An Approximation of the Cost Function for Multi-Echelon Inventory Model

For an inventory model with a central warehouse that supplies two satellite warehouses an approximation of the cost function by upper and lower bounds is presented under the assumption that the satellites follow (s, S) policies that are optimal for the satellites alone. The difference between these upper and lower bounds for each period is less than a fixed number. In the infinite horizon model with a discount rate less than one this difference is less than a constant that depends on the mean of the demands, the holding, and the penalty costs. The results are shown for two satellites, they can easily be generalized to k satellites.