We consider a model for decentralized inventory control in a two-level distribution system with one central warehouse and N non-identical retailers. All installations use continuous review installation stock (R,Q)-policies for replenishing their inventories. Our approach is based on an approximate cost evaluation technique, where the retailers replace their stochastic lead-times by correct averages. By introducing a modified cost-structure at the warehouse, the multi-level inventory control problem can be decomposed into N+1 single level sub-problems, one problem for each installation. The sub-problems are then solved in an iterative manner by a simple coordination procedure, which can be interpreted as a negotiation process. In the case of normally distributed demand we show that the procedure converges to a near optimal solution. To assess the quality of the involved approximation an upper bound for the relative cost increase of using the obtained solution is derived. We also provide a numerical study illustrating the performance of our approach.
