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

• Published in: International journal of production research Vol. 57; no. 5; pp. 1427 - 1457
• Main Authors: Benttaleb, Mourad, Hnaien, Faicel, Yalaoui, Farouk
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 04-03-2019; Taylor & Francis LLC
• Subjects: Availability; availability constraints; branch and bound; Branch and bound methods; Completion time; Computer Science; Integer programming; Job shop scheduling; Job shops; Linear programming; makespan; Mixed integer; mixed integer linear programming; Operations Research; Permutations; Preempting; Production scheduling; makespan; branch and bound; mixed integer linear programming; availability constraints; job shop scheduling
• ISSN: 0020-7543; 1366-588X
• DOI: 10.1080/00207543.2018.1489160

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.