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The two-machine flowshop total completion time problem: Branch-and-bound algorithms based on network-flow formulation

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  • Detienne, Boris
  • Sadykov, Ruslan
  • Tanaka, Shunji

Abstract

We consider the flowshop problem on two machines with sequence-independent setup times to minimize total completion time. Large scale network flow formulations of the problem are suggested together with strong Lagrangian bounds based on these formulations. To cope with their size, filtering procedures are developed. To solve the problem to optimality, we embed the Lagrangian bounds into two branch-and-bound algorithms. The best algorithm is able to solve all 100-job instances of our testbed with setup times and all 140-job instances without setup times, thus significantly outperforming the best algorithms in the literature.

Suggested Citation

  • Detienne, Boris & Sadykov, Ruslan & Tanaka, Shunji, 2016. "The two-machine flowshop total completion time problem: Branch-and-bound algorithms based on network-flow formulation," European Journal of Operational Research, Elsevier, vol. 252(3), pages 750-760.
    • Handle: RePEc:eee:ejores:v:252:y:2016:i:3:p:750-760
    DOI: 10.1016/j.ejor.2016.02.003
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    References listed on IDEAS

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    1. Amin Hosseininasab & Willem-Jan van Hoeve, 2021. "Exact Multiple Sequence Alignment by Synchronized Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 721-738, May.

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