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Allocating the gains from resource pooling with the Shapley Value

Author

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  • G Reinhardt

    (DePaul University)

  • M Dada

    (Purdue University)

Abstract

To make their cost structure more efficient, firms often pool their critical resources: small divisions of a large firm may negotiate a joint contract to benefit from volume discounts; or firms may outsource their call centres to an independent provider who is able to increase utilization by reducing variability since demand is now pooled. Since pooling demand reduces total joint costs, an immediate question is how the realized savings should be shared. We model the problem as a cooperative game and use the resulting allocation schemes to distribute the savings. One popular scheme is the Shapley Value, which always exists and, we show, represents each player's incremental value to the pool. When the pooled savings depend on the sum of each player's demand, we label the game coalition symmetric and propose, for those games, an algorithm that makes pseudo-polynomial the computation of the Shapley Value.

Suggested Citation

  • G Reinhardt & M Dada, 2005. "Allocating the gains from resource pooling with the Shapley Value," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(8), pages 997-1000, August.
    • Handle: RePEc:pal:jorsoc:v:56:y:2005:i:8:d:10.1057_palgrave.jors.2601929
    DOI: 10.1057/palgrave.jors.2601929
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    References listed on IDEAS

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    1. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
    2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    3. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
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    Cited by:

    1. Hennet, Jean-Claude & Mahjoub, Sonia, 2010. "Toward the fair sharing of profit in a supply network formation," International Journal of Production Economics, Elsevier, vol. 127(1), pages 112-120, September.
    2. Robin Molinier & Pascal da Costa, 2019. "Infrastructure sharing synergies and industrial symbiosis: optimal capacity oversizing and pricing," Post-Print hal-01792032, HAL.
    3. Chen, Kebing, 2012. "Procurement strategies and coordination mechanism of the supply chain with one manufacturer and multiple suppliers," International Journal of Production Economics, Elsevier, vol. 138(1), pages 125-135.
    4. Nagarajan, Mahesh & Sosic, Greys, 2008. "Game-theoretic analysis of cooperation among supply chain agents: Review and extensions," European Journal of Operational Research, Elsevier, vol. 187(3), pages 719-745, June.
    5. An, Qingxian & Wen, Yao & Ding, Tao & Li, Yongli, 2019. "Resource sharing and payoff allocation in a three-stage system: Integrating network DEA with the Shapley value method," Omega, Elsevier, vol. 85(C), pages 16-25.

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