# An Integrated Capacity Allocation and Dynamic Pricing Model Designed for Air Cargo Transportation
## 2 Materials, Methods, and Models
### Demand Forecasting  
Prior to initiating the dynamic pricing model, a demand forecasting model was developed to serve as an input to the model. The inputs utilized by the demand forecasting model were determined through interviews with experts (see Table 1) in the sector who have been employed in this field for an extended period. The resultant inputs for the model were determined as destination point, flight date, aircraft type (passenger or cargo aircraft), total capacity in the relevant period, and capacity allocation rate, which was generated from the capacity allocation model. In order to include economic expectations in the study, an attempt was made to add GDP rates to the model as input. However, since the GDP \begin{table}
\begin{tabular}{c c c} \hline \hline
**Measure** & **CVaR Model** & **ANN Model** \\ \hline ME & \(-0.229\) & \(-0.024\) \\ MAD & 0.231 & 0.028 \\ MSE & 0.058 & 0.001 \\ RMSE & 0.242 & 0.032 \\ MNB & \(-13.856\) & \(-1.872\) \\ MdAE & 0.247 & 0.028 \\ MAxAE & 0.348 & 0.063 \\ MARE & 13.981 & 1.888 \\ GMAE & 0.202 & 0.021 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical comparison of capacity allocation models. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Network Type** & **Number of Layers** & **Number of Neurons** & **R\({}^{2}\)** \\ \hline NARX & 5 & 9 & 54\% \\ NARX & 5 & 10 & 11\% \\ NARX & 6 & 7 & 71\% \\ NARX & 6 & 9 & 41\% \\ NARX & 6 & 10 & 65\% \\ NARX & 7 & 2 & 1\% \\ NARX & 7 & 3 & 35\% \\ NARX & 7 & 5 & 17\% \\ NARX & 7 & 6 & 84\% \\ NARX & 7 & 7 & 33\% \\ NARX & 7 & 8 & 66\% \\ NARX & 7 & 9 & 57\% \\ NARX & 7 & 10 & 93\% \\ NARX & 7 & 11 & 50\% \\ NARX & 8 & 10 & 38\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results produced by different ANN models for capacity allocation. input did not produce a statistically significant result in the demand forecasting models of the selected destinations, the GDP parameter was removed from the data set. The demand forecast produced in this section will be entered into both the capacity allocation model and the dynamic pricing model. In order to ensure the proximity of future predictions to reality, it is necessary to select the prediction technique that is suitable for the structure of the problem to be predicted [20]. A taxonomy of forecasting methods can be classified into three broad categories: quantitative forecasting methods, qualitative forecasting methods, and intelligent forecasting methods [21]. Quantitative forecasting methods are based on a thorough analysis of the data, with the input of the method being real data collected at different times. Qualitative forecasting methods, on the other hand, employ the expertise and experience of experts [22]. In certain instances, both qualitative and quantitative methods can be utilized in conjunction. In addition to these conventional methods, intelligent methods such as artificial neural networks (ANNs), genetic algorithms, and fuzzy logic have also been employed in academic literature to predict future outcomes [23]. In our study, we developed a demand forecasting model using historical data. We implemented time series analysis and regression analysis, which are quantitative methods, in our data-based forecasting models. The ANN model, an intelligent method, was employed, and the results of all three models were statistically analyzed. As a result, the model that gave the best results among the tested models was determined. Regression analysis is a statistical analysis method that has been applied in a wide array of fields, including medicine, chemistry, economics, physics, social sciences, and biology. The objective of regression analysis is to ascertain the relationship between variables (two or more) that may be interrelated. In the model, the variable is divided into two categories: dependent and independent. The variable to be estimated is the dependent variable, while the other variables used to predict the value of the dependent variable are considered independent variables [23].