An effective methodology is reported for the optimal design of multisite batch production/transportation and storage networks under uncertain demand forecasting. We assume that any given storage unit can store one material type that can be purchased from suppliers, internally produced, internally consumed, transported to or from other plant sites, and/or sold to customers. We further assume that a storage unit is connected to all processing and transportation stages that consume/produce or move the material to which that storage unit is dedicated Each processing stage transforms a set of feedstock materials or intermediates into a set of products with constant conversion factors. A batch transportation process can transfer one material or multiple materials at once between plant sites. The objective for optimization is to minimize the probability averaged total cost, which consists of the raw material procurement cost, the cost of setting up processes, inventory holding costs of the storage units, and the capital costs of processes and storage units. A novel production and inventory analysis formulation, the PSW (periodic square wave) model, provides useful expressions for the upper/lower bounds and average level of the storage inventory. The expressions for the Kuhn-Tucker conditions of the optimization problem can be reduced to two sub-problems. The first yields analytical solutions for determining lot sizes, and the second is a separable concave minimization network flow sub-problem whose solution yields the average material flow rates through the networks for the given demand forecast scenario. The result of this study will contribute to the optimal design and operation of large-scale supply chain systems.