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An algorithm for the maximum revenue jobshop problem

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  • Penn, Michal
  • Raviv, Tal

Abstract

In this paper, we state and study the problem of selecting a product mix and a dispatching rule for a jobshop system to maximize its revenue rate over an infinite planning horizon. We solve the problem of obtaining maximum revenue by selecting a product mix and determine a schedule. The designed algorithm appropriately rounds an optimal solution to a fluid relaxation in which we replace discrete jobs with the flow of a continuous fluid. The algorithm solves the fluid relaxation optimally and then aims to keep the discrete schedule close to the continuous one obtained by the fluid solution. The schedule obtained is cyclic, with bounded WIP and asymptotically optimal. A secondary aim is to further reduce the WIP and the buffers' sizes by shortening the cycle length. This is achieved at the cost of a slight compromise on the revenue. We report on satisfactory computational results on some benchmark instances.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:193:y:2009:i:2:p:437-450
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    References listed on IDEAS

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    1. Joseph Adams & Egon Balas & Daniel Zawack, 1988. "The Shifting Bottleneck Procedure for Job Shop Scheduling," Management Science, INFORMS, vol. 34(3), pages 391-401, March.
    2. Hanen, Claire, 1994. "Study of a NP-hard cyclic scheduling problem: The recurrent job-shop," European Journal of Operational Research, Elsevier, vol. 72(1), pages 82-101, January.
    3. 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.
    4. Kamoun, H. & Sriskandarajah, C., 1993. "The complexity of scheduling jobs in repetitive manufacturing systems," European Journal of Operational Research, Elsevier, vol. 70(3), pages 350-364, November.
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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. 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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