In the fast-changing business environment, supply chains are affected by the production and inventory strategies, which influence the amount of information needed by the chains. The firms must therefore determine the best supply chain inventory strategies for their products. The lack of precise market demand and reliable supplier’s stock level makes it inappropriate to use the statistically-based inventory model to determine inventory strategies for the new product supply chain. This paper therefore presents a fuzzy neural network model to describe the uncertain market demand and supply reliability. By the joint replenishment and periodic review, we determine, under the consideration of long-term effect, the possible quantities of supply and customer’s demands in the multi-echelon acyclic network supply chain.