# 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 Feedback Yield Estimation  
The cost of biodiesel is greatly influenced by the feedstock used to produce biodiesel [53]. Therefore, predicting feedstock yield is a significant factor for the efficient supply chain management of biodiesel. Figure 1 illustrates a general process of crop yield estimation model development via a machine learning algorithm. Since each machine learning algorithm requires observed data for its modeling process, most studies collect data (e.g., climate data, climate change data, soil parameter data, and crop data) from a field experiment. Remote sensors such as a thermometer and a photosynthetically active radiation (PAR) sensor can be utilized for the data collection [54]. Once the dataset is built, supervised learning is conducted to develop a yield estimation model for a certain crop. The validated machine learning model is used to estimate crop yield under a designed scenario (e.g., a climate change scenario), and researchers can analyze the estimated results. [PERSON] et al. [55] sought to predict the yields of corn, soybean, winter wheat, spring wheat, cotton, and alfalfa using a two-step machine learning approach consisting of GPM and RF. In order to derive land productivity index and identify potential marginal lands, county-level crop yield data and remote sensed gross primary productivity (_GPP_) data are preprocessed and downscaled for machine learning. To be more specific, GPM estimated the ratio \(\alpha_{i}\) for a specific crop \(i\) in Equation (1):  
\[\alpha_{i}=YD_{i}/GPP_{i} \tag{1}\]  
where \(YD_{i}\) is a crop yield, and \(GPP_{i}\) is the growing season _GPP_ value of a specific crop \(i\). County-level crop yield data averaged over the years 2008-2017, county average temperature, water availability involving the ratio of evapotranspiration (ET) over precipitation, and the percentage of land being irrigated were used to train GPM. The estimated ratio \(\hat{\alpha}_{i}\) was applied to train the RF for each crop \(i\) (see Equation (2)), and each trained RF was applied to estimate the yield of each feedstock:  
\[\hat{YD}_{i}=\hat{\alpha}_{i}GPP_{i} \tag{2}\]  
Figure 2 shows that RF generates bootstrap samples (i.e., \(L_{1},L_{2},\ldots,L_{B}\)) from the original dataset \(L\) involving the independent variable \(x\) and dependent variable \(y\). The bootstrap samples are used to train the individual decision tree \(\phi(x,L_{b})\), and the aggregation process in RF generates \(\phi(x)\) via Equation (3) to estimate the value of \(y\)[56]:  
\[\phi(x)=\frac{1}{B}{\sum_{b=1}^{B}\phi(x,L_{b})} \tag{3}\]  
As a result, the two-step machine learning approach showed that the coefficient of determination (\(R^{2}\)) values of corn, soybean, winter wheat, spring wheat, cotton, and alfalfa were (0.95, 0.90, 0.92, 0.93, 0.86 and 0.83), respectively [55]. Since this approach narrows down the scope of modeling training, it is possible to accurately capture uncertainty associated with the production of each crop type. [PERSON] et al. [57] estimated the soybean yield in Brazil based on three different machine learning algorithms of RF, ANN, and SVM. The study collected the meteorological information and soybean yield data from 2008 to 2017, and seven independent variables (i.e., temperature, precipitation, crop evapotranspiration, real crop evapotranspiration, storage, deficit, and surplus) were considered for the yield prediction. Particularly, the NASA  
Figure 1: General process of crop yield estimation via machine learning model. POWER platform was used to collect meteorological data., and [PERSON]'s 1971 method was used to compute potential evapotranspiration and cultivation evapotranspiration. Table 1 describes the database matrix of 36 columns by 936 rows. In Table 1, each independent variable was stratified into five sub-variables from November to March (i.e., five months) according to the grain planting and harvesting calendar in Brazil [57]. The preprocessed database matrix was used for machine learning with RF, ANN, and SVM.