本文以Onsale网上拍卖公司的拍卖方式为背景,研究了在给定拍卖时间长度与拍卖总供给量的条件下,将拍卖品分若干批拍卖这一问题.建立了其马尔可夫决策过程模型,分别在公开保留价与不公开保留价的两种情况下,研究了每批拍卖品数量的最优问题,并证明了网上拍卖中商家不公开保留价时获得的最大期望利润多于公开时的最大期望利润.

On the basis of the auction formalism in Onsale, Inc., we study the following optimization problem. Here a given total number of items should be sold in a given time horizon which is divided into several time periods, and at each period there is an auction to sell the items offered optimally. The remaining items at each period can be sold at the next period until the time horizon is ended. It is formulated as a Markov decision process and its optimality equation is solved separately for two types of the reserve price which is announced or private. Finally, we conclude that the auctioneer can gain more expected total profit if he doesn't open the reserve price, which is, moreover, validated by numerical examples.