Cooperation in an Arrow-Karlin Type Supply Chain

Imre Dobos


In this paper we apply cooperative game theory concepts to analyze vertical supply chains. The bullwhip effect in a two-stage supply chain (supplier-manufacturer) in the framework of the Arrow-Karlin model with linear-convex cost functions is considered. It is assumed that both firms minimize their relevant costs, and two cases are examined: the supplier and the manufacturer minimize their relevant costs in a decentralized and in a centralized (cooperative) way. The question of how to share the savings of the decreased bullwhip effect in the centralized (cooperative) model is answered by transferable utility cooperative game theory tools.


Optimal control, Supply chain, Bullwhip effect, Cooperative game theory

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ISSN: 2062-087X

DOI: 10.14267/issn.2062-087X