Optimal co-investment in supply chain infrastructure

This paper considers co-investment in a supply chain infrastructure using an inter-temporal model. We assume that firms' capital is essentially the supply chain's infrastructure. As a result, firms' policies consist in selecting an optimal level of employment as well as the level of co-investment in the supply chain infrastructure. Several applications and examples are presented and open-loop, as well as feedback solutions are found for non-cooperating firms, long- and short-run investment cooperation and non-simultaneous moves (Stackelberg) firms. In particular, we show that a solution based on Nash and Stackelberg differential games provides the same level of capital investment. Thus, selecting the leader and the follower in a co-investment program does not matter. We show that in general, co-investments by firms vary both over time and across firms, and thereby render difficult the implementation of co-investment programs for future capital development. To overcome this problem, we derive conditions for firms' investment share to remain unchanged over time and thus be easily planned.