## 3 Materials and Methods
### Proposed Approach
#### 3.2.1 Data Management Stage  
Following ref [22], three steps are considered in the data management phase: data collection, data augmentation, and data preprocessing. First, domain expert interviews are proposed as the means of data collection that effectively restrict the possibly infinite number of macroeconomic data to those considered to most affect the delivery performance of suppliers. Indeed, experts' interviews have proven to be effective in refrigering macroeconomic indicators [19]. In particular, the external cues-based methodology suggested in [32] is proposed to select experts. According to [32], the external cues-based methodology should be preferred when tasks are related to highly specialized markets. Afterward, a data augmentation step based on a linear interpolation of macroeconomic data is proposed to reconstruct the daily value of the macroeconomic variables. Indeed, while the problem statement requires the delivery delay performance of each supplied component to be predicted at a daily level, macroeconomic variables are usually recorded with a monthly frequency. Once the data augmentation has been executed, a data preprocessing step is proposed involving feature engineering, feature selection, and feature scaling. A lag transformation is proposed for the feature engineering step. Considering a variable \(X\), the lag transformation \(L(X,\alpha)\) creates a new variable whose \(t\)-th value is equal to \(X_{t-\alpha}\) for \(t>\alpha\), while for \(t\leq\alpha\), the new variable contains missing values. The lag transformation is proposed because macroeconomic variables usually affect local systems with a certain delay in time. Thus, generating different lagged values for the collected macroeconomic data is considered necessary under the requirement identified in the problem statement. However, considering all possible combinations for the parameter \(\alpha\) and all macroeconomic variables at a daily level can easily lead to long computational times for dataset generation as well as memory storage problems. To overcome these problems, the proposed feature engineering step will generate only those lagged variables resulting from considering \(\alpha\) in a limited discrete subset. Furthermore, it is proposed that for each separate component, only the observations for which delivery delay data are recorded and not those observations containing missing data generated from the lag transformation will be considered for each macroeconomic variable. A univariate feature selection based on the K-best algorithm implemented [33] separately for each component in Sklearn is proposed for the feature selection step. The proposed feature selection algorithm selects only the K features from the entire subset of features, reporting the highest scores according to the algorithm rank, in which the parameter K must be found experimentally. This technique is suggested for two main reasons. First,  
Figure 1: Proposed approach. compared to the heuristic approach proposed in [18], this technique does not require the choice of macroeconomic indicators to be limited to those related to the location in which a specific supplier is located. Rather, the proposed technique automatically identifies the macroeconomic variables that are most relevant to the supplier's delivery performance. On the other hand, compared to the other feature selection methods, its reduced computational complexity guarantees a fast application even when a large number of macroeconomic variables are considered. Lastly, a data scaling step based on the MinMax scaler is proposed to scale each variable in the dataset in the range [0, 1] according to the equation below:  
\[x_{scaled}=\frac{x-\min(x)}{\max(x)-\min(x)} \tag{1}\]  
Here, for a given variable, \(x_{scaled}\) represents the scaled vector, \(x\) represents the original vectors, and \(\max(x)\) and \(\min(x)\) represent, respectively, the maximum and minimum values of the vectors.