具有日历感知和依赖需求的收益管理：渐近紧的流体近似
Revenue Management with Calendar-Aware and Dependent Demands: Asymptotically Tight Fluid Approximations
AI总结：
本文研究具有日历阶段划分及跨阶段依赖、任意分布需求的收益管理，提出以紧邻前期需求为条件的正确流体近似，并证明其策略渐近最优且实践效果显著。
摘要：
在对收益管理系统中的需求进行建模时，一种自然的方法是关注一个标准时间区间，例如一周，以便我们预测销售周期内每一周的需求。理想情况下，我们希望使用具有一般分布的随机变量来建模每周的需求。当前需求可以为未来需求提供信号，因此我们也希望捕捉不同周需求之间的依赖性。文献中流行的需求模型基于对 Poisson 过程的离散时间近似，无法兼容这些需求。本文聚焦于与一种自然需求预测方法相兼容的收益管理模型。通过动态规划构建此类模型并不困难。我们将销售周期划分为多个阶段，每个阶段都是日历上的一个标准时间区间。每个阶段中我们有随机数量的顾客到达，其分布是任意的，并依赖于前一阶段的到达数量。我们试图回答的问题是相应流体近似的形式。我们给出了正确的流体近似，其含义是它能产生渐近最优策略。我们的流体近似形式令人惊讶，因为其约束使用了某一资源截至特定时间段的期望容量消耗，并以所讨论时间段之前紧邻阶段的需求为条件。随着资源容量和阶段数量以相同速率增长，我们的性能保证收敛至一。据我们所知，该结果给出了在具有任意分布的依赖需求下的首个渐近最优策略。我们的计算实验表明，使用正确的流体近似在实践中能够产生显著影响。
英文摘要：
When modeling the demand in revenue management systems, a natural approach is to focus on a canonical interval of time, such as a week, so that we forecast the demand over each week in the selling horizon. Ideally, we would like to use random variables with general distributions to model the demand over each week. The current demand can give a signal for the future demand, so we also would like to capture the dependence between the demands over different weeks. Prevalent demand models in the literature, which are based on a discrete-time approximation to a Poisson process, are not compatible with these needs. In this paper, we focus on revenue management models that are compatible with a natural approach for forecasting the demand. Building such models through dynamic programming is not difficult. We divide the selling horizon into multiple stages, each stage being a canonical interval of time on the calendar. We have random number of customer arrivals in each stage, whose distribution is arbitrary and depends on the number of arrivals in the previous stage. The question we seek to answer is the form of the corresponding fluid approximation. We give the correct fluid approximation in the sense that it yields asymptotically optimal policies. The form of our fluid approximation is surprising as its constraints use expected capacity consumption of a resource up to a certain time period, conditional on the demand in the stage just before the time period in question. As the resource capacities and number of stages increase with the same rate, our performance guarantee converges to one. To our knowledge, this result gives the first asymptotically optimal policy under dependent demands with arbitrary distributions. Our computational experiments indicate that using the correct fluid approximation can make a dramatic impact in practice.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
