On the convexity of a function related to the Wagner-Whitin model

The classical Economic Order Quantity (EOQ) model of Harris and Wilson exhibits a convex objective function. The Dynamic Lot Size (DLS) model of Wagner and Whitin exhibits a concave objective function. In this paper, the authors reconcile these two results by showing that a reformulation of the DLS model along the lines of EOQ model exhibits a convex objective function provided only that unit production costs are stationary. A counterexample is provided to show the necessity of the condition.