# Machine Learning Technologies in the Supply Chain Management Research of Biodiesel: A Review
## 3 Machine Learning in Supply Chain Management of Biodiesel
### Machine Learning Algorithms for Biodiesel Productivity Prediction  
Similar to the yield prediction, multiple machine learning algorithms have been used for biodiesel productivity prediction. [PERSON] et al. (2018) estimated the biodiesel production quantity using four different machine learning algorithms of RF, KNN, SVM, and AdaBoost regression. The dataset involving 381 individual observations with 13 distinct experimental cases was collected under five independent variables of catalyst loading (wt.%), feedstock type, molar ratio of methanol to oil, reaction time (min), and reaction temperature (\({}^{\circ}\)C). Table 3 describes the input and output variables used in the study. In the study, the performance of the four machine learning algorithms was evaluated via _RMSE_ (see Equation (5)). Equation (12) is used to estimate the output \(y\) via the average of the nearest neighbor output \(y_{k}(x)\) in KNN. Unlike RF and SVM (see Section 3.1 for more detail about the algorithms), KNN computes distance (e.g., Euclidian distance and Manhattan distance) between data points for its modeling training:  
\[\hat{y}=\frac{1}{K}{\sum_{k=1}^{K}y_{k}(x)} \tag{12}\]  
In KNN, the selection of k-nearest neighbors is the most critical task because it significantly affects the estimation accuracy of the algorithm. To this end, the interest-specific classification technique selects \(k\) by evaluating the prediction accuracy over different k values. Table 4 describes the selection result of k-nearest neighbors in the study ([PERSON] et al., 2018). The optimum value of \(k\) was selected in terms of RMSE so that the devised KNN has the minimum deviation between observed data and estimated data when \(k=3\) in Table 4.  
On the other hand, AdaBoost regression trains weight via multiple iterations with different sub-training datasets. Initially, a model has an equal weight as dataset D, and replace sampling is performed on D to obtain an adjusted weight with sub-dataset D\({}_{1}\). This replace sampling continues until the best weight with the least value of a loss function is identified. Figure 3 illustrates the overall process of AdaBoost regression ([PERSON] et al., 2018). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\(k\)**Values**} & \multicolumn{3}{c}{**RMSE**} \\ \cline{2-4}  & **Training** & **Validation** & **Result** \\ \hline
3 & 4.081 & 6.332 & Optimum \\
4 & 4.567 & 6.444 & \\
5 & 4.848 & 6.895 & \\
6 & 5.186 & 7.166 & \\
8 & 5.399 & 6.805 & \\
10 & 5.670 & 6.520 & \\
12 & 5.883 & 6.630 & \\
16 & 6.101 & 6.969 & \\
20 & 6.196 & 7.148 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Root mean square error (RMSE) of k-nearest neighbor (KNN) with different \(k\) values ([PERSON] et al., 2018). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **No.** & **Variables** & **Unit** & **Description** \\ \hline \multirow{4}{*}{Inputs} & 1 & Reaction time (\(t\)) & min & Numerical variable, 20–180 min \\  & 2 & Reaction temperature (\(T\)) & \({}^{\circ}\)C & Numerical variable, 30–70 \({}^{\circ}\)C \\ \cline{1-1}  & 3 & Catalyst weight (Wc) & wt.% & Numerical variable, 0.4–2\% \\ \cline{1-1}  & 4 & Methanol/oil molar ratio (\(M\)) & Not applicable & Numerical variable 3–15 \\ \cline{1-1}  & 5 & Feedstock types (\(F\)) & Not applicable & Categorical variable, different biomass oil \\ \hline Outputs & 1 & Biodiesel yield (\(\gamma\)) & \% & Numerical variable, 53.12–98.92\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Description of input and output variables ([PERSON] et al., 2018). Among the four algorithms, RF was selected as the best algorithm to predict biodiesel production quantity with the lowest values of RMSE for both the training (2.778) and validation (5.178) datasets. In the training dataset, the RMSE values of KNN, SVM, and AdaBoost were 4.081, 8.650, and 6.941, while in the validation dataset, the RMSE values were 6.332, 12.122, and 8.332, respectively. [PERSON] et al.