Approximation algorithms for the multiprocessor open shop scheduling problem

  • Authors:

  • Petra Schuurman;Gerhard J. Woeginger

  • Affiliations:

  • Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands;Institut für Mathematik B, TU Graz, Steyrergasse 30, A-8010 Graz, Austria

  • Venue:
  • Operations Research Letters
  • Year:
  • 1999

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Abstract

We investigate the multiprocessor multi-stage open-shop scheduling problem. In this variant of the open-shop model, there are s stages, each consisting of a number of parallel identical machines. Each job consists of s operations, one for each stage, that can be executed in any order. The goal is to find a non-preemptive schedule that minimizes the makespan. We derive two approximation results for this NP-hard problem. First, we demonstrate the existence of a polynomial-time approximation algorithm with worst case ratio 2 for the case that the number s of stages is part of the input. This algorithm is based on Racsmany's concept of dense schedules. Secondly, for the multiprocessor two-stage open-shop problem we derive a family of polynomial-time approximation algorithms whose worst-case ratios can be made arbitrarily close to 32.