## 3 Materials and Methods
### Experiment Setup  
The experimental setup remained consistent across all the eight components outlined in Section 3.2.1. The historical data of the delivery performance reported by each supplier for a specific component are divided into three consecutive subsets, as illustrated in Figure 2.  
The three subsets, referred to as the training set (comprising 60% of the historical data), the validation set (comprising 20% of the historical data), and the test set (containing the remaining data), were utilized to achieve distinct objectives. The training set facilitated the initial learning phase of the models constituting the predictive module. During this phase, the models learned the relationship between the selected features and the label to predict. The hyperparameters used for the models are detailed in Table 5 and have been obtained following a trial-and-error procedure. Although other strategies could have been adopted for the hyperparameter tuning phase, selecting a more basic tuning procedure was preferred, as the extensive optimization of the hyperparameters was assumed not to be this study's primary goal. The validation set is instead adopted only when considering the proposed approach to find the best value of parameter \(\theta^{data\ benefit}_{i}\). A Bayesian optimization (BO) strategy [36] is proposed to find the best value of the parameter \(\theta^{data\ benefit}_{i}\) within a prespecified research space 0. A BO strategy is adopted, as it represents a valuable iterative optimization technique for finding the maximum or minimum of an objective function when it is expensive to evaluate. This feature is particularly useful, considering that the optimal value of the  
Figure 2: Temporal splitting of historical data related to the delivery performance reported for each supplier for a specific component. tunable parameter \(\theta_{i}^{data\ benefit}\) needs to be found by looking for a value in research space \(\theta\) that minimizes the following result of Equation (11):  
\[ \begin{split}\text{M}in\sum_{t^{\prime}=0}^{T}\sum_{t^{\prime}+1 \geq t>t^{\prime}}^{T}\sum_{i=1}^{M}\hat{Y}_{itt^{\prime}}\Big{(}c_{i}^{ purchasing}+c^{delay}true_{it}^{delay}+c^{advance}true_{it}^{advance}\Big{)}+\\ \sum_{t^{\prime}=0}^{T}\sum_{t^{\prime}+1\geq t>t^{\prime}}^{T} \sum_{i=1}^{M}\hat{Z}_{itt^{\prime}}\Big{(}c_{i}^{order\ emission}-\hat{\theta}_{i}^{ data\ benefit}\Big{)}\end{split}  \tag{11}\]  
In Equation (11), \(\hat{Y}_{itt^{\prime}}\) and \(\hat{Z}_{itt^{\prime}}\) represent the optimal decisions obtained from the prescriptive module when considering a specific value, and \(\hat{\theta}_{i}^{data\ benefit}\) indicates the data acquisition benefit and forecast updated on day \(t^{\prime}\). Conversely, \(true_{it}^{advance}\) and \(true_{it}^{delay}\) represent the ex-post real amount of advance or delay of supplier deliveries. The computation of Equation (11) cannot be considered cheap. First, it requires solving the multiperiod SSOA defined in Section 3.2.1 based on the forecast provided by the predictive module described in Section 3.2.2 to find the optimal values of \(\hat{Y}_{itt^{\prime}}\) and \(\hat{Z}_{itt^{\prime}}\). Afterwards, it requires performing an ex-post evaluation of the decisions based on the true values of delivery performance experienced by the selected suppliers in each considered period (\(true_{it}^{advance}\) and \(true_{it}^{delay}\)). The predictive module is thus initially trained using the training set's past historical data. Then, a value of parameter \(\theta_{i}^{data\ benefit}\) is selected within search space \(\theta\) following the BO strategy, and the prescriptive module is executed considering these inputs. Order allocation decisions are thus generated, new data points are acquired, and the predictive models are updated in the validation set following the order allocation decisions.