A simple decision rule for decentralized two-echelon inventory control

We consider a two-echelon distribution inventory system with a central warehouse and a number of retailers. The retailers face stochastic demand. The system is controlled by continuous review installation stock (R,Q) policies with given batch quantities. One way to decentralize the system control is to provide a backorder cost to the warehouse, and let the warehouse choose its reorder point so that the sum of the expected holding and backorder costs are minimized. Given the resulting warehouse policy, the retailers similarly optimize their costs with respect to the reorder points. This paper provides a simple approximate technique for determining the backorder cost to be used by the warehouse.