, say N , on each route. The heuristic uses safety stocks and keeps the bottleneck machine busy at almost all times, while the other machines are paced by the bottleneck machine. We perform a probabilistic analysis of the heuristic, under some assumptions on the distributions of the processing times. We show that our heuristic produces makespan, which exceeds the optimal makespan by no more than c log N with a probability that exceeds 1-1/ N for all N (ge) 1, where c is some constant independent of N .

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:4:p:692-707
    DOI: 10.1287/opre.50.4.692.2860
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    References listed on IDEAS

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    1. Imre Bárány, 1981. "A Vector-Sum Theorem and its Application to Improving Flow Shop Guarantees," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 445-452, August.
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    Cited by:

    1. 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.
    2. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    3. 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.
    4. 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.
    5. Wei-Min Lan & Tava Lennon Olsen, 2006. "Multiproduct Systems with Both Setup Times and Costs: Fluid Bounds and Schedules," Operations Research, INFORMS, vol. 54(3), pages 505-522, June.
    6. 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.
    7. Jinwei Gu & Manzhan Gu & Xiwen Lu & Ying Zhang, 2018. "Asymptotically optimal policy for stochastic job shop scheduling problem to minimize makespan," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 142-161, July.

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