A deterministic multiproduct, facility-in series multiperiod production planning model is analyzed, where each period demand for the product of a facility appear in a fixed proportion of that for the product of the immediately following facility. The model considers concave production and inventory costs, which can depend upon the production in different facilities. No backlogging is allowed. It is shown that the model is represented via a single source network, which facilitates development of efficient dynamic programming algorithms for computing the optimal production schedule.