review, order-up-to policy, under both stochastic demand and lead times.

The main purpose of Iida’s paper is to show that near-myopic policies are acceptable for a multi-echelon inventory problem. It is assumed that lead times at each echelon are constant. Chen and Song’s objective is to minimize the long-run average costs in the system. In the system by Chen et al., each location employs a periodic-review, or lot-size reorder point inventory policy. They show that each location’s inventory positions are stationary and the stationary distribution is uniform and independent of any other. In the study by Minner et al., the impact of manufacturing flexibility on inventory investments in a distribution network consisting of a central depot and a number of local stock points is investigated. Chiang and Monahan present a two-echelon dual-channel inventory model in which stocks are kept in both a manufacturer warehouse (upper echelon) and a retail store (lower echelon), and the product is available in two supply channels: a traditional retail store and an internet-enabled direct channel. Johansen’s system is assumed to be controlled by a base-stock policy. The independent and stochastically dependent lead times are compared.

To sum up, these papers consider two- or N-echelon inventory systems, with generally stochastic demand, except for one study that considers Markov-modulated demand. They generally assume constant lead time, but two of them accept it to be stochastic. They gain exact or approximate solutions.

In multi-echelon inventory management there are some other research techniques used in literature, such as heuristics, vary-METRIC method, fuzzy sets, model predictive control, scenario analysis, statistical analysis, and GAs. These methods are used rarely and only by a few authors.

A multi-product, multi-stage, and multi-period scheduling model is proposed by Chen and Lee to deal with multiple incommensurable goals for a multi-echelon SC network with uncertain market demands and product prices. The uncertain market demands are modeled as a number of discrete scenarios with known probabilities, and the fuzzy sets are used for describing the sellers’ and buyers’ incompatible preference on product prices.