An Approximate Dynamic Programming Approach to Dynamic Pricing for Network Revenue Management

Much of the network revenue management (NRM) literature considers capacity control problems where product prices are fixed and the product availability is controlled over time. However, for industries with imperfect competition, firms typically retain some pricing power and dynamic pricing models are more realistic than capacity control models. Dynamic pricing problems are more challenging to solve; even the deterministic version is typically nonlinear. In this study, we consider a dynamic programming model and use approximate linear programs (ALPs) to solve the problem. Unlike capacity control problems, the ALPs are semi-infinite linear programs, for which we propose a column generation algorithm. Furthermore, for the affine approximation under a linear independent demand model, we show that the ALPs can be reformulated as compact second order cone programs (SOCPs). The size of the SOCP formulation is linear in model primitives, including the number of resources, the number of products, and the number of periods. In addition, we consider a version of the model with discrete price sets and show that the resulting ALPs admit compact reformulations. We report numerical results on computational and policy performance on a set of hub-and-spoke problem instances.