Coordination of co-investments in supply chain infrastructure

This paper considers co-investments in a supply chain infrastructure using an inter-temporal investment model. We assume that the supply chain firms' capital consists essentially of an investment in the supply chain's infrastructure. As a result, firms' policies consist in selecting both an optimal level of employment and the level of co-investment in the supply chain infrastructure. Recent papers by Kogan and Tapiero (Eur J Oper Res 2009; Supply chain games: Operations management and risk valuation. Springer, Boston 2007) have presented open-loop and feedback solutions for non-cooperating firms and have shown that these solutions differ from a unique system-wide optimal solution, which maximizes the overall supply chain profit. To overcome this problem and thereby improve the supply chain performance, this paper suggests a coordination approach. Such an approach is consistent with a recent practice which consists in the creation of a supply chain shared capital (or joint funding of selected activities) with a temporal reward (or penalties) offered to non-cooperating firms for each dollar investment they make. In addition, this paper provides a closed form expression for the time sensitive rewards function expressed in terms of the system parameters. We show that when these rewards are offered, the Nash co-investment equilibrium is equal to the system-wide optimal solution.