Research Article

The complexity of two group scheduling problems

  1. Jacek Blazewicz1,
  2. Mikhail Y. Kovalyov2,*

Article first published online: 7 NOV 2002

DOI: 10.1002/jos.118

Issue

Journal of Scheduling

Journal of Scheduling

Special Issue: Special Issue of Selected Papers from the Dagstuhl Workshop on Scheduling in Computer and Manufacturing Systems

Volume 5, Issue 6, pages 477–485, November/December 2002

Additional Information

How to Cite

Blazewicz, J. and Kovalyov, M. Y. (2002), The complexity of two group scheduling problems. J. Sched., 5: 477–485. doi: 10.1002/jos.118

Author Information

  1. 1

    Instytut Informatyki, Politechnika Poznanska, and Instytut Biochemii, Polska Akademia Nauk, Poznan, Poland

  2. 2

    Institute of Engineering Cybernetics, National Academy of Sciences of Belarus, Minsk, Belarus

*Institute of Engineering Cybernetics, National Academy of Sciences of Belarus, Surganova 6, 220012 Minsk, Belarus

Publication History

  1. Issue published online: 7 NOV 2002
  2. Article first published online: 7 NOV 2002

Funded by

  • Polish Government. Grant Number: KBN 8T11A01618
  • International Association for Promotion of Cooperation with Scientists from Former Soviet Union. Grant Number: INTAS 00-217

SEARCH

SEARCH BY CITATION

ARTICLE TOOLS

Get PDF (94K)

Keywords:

  • scheduling;
  • group technology;
  • parallel machines;
  • open shop

Abstract

The problems of scheduling groups of jobs under the group technology assumption are studied. The two remaining open questions posed in the literature a decade ago about the computational complexity of these problems (J. Oper. Res. Soc., 1992; 43:395–406), are answered. The parallel machine problem to minimize the total job completion time is proved to be NP-hard in the strong sense, even if group set-up times are equal to zero. A dynamic programming algorithm is presented to solve this problem, which is polynomial if the number of machines is fixed. The two-machine open-shop problem to minimize the makespan is proved to be NP-hard in the ordinary sense, even if there are zero group set-up times and equal job processing times on both machines. It is shown that the latter problem under the condition that any group can be split into batches does not reduce to the problem where the splittings are not allowed, i.e. the group technology assumption is satisfied. Copyright © 2002 John Wiley & Sons, Ltd.

Get PDF (94K)