On the incorporation of upgrades into airline network revenue management

Recently, the standard dynamic programming model of network revenue management has been extended for integrated upgrade decision-making. However, opposed to the original model, heuristically breaking the extended model down into a series of single-leg problems by dynamic programming decomposition in order to allow for real-world application is not possible. This is because the model's state space does not incorporate resources but commitments reflecting already sold products and capacity consumption is only resolved at the end of the booking horizon, thereby considering upgrade options. In this paper, we consider arbitrary airline networks with upgrades being performed separately on each flight leg. We show that in this case, there are two reformulations of the extended model. First, we prove that an ad hoc formulation, in which upgrades are technically performed immediately after a sale, is completely equivalent. Second, we present another reformulation whose idea is adapted from linear programing-based production planning with alternative machine types. We prove that the resulting dynamic program is also equivalent. The advantage of both reformulations is that their state space is based on either real or virtual resources instead of commitments. Thus, dynamic programming decomposition techniques can again be applied. Despite the formal equivalence of both reformulations, applying decomposition techniques leads to different approximations and thus to potentially different results when applied in practice. Therefore, we finally numerically examine the approaches regarding revenue performance and discuss airline revenue management settings in which they differ.