Abstract: Based on the famous reverse auction website Priceline, this paper studies a problem of how to dynamically set reserve prices for some goods of the seller in a period of continuous time when customers arrive at Priceline one after another according to a non-stationary Poisson process, so that the seller can gain a maximal expected revenue. With the comparability of both revenue management and reverse auction, and the uniqueness of reverse auction, the optimal control model of the expected revenue for sellers is set up, and the following properties are obtained: 1) the concavity and monotonicity of the maximal expected revenue function, 2) the monotonicity of the marginal expected revenue function, and 3) the concavity of the optimal price. The results of numerical analysis are consistent with theoretical ones. It is also illustrated that the closer the bidding price is to the valuation, the more dominant Priceline will be to revenue management.

Key words: on-line auctions, reverse auctions, optimal control, revenue management, Priceline