Combinatorial Auctions for Coordination and Control of Manufacturing MAS: Updating Prices Methods

  • Juan José Lavios Villahoz
  • Ricardo del Olmo Martínez
  • Alberto Arauzo Arauzo
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 73)


We use the paradigm of multiagent systems to solve the Job Shop problem. It concerns the allocation of machines to operations of some production process over time periods and its goal is the optimization of one or several objectives. We propose a combinatorial auction mechanism to coordinate agents. The “items” to be sold are the time slots that we divide the time horizon into. In tasks scheduling problems tasks need a combination of time slots of multiple resources to do the operations. The use of auctions in which different valuations of interdependent items are considered (e.g. combinatorial auctions) is necessary. The auctioneer fixes prices comparing the demand over a time slot of a resource with the capacity of the resource in this time slot. Our objective is to find an updating price method for combinatorial auctions that meet the needings of scheduling manufacturing systems in dynamic environments, e.g. robustness, stability, adaptability, and efficient use of available resources.


Time Slot Multiagent System Lagrangian Relaxation Combinatorial Auction Subgradient Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Pinedo, E.P.M.L.: Scheduling, 2nd edn. Springer, New York (2008)zbMATHGoogle Scholar
  2. 2.
    Shen, W.: Distributed manufacturing scheduling using intelligent agents. Intelligent Systems 17(1), 88–94 (2002)CrossRefGoogle Scholar
  3. 3.
    Shen, W., et al.: Applications of agent-based systems in intelligent manufacturing: An updated review. Advanced Engineering Informatics 20(4), 415–431 (2006)CrossRefGoogle Scholar
  4. 4.
    Lee, Kim: Multi-agent systems applications in manufacturing systems and supply chain management: a review paper. International Journal of Production Research 46(1), 233–265 (2008)zbMATHCrossRefGoogle Scholar
  5. 5.
    Ouelhadj, D., Petrovic, S.: A survey of dynamic scheduling in manufacturing systems. Journal of Scheduling 12(4), 417–431 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Kutanoglu, E., Wu, S.D.: On combinatorial auction and Lagrangean relaxation for distributed resource scheduling. IIE Transactions 31(9), 813–826 (1999)Google Scholar
  7. 7.
    Wellman, M.P., et al.: Auction Protocols for Decentralized Scheduling. Games and Economic Behavior 35(1-2), 271–303 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    de Vries, S., Vohra, R.V.: Combinatorial Auctions: A Survey. Informs Journal on Computing 15(3), 284–309 (2003)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Dewan, P., Joshi, S.: Auction-based distributed scheduling in a dynamic job shop environment. International Journal of Production Research 40(5), 1173–1191 (2002)zbMATHCrossRefGoogle Scholar
  10. 10.
    Duffie, N.A.: Synthesis of heterarchical manufacturing systems. Comput. Ind. 14(1-3), 167–174 (1990)CrossRefGoogle Scholar
  11. 11.
    Wang, J., et al.: An optimization-based algorithm for job shop scheduling. SADHANA 22, 241–256 (1997)CrossRefGoogle Scholar
  12. 12.
    Geoffrion, A.M.: Lagrangean relaxation for integer programming. En Approaches to Integer Programming, 82–114 (1974), (Accedido Mayo 20, 2009)
  13. 13.
    Fisher, M.L.: The Lagrangian Relaxation Method for Solving Integer Programming Problems. Management Science 50(suppl.12), 1861–1871 (2004)CrossRefGoogle Scholar
  14. 14.
    Guignard, M.: Lagrangean relaxation. TOP 11(2), 151–200 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Camerini, P.M., Fratta, L., Maffioli, F.: On improving relaxation methods by modified gradient techniques. En Nondifferentiable Optimization, 26–34 (1975), (Accedido Junio 3, 2009)
  16. 16.
    Brännlund, U.: A generalized subgradient method with relaxation step. Mathematical Programming 71(2), 207–219 (1995)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Zhao, X., Luh, P., Wang, J.: The surrogate gradient algorithm for Lagrangian relaxation method. In: Proceedings of the 36th IEEE Conference on Decision and Control, vol. 1, pp. 305–310 (1997)Google Scholar
  18. 18.
    Chen, H., Luh, P.: An alternative framework to Lagrangian relaxation approach for job shop scheduling. European Journal of Operational Research 149(3), 499–512 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Demirkol, E., Mehta, S., Uzsoy, R.: Benchmarks for shop scheduling problems. European Journal of Operational Research 109(1), 137–141 (1998)zbMATHCrossRefGoogle Scholar
  20. 20.
    Kreipl, S.: A large step random walk for minimizing total weighted tardiness in a job shop. Journal of Scheduling 3(3), 125–138 (2000)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Juan José Lavios Villahoz
    • 1
  • Ricardo del Olmo Martínez
    • 1
  • Alberto Arauzo Arauzo
    • 2
  1. 1.INSISOC. Escuela Politécnica SuperiorUniversidad de BurgosSpain
  2. 2.INSISOC. ETSIIUniversidad de ValladolidSpain

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