バイアップがある静的レベニューマネジメントモデル (不確実・不確定性の下における数理的意思決定の理論と応用)

Abstract

In the classical Littlewood's two-period model of static revenue management for airline seat reservation as well as its extensions to multi-period models by others, it is assumed that the demands in each period are independent and that customers whose request for reservation are once rejected disappear immediately. This assumption does not reflect a common behavior of customers in practice that they tend to seek booking again at higher fare. The theoretical treatment of such buy-up behavior is not simple because of the resultant mutual dependence of the demands over several periods. Some literature heuristically (incorrectly) treats the two-period model with customers'buy-up behavior. In this paper, we study the optimal booking limits in the two-and three-period static revenue management models with customers'buy-up behavior in which a given fraction of customers whose request for seat reservation are rejected in each period try to book in the following periods at higher fare with some probability successively. Specifically, for the three-period model with buy-up factor a from the third to the second period and another factor β from the second to the first period, we derive a set of simultaneous equations for the optimal booking limits for the third and second periods in terms of the multiple integrals involving the distribution functions for the original demands in the three periods. Numerical examples are provided to illustrate the dependence of the optimal booking limits on α and β. It is observed that the maximized expected revenue increases as α and β increase by reducing the optimal booking limits accordingly.