# 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 Quality Prediction  
In general, the quality of biodiesel is evaluated in terms of density, viscosity, and cetane number. These properties play a crucial role in fuel combustion [62]. According to [PERSON] et al. [63], ANN can be adapted to predict the density, dynamic viscosity, and cetane number of biodiesel from four independent variables involving the temperature, composition of methyl esters (C8:0, C10:0, C12:0, C14:0, C16:0, C16:1, C18:0, C18:1, C18:2, C18:3, C20:0, C20:1, C22:0, C22:1, C24:0), number of carbon atoms, and number of hydrogen atoms. Since ANN requires many data points for its training, the study collected 780 experimental points from different scientific articles. The collected data were randomly divided into a training set (60%), testing set (20%), and validation set (20%). Figure 5 illustrates the general modeling procedure of ANN consisting of experimental data collection, ANN modeling, and validation and statistical analysis between the simulated and experimental outputs [64]. [PERSON] et al. [63] utilized Matlab software (2015a) with a neural network toolbox for the ANN modeling, and they conducted sensitivity analysis on independent variables to identify the impact of independent variables on the response variables. The results showed that the correlation coefficient values for density, dynamic viscosity, and cetane number were 0.99208, 0.98255, and 0.91946, respectively. ANN provided high prediction accuracy for the three performance measures representing biodiesel quality. [PERSON] et al. [65] predicted the density (kg/m\({}^{3}\)), higher heating value (MJ/kg), viscosity at 40 \({}^{\circ}\)C (mm\({}^{2}\)/s), flash point (\({}^{\circ}\)C), and oxidative stability (min) of biodiesel via multiple linear regression (or multivariate linear regression), which is a well-known traditional statistical model. Three independent variables of feedstock polyunsaturated/monounsaturated fatty acids balance (_PUI/MU_), iodine value (_IV_), and saponification value (_SV_) were considered. Seventeen oil types involving sunflower oil, peanut oil, hydrogenated coconut oil, hydrogenated copra oil, beef tallow, rapeseed oil, walnut oil, and another 10 blends, were considered. The study demonstrated strong correlations among most parameters except for flash point and oxidative stability. Equations (14)-(18) show the five multiple linear regression models. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**NPLME**} & \multicolumn{2}{c}{**WPLME**} & \multicolumn{2}{c}{**EPLME**} \\ \cline{2-7}  & \(\mathbf{R^{2}}\) & _MAPE_ & \(\mathbf{R^{2}}\) & _MAPE_ & \(\mathbf{R^{2}}\) & _MAPE_ \\ \hline LR & 0.7309 & 14.4841 & 0.6824 & 9.8820 & 0.6959 & 9.1998 \\ KNN & 0.8680 & 7.9753 & 0.8217 & 5.5745 & 0.8765 & 4.7121 \\ MLP & 0.8415 & 8.5512 & 0.7761 & 7.9917 & 0.7417 & 7.6580 \\ \hline \end{tabular}
\end{table} 
Table 5: Estimation performance of linear regression (LR), multilayer perceptron (MLP), and k-nearest neighbor (KNN) [60]. \[ \begin{split} Density=993-0.899(IV)-1.091(SV)+78.87(PU/MU)+\\ 32.5\times 10^{-4}(IV)(SV)-0.189(IV)(PU/MU)-0.29(SV)(PU/MU)+\\ 28.4\times 10^{-4}(IV)^{2}+22.95\times 10^{-4}(SV)^{2}+0.22(PU/MU)^{2} \\ Higher\ heating\ value=41.76+0.0045 IV-0.01395V\\ Viscosity=9.152+0.00572 IV-3.522(PU/MU)-1.37\times 10^{-5}(IV)(SV)+\\ 0.00533(IV)(PU/MU)+0.013(SV)(PU/MU)\\ Flash\ point=-11749-4.364(IV)+173.76(SV)-8.07(PU/MU)+\\ 0.0276(IV)(SV)-0.418(IV)(PU/MU)-0.0149(SV)(PU/MU)-\\ 0.0249(IV)^{2}-0.833(SV)^{2}+17.718(PU/MU)^{2}+0.00016(IV)^{3}+\\ 0.00131(SV)^{3}-1.8135(PU/MU)^{3}\\ Oxidative\ stability=15.157-0.0169(IV)-10.284(PU/MU)+\\ 0.0214(IV)(PU/MU)+0.00084(IV)^{2}+4.54(PU/MU)^{2}-5.37\times 10^{-6}( IV)^{3}-\\ 0.688(PU/MU)^{3}\end{split}  \tag{14}\]  
The \(R^{2}\) value of the density model was 95.4%, so the prediction model offers high prediction accuracy.