# An Integrated Capacity Allocation and Dynamic Pricing Model Designed for Air Cargo Transportation
## 2 Materials, Methods, and Models
### Demand Forecasting
The selection of independent variables is paramount for optimizing the regression equation, and the relationship between the dependent and independent variables must be meticulously evaluated during analysis. A robust correlation between the dependent and independent variables is essential, and it is equally crucial that the data set is sufficiently large and free of outliers [24]. The structuring of numerical observations in a time-dependent manner is referred to as a time series [25]. The objective of a time series is to construct a model utilizing existing data, with time generally exhibiting equal intervals, such as daily or hourly. Examining the factors influencing realized events facilitates predictions for the future and offers insights into subsequent periods. Time series analysis is a distinctive analytical method that differs from regression analysis. In time series analysis, the temporal dimension is paramount, as successive observations are typically dependent. This interdependence enables enhanced prediction of future values [26]. When consistent historical data are available, it is feasible to utilize time series analysis methods to model the data and make future predictions. Time series analysis is employed for non-stationary data that exhibits fluctuations over time. Time series analysis is frequently employed in various sectors, including finance, economics, and retail. However, it should be noted that using time series can pose significant challenges because it is difficult to manage market volatility and capture changes in non-stationary data in financial forecasting. Prior to the selection of an appropriate time series method for our study, a comprehensive investigation was conducted to ascertain the most suitable approach. This investigation entailed a meticulous analysis of the data over a four-year period to discern the characteristics of the series. The findings revealed the presence of comparable patternsin the data on a monthly basis, indicating the existence of a seasonal effect. In addition to the seasonal effect, an upward trend was observed in the demand series. Given the presence of both seasonality and trend in the series, we opted to utilize an exponential smoothing method. Winters' method is one of the exponential smoothing methods that can be used when there is a trend, tendency, and seasonality in the series. This method dynamically estimates the trend, the effect of seasonal changes, and cyclical movements. It uses three different correction factors: the correction factor for seasonal variation, the correction factor for cyclical movements, and the correction factor for the trend. Since our data set has seasonality and trend tendency, we chose [PERSON] method to use in our model. In the process of engineering the artificial neural network (ANN) model, a comprehensive evaluation of numerous ANN algorithms was conducted to ascertain their respective degrees of suitability. This evaluation process culminated in the selection of the NARX model for incorporation into our study, a decision that was guided by the observation that the outputs of the NARX model exhibited a greater degree of alignment with the actual data. The tested models' results can be found in Table 5.  
This study aims to forecast the future demand for the four selected destinations. To this end, the past twenty-four months of data were used to predict four months of data. A total of 627 observations were considered in the data set, and it was found that the results of the time series model yielded the worst R\({}^{2}\) result when compared to the actual data. Upon examining the data set and its outputs, it was observed that the predictions generated by the time series model were not significantly deficient; however, for a few extreme values, the results exhibited a substantial deviation from the actual data. Consequently, the time series model was modified by excluding these data points, resulting in the acquisition of the corrected time series model results.