A Re-Solving Heuristic with Bounded Revenue Loss for Network Revenue Management with Customer Choice

We consider a network revenue management problem with customer choice and exogenous prices. We study the performance of a class of certainty equivalent heuristic control policies. These heuristics periodically re-solve the deterministic Linear Program (DLP) that results when all future random variables are replaced by their average values and implement the solutions in a probabilistic manner. We provide an upper bound for the expected revenue loss under such policies when compared to the optimal policy. Using this bound, we construct a schedule of re-solving times such that the resulting expected revenue loss, obtained by re-solving the DLP at these times and implementing the solution as a probabilistic scheme, is bounded by a constant that is independent of the size of the problem.