In this paper we study the Common Cycle Scheduling Problem (CCSP). This classic production problem is concerned with determining optimal production lot sizes for a given set of products using a common facility. CCSP is based on scheduling all products using a common (base) cycle time, so that the lot size for each product is the forecasted demand for that product over the base cycle time. This research provides an optimizing framework for CCSP for a multi-stage, multi-product, flow-shop environment under deterministic and stationary conditions, assuming a fixed sequence is maintained across all processing stages. The framework presented considers the costs of work-in-process inventory and determines a jointly optimal common cycle time and production schedule (start and finish times for each product's production lot-size) for the multi-stage facility in question. The paper also reports some results on the impact of alternative sequencing rules for the CCSP context.