Abstract
As a type of scheduling problem, the flowshop problem has been largely studied for 60 years. The total completion time is a very interesting criterion because it reflects “the total manufacturing waiting time experienced by all customers”(Emmons and Vairaktarakis). There have been many studies in the past but they focused on a limited number of machines and/or on specific constraints. Therefore, this study presents a new approach to tackle a general permutation flowshop problem, with various additional constraints, to elaborate on lower bounds for the total completion time. These lower bounds can take into account several constraints, like delays, blocking or setup times, but they imply solving a Traveling Salesman Problem. The theory is developed first, based on a MaxPlus modeling of flowshop problems and experimental results of a branch-and-bound procedure with a lower bound selection strategy are then presented.
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Vo, N.V., Fouillet, P., Lenté, C. (2015). Elaboration of General Lower Bounds for the Total Completion Time in Flowshop Scheduling Problems through MaxPlus Approach. In: Pinson, E., Valente, F., Vitoriano, B. (eds) Operations Research and Enterprise Systems. ICORES 2014. Communications in Computer and Information Science, vol 509. Springer, Cham. https://doi.org/10.1007/978-3-319-17509-6_19
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DOI: https://doi.org/10.1007/978-3-319-17509-6_19
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