Up then down:bid-price trends in revenue management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price-sensitive non-strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this paper aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid-price processes. We show that an optimal bid-price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up-then-down pattern of bid-price processes is related to two fundamental static properties of the optimal bid prices: (1) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (2) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid-price process is mainly driven by the resource scarcity effect while the downward trend implies that the bid-price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal-price process. The results are also extended to the network RM problems