Dynamic Pricing and Inventory Management Under Inventory-Dependent Demand

We analyze a finite horizon periodic review joint pricing and inventory management model for a firm that replenishes and sells a product under the scarcity effect of inventory. The demand distribution in each period depends negatively on the sales price and customer-accessible inventory level at the beginning of the period. The firm can withhold or dispose of its on-hand inventory to deal with the scarcity effect. We show that a customer-accessible-inventory-dependent order-up-to/dispose-down-to/display-up-to list-price policy is optimal. Moreover, the optimal order-up-to/display-up-to and list-price levels are decreasing in the customer-accessible inventory level. When the scarcity effect of inventory is sufficiently strong, the firm should display no positive inventory and deliberately make every customer wait. The analysis of two important special cases wherein the firm cannot withhold (or dispose of) inventory delivers sharper insights showing that the inventory-dependent demand drives both optimal prices and order-up-to levels down. In addition, we demonstrate that an increase in the operational flexibility (e.g., a higher salvage value or the inventory withholding opportunity) mitigates the demand loss caused by high excess inventory and increases the optimal order-up-to levels and sales prices. We also generalize our model by incorporating responsive inventory reallocation after demand realizes. Finally, we perform extensive numerical studies to demonstrate that both the profit loss of ignoring the scarcity effect and the value of dynamic pricing under the scarcity effect are significant.