How the Difference in Travel Times Affects the Optima Localization for the Routing Open Shop

  • Ilya ChernykhEmail author
  • Ekaterina Lgotina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)


The routing open shop problem, being a generalization of the metric TSP and the open shop scheduling problem, is known to be NP-hard even in case of two machines with a transportation network consisting of two nodes only. We consider a generalization of this problem with unrelated travel times of each machine. We determine a tight optima localization interval for the two-machine problem in the case when the transportation network consists of at most three nodes. As a byproduct of our research, we present a linear time \(\frac{5}{4}\)-approximation algorithm for the same problem. We prove that the algorithm has the best theoretically possible approximation ratio with respect to the standard lower bound.


Scheduling Routing open shop Unrelated travel times Optima localization Approximation algorithm 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Novosibirsk State Technical UniversityNovosibirskRussia

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