Mathematical programming issues related to pricing and revenue management

这项提案涉及围绕定价和收入管理这一当前运筹学最活跃的领域之一的主题的问题。这在航空公司希望在竞争环境中提高盈利能力的背景下解释得最好，传统上涉及四个组成部分：需求预测、超额预订政策、座位库存控制和定价。这些组成部分的共同主线是，与购买飞机或修改航线等棘手问题不同，它们不需要资本投资，对成本的影响很小，尽管它们对收入有直接影响。我在这个领域的研究受到了早期对双层规划的研究的推动，双层规划是数学的一个分支，在这个分支中，决策者(政府、公司)将其他代理人(竞争对手、客户)对自己行动过程的反应纳入其决策过程。这种方法虽然在收入管理方面是自然的，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.