Reallocation of Logistics Costs in a Cooperative Network of Sawmills

  • Patrik Flisberg
  • Mikael Frisk
  • Mario Guajardo
  • Mikael Rönnqvist
Conference paper
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 45)


While collaborative logistics has the potential to provide savings to organizations, the individual result of sub-units within an organization might not directly benefit from the collaboration. This cause problems as the sub-units may be their own result or profit centers. We face this problem in the context of an organized network of sawmills. The organization benefits from timbering exchange and joint transports with an external company. The collaboration with this external company, however, implies an increase in the direct cost of supplying some of the sawmills. This occurs because some of the flows which would be used to supply these sawmills in absence of the collaboration, are assigned to the external company in the collaborative solution. In order to make the collaboration profitable for all sawmills, the organization must reallocate the cost among the different members in the network. We address this problem by using concepts of cooperative game theory. We apply these concepts in a case involving a network of 12 Scandinavian sawmills which together cooperate with an external procurement company. The collaboration in this case results in 3.3% savings for the network. A slightly modified version of the equal profit method allows to reallocate the cost of the collaborative solution in such a way that the cost of all sawmills is reduced with respect to their direct cost in absence of collaboration, while also assures the stability of the cooperation.


  1. Audy J-F, Di Amours S, Rousseau L-M (2011) Cost allocation in the establishment of a collaborative transportation agreement an application in the furniture industry. J Oper Res Soc 62(6):960–970CrossRefGoogle Scholar
  2. Flisberg P, Frisk M, Rönnqvist M, Guajardo M (2015) Potential savings and cost allocations for forest fuel transportation in Sweden: a country-wide study. Energy 85:353–365CrossRefGoogle Scholar
  3. Flisberg P, Frisk M, Guajardo M, Rönnqvist M (2016) The aftermath of implementing collaboration in a network of sawmills: a retrospective analysis on logistics costs. In: ILS Conference Information Systems, Logistics and Supply Chain, Bordeaux, France, June 1–4, 2016.
  4. 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(2):101–114Google Scholar
  5. Frisk M, Göthe-Lundgren M, Jörnsten K, Rönnqvist M (2010) Cost allocation in collaborative forest transportation. Euro J Oper Res 205(2):448–458CrossRefzbMATHGoogle Scholar
  6. Fromen B (1997) Reducing the number of linear programs needed for solving the nucleolus problem of n-person game theory. Euro J Oper Res 98(3):626–636CrossRefzbMATHGoogle Scholar
  7. Guajardo M, Jörnsten K (2015) Common mistakes in computing the nucleolus. Euro J Oper Res 241(3):931–935MathSciNetCrossRefzbMATHGoogle Scholar
  8. Guajardo M, Rönnqvist M (2015) Operations research models for coalition structure in collaborative logistics. Euro J Oper Res 240(1):147–159MathSciNetCrossRefzbMATHGoogle Scholar
  9. Guajardo M, Rönnqvist M (2016) A review on cost allocation methods in collaborative transportation. Int Trans Oper Res 23(3):371–392MathSciNetCrossRefzbMATHGoogle Scholar
  10. Guajardo M, Jörnsten K, Rönnqvist M (2016) Constructive and blocking power in collaborative transportation. OR Spectr 38(1):25–50MathSciNetCrossRefzbMATHGoogle Scholar
  11. Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20(1):224–230MathSciNetCrossRefzbMATHGoogle Scholar
  12. Schmeidler D (1969) The nucleolus of a characteristic function game. SIAM J Appl Math 17(6):1163–1170MathSciNetCrossRefzbMATHGoogle Scholar
  13. Shapley LS (1953) A values for n-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games, vol II (Annal of Mathematics Studies)Google Scholar
  14. Temponi C, Vandaele N (eds) LNBIP 262: ILS 2016. Springer (under review)Google Scholar
  15. Tolstoi AN (1930) Methods of finding the minimal total kilometrage in cargo transportation planning in space. TransPress of the National Commissariat of Transportation, pp 23–55Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Patrik Flisberg
    • 1
  • Mikael Frisk
    • 1
  • Mario Guajardo
    • 2
  • Mikael Rönnqvist
    • 3
  1. 1.The Forestry Research Institute of SwedenUppsalaSweden
  2. 2.Department of Business and Management ScienceNHH Norwegian School of EconomicsBergenNorway
  3. 3.Département de génie mécaniqueUniversité LavalQuébecCanada

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