Using Shapley Value to Allocate Savings in A Supply Chain

  • John J. BartholdiIII
  • Eda Kemahlioğlu-Ziya
Part of the Applied Optimization book series (APOP, volume 98)


Consider two retailers, whose inventory is provided by a common supplier who bears all the inventory risk. We model the relationship among the retailers and supplier as a single-period cooperative game in which the players can form inventory-pooling coalitions. Using the Shapley value to allocate the profit, we analyze various schemes by which the supplier might pool inventory she holds for the retailers. We find, among other things, that the Shapley value allocations are individually rational and are guaranteed to coordinate the supply chain; but they may be perceived as unfair in that the retailers’ allocations can, in some situations, exceed their contribution to supply chain profit. Finally we analyze the effects of demand variance and asymmetric service level requirements on the allocations.


Supply Chain Service Level Inventory Level Expected Profit Stock Level 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • John J. BartholdiIII
    • 1
  • Eda Kemahlioğlu-Ziya
    • 2
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlanta
  2. 2.Kenan-Flagler Business SchoolUniversity of North CarolinaChapel Hill

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