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Minimising the makespan in the two-machine job shop problem under availability constraints

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  • Mourad Benttaleb
  • Faicel Hnaien
  • Farouk Yalaoui

Abstract

Classical scheduling problem assumes that machines are available during the scheduling horizon. This assumption may be justified in some situations but it does not apply if maintenance requirements, machine breakdowns or other availability constraints have to be considered. In this paper, we treat a two-machine job shop scheduling problem with one availability constraint on each machine to minimise the maximum completion time (makespan). The unavailability periods are known in advance and the processing of an operation cannot be interrupted by an unavailability period (non-preemptive case). We present in our approach properties dealing with permutation dominance and the optimality of Jackson's rule under availability constraints. In order to evaluate the effectiveness of the proposed approach, we develop two mixed integer linear programming models and two schemes for a branch and bound method to solve the tackled problem. Computational results validate the proposed approach and prove the efficiency of the developed methods.

Suggested Citation

  • Mourad Benttaleb & Faicel Hnaien & Farouk Yalaoui, 2019. "Minimising the makespan in the two-machine job shop problem under availability constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 57(5), pages 1427-1457, March.
    • Handle: RePEc:taf:tprsxx:v:57:y:2019:i:5:p:1427-1457
    DOI: 10.1080/00207543.2018.1489160
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    Cited by:

    1. Faicel Hnaien & Taha Arbaoui, 2023. "Minimizing the makespan for the two-machine flow shop scheduling problem with random breakdown," Annals of Operations Research, Springer, vol. 328(2), pages 1437-1460, September.
    2. Berti, Nicola & Finco, Serena & Battaïa, Olga & Delorme, Xavier, 2021. "Ageing workforce effects in Dual-Resource Constrained job-shop scheduling," International Journal of Production Economics, Elsevier, vol. 237(C).

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