Dynamic Pricing for Air Cargo Revenue Management

We address a dynamic pricing problem for airlines aiming to maximize expected revenue from selling cargo space on a single-leg flight. The cargo shipments' weight and volume are uncertain and their precise values remain unavailable at the booking time. We model this problem as a Markov decision process, and further derive a necessary condition for its optimal pricing strategy. To break the curse of dimensionality, we develop two categories of approximation methods and pricing strategies. One category is based on the quantity of accepted bookings, while the other is founded on the expected weight and volume of accepted bookings. We prove that the pricing strategy of the quantity-based method possesses several inherent structural properties, which are crucial for analytically validating the model and accelerating the computational process. For the weight-volume-based approximation method, we derive a theoretical upper bound for the optimality gap of total expected revenue. For both methods, we further develop augmented strategies to address the extreme pricing issues in scenarios with high product heterogeneity and incorporate the second moment to enhance performance in the scenarios of high uncertainty, respectively. We utilize realistic dataset to conduct extensive numerical tests, and the results show that the average performance gap between the optimal expected revenue and that of each proposed pricing strategy is less than 10%. The quantity-based method requires the least computation, and performs quite well in the scenarios with low product heterogeneity. The augmented quantity-based method and the weight-volume-based method further enhance the resilience to product heterogeneity. The augmented weight-volume-based method significantly improves the revenue when there are high penalties for overbooking and high uncertainty.