Open shops with jobs overlap-revisited

Joseph Leung, Haibing Li, Michael Pinedo, Chelliah Sriskandarajah

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

In this communication we consider a two machine open shop in which a job requires processing on both machines. However, in contrast to the classical open shop, the two operations of any given job may overlap in time. The objective function under consideration is the minimization of the total completion time. This model has been considered before by Wagneur and Sriskandarajah [Eur. J. Oper. Res. 71 (1993) 366] and they presented a proof showing that minimizing the total completion time in a two machine open shop with jobs overlap is strongly NP-hard. Their proof is based on a reduction of the numerical matching with target sums (NMTS) problem; however, their proof is unfortunately not correct. In this communication we provide a counterexample that shows that their reduction does not hold. Our counterexample implies that the complexity status of the two machine open shop with job overlap remains open.

Original languageEnglish (US)
Pages (from-to)569-571
Number of pages3
JournalEuropean Journal of Operational Research
Volume163
Issue number2
DOIs
StatePublished - Jun 1 2005

All Science Journal Classification (ASJC) codes

  • Information Systems and Management
  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research

Keywords

  • Open shops
  • Strongly NP-hard
  • Total completion time

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    Leung, J., Li, H., Pinedo, M., & Sriskandarajah, C. (2005). Open shops with jobs overlap-revisited. European Journal of Operational Research, 163(2), 569-571. https://doi.org/10.1016/j.ejor.2003.11.023