is the first multi-echelon inventory model for managing the inventory of service parts. Thereafter, a large set of models which generally seek to identify optimal lot sizes and safety stocks in a multi-echelon framework, were produced by many researchers. In addition to analytical models, simulation models have also been developed to capture the complex interaction of the multi-echelon inventory problems.

So far literature has devoted major attention to the forecasting of lumpy demand, and to the development of stock policies for multi-echelon SCs Inventory control policy for multi-echelon system with stochastic demand has been a widely researched area. More recent papers have been covered by Silver and Pyke. The advantage of centralized planning, available in periodic review policies, can be obtained in continuous review policies, by defining the reorder levels of different stages, in terms of echelon stock rather than installation stock.

Rau et al. , Diks and de Kok , Dong and Lee ,Mitra and Chatterjee , Hariga , Chen ,Axsater and Zhang , Nozick and Turnquist ,and So and Zheng use a mathematic modeling technique in their studies to manage multi-echelon inventory in SCs. Diks and de Kok’s study considers a divergent multi-echelon inventory system, such as a distribution system or a production system, and assumes that the order arrives after a fixed lead time. Hariga, presents a stochastic model for a single-period production system composed of several assembly/processing and storage facilities in series. Chen, Axsater and Zhang, and Nozick and Turnquist consider a two-stage inventory system in their papers. Axsater and Zhang and Nozickand Turnquist assume that the retailers face stationary and independent Poisson demand. Mitra and Chatterjee examine De Bodt and Graves’ model (1985), which they developed in their paper’ Continuous-review policies for a multi-echelon inventory problem with stochastic demand’, for fast-moving items from the implementation point of view. The proposed modification of the model can be extended to multi-stage serial and two -echelon assembly systems. In Rau et al.’s model, shortage is not allowed, lead time is assumed to be negligible, and demand rate and production rate is deterministic and constant. So and Zheng used an analytical model to analyze two important factors that can contribute to the high degree of order-quantity variability experienced by