# An Integrated Capacity Allocation and Dynamic Pricing Model Designed for Air Cargo Transportation
## 3 Results, Discussion, and Conclusions
### Methodology and Generalization of Findings  
Air cargo management is an important element of modern global logistics and supply chain operations. Air cargo management is a highly complex and challenging endeavor as it requires planning and coordination in many areas. One of these challenging processes is the management of limited cargo capacity. Since the capacity is not available for sale after the flight, it must be sold before the flight. It can be said that air cargo capacity planning is at the forefront of revenue management strategies [37]. There are two main methods of selling capacity: contract sales and free sales. 1. Contract sales: Contract sales are agreements between the airline and the customer that guarantee the customer a certain capacity on a certain flight. \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameters** & **Value** \\ \hline \(\alpha\) & 0.1 \\ \(\gamma\) & 0.9 \\ \(\epsilon\) & 0.1 \\ Episodes & 25.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Hyperparameters used in the model as a result of the grid search method. \begin{table}
\begin{tabular}{c c} \hline \hline
**Destination** & **MAE Value** \\ \hline
1 & 1.15 \\
2 & 0.8 \\
3 & 0.94 \\
4 & 0.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: SARSA model results by destination. Free sales: There is no allocation of capacity. Capacity is offered for direct sale. There is no guarantee that the capacity will be sold. Demand forecasting, capacity determination for contract sales, and pricing are some of the important areas of research in revenue management. In air cargo, there are two main dimensions of capacity: weight and volume. For passenger aircraft, the capacity that can be used for carriage is not fixed; it can be affected by the number of passengers, the total amount of baggage, etc. Demand is also different in the two sectors; while passenger demand can be characterized by seasonal fluctuations, on the cargo side, there are many parameters affecting demand, and it is much more difficult to forecast. As a result of all these difficulties, although there are many articles on revenue management in air passenger transport, there are very few on air cargo. Our first objective in the study is to accurately determine the ratio of allotment capacity for capacity planning. Our second objective is to dynamically price the capacity allocated for free sales. To build the dynamic pricing model, we first built the demand forecasting model. Capacity management is very critical for the air cargo industry. By allocating capacity correctly, it is possible to increase the load factor and thus the total revenue that can be generated. In the highly competitive air cargo sector, it is essential for companies to get their pricing strategies right in order to stay afloat, gain a competitive advantage, and increase profitability. In order to correctly perform the capacity allocation, which is the first step of our study, we have built two models, CVaR and ANN. The CVaR model we built is based on the capacity allocation study conducted in 2022 [7]. In our study, we built the CVaR model using GAMS and the ANN model (NARX) using MATLAB (R2024a). We determined the inputs to be used in the ANN model based on a literature review and expert opinion. We compared the model results with real results using two years of data for four different destinations. The R\({}^{2}\) results were 0.4598 for the CVaR model and 0.9335 for the ANN model. Based on the results, we decided to use the ANN model that we created for the first stage. In business, dynamic pricing is defined as a strategy that adjusts the price of a product or service in real time based on a variety of factors. Examples of factors that affect price include market demand, seasonality, competitive pressures, and other external factors. The aim of dynamic pricing is to maximize revenue and meet sales targets by charging the highest price customers are willing to pay.