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


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.


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


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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

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