semiconductor manufacturers: supplier’s lead time and forecast demand updating. They assume that the external demands faced by there tailor are correlated between two successive time periods and that the retailer uses the latest demand information to update its future demand forecasts. Furthermore, they assume that the supplier’s delivery lead times are variable and are affected by the retailer’s order quantities. Dong and Lee’s paper revisits the serial multi-echelon inventory system of Clark and Scarf and develops three key results. First, they provide a simple lower-bound approximation to the optimal echelon inventory levels and an upper bound to the total system cost for the basic model of Clark and Scarf. Second, they show that the structure of the optimal stocking policy of Clark and Scarf holds under time-correlated demand processing using a Martingale model of forecast evolution. Third, they extend the approximation to the time-correlated demand process and study, in particular for an autoregressive demand model, the impact of lead times, and autocorrelation on the performance of the serial inventory system.

After reviewing the literature about multi-echelon inventory management in SCs using mathematic modeling technique, it can be said that, in summary, these papers consider two, three, or N-echelon systems with stochastic or deterministic demand. They assume lead times to be fixed, zero, constant, deterministic, or negligible. They gain exact or approximate solutions.

Dekker et al. analyses the effect of the break-quantity rule on the inventory costs. The break-quantity rule is to deliver large orders from the warehouse, and small orders from the nearest retailer, where a so-called break quantity determines whether an order is small or large. In most l-warehouse–N-retailers distribution systems, it is assumed that all customer demand takes place at the retailers. However, it was shown by Dekker et al. that delivering large orders from the warehouse can lead to a considerable reduction in the retailer’s inventory costs. In Dekker et al. the results of Dekker et al. were extended by also including the inventory costs at the warehouse. The study by Mohebbi and Posner’s contains a cost analysis in the context of a continuous-review inventory system with replenishment orders and lost sales. The policy considered in the paper by Vander Heijden et al. is an echelon stock, periodic