Mathematical Programming

, Volume 82, Issue 1, pp 191–198

Makespan minimization in open shops: A polynomial time approximation scheme

  • Sergey V. Sevastianov
  • Gerhard J. Woeginger
Article

DOI: 10.1007/BF01585871

Cite this article as:
Sevastianov, S.V. & Woeginger, G.J. Mathematical Programming (1998) 82: 191. doi:10.1007/BF01585871

Abstract

In this paper, we demonstrate the existence of a polynomial time approximation scheme for makespan minimization in the open shop scheduling problem with an arbitrary fixed numberm of machines. For the variant of the problem where the number of machines is part of the input, it is known that the existence of an approximation scheme would implyP = NP. Hence, our result draws a precise separating line between approximable cases (i.e., withm fixed) and non-approximable cases (i.e., withm part of the input) of this shop problem. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

Keywords

SchedulingApproximation algorithmApproximation schemeWorst-case analysisOpen shopMakespan

Copyright information

© The Mathematical Programming Society, Inc. 1998

Authors and Affiliations

  • Sergey V. Sevastianov
    • 1
  • Gerhard J. Woeginger
    • 2
  1. 1.Siberian Branch of the Russian Academy of SciencesInstitute of MathematicsNovosibirsk-90Russian Federation
  2. 2.TU GrazInstitut für Mathematik BGrazAustria