This study sought to find analytic solutions to the problem of determining the optimal capacity of a batch-storage network to meet demand for finished products in a system undergoing joint random variations of operating time and batch quantity. The raw material purchasing flow and final product demand flow are susceptible to joint random variations in the order cycle time and batch size. The production processes also have joint random variations in production cycle time and product quantity. Waste regeneration or disposal processes are included into the network to treat the spoiled materials from failed batches. The objective function of the optimization is minimizing the expected total cost, which is composed of setup and inventory holding costs as well as the capital costs of constructing processes and storage units. A production and inventory method, the PSW (periodic square wave) model, provides a unique graphical method to find the upper/lower bounds and average of random flows, which are used to construct terms of the objective function and constraints of the optimization model. The advantage of this model is that it provides a set of simple analytic solutions while also maintaining a realistic description of the random material flows between processes and storage units; as a consequence of these analytic solutions, the computation burden is significantly reduced. The proposed method has the potential to rapidly provide very useful data on base investment decisions during the early plant design stage. It should be particularly useful when these decisions must be made in a highly uncertain business environment. (C) 2008 American Institute of Chemical Engineers.