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Mean‐variance trade‐offs in supply contracts


  • Victor Martínez‐de‐Albéniz
  • David Simchi‐Levi


We study the trade‐offs faced by a manufacturer signing a portfolio of long‐term contracts with its suppliers and having access to a spot market. The manufacturer incurs inventory risk when purchasing too many contracts and spot price risk when buying too few. We quantify these risks for a single selling period by studying the profit mean and variance for a given portfolio of option contracts. We characterize the set of efficient portfolios that the manufacturer must hold in order to obtain dominating mean‐variance pairs. Among these, we emphasize the maximum expectation portfolio, obtained by solving the classical newsvendor problem, and the corresponding minimum variance portfolio. We show that the upper‐level sets of a mean‐variance utility function are connected. Hence, a greedy method will find the portfolios on the efficient frontier. Finally, we provide a comparison with standard hedging strategies and show that the approximation associated with financial hedging can be relatively inaccurate. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 2006

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  • Victor Martínez‐de‐Albéniz & David Simchi‐Levi, 2006. "Mean‐variance trade‐offs in supply contracts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(7), pages 603-616, October.
  • Handle: RePEc:wly:navres:v:53:y:2006:i:7:p:603-616
    DOI: 10.1002/nav.20186

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    References listed on IDEAS

    1. Wu, D. J. & Kleindorfer, P. R. & Zhang, Jin E., 2002. "Optimal bidding and contracting strategies for capital-intensive goods," European Journal of Operational Research, Elsevier, vol. 137(3), pages 657-676, March.
    2. Mokrane Bouakiz & Matthew J. Sobel, 1992. "Inventory Control with an Exponential Utility Criterion," Operations Research, INFORMS, vol. 40(3), pages 603-608, June.
    3. Serel, Dogan A. & Dada, Maqbool & Moskowitz, Herbert, 2001. "Sourcing decisions with capacity reservation contracts," European Journal of Operational Research, Elsevier, vol. 131(3), pages 635-648, June.
    4. Seifert, Ralf W. & Thonemann, Ulrich W. & Hausman, Warren H., 2004. "Optimal procurement strategies for online spot markets," European Journal of Operational Research, Elsevier, vol. 152(3), pages 781-799, February.
    5. Minner, Stefan, 2003. "Multiple-supplier inventory models in supply chain management: A review," International Journal of Production Economics, Elsevier, vol. 81(1), pages 265-279, January.
    6. K. Borch, 1969. "A Note on Uncertainty and Indifference Curves," Review of Economic Studies, Oxford University Press, vol. 36(1), pages 1-4.
    7. Wedad J. Elmaghraby, 2000. "Supply Contract Competition and Sourcing Policies," Manufacturing & Service Operations Management, INFORMS, vol. 2(4), pages 350-371, April.
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