Two-dimensional air cargo overbooking models under stochastic booking request level, show-up rate and booking request density

• We present two-dimensional air cargo overbooking model to find optimal overbooking level.
• Sensitivity analysis is done to observe impacts of parameters on optimal solution.
• We present two simplified models which are used to predict the optimal solution.
• The simplified models are multiple regression (R-sq(adj) = 98.3%)and the naïve model.
• The naïve model is at its best when the booking request mean is at the capacity level.

Overbooking is a revenue management technique which offers products more than the amount that is available because there is a chance that some purchasers may withdraw their bookings. For air cargo industry, overbooking decision is more complex to be made because of the two-dimensional characteristic: volume and weight of the booking requests. This paper develops two-dimensional air cargo overbooking models to find the optimal overbooking level in order to minimize the total cost, which consists of spoilage and offloading costs. Booking request level, show-up rate, and booking request density are random variables with known distributions. Computational experiments are conducted to explore the impact of model parameters (such as the ratio between spoilage and offloading costs, capacities and booking requests) on the optimal overbooking level. As the optimal overbooking level finding is complicated, we present simplified methods to estimate the solutions of the problem. It is found that the overbooking level obtained from the simplified method using regression model is very close to the optimal solutions (with R-sq(adj) value of 98.3%). A naïve method to find solution is also presented in this paper and we identify situations when it is appropriate to use each method.