Managing a supply chins is very difficult, since complex interrelationships at various levels between various entities and uncertainties exist in the supply chain. The objective of this paper is to determine the optimal inventory strategy for the new product supply chain. Since there may be no historical data available for these products, fuzzy set theory is used to represent the uncertain customer demands and unreliable supply delivery. An algorithm is developed to estimate the total inventory cost of the entire supply chain, according to a set of order-up-to-levels for stock-keeping units on the supply chain. Genetic algorithm is applied to determine the optimal set of order-up-to levels that minimize the total supply chain inventory cost. An example is used to illustrate the concept developed.