An Approximation Algorithm for Network Revenue Management Under Nonstationary Arrivals

We provide an approximation algorithm for network revenue management problems. In our approximation algorithm, we construct an approximate policy using value function approximations that are expressed as linear combinations of basis functions. We use a backward recursion to compute the coefficients of the basis functions in the linear combinations. If each product uses at most L resources, then the total expected revenue obtained by our approximate policy is at least $1/\left(1+L\right)$ of the optimal total expected revenue. In many network revenue management settings, although the number of resources and products can become large, the number of resources used by a product remains bounded. In this case, our approximate policy provides a constant-factor performance guarantee. Our approximate policy can handle nonstationarities in the customer arrival process. To our knowledge, our approximate policy is the first approximation algorithm for network revenue management problems under nonstationary arrivals. Our approach can incorporate the customer choice behavior among the products, and allows the products to use multiple units of a resource, while still maintaining the performance guarantee. In our computational experiments, we demonstrate that our approximate policy performs quite well, providing total expected revenues that are substantially better than its theoretical performance guarantee.