A Generalized Order-Up-To Policy and Altruistic Behaviour in a Three-Level Supply Chain

An order coordination policy based on the order-up-to (OUT) policy that minimizes the total inventory costs for a three-level supply chain will be examined. For a single level of a supply chain, Vassian (1955) introduced an ordering policy with a work in progress (WIP) feedback loop and showed that this ordering policy minimizes the variance of the end of period net stock levels. In addition, Vassian showed that the minimized variance of the end-period net inventory level is identical to the variance of the error in the forecast of demand over the lead time plus review period. In this research, Vassian’s ordering policy is called as the traditional OUT policy.1 From Vassian’s seminal contribution, it is obvious that in a single-level supply chain case, the traditional OUT policy is an optimal policy for minimizing the variance of the end of period net stock levels over time. In a multi-level supply chain scenario, however, it might be reasonable to assume that a sequence of traditional OUT policies may not be optimal any more as there is no guarantee that a succession of local minimizations will result in a global optimum, as shown in Hosoda and Disney (2006a). Since the traditional OUT policy does not provide much freedom to manipulate the dynamics of the ordering process, Hosoda and Disney (2006a) have investigated a two-level supply chain using the traditional OUT policy modified to include a proportional controller.