Advertisement

Implementation of optimal schedules in outsourcing with identical suppliers

  • Herbert Hamers
  • Flip Klijn
  • Marco Slikker
Original Article
  • 45 Downloads

Abstract

This paper deals with decentralized decision-making situations in which firms outsource production orders to multiple identical suppliers. Each firm aims to minimize the sum of its completion times. We study whether a central authority can install a mechanism such that strategic interaction leads to a socially optimal schedule. For the case of single demand the shortest-first mechanism implements optimal schedules in Nash equilibrium. We show that for the general case there exists no anonymous mechanism that implements optimal schedules in correlated equilibrium.

Keywords

Game theory Outsourcing Scheduling Efficiency Implementation Nash equilibrium Correlated equilibrium Price of stability 

JEL Classification

C72 D71 D82 

References

  1. Abed F, Correa JR, Huang CC (2014) Optimal coordination mechanisms for multi-job scheduling games. In: Schulz AS, Wagner D (eds) Algorithms—ESA 2014. Lecture notes in computer science, vol 8737. Springer, Berlin, Heidelberg, pp 13–24Google Scholar
  2. Agussurja L, Lau HC (2009) The price of stability in selfish scheduling games. Web Intell Agent Syst 7(4):305–311Google Scholar
  3. Angel E, Bampis E, Pascual F, Thibault N (2016) Truthfulness for the sum of weighted completion times. In: Dinh T, Thai M (eds) Computing and combinatorics. COCOON 2016. Lecture notes in computer science, vol 9797. Springer, Cham, pp 15–26Google Scholar
  4. Anshelevich E, Dasgupta A, Kleinberg J, Tardos É, Wexler T, Roughgarden T (2008) The price of stability for network design with fair cost allocation. SIAM J Comput 38(4):1602–1623MathSciNetCrossRefzbMATHGoogle Scholar
  5. Arrow KJ (1950) A difficulty in the concept of social welfare. J Polit Econ 58(4):328–346CrossRefGoogle Scholar
  6. Aumann Y, Dombb Y (2010) Pareto efficiency and approximate pareto efficiency in routing and load balancing games. In: Proceedings of the 3rd international symposium on algorithmic game theory. pp 66–77Google Scholar
  7. Braat J, Hamers H, Klijn F, Slikker M (2016) A selfish allocation heuristic in scheduling: equilibrium and inefficiency bound analysis. Tilburg University, Working PaperGoogle Scholar
  8. Bukchin Y, Hanany E (2007) Decentralization cost in scheduling: a game-theoretic approach. Manuf Serv Oper Manag 9(3):263–275CrossRefGoogle Scholar
  9. Bukchin Y, Hanany E (2011) Decentralization cost in supply chain jobshop scheduling with minimum flowtime objective. Tel Aviv University, Working PaperGoogle Scholar
  10. Cachon GP, Netessine S (2004) Game theory in supply chain analysis. In: Simchi-Levi D, Wu SD, Shen Z-J (eds) Handbook of quantitative supply chain analysis, vol 34. Springer, New York, pp 13–65Google Scholar
  11. Caragiannis I (2013) Efficient coordination mechanisms for unrelated machine scheduling. Algorithmica 66(3):512–540MathSciNetCrossRefzbMATHGoogle Scholar
  12. Cohen J, Pascual F (2015) Scheduling tasks from selfish multi-tasks agents. In: Träff J, Hunold S, Versaci F (eds) Euro-Par 2015: Parallel Processing. Euro–Par 2015. Lecture Notes in Computer Science, vol 9233. Springer, Berlin, Heidelberg, pp 183–195Google Scholar
  13. Cole R, Correa J, Gkatzelis V, Mirrokni V, Olver N (2015) Decentralized utilitarian mechanisms for scheduling games. Games Econ Behav 92:306–326MathSciNetCrossRefzbMATHGoogle Scholar
  14. Correa JR, Queyranne M (2012) Efficiency of equilibria in restricted uniform machine scheduling with total weighted completion time as social cost. Naval Res Logist 59(5):384–395MathSciNetCrossRefGoogle Scholar
  15. Dubey P (1986) Inefficiency of Nash equilibria. Math Oper Res 11(1):1–8MathSciNetCrossRefzbMATHGoogle Scholar
  16. Epstein L, Kleiman E (2011) On the quality and complexity of pareto equilibria in the job scheduling game. In: Proceedings of the 10th international conference on autonomous agents and multiagent systems, vol 2. pp 525–532Google Scholar
  17. Hoeksma R, Uetz M (2012) The price of anarchy for minsum related machine scheduling. In: Solis–Oba R, Persiano G (eds) 9th Workshop on approximation and online algorithms. lecture notes in computer science studies in economic theory, vol 7164. Springer, Berlin, pp 261–273Google Scholar
  18. Horowitz E, Sahni S (1976) Exact and approximate algorithms for scheduling nonidentical processors. J ACM 23(2):317–327MathSciNetCrossRefzbMATHGoogle Scholar
  19. Ibarra O, Kim C (1977) Heuristic algorithms for scheduling independent tasks on nonidentical processors. J ACM 24(2):280–289MathSciNetCrossRefzbMATHGoogle Scholar
  20. Immorlica N, Li L, Mirrokni V, Schulz A (2009) Coordination mechanisms for selfish scheduling. Theor Comput Sci 410(17):1589–1598MathSciNetCrossRefzbMATHGoogle Scholar
  21. Jackson MO (2001) A crash course in implementation theory. Soc Choice Welf 18(4):655–708MathSciNetCrossRefzbMATHGoogle Scholar
  22. Koutsoupias E, Papadimitriou C (2009) Worst-case equilibria. Comput Sci Rev 3(2):65–69CrossRefGoogle Scholar
  23. Lee K, Leung JY-T, Pinedo ML (2012) Coordination mechanisms for parallel machine scheduling. Eur J Oper Res 220(2):305–313MathSciNetCrossRefzbMATHGoogle Scholar
  24. Li X, Wang Q (2007) Coordination mechanisms of supply chain systems. Eur J Oper Res 179(1):1–16MathSciNetCrossRefzbMATHGoogle Scholar
  25. Li L, Whang S (2001) Game theory models in operations management and information systems. In: Chatterjee K, Samuelson WF (eds) Game theory and business applications. Kluwer Academic Publishers, New York, pp 95–131Google Scholar
  26. Maskin E (1985) The theory of implementation in nash equilibrium: a survey. In: Hurwicz L, Schmeidler D, Sonnenschein H (eds) Social goals and social organization: volume in memory of Elisha Pazner. Cambridge University Press, Cambridge, pp 173–204Google Scholar
  27. Myerson RB, Satterthwaite MA (1983) Efficient mechanisms for bilateral trading. J Econ Theory 29(2):265–281MathSciNetCrossRefzbMATHGoogle Scholar
  28. Papadimitriou C (2001) Algorithms, games, and the internet. In: Proceedings of the 33rd annual acm symposium on the theory of computing, pp 749–753Google Scholar
  29. Perakis G, Roels G (2007) The price of anarchy in supply chains: quantifying the efficiency of price-only contracts. Manag Sci 53(8):1249–1268CrossRefzbMATHGoogle Scholar
  30. Schulzan A, Stier Moses N (2003) On the performance of user equilibria in traffic networks. In: Proceedings of the 14th annual ACM-SIAM symposium on discrete algorithms, pp 86–87Google Scholar
  31. Smith W (1956) Various optimizers for single-stage production. Naval Res Logist Q 3(1–2):59–66MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CentER and Department of Econometrics and Operations ResearchTilburg UniversityTilburgThe Netherlands
  2. 2.Institute for Economic AnalysisCSICBellaterraSpain
  3. 3.Barcelona GSE CenterBarcelonaSpain
  4. 4.CentERTilburg UniversityTilburgThe Netherlands
  5. 5.Industrial Engineering and Innovation SciencesEindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations