An optimally designed of batch-storage network that uses a periodic square wave model provides analytical lot-sizing equations for a complex supply chain network characterized as a multisupplier, multiproduct, multi-stage, nonserial, multicustomer, cyclic system, with recycling or remanufacturing. The network structure includes multiple currency flows and material flows. The processes involve multiple feedstock and product materials with fixed compositions that are highly suitable for production processes. Transportation processes that carry multiple materials of unknown composition are included in this study, and the time frame is varied from a single infinite period to multiple finite periods to accommodate non periodic parameter variations. The objective function in the optimization is chosen to minimize the difference between the opportunity costs of currency/material inventories and stockholder benefits given in the numeraire currency. Expressions for the Kuhn-Tucker conditions for the optimization problem are reduced to a multiperiod subproblem describing the average flow rates and the analytical lot-sizing equations. The multiperiod lot-sizing equations are shown to differ from their single-period counterparts. The multiperiod subproblem yields a multiperiod planning model that has many advantages over existing planning models. For example, it contains terms that represent operation frequency dependent costs. Realistically sized numerical examples that deal with multinational corporations are formulated and tested. The effects of corporate income taxes, interest rates, and exchange rates are presented. (C) 2011 American Institute of Chemical Engineers AIChE J, 57: 2821-2840, 2011