The Network Revenue Management (NRM) problem is a well-known challenge in dynamic decision-making under uncertainty. In this problem, fixed resources must be allocated to serve customers over a finite horizon, while customers arrive according to a stochastic process. The typical NRM model assumes that customer arrivals are independent over time. However, in this paper, we explore a more general setting where customer arrivals over different periods can be correlated. We propose a new model that assumes the existence of a system state, which determines customer arrivals for the current period. This system state evolves over time according to a time-inhomogeneous Markov chain. Our model can be used to represent correlation in various settings and synthesizes previous literature on correlation models. To solve the NRM problem under our correlated model, we derive a new linear programming (LP) approximation of the optimal policy. Our approximation provides a tighter upper bound on the total expected value collected by the optimal policy than existing upper bounds. We use our LP to develop a new bid price policy, which computes bid prices for each system state and time period in a backward induction manner. The decision is then made by comparing the reward of the customer against the associated bid prices. Our policy guarantees to collect at least $1/(1+L)$ fraction of the total reward collected by the optimal policy, where $L$ denotes the maximum number of resources required by a customer. In summary, our work presents a new model for correlated customer arrivals in the NRM problem and provides an LP approximation for solving the problem under this model. We derive a new bid price policy and provides a theoretical guarantee on the performance of the policy.

翻译：网络收益管理（NRM）问题是不确定环境下动态决策中的经典挑战。在该问题中，固定资源需在有限时间范围内分配给顾客，而顾客根据随机过程到达。典型的NRM模型假设顾客到达独立于时间。然而，本文探讨了一种更一般的场景，其中不同时期的顾客到达可能存在相关性。我们提出了一种新模型，假设存在一个系统状态，该状态决定当前时期的顾客到达。系统状态根据时间非齐次马尔可夫链随时间演化。我们的模型可用于表示多种场景下的相关性，并综合了以往关于相关性模型的文献。为了解决相关性模型下的NRM问题，我们推导了一种新的线性规划（LP）近似最优策略。与现有上界相比，我们的近似提供了最优策略总期望收益更紧的上界。我们利用LP开发了一种新的投标价格策略，该策略通过逆向归纳方式为每个系统状态和时间段计算投标价格，然后通过比较顾客收益与对应投标价格做出决策。该策略保证能收集到最优策略总收益的至少$1/(1+L)$比例，其中$L$表示顾客所需的最大资源数。总之，本文为NRM问题中的相关性顾客到达提出了新模型，并提供了该模型下求解问题的LP近似。我们推导了新的投标价格策略，并给出了该策略性能的理论保证。