The open shop problem with routing at a two-node network and allowed preemption

Article

Abstract

The open shop problem with routing and allowed preemption is a generalization of the two classical discrete optimization problems: the NP-hard metrical traveling salesman problem and the polynomially solvable scheduling problem, i.e., the open shop with allowed preemption. In the paper, a partial case of this problem is considered when the transportation network consists of two nodes. It is proved that the problem with two machines is polynomially solvable, while the problem is NP-hard in the strong sense in the case of not fixed number of machines.

Keywords

open shop problem with routing preemption of the operations NP-completeness 

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References

  1. 1.
    I. Averbakh, O. Berman, and I. Chernykh, “A \(\tfrac{6} {5}\)-Approximation Algorithm for the Two-Machine Routing Open-Shop Problem on a 2-Node Network,” European J. Oper. Res. 166(1), 3–24 (2005).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    I. Averbakh, O. Berman, and I. Chernykh, “The Routing Open-Shop Problem on a Network: Complexity and Approximation,” European J. Oper. Res. 173(2), 531–539 (2006).MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    I. Chernykh, N. Dryuck, A. Kononov, and S. Sevastyanov, “The Routing Open Shop Problem: New Approximation Algorithms,” in Approximation and Online Algorithms: 7th International Workshop WAOA 2009 (Copenhagen, Denmark, September 10–11, 2009). Revised Papers (Berlin, Springer, 2010), pp.75–85.Google Scholar
  4. 4.
    T. Gonzalez and S. Sahni, “Open Shop Scheduling to Minimize Finish Time,” J. ACM 23(4), 665–679 (1976).MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and G. B. Shmoys, “Sequencing and Scheduling: Algorithms and Complexity,” in Logistics of Production and Inventory (Elsevier, Amsterdam, 1993), pp. 445–522.CrossRefGoogle Scholar
  6. 6.
    D. P. Williamson, L. A. Hall, J. A. Hoogeveen, C. A. J. Hurkens, J. K. Lenstra, S. V. Sevastianov, and D. B. Shmoys, “Short Shop Schedules,” Oper. Res. 45(2), 288–294 (1997).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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