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OR Spectrum

, Volume 38, Issue 1, pp 25–50 | Cite as

Constructive and blocking power in collaborative transportation

  • Mario Guajardo
  • Kurt Jörnsten
  • Mikael Rönnqvist
Regular Article

Abstract

We empirically investigate constructive and blocking power concepts in transportation planning. Our main question is what do these concepts represent in collaborative transportation. We address it by studying cost allocation and coalition structure problems in a real-world case on forest transportation involving eight companies. The potential savings of collaboration in this case account for about 9 %. We find that players more centrally located tend to benefit from the nucleolus allocation, which takes into account only the constructive power. Other methods, which take into account the blocking power, namely the modiclus and the SM-nucleolus, correct the relative importance of the central players with respect to those in more peripheral areas. The blocking power acknowledges that the more peripheral companies, as a block, are still crucial to the collaboration, despite among themselves they have little opportunities for collaboration. Our main conclusion is that incorporating the blocking power as a criterion in a cost sharing rule for collaborative planning in transportation is important specially in the case where the coalition consists of one or few centrally located companies and several peripheral companies. A method based merely on the constructive power might extremely benefit the central companies, hurting the possibilities of sustaining the coalition.

Keywords

Collaborative logistics Game theory Forest transportation Nucleolus Modiclus 

Notes

Acknowledgments

We would like to thank the anonymous reviewers for their insightful comments which allowed us to considerably improve our article. We would also like to thank Kaja Lorentzen and Tone Lund for fruitful discussion which helped us to elaborate this article.

References

  1. Alonso-Meijide JM, Carreras F, Costa J, García-Jurado I (2015) The proportional partitional Shapley value. Discrete Appl Math 187:1–11CrossRefGoogle Scholar
  2. Audy JF, Marques AS, Rönnqvist M, Epstein R, Weintraub A (2014) Transportation and routing. In: Borges JG, Diaz-Balteiro L, McDill ME, Rodriguez LCE (eds) The Management of Industrial Forest Plantations. Springer, Netherlands, pp 269–295Google Scholar
  3. Audy JF, D’Amours S, Rönnqvist M (2012) An empirical study on coalition formation and cost/savings allocation. Int J Prod Econ 136(1):13–27CrossRefGoogle Scholar
  4. Aumann RJ, Drèze JH (1974) Cooperative games with coalition structures. Int J Game Theory 3:217–237CrossRefGoogle Scholar
  5. Carlsson D, Rönnqvist M (2007) Backhauling in forest transportation: models, methods, and practical usage. Canad J For Res 37(12):2612–2623CrossRefGoogle Scholar
  6. Casajus A (2009) Outside options, component efficiency, and stability. Games Econ Behav 65(1):49–61CrossRefGoogle Scholar
  7. Çetiner D (2013) Approximate Nucleolus-Based Revenue Shares for Airline Alliances. In: Fair Revenue Sharing Mechanisms for Strategic Passenger Airline Alliances, Lecture Notes in Economics and Mathematical Systems 668, Springer, Berlin Heidelberg, pp 83–109Google Scholar
  8. D’Amours S, Rönnqvist M (2010) Issues in collaborative logistics. In: Bjørndal E, Bjørndal M, Pardalos PM, Rönnqvist M (eds) Energy, natural resources and environmental economics. Springer, Berlin, Heidelberg, pp 115–130Google Scholar
  9. D’Amours S, Rönnqvist M (2013) An educational game in collaborative logistics. INFORMS Trans Edu 13(2):102–113CrossRefGoogle Scholar
  10. Forsberg M, Frisk M, Rönnqvist M (2005) Flowopt—a decision support tool for strategic and tactical transportation planning in forestry. Int J For Eng 16:101–114Google Scholar
  11. Frisk M, Göthe-Lundgren M, Jörnsten K, Rönnqvist M (2010) Cost allocation in collaborative forest transportation. Eur J Oper Res 205(2):448–458CrossRefGoogle Scholar
  12. Fromen B (1997) Reducing the number of linear programs needed for solving the nucleolus problem of \(n\)-person game theory. Eur J Oper Res 98(3):626–636CrossRefGoogle Scholar
  13. Greenberg J (1994) Coalition structures. In: Aumann RJ, Hart S (eds) Handbook of Game Theory with Economic Applications. vol 2. Elsevier Science B.V., Amsterdam, pp 1305–1337Google Scholar
  14. Guajardo M, Jörnsten K (2015) Common mistakes in computing the nucleolus. Eur J Oper Res 241(3):931–935CrossRefGoogle Scholar
  15. Guajardo M, Rönnqvist M (2015) Operations research models for coalition structure in collaborative logistics. Eur J Oper Res 240(1):147–159CrossRefGoogle Scholar
  16. Guo P, Leng M, Wang Y (2013) A fair staff allocation rule for the capacity pooling of multiple call centers. Oper Res Lett 41(5):490–493CrossRefGoogle Scholar
  17. Khmelnitskaya A (2014) Values for games with two-level communication structures. Discrete Appl Math 166:34–50CrossRefGoogle Scholar
  18. Kohlberg E (1972) The nucleolus as a solution of a minimization problem. SIAM J Appl Math 23(1):34–39CrossRefGoogle Scholar
  19. Kopelowitz A (1967) Computation of the kernels of simple games and the nucleolus of \(n\)-person games. Research memorandum 31, Department of Mathematics, The Hebrew University of JerusalemGoogle Scholar
  20. Krajewska MA, Kopfer H, Laporte G, Ropke S, Zaccour G (2008) Horizontal cooperation among freight carriers: request allocation and profit sharing. J Oper Res Soc 59(11):1483–1491CrossRefGoogle Scholar
  21. Leng M, Parlar M (2009) Allocation of cost savings in a three-level supply chain with demand information sharing: A cooperative-game approach. Oper Res 57:200–213CrossRefGoogle Scholar
  22. Lozano S, Moreno P, Adenso-Díaz B, Algaba E (2013) Cooperative game theory approach to allocating benefits of horizontal cooperation. Eur J Oper Res 229(2):444–452CrossRefGoogle Scholar
  23. Nagarajan M, S\(\breve{\rm o}\)sić G (2009) Coalition stability in assembly models. Oper Res 57:131–145Google Scholar
  24. Potters JAM, Reijnierse JH, Ansing M (1996) Computing the nucleolus by solving a prolonged simplex algorithm. Math Oper Res 21(3):757–768CrossRefGoogle Scholar
  25. Puettmann C, Stadtler H (2010) A collaborative planning approach for intermodal freight transportation. OR Spectr 32(3):809–830CrossRefGoogle Scholar
  26. Rosenmüller J, Sudhölter P (2002) Formation of cartels in glove markets and the modiclus. J Econ 76(3):217–246CrossRefGoogle Scholar
  27. Schmeidler D (1969) The nucleolus of a characteristic function game. SIAM J Appl Math 17(6):1163–1170CrossRefGoogle Scholar
  28. Shapley LS (1953) A value for n-person games. Ann Math Stud 28:307–317Google Scholar
  29. Stadtler H (2009) A framework for collaborative planning and state-of-the-art. OR Spectr 31(1):5–30CrossRefGoogle Scholar
  30. Stein HD (2010) Allocation rules with outside option in cooperation games with time-inconsistency. J Bus Econ 11:56–96Google Scholar
  31. Sudhölter P (1996) The modified nucleolus as canonical representation of weighted majority games. Math Oper Res 21(3):734–756CrossRefGoogle Scholar
  32. Sudhölter P (1997) The modified nucleolus: properties and axiomatizations. Int J Game Theory 26(2):147–182CrossRefGoogle Scholar
  33. S\(\breve{\rm o}\)sić G (2006) Transshipment of inventories among retailers: Myopic vs. farsighted stability. Manag Sci 52:1493–1508Google Scholar
  34. S\(\breve{\rm o}\)sić G (2010) Stability of information-sharing alliances in a three-level supply chain. Naval Res Logist 57:279–295Google Scholar
  35. Tarashnina S (2011) The simplified modified nucleolus of a cooperative tu-game. Top 19(1):150–166CrossRefGoogle Scholar
  36. van den Brink R, van der Laan G, Moes N (2015) Values for transferable utility games with coalition and graph structure. Top 23(1):77–99CrossRefGoogle Scholar
  37. Vázquez-Brage M, García-Jurado I, Carreras F (1996) The Owen value applied to games with graph-restricted communication. Games Econ Behav 12(1):42–53CrossRefGoogle Scholar
  38. Wang X, Kopfer H (2014) Collaborative transportation planning of less-than-truckload freight. OR Spectr 36(2):357–380CrossRefGoogle Scholar
  39. Wiese H (2007) Measuring the power of parties within government coalitions. Int Game Theory Rev 9(2):307–322CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Mario Guajardo
    • 1
  • Kurt Jörnsten
    • 1
  • Mikael Rönnqvist
    • 1
    • 2
  1. 1.Department of Business and Management ScienceNHH Norwegian School of EconomicsBergenNorway
  2. 2.Département de génie mécaniqueUniversité LavalQuébecCanada

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