Stockout compensation: Joint inventory and price optimization in electronic retailing

Delays in product availability are common in e-commerce where electronic retailers try to manage with very low inventories. While this lowers inventory costs, the negative effect of increased stockouts is to reduce net demand for the product. We analyze the effect of offering a lower price during stockout to compensate for a customer's waiting time, using an EOQ-type inventory-modeling framework but solving simultaneously for both the optimal prices and the lengths of the in-stock and stockout periods. The lower price recaptures some lost demand and has an important synergistic effect: the increased sales rate leads to lower unit costs for inventory holding and product ordering. Stockout compensation improves market efficiency and increases the retailer's sales and profit. The optimal stockout-compensation policy is to choose period lengths and prices such that the two periods have equal effective prices (i.e., the optimal stockout compensation equals the average waiting cost for a customer). Compared with the pure wait-free and stockless-operation policies, stockout compensation not only yields greater profits, but also greater revenues, lower unit costs, and increased consumer surplus and market coverage. Compared with a backorder policy without compensation, the stockout compensation policy improves profits and social welfare but at the expense of consumer surplus. Allowing for strategic consumer behavior under knowledge of future prices, the equal-effective-prices solution defines a rational-expectations equilibrium.