Using decomposition methods to solve pricing problems in network revenue management

In this article, we develop two methods for making pricing decisions in network revenue management problems. We consider a setting where the probability of observing a request for an itinerary depends on the prices and the objective is to dynamically adjust the prices so as to maximize the total expected revenue. The idea behind both of our methods is to decompose the dynamic programming formulation of the pricing problem by the flight legs and to obtain value function approximations by focusing on one flight leg at a time. We show that our methods provide upper bounds on the optimal total expected revenue and these upper bounds are tighter than the one provided by a deterministic linear program commonly used in practice. Our computational experiments yield two important results. First, our methods provide substantial improvements over the deterministic linear program. The average gap between the total expected revenues obtained by our methods and the deterministic linear program is 7.11 per cent. On average, our methods tighten the upper bounds obtained by the deterministic linear program by 3.66 per cent. Second, the two methods that we develop have different strengths. In particular, while one method is able to obtain tighter upper bounds, the other one is able to obtain pricing policies that yield higher total expected revenues.