Prior work has investigated time-and inventory-level-dependent pricing of limited inventories with finite selling horizons. We consider a third dimension-in addition to time and inventory level-that the firms can use in setting their prices: the information that the firm has at the individual customer level. An arriving customer provides a signal to the firm, which is an imperfect indicator of the customer's willingness to pay, and the firm makes a personalized price offer depending on the signal, inventory level, and time. We consider two different models: full personalization and partial personalization. In the full personalization model, the firm charges any price it wishes given the customer signal, while in the partial personalization model, the firm can charge one of two prices. We find that a mere correlation between the signals and customers' willingness to pay is not sufficient to ensure intuitive relationships between the signal and the optimal prices. We determine a stronger condition, which leads to several structural properties, including the monotonicity of the optimal price with respect to the signal in the full personalization model. For the partial personalization model, we show that the optimal pricing policy is of threshold-type and that the threshold is monotonic in the inventory level and time.
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