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A dynamic programming algorithm for scheduling jobs in a two-machine open shop with an availability constraint

Author

Listed:
  • T Lorigeon

    (Université de Tours)

  • J-C Billaut

    (Université de Tours)

  • J-L Bouquard

    (Université de Tours)

Abstract

This paper studies a two-machine open shop scheduling problem with an availability constraint, ie we assume that a machine is not always available and that the processing of the interrupted job can be resumed when the machine becomes available again. We consider the makespan minimization as criterion. This problem is NP-hard. We develop a pseudo-polynomial time dynamic programming algorithm to solve the problem optimally when the machine is not available at time s>0. Then, we propose a mixed integer linear programming formulation, that allows to solve instances with up to 500 jobs optimally in less than 5 min with CPLEX solver. Finally, we show that any heuristic algorithm has a worst-case error bound of 1.

Suggested Citation

  • T Lorigeon & J-C Billaut & J-L Bouquard, 2002. "A dynamic programming algorithm for scheduling jobs in a two-machine open shop with an availability constraint," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1239-1246, November.
    • Handle: RePEc:pal:jorsoc:v:53:y:2002:i:11:d:10.1057_palgrave.jors.2601421
    DOI: 10.1057/palgrave.jors.2601421
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    Cited by:

    1. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    2. Yuan Yuan & Yan Lan & Ning Ding & Xin Han, 2022. "A PTAS for non-resumable open shop scheduling with an availability constraint," Journal of Combinatorial Optimization, Springer, vol. 43(2), pages 350-362, March.

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