This paper is concerned with inventory control in assembly systems for minimizing production costs. The system manufactures multiple products assembled from various components, and it operates according to a cyclic schedule. At the start of each cycle time, two decisions are made: the product volumes to be assembled during the current cycle, and the component-stock levels to be ordered. For a given decision, there is an associated cost incurred by backlogging of the finished products on one hand, and the component inventory holding cost, on the other hand. The objective here is to balance the two costs so as to minimize their sum. One complicating factor stems from uncertainties in both product demand levels and components yield times. These uncertainties can be modeled by probabilistic means, and hence the cost minimization problem becomes a stochastic problem. This problem can be quite difficult due to the nonlinearity of the equations involved, the mix of integer and continuous parameters, and their large number in moderate-size problems. Our approach in this paper is to first define certain control parameters and thus reduce the number of the variables involved in the optimization problem, and then solve the latter problem by using sophisticated optimization techniques in conjunction with heuristic modeling. We will demonstrate, by numerical means, the resolution of fairly difficult problems and thus establish the viability of the proposed numerical techniques