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    Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management

    200385_200385.pdf (149.7Kb)
    Access Status
    Open access
    Authors
    Ang, J.
    Fukushima, M.
    Meng, F.
    Noda, T.
    Sun, Jie
    Date
    2013
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Ang, J. and Fukushima, M. and Meng, F. and Noda, T. and Sun, J. 2013. Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management. Journal of Global Optimization. 56 (4): pp. 1297-1312.
    Source Title
    Journal of Global Optimization
    DOI
    10.1007/s10898-012-9894-3
    ISSN
    09255001
    Remarks

    The final publication is available at Springer via http://doi.org/10.1007/s10898-012-9894-3.

    URI
    http://hdl.handle.net/20.500.11937/22402
    Collection
    • Curtin Research Publications
    Abstract

    We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier’s profit depends not only on its own delivery frequency, but also on other suppliers’ frequencies through their impact on manufacturer’s purchase allocation to the suppliers. We first solve the follower’s (manufacturer’s) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders’ (suppliers’) game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved.

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