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

Abstract

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.