Abstract
We address the two-machine flow-shop scheduling problem with time delays in order to minimize the makespan, i.e., the maximum completion time. We present a comprehensive theoretical analysis of the different lower bounds of the state of the art and we elucidate dominance relationships between them. We then introduce an exact method based on a branch-and-bound scheme. This method includes a local search-based heuristic and three dominance rules. Finally, a computer simulation of the branch-and-bound method is given on a set of 480 instances. We point out the good performance of our branch-and-bound method that outperforms the state of the art exact method. Precisely, we manage to solve all the state of the art instances except one in a very short time.
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Acknowledgements
This work is carried out in the framework of the Labex MS2T, which was funded by the French Government, through the program Investments for the future managed by the National Agency for Research (Reference ANR-11-IDEX-0004-02). It is also partially supported by the ATHENA Project (ANR-13-BS02-0006-02).
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Mkadem, M.A., Moukrim, A. & Serairi, M. Exact method for the two-machine flow-shop problem with time delays. Ann Oper Res 298, 375–406 (2021). https://doi.org/10.1007/s10479-018-3082-x
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DOI: https://doi.org/10.1007/s10479-018-3082-x