The theory and practice of dynamic-programming-based bid prices

Others have mentioned dynamic programming (DP) as an elegant, theoretical solution that could be applied to the complex problem of airline network revenue management. In this article, we examine how the general DP theory is applied in practice to the airline problem. We use simulation analysis to show the difference in the expected revenue performance of such deterministic DP-based bid prices, compared to linear programming (LP)-based bid price control and EMSRb leg control. The results show that deterministic DP outperforms the other methods when uncertainty in the demand (variance) is lower. Only at the highest level of variance, in a few cases the LP method is best. On average though, across all 25 simulations run (representing different combinations of parameters and variance levels), DP beat LP by an impressive 3.5 per cent. DP also beat leg control by 5.4 per cent on average. We also present results which show that the time to fully solve such DPs without shortcuts and generate the associated bid prices, even in small networks (for example, two legs with 30 seat capacity) is prohibitive. We then show an innovative shortcut that generates an enormous time savings and allows us to solve much larger and more realistic airline networks (for example, 11 legs, 66 origin-destinations, 5 fare classes and leg capacities greater than or equal to 500 seats). Finally, we explore the revenue advantage of using stochastic DP over deterministic DP. We find that stochastic DP beats deterministic DP by 0.7 per cent on average across all 25 simulations run (again, representing different combinations of parameters and variance levels).