Dynamic pricing for air cargo revenue management

Revenue management for air cargo has gained increasing importance due to its significant contribution to the global freight industry. Compared to capacity control methods with fixed prices, dynamic pricing offers the flexibility to adjust prices based on price-demand relationships, thereby enhancing profitability. However, implementing dynamic pricing in air cargo presents unique challenges, such as heterogeneous cargo types, uncertain weight and volume, and overbooking, which lead to the curse of dimensionality. To address these issues, we model the dynamic pricing problem for airlines selling cargo space on a single-leg flight as a Markov decision process, and develop two categories of approximation methods for pricing strategies. The first category is based on the summed quantity of accepted bookings, for which we establish structural properties of the pricing strategy. The second category is founded on the expected weight and volume of accepted bookings, and we derive a theoretical upper bound for the optimality gap of total expected revenue. Due to the possible performance deterioration caused by high product heterogeneity or uncertainty, we further develop augmented methods for either category to enhance performance, employing constructive terms or second moments. Numerical experiments based on a realistic dataset show that the average optimality gap for each proposed pricing strategy is less than 10%, while the gap narrows to below 5% for each augmented strategy. Our findings suggest that using information on distributions of cargo weight and volume and conservative estimations of them can effectively enhance revenue.