A multi-period pricing and inventory control model

The authors analyze a finite horizon, single product, period review model in which pricing and inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortage are backlogged. Ordering cost is a convex function of the amount ordered. The objective is to find an inventory and pricing policy maximizing expected discounted profit over the finite horizon. The authors characterize the structure of the optimal combined pricing and inventory strategy for this model. Moreover, the authors demonstrate how the profit-to-go function, order up to level, reorder point and optimal price change with respect to state and time.