On the complexity of non-preemptive shop scheduling with two jobs

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this note, we investigate the time complexity of non-preemptive shop scheduling problems with two jobs. First we study mixed shop scheduling where one job has a fixed order of operations and the operations of the other job may be executed in arbitrary order. This problem is shown to be binary NP-complete with respect to all traditional optimality criteria even if distinct operations of the same job require different machines. Moreover, we devise a pseudo-polynomial time algorithm which solves the problem with respect to all non-decreasing objective functions. Finally, when the job with fixed order of operations may visit a machine more than once, the problem becomes unary NP-complete. Then we discuss shop scheduling with two jobs having chain-like routings. It is shown that the problem is unary NP-complete with respect to all traditional optimality criteria even if one of the jobs has fixed order of operations and the jobs cannot visit a machine twice.

Original languageEnglish
Pages (from-to)37-49
Number of pages13
JournalComputing (Vienna/New York)
Volume69
Issue number1
DOIs
Publication statusPublished - Oct 19 2002

Keywords

  • Computational complexity
  • Mixed shop scheduling
  • Pseudo-polynomial time algorithm

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computational Mathematics

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