Journal of Scheduling

, Volume 21, Issue 2, pp 227–233 | Cite as

Exact exponential algorithms for 3-machine flowshop scheduling problems

  • Lei Shang
  • Christophe Lenté
  • Mathieu Liedloff
  • Vincent T’Kindt


In this paper, we focus on the design of an exact exponential time algorithm with a proved worst-case running time for 3-machine flowshop scheduling problems considering worst-case scenarios. For the minimization of the makespan criterion, a Dynamic Programming algorithm running in \({\mathcal {O}}^*(3^n)\) is proposed, which improves the current best-known time complexity \(2^{{\mathcal {O}}(n)}\times \Vert I\Vert ^{{\mathcal {O}}(1)}\) in the literature. The idea is based on a dominance condition and the consideration of the Pareto Front in the criteria space. The algorithm can be easily generalized to other problems that have similar structures. The generalization on two problems, namely the \(F3\Vert f_\mathrm{max}\) and \(F3\Vert \sum f_i\) problems, is discussed.


Moderately exponential algorithms Dynamic programming Flowshop 


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Laboratoire d’Informatique (EA 6300), ERL CNRS OC 6305Université François-Rabelais de ToursToursFrance
  2. 2.INSA Centre Val de Loire, LIFO EA 4022Université d’OrléansOrléansFrance

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