Abstract
In this paper, we consider a three-machine permutation flow-shop scheduling problem where the criterion is to minimize the total completion time without idle times subject to the minimum makespan on the second machine. This problem is NP-hard while each of the objective functions alone can be optimized in polynomial time. We develop a branch-and-bound algorithm with effective branching rules and dominance properties which help to reduce the search space. By our computational experiments, the branch-and-bound algorithm is comparable to a recent mixed integer programming solver and, for some kinds of problem instances, the branch-and-bound algorithm outperforms the solver. On the other hand, the computational result would indicate that the hierarchical scheduling problems are essentially hard in both theoretical and computational points of view.
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Acknowledgements
We thank anonymous referees for their valuable comments and suggestions. We are also grateful to Professors Teruhiko Yoshida, Toshio Hamada and Kensaku Kikuta for their helpful comments.
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Yanai, S., Fujie, T. A three-machine permutation flow-shop problem with minimum makespan on the second machine. J Oper Res Soc 57, 460–468 (2006). https://doi.org/10.1057/palgrave.jors.2602014
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DOI: https://doi.org/10.1057/palgrave.jors.2602014