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The no-wait job shop with regular objective: a method based on optimal job insertion

Author

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  • Reinhard Bürgy

    (Polytechnique Montréal)

  • Heinz Gröflin

    (University of Fribourg)

Abstract

The no-wait job shop problem (NWJS-R) considered here is a version of the job shop scheduling problem where, for any two operations of a job, a fixed time lag between their starting times is prescribed. Also, sequence-dependent set-up times between consecutive operations on a machine can be present. The problem consists in finding a schedule that minimizes a general regular objective function. We study the so-called optimal job insertion problem in the NWJS-R and prove that this problem is solvable in polynomial time by a very efficient algorithm, generalizing a result we obtained in the case of a makespan objective. We then propose a large neighborhood local search method for the NWJS-R based on the optimal job insertion algorithm and present extensive numerical results that compare favorably with current benchmarks when available.

Suggested Citation

  • Reinhard Bürgy & Heinz Gröflin, 2017. "The no-wait job shop with regular objective: a method based on optimal job insertion," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 977-1010, April.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:3:d:10.1007_s10878-016-0020-1
    DOI: 10.1007/s10878-016-0020-1
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    References listed on IDEAS

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    1. Christoph Schuster, 2006. "No-wait Job Shop Scheduling: Tabu Search and Complexity of Subproblems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 473-491, July.
    2. Robert H. Storer & S. David Wu & Renzo Vaccari, 1992. "New Search Spaces for Sequencing Problems with Application to Job Shop Scheduling," Management Science, INFORMS, vol. 38(10), pages 1495-1509, October.
    3. Mati, Yazid & Dauzère-Pérès, Stèphane & Lahlou, Chams, 2011. "A general approach for optimizing regular criteria in the job-shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 212(1), pages 33-42, July.
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