Journal of Scheduling

, Volume 18, Issue 3, pp 243–261 | Cite as

Scheduling two agent task chains with a central selection mechanism

  • Alessandro Agnetis
  • Gaia Nicosia
  • Andrea PacificiEmail author
  • Ulrich Pferschy


In this paper, we address a deterministic scheduling problem in which two agents compete for the usage of a single machine. Each agent decides on a fixed order to submit its tasks to an external coordination subject, who sequences them according to a known priority rule. We consider the problem from different perspectives. First, we characterize the set of Pareto-optimal schedules in terms of size and computational complexity. We then address the problem from the single-agent point-of-view, that is, we consider the problem of deciding how to submit one agent’s tasks only taking into account its own objective function against the other agent, the opponent. In this regard, we consider two different settings depending on the information available to the agents: In one setting, the considered agent knows in advance all information about the submission sequence of the opponent; and in the second setting (as in minimax strategies in game theory), the agent has no information on the opponent strategy and wants to devise a strategy that minimizes its solution cost in the worst possible case. Finally, we assess the performance of some classical single-agent sequencing rules in the two-agent setting.


Scheduling Multi-agent optimization Bicriteria optimization Best response Computational complexity 



This work was supported by the Austrian Science Fund (FWF): [P 23829-N13] and by the Italian Ministry MIUR Project PRIN 2009XN4ZRR_002.


  1. Agnetis, A., Billaut, J.-C., Gawiejnowicz, S., Pacciarelli, D., & Soukhal, A. (2014). Multiagent scheduling: Models and algorithms. Berlin: Springer.CrossRefGoogle Scholar
  2. Agnetis, A., Mirchandani, P. B., Pacciarelli, D., & Pacifici, A. (2004). Scheduling problems with two competing agents. Operations Research, 52(2), 229–242.CrossRefGoogle Scholar
  3. Agnetis, A., Nicosia, G., Pacifici, A., & Pferschy, U. (2013). Two agents competing for a shared machine. In Proceedings of the 3rd international conference on algorithmic decision theory (ADT 2013), Lecture notes in computer science 8176, pp. 1–14, Springer: Berlin.Google Scholar
  4. Agnetis, A., Pacciarelli, D., & Pacifici, A. (2007). Combinatorial models for multi-agent scheduling problems, in multiprocessor scheduling: Theory and applications. Vienna, Austria: I-Tech Education and Publishing.Google Scholar
  5. Agnetis, A., De Pascale, G., & Pranzo, M. (2009). Computing the Nash solution for scheduling bargaining problems. International Journal of Operational Research, 6(1), 54–69.CrossRefGoogle Scholar
  6. Arbib, C., Smriglio, S., & Servilio, M. (2004). A competitive scheduling problem and its relevance to UMTS channel assignment. Networks, 44(2), 132–141.Google Scholar
  7. Baker, K., & Smith, J. C. (2003). A multiple criterion model for machine scheduling. Journal of Scheduling, 6(1), 7–16.CrossRefGoogle Scholar
  8. Cohen, J., Cordeiro, D., Trystram, D., & Wagner, F. (2011). Multi-organization scheduling approximation algorithms. Concurrency and computation: Practice and experience, 23(17), 2220–2234.CrossRefGoogle Scholar
  9. Darmann, A., Nicosia, G., Pferschy, U., & Schauer, J. (2014). The subset sum game. European Journal of Operational Research, 233(3), 539–549.CrossRefGoogle Scholar
  10. Ding, G., & Sun, S. (2010). Single-machine scheduling problems with two agents competing for makespan (pp. 244–255). Lecture notes in computer science, 6328, Berlin: Springer.Google Scholar
  11. Garey, M. R., Tarjan, R. E., & Wilfong, G. T. (1988). One-processor scheduling with symmetric earliness and tardiness penalties. Mathematics of Operations Research, 13(2), 330–348.CrossRefGoogle Scholar
  12. Hall, N. G., & Liu, Z. (2013). Market good flexibility in capacity auctions. Production and Operations Management, 22(2), 459–472.CrossRefGoogle Scholar
  13. Huynh, Tuong N., Soukhal, A., & Billaut, J.-C. (2012). Single-machine multi-agent scheduling problems with a global objective function. Journal of Scheduling, 15(1), 311–321.Google Scholar
  14. Jayasudha, A. R., & Purusothaman, T. (2012). Job scheduling model with job sequencing and prioritizing strategy in grid computing. International Journal of Computer Applications, 46(24), 29–32.Google Scholar
  15. Leung, J. Y.-T., Dror, M., & Young, G. H. (2001). A note on an open-end bin packing problem. Journal of Scheduling, 4, 201–207.CrossRefGoogle Scholar
  16. Marini, C., Nicosia, G., Pacifici, A., & Pferschy, U. (2013). Strategies in competing subset selection. Annals of Operations Research, 207(1), 181–200.CrossRefGoogle Scholar
  17. Nicosia, G., Pacifici, A., & Pferschy, U. (2009). Subset weight maximization with two competing agents. In Proceedings of algorithmic decision theory: ADT 2009, Lecture notes in computer science 5783, pp. 74–85, Berlin: Springer.Google Scholar
  18. Nicosia, G., Pacifici, A., & Pferschy, U. (2011). Competitive subset selection with two agents. Discrete Applied Mathematics, 159(16), 1865–1877.CrossRefGoogle Scholar
  19. Nicosia, G., Pacifici, A., & Pferschy, U. (2014). Scheduling the tasks of two agents with a central selection mechanism, submitted. available as: Optimization Online 2014–02-4222.Google Scholar
  20. Pessan, C., Bouquard, J.-L., & Neron, E. (2008). An unrelated parallel machines model for an industrial production resetting problem. European Journal of Industrial Engineering, 2, 153–171.CrossRefGoogle Scholar
  21. Soomer, M. J., & Franx, G. J. (2008). Scheduling aircraft landings using airlines’ preferences. Mathematical Programming, 190, 277–291.Google Scholar
  22. T’Kindt, V., & Billaut, J.-C. (2006). Multicriteria scheduling. Theory, models and algorithms. Berlin: Springer.Google Scholar
  23. Wellman, M. P., Walsh, W. E., Wurman, P. R., & MacKie-Mason, J. K. (2001). Auction protocols for decentralized scheduling. Games and Economic Behavior, 35(1/2), 271–303.CrossRefGoogle Scholar
  24. Ye, D., & Zhang, G. (2012). Coordination mechanisms for selfish parallel jobs scheduling. In M. Agrawal, et al. (Eds.), 9th Annual conference on theory and applications of models of computation, 2012 (pp. 225–236). Lecture notes in computer science 7287. Berlin:Springer.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Alessandro Agnetis
    • 1
  • Gaia Nicosia
    • 2
  • Andrea Pacifici
    • 3
    Email author
  • Ulrich Pferschy
    • 4
  1. 1.Dipartimento di Ingegneria dell’Informazione e Scienze MatematicheUniversità degli Studi di SienaSienaItaly
  2. 2.Dipartimento di IngegneriaUniversità degli Studi Roma TreRomeItaly
  3. 3.Dipartimento di Ingegneria Civile e Ingegneria InformaticaUniversità degli Studi di Roma “Tor Vergata”RomeItaly
  4. 4.Department of Statistics and Operations ResearchUniversity of GrazGrazAustria

Personalised recommendations