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A branch and bound method for the job-shop problem with sequence-dependent setup times

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Abstract

This paper deals with the job-shop scheduling problem with sequence-dependent setup times. We propose a new method to solve the makespan minimization problem to optimality. The method is based on iterative solving via branch and bound decisional versions of the problem. At each node of the branch and bound tree, constraint propagation algorithms adapted to setup times are performed for domain filtering and feasibility check. Relaxations based on the traveling salesman problem with time windows are also solved to perform additional pruning. The traveling salesman problem is formulated as an elementary shortest path problem with resource constraints and solved through dynamic programming. This method allows to close previously unsolved benchmark instances of the literature and also provides new lower and upper bounds.

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Authors and Affiliations

  1. Université de Toulouse, LAAS–CNRS, 7 Avenue du Colonel Roche, 31077, Toulouse, France

    Christian Artigues

  2. LIA—Université d’Avignon, 339 Chemin Meinajariés, Agroparc, BP 1228, 84911, Avignon Cedex 9, France

    Dominique Feillet

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  1. Christian Artigues
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  2. Dominique Feillet
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Correspondence to Christian Artigues.

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Artigues, C., Feillet, D. A branch and bound method for the job-shop problem with sequence-dependent setup times. Ann Oper Res 159, 135–159 (2008). https://doi.org/10.1007/s10479-007-0283-0

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