# An Integrated Capacity Allocation and Dynamic Pricing Model Designed for Air Cargo Transportation
###### Abstract
A review of the literature on revenue management reveals that the concept was initially applied to the airline industry but was subsequently adopted by other sectors. With the application of revenue management to air transportation, benefits such as increased profitability, better use of resources, meeting the needs of different types of customers, digitalization of systems, and increased customer satisfaction and loyalty are achieved. However, due to the significant differences between air cargo and passenger transportation, the application of revenue management practices in the former has been relatively limited in comparison to the latter. The analysis of revenue management in air cargo can be divided into four main categories: forecasting, capacity control, overbooking, and pricing. All of the aforementioned components are correlated and interact with one another. Figure 1 illustrates the interrelationship between the components of air cargo revenue management. When the figure is analyzed, it can be seen that the air cargo revenue management process starts with forecasting. In the context of forecasting, it is possible to estimate a number of variables, including demand, capacity, cancelation, and no-show rates. Forecasting data is a prerequisite for the capacity control phase. While forecasting demand, holidays, market data, existing bookings, and data from the past period can be used. In order to accurately forecast capacity, it is essential to evaluate cargo and passenger aircraft separately. Since factors such as the number of passengers and baggage weight affect the cargo capacity of passenger aircraft, it is more difficult to make capacity forecasts for passenger aircraft. In the capacity control phase, it is essential to ascertain both the contracted sales capacity and the free sales capacity. The data obtained after the capacity control phase will be employed for both the evaluation of allocation requests and the determination of pricing. The financial success of air cargo companies is dependent upon their capacity to utilize their limited resources in an optimal manner. The evaluation of capacity in the air cargo sector can be conducted according to three distinct criteria: tonnage, volume, and position. The multidimensional nature of capacity renders capacity management a challenging endeavor. Given the importance of capacity utilization in several fields, it is necessary to investigate the optimal means of maximizing this utilization. Despite the extensive literature on the topic of resource allocation using nonlinear programming, there is a lack of research in the field of mathematical models for the allocation of air cargo capacity [7]. In a previous study, [PERSON] and colleagues [8] proposed a multi-stage stochastic programming model for the optimal allocation of cargo to the passenger network, intending to maximize profits. Firstly, the authors considered the uncertainty pertaining to the cargo capacity of passenger aircraft and the uncertainty of demand. Subsequently, they concentrated on the distribution of the reserved capacity across different legs, utilizing the fuselage of passenger aircraft as the sole mode of transportation. In their model, the researchers incorporated demand as a chance constraint, assuming that it follows a normal distribution and requiring that there should be no shortages with high probability. In our model, we have also incorporated demand forecasting in order to enhance the model's accuracy. In their study, [PERSON] et al. [9] addressed the issue of single-leg capacity allocation in cargo revenue management, with a particular focus on the management of reservations based on free sales capacity. A Markov model was proposed as a means of managing this process. However, the authors did not address the question of determining the optimal allocation of capacity between contracted sales and free sales. In the initial phase of our  
Figure 1: Relationships between air cargo revenue management components.