Constant Approximation for Network Revenue Management with Markovian-Correlated Customer Arrivals

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.