Decentralized multiechelon inventory control

This paper considers a model for decentralized control of an inventory system consisting of 1 central warehouse and a number of retailers. The cost structure includes holding costs at both echelons and shortage costs proportional to the time until delivery at the retailers. We analyze a procedure for coordinated but still decentralized control of the system. The procedure is based on a simple approximation, in which the stochastic lead times perceived by the retailers are replaced by their correct averages. The approximation enables us to decompose the considered multiechelon inventory problem into a number of single echelon problems, 1 for each installation. The information about how a certain decision at the warehouse affects the retailers is conveyed through the marginal cost increase with respect to a change of the expected lead time. This information about the retailer costs is used as a shortage cost at the warehouse. We show that a coordination procedure based on this information can be used for finding near-optimal reorder points for the system and provide bounds for the approximation errors.