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A branch-and-bound method for the single-machine scheduling problem under a non-availability constraint for maximum delivery time minimization

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  • Hfaiedh, Walid
  • Sadfi, Chérif
  • Kacem, Imed
  • Hadj-Alouane, Atidel

Abstract

We consider the single machine scheduling problem with release dates and tails, provided that the machine is unavailable during a fixed interval. We aim to minimize the maximum delivery time under the nonresumable senario. This problem is strongly NP-hard. The proposed algorithm is based on a branch-and-bound method. We use Jackson’s preemptive algorithm with precedence constraints to compute the lower bound and Schrage’s sequence as an upper bound. Numerical experiments show that the algorithm can solve large-size instances with up to 1000 jobs.

Suggested Citation

  • Hfaiedh, Walid & Sadfi, Chérif & Kacem, Imed & Hadj-Alouane, Atidel, 2015. "A branch-and-bound method for the single-machine scheduling problem under a non-availability constraint for maximum delivery time minimization," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 496-502.
    • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:496-502
    DOI: 10.1016/j.amc.2014.11.103
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    References listed on IDEAS

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    1. Carlier, Jacques, 1982. "The one-machine sequencing problem," European Journal of Operational Research, Elsevier, vol. 11(1), pages 42-47, September.
    2. C. N. Potts, 1980. "Technical Note—Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times," Operations Research, INFORMS, vol. 28(6), pages 1436-1441, December.
    3. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    4. Imed Kacem, 2009. "Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 117-133, February.
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