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

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 This paper was presented at The Eighth International Conference on Optimization: Techniques and Applications (ICOTA8) in Shanghai, December 2010. James Ang Department of Decision Sciences, National University of Singapore. E-mail: [email protected] Masao Fukushima Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University. E-mail: [email protected] Fanwen Meng Centre for Maritime Studies, National University of Singapore. E-mail: [email protected] Takahiro Noda Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University. E-mail: [email protected] Jie Sun Department of Decision Sciences and Risk Management Institute, National University of Singapore. Tel.: +65-6516-6448 Fax: +65-6779-2621 E-mail: [email protected] Manuscript Click here to download Manuscript: JGO-11-2273R1.tex Click here to view linked References