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We extend the guaranteed service, supply chain modeling framework to allow for an arbitrary, integer review period or ordering frequency at each stage. We define a notation for the cyclic inventory dynamics that review periods introduce and generalize inventory-balance equations to accommodate three different periodic-review operating policies---constant base stock, constant safety stock, and adaptive base stock. As a form of validation, we apply the model to the Celanese acetic acid supply chain and show that inventory metrics of the new model differ by more than 30 percent from those derived through the simpler modeling approach of aggregating a review period into lead time.