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）问题是不确定性下动态决策中的一个经典挑战。在此问题中，有限资源必须在有限时间内分配给服务客户，而客户根据随机过程到达。典型的NRM模型假设客户到达在时间上相互独立。然而，本文探索了一个更一般的场景，其中不同时期内的客户到达可能存在相关性。我们提出了一种新模型，该模型假设存在一个决定当期客户到达的系统状态。此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各种情景下的相关性，并综合了关于相关性模型的先前文献。为解决相关模型下的NRM问题，我们推导出最优策略的一个新线性规划（LP）近似。我们的近似比现有上界提供了最优策略所收集总期望值的更紧上界。我们利用LP开发了一种新的投标价格策略，该策略通过反向归纳方式为每个系统状态和时间段计算投标价格。然后，通过将客户奖励与相应投标价格进行比较来做出决策。我们的策略保证至少收集最优策略所获总奖励的$1/(1+L)$部分，其中$L$表示客户所需的最大资源数量。总之，我们的工作为NRM问题中的相关客户到达提出了一个新模型，并提供了在该模型下求解该问题的LP近似。我们推导了一种新的投标价格策略，并给出了该策略性能的理论保证。