Advertisement

Journal of Scheduling

, Volume 12, Issue 4, pp 401–415 | Cite as

A Lagrangian approach to single-machine scheduling problems with two competing agents

  • Alessandro Agnetis
  • Gianluca de Pascale
  • Dario Pacciarelli
Article

Abstract

In this paper, we develop branch-and-bound algorithms for several hard, two-agent scheduling problems, i.e., problems in which each agent has an objective function which depends on the completion times of its jobs only. Our bounding approach is based on the fact that, for all problems considered, the Lagrangian dual gives a good bound and can be solved exactly in strongly polynomial time. The problems addressed here consist in minimizing the total weighted completion time of the jobs of agent A, subject to a bound on the cost function of agent B, which may be: (i) total weighted completion time, (ii) maximum lateness, (iii) maximum completion time. An extensive computational experience shows the effectiveness of the approach.

Keywords

Branch-and-bound Lagrangian relaxation Multi-agent scheduling Single-machine scheduling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albino, V., Carbonara, N., & Giannoccaro, I. (2006). Innovation in industrial districts: an agent-based simulation model. International Journal of Production Economics, 104, 30–45. CrossRefGoogle Scholar
  2. Arbib, C., Servilio, M., & Smriglio, S. (2004). A competitive scheduling problem and its relevance to UMTS channel assignment. Networks, 44(2), 132–141. CrossRefGoogle Scholar
  3. Agnetis, A., Mirchandani, P. B., Pacciarelli, D., & Pacifici, A. (2000). Nondominated schedules for a job-shop with two competing agents. Computational and Mathematical Organization Theory, 6(2), 191–217. CrossRefGoogle Scholar
  4. Agnetis, A., Mirchandani, P. B., Pacciarelli, D., & Pacifici, A. (2004). Scheduling problems with two competing agents. Operations Research, 52(2), 229–242. CrossRefGoogle Scholar
  5. Baker, K. R., & Cole Smith, J. (2003). A multiple-criterion model for machine scheduling. Journal of Scheduling, 6(1), 7–16. CrossRefGoogle Scholar
  6. Cheng, T. C. E., Ng, C. T., & Yuan, J. J. (2006). Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theoretical Computer Science, 362, 273–281. CrossRefGoogle Scholar
  7. Cheng, T. C. E., Ng, C. T., & Yuan, J. J. (2008). Multi-agent scheduling on a single machine with max-form criteria. European Journal of Operational Research, 188, 603–609. CrossRefGoogle Scholar
  8. Ng, C. T., Cheng, T. C. E., & Yuan, J. J. (2006). A note on the complexity of the problem of two-agent scheduling on a single machine. Journal of Combinatorial Optimization, 12(4), 387–394. CrossRefGoogle Scholar
  9. Pan, Y. (2003). An improved branch and bound algorithm for single machine scheduling with deadlines to minimize total weighted completion time. Operations Research Letters, 31, 492–496. CrossRefGoogle Scholar
  10. Peha, J. M. (1995). Heterogeneous-criteria scheduling: minimizing weighted number of tardy jobs and weighted completion time. Journal of Computers and Operations Research, 22(10), 1089–1100. CrossRefGoogle Scholar
  11. Posner, M. E. (1985). Minimizing weighted completion times with deadlines. Operations Research, 33(3), 562–574. CrossRefGoogle Scholar
  12. Smith, W. E. (1956). Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3(1), 59–66. CrossRefGoogle Scholar
  13. Sourd, F. (2008). Private communication. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Alessandro Agnetis
    • 1
  • Gianluca de Pascale
    • 1
  • Dario Pacciarelli
    • 2
  1. 1.Dipartimento di Ingegneria dell’InformazioneUniversità di SienaSienaItaly
  2. 2.Dipartimento di Informatica e AutomazioneUniversità Roma TreRomaItaly

Personalised recommendations