An open shop scheduling problem with a non-bottleneck machine

  • Authors:

  • V. A. Strusevich;L. A. Hall

  • Affiliations:

  • School of Computing and Mathematical Sciences, University of Greenwich, Wollwich Campus, Wellington Street, SE18 6PF London, UK;Department of Mathematical Sciences, The John Hopkins University, Baltimore, MD 21218, USA

  • Venue:
  • Operations Research Letters
  • Year:
  • 1997

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Abstract

This paper considers the problem of processing n jobs in a two-machine non-preemptive open shop to minimize the makespan, i.e., the maximum completion time. One of the machines is assumed to be non-bottleneck. It is shown that, unlike its flow shop counterpart, the problem is NP-hard in the ordinary sense. On the other hand, the problem is shown to be solvable by a dynamic programming algorithm that requires pseudopolynomial time. The latter algorithm can be converted into a fully polynomial approximation scheme that runs in O(n^2@e) time. An O(n log n) approximation algorithm is also designed whi finds a schedule with makespan at most 5/4 times the optimal value, and this bound is tight.