Mathematical programming issues related to pricing and revenue management

本提案所关注的是围绕定价和收益管理这一主题的问题，这是目前运筹学中最活跃的领域之一。最好的解释是，航空公司希望在竞争环境中提高盈利能力，传统上包括四个组成部分：需求预测、超售政策、座位库存控制和定价。这些组成部分的共同点是，与购买飞机或修改航线等战略问题相比，它们不需要资本投资，对成本的影响也很低，尽管它们对收入有直接影响。我在这一领域的研究受到了早期双层规划研究的启发，双层规划是数学的一个分支，决策者（政府、公司）在其决策过程中纳入了其他代理人（竞争对手、客户）对其自身行动的反应。这种方法虽然在收入管理环境中很自然，但从计算的角度来看，产生的数学公式极具挑战性。

This proposal is concerned with issues revolving around the theme of pricing and revenue management, currently one of the most active fields in operations research. It is best explained in the context of an airline that wishes to improve its profitability in a competitive environment, and traditionally involves four components: demand forecasting, overbooking policy, seat inventory control, and pricing. The common thread to these components is that, in contrast with stretegic issues such as aircraft purchasing or route modifications, they do not require capital investment and have a low impact on costs, although they have a direct impact on revenues. My research in this field has been motivated by earlier studies in bilevel programming, a branch of mathematics where a decision maker (a government, a firm) incorporates within its decision process the reaction of other agents (competitors, customers) to its own course of action. This approach, although natural in the revenue management context, yields mathematical formulations that are extremely challenging from the computational point of view.