2.1. Experimental methodology

In the year 2012, an experiment to find insights related to the physical and chemical properties of switchgrass was designed and implemented at the Biomass Innovation Park in Vonore, Tennessee. The type of biomass was from Alamo switchgrass and the samples were harvested and then baled in squared shape (1.2 m 0.9 m 2.4 m) with a baler machine New Holland BB9080 (New Holland Agriculture, New Holland, PA, USA). New Holland BB9080 is a square baler without a cutter that was used to process the batch of lignocellulosic biomass in the second week of January of that year. After processing the biomass to form square bales, the biomass was transported to other covered location before the beginning of the pre-processing.

A Vermeer TG5000 tub grinder (Vermeer Corporation, Pella, IA, USA) was utilized to unpack and grind the switchgrass in January 2012. Once the biomass was ground, the next step was to sample the moisture content and the chemical composition; the measures for the chemical composition were obtained with a near-infrared (NIR) technology. A machine BT3 industrial baler (TLA Bale Tech LLC, South Orange, NJ, USA) was employed to bale the switchgrass one more time after measuring the chemical properties. Round bales (1.2 m of diameter 1.5 m of width) were made with the BT3 and then they were moved to storage before the next phase of the experiment.

Four controllable factors were introduced in the analysis that utilizes a split-split plot design. The factors in the analysis were: (1) the number of days in storage, (2) the particle size of the feedstock, (3) the wrap type of the bale, and (4) the weight of the bale. The number of days has three groups or levels, same as particle size. The wrap type and the weight of the bale have two groups. The database utilized for this study presented the necessary conditions of normality, homogeneity and heteroscedasticity as discussed in Kline et al. [8].


Table 1. Factors and variables for PCA.

biomass that does not meet the specifications could lead to extra costs as a consequence of

The reduction of the variance within the physical and chemical properties of the biomass helps to avoid extra operational cost due to re-processing of feedstock that is out of the specifications. Identifying the factors, which are involved in production and distribution activities that affect the physical/chemical properties, is necessary to design an efficient SC. Researchers in the field have studied baling effects in feedstock properties [5–7]. In previous works, Aboytes-Ojeda et al. [3] proposes a PCA to detect those factors that have a significant impact on properties of interest and that should be approached by implementing novel operations and

The multivariate methodology proposed by Aboytes-Ojeda et al. [3] intends to: (1) introduce the covariance information analysis to draw systematic insights about the factors under study, and (2) present a novel methodology to identify the contribution of every factor in the analysis with respect to the total system variability. The variables introduced in the analysis were cellulose, hemicellulose, lignin, ash and extractives content; whereas the factors were the particle size in the bale, the wrap material, the days in storage and the weight of the bale.

In the year 2012, an experiment to find insights related to the physical and chemical properties of switchgrass was designed and implemented at the Biomass Innovation Park in Vonore, Tennessee. The type of biomass was from Alamo switchgrass and the samples were harvested and then baled in squared shape (1.2 m 0.9 m 2.4 m) with a baler machine New Holland BB9080 (New Holland Agriculture, New Holland, PA, USA). New Holland BB9080 is a square baler without a cutter that was used to process the batch of lignocellulosic biomass in the second week of January of that year. After processing the biomass to form square bales, the biomass was transported to other covered location before the beginning of the pre-processing. A Vermeer TG5000 tub grinder (Vermeer Corporation, Pella, IA, USA) was utilized to unpack and grind the switchgrass in January 2012. Once the biomass was ground, the next step was to sample the moisture content and the chemical composition; the measures for the chemical composition were obtained with a near-infrared (NIR) technology. A machine BT3 industrial baler (TLA Bale Tech LLC, South Orange, NJ, USA) was employed to bale the switchgrass one more time after measuring the chemical properties. Round bales (1.2 m of diameter 1.5 m of width) were made with the BT3 and then they were moved to storage before the next phase of

Four controllable factors were introduced in the analysis that utilizes a split-split plot design. The factors in the analysis were: (1) the number of days in storage, (2) the particle size of the feedstock, (3) the wrap type of the bale, and (4) the weight of the bale. The number of days has three groups or levels, same as particle size. The wrap type and the weight of the bale have two groups. The database utilized for this study presented the necessary conditions of normality,

homogeneity and heteroscedasticity as discussed in Kline et al. [8].

re-processing the biomass up to meeting the specifications.

strategies in order to fulfill the conversion specifications.

2.1. Experimental methodology

42 Advances in Biofuels and Bioenergy

the experiment.

Table 1 identifies the factors and variables included in the analysis. The storage days were classified in three groups or levels: 75, 150 and 225 days of storage. The particle size was defined in three groups or levels: PS1 (243.84 cm), PS2 (7.62 cm) and PS3 (1.27–1.91 cm). The wrap type was categorized in two levels: (i) net mesh and net (excluding the two ending parts of the bale), and (ii) the high tensile strength film wrapping for the complete bale (net and film). The bale weight has two levels for this study; the lower level was for bale with a weight between 957.65 and 1715.20 lb., whereas the high level was for bale with a weight between 1715.21 and 2455.10 lb. The weight in the bale has repercussions in logistic operations such as handling, storage, and transportation.

Five variables were included in the analysis. The cellulose is a glucose polymer linked by glycosidic bonds and the hemicellulose is a branched polymer of carbon sugars. The lignin refers to a structural component of plants, consisting of an aromatic system made of phenyl proposal units. The ash is considered as the inorganic leftover after the combustion process at 550–600C. The extractives are non-structural components that can include free sugars, proteins, chlorophyll, and waxes. The PCA methodology proposed uses the variability within the variables (i.e., variance and covariance) to create artificial variables and then it groups the data according to their corresponding factor group/level. Finally, a statistical comparison of means is utilized to conclude if there is a significant difference between the means of every factor group/level. Figure 1 shows the methodology to perform the PCA which consists of five basic steps.

#### 2.2. Principal component analysis (PCA)

In order to implement the PCA [9, 10], it is necessary to test the required data conditions to perform the analysis, then, the covariance/correlation matrix needs to be calculated. A Bartlett's test of sphericity is utilized next to determine if the correlation information for the analysis is significant. With the covariance/correlation matrix, eigenvalues and eigenvectors are computed. The eigenvalue is utilized to determine the portion of variance attributed to the corresponding eigenvector. The components of the eigenvectors known as loadings are used to transform the original data into the components scores. The variance matrix is shown in Table 2; there is no need to compute the correlation matrix since all the measures for every variable are in the same scale.

The portion of variance in PCA is calculated according to the eigenvalues obtained in the analysis. The idea behind the PCA is to detect those components with the higher eigenvalues;

Figure 2 and Table 3, PC1 and PC2 are the main components since their eigenvalues are above one and the amount of variance represents up to approximately 80% of the total variance. The eigenvalues are also attached to the eigenvectors which are the directions where the largest variance is presented. The loadings are the values that indicate the correlation between the original value and the score value. A high value means that the original variable and the compo-

Eigenvalue 1.448 1.266 0.777 0.527 0.318 Variance (%) 45 34 13 6 2 Cumulative (%) 45 79 92 98 100

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Modeling and Optimization of Quality Variability for Decision Support Systems in Biofuel Production

With the loadings values, it is possible to transform the original data into scores. Scores are the representation of the original data points under the principal components basis. These scores can be plotted in a graph called bi-plot and then explored (exploratory data analysis) in order to find some insights related to the segregation within the groups of data. In the results section,

Sometimes it is not possible to detect any pattern in the exploratory analysis (i.e., segregation in the data cannot be visually identified). For those occasions, a statistical analysis is needed to determine if there is a significant effect in the principal components due to the factors that were previously introduced. The statistical analysis in this work was performed with a t-test; the means for every group/level within a factor are compared to see if there is any significant difference between them, if so, it can be concluded that there is some evidence to claim that there is a significant effect in the data due to the factors. The statistical test has the following assumptions: unknown but equal population variances, known sample means and not equal sample variances. The following equations are defined for the t-distribution and the corres-

<sup>t</sup> <sup>¼</sup> <sup>x</sup><sup>1</sup> � <sup>x</sup><sup>2</sup> � <sup>μ</sup><sup>1</sup> � <sup>μ</sup><sup>2</sup>

The following set of bi-plot graphs are introduced to show the relevant information about the groups/levels within each one of the factors under study. Figure 3 presents the data classification according to the wrap type that was utilized to wrap the switchgrass. As it can be

sp

ð Þ <sup>n</sup><sup>1</sup> � <sup>1</sup> <sup>s</sup><sup>2</sup>

� �

<sup>1</sup> <sup>þ</sup> ð Þ <sup>n</sup><sup>2</sup> � <sup>1</sup> <sup>s</sup><sup>2</sup>

2

<sup>q</sup> (1)

(2)

ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 <sup>n</sup><sup>1</sup> <sup>þ</sup> <sup>1</sup> n2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

n<sup>1</sup> þ n<sup>2</sup> � 2

several bi-plots are presented to show some of the insights found in the analysis.

nent are close. Table 4 represents the loadings values.

Table 3. Variance analysis in PCs.

Principal component

ponding estimator is introduced with the expressions:

2.3. Exploratory data analysis and statistical test results

sp ¼

s

Figure 1. Flow chart for PCA.


Table 2. Chemical components covariance.

Figure 2. Scree plot for PCA.

therefore, it is possible to identify the principal components due to their share in the total variance. Figure 2 shows that the first two components contain almost 80% of the total variance; Table 3 presents the eigenvalues for all the components as well as their share in the total variance. As a rule of thumb, those components above the value of one in Figure 2 must be considered as the principal components of the analysis.


Table 3. Variance analysis in PCs.

Figure 2 and Table 3, PC1 and PC2 are the main components since their eigenvalues are above one and the amount of variance represents up to approximately 80% of the total variance. The eigenvalues are also attached to the eigenvectors which are the directions where the largest variance is presented. The loadings are the values that indicate the correlation between the original value and the score value. A high value means that the original variable and the component are close. Table 4 represents the loadings values.

With the loadings values, it is possible to transform the original data into scores. Scores are the representation of the original data points under the principal components basis. These scores can be plotted in a graph called bi-plot and then explored (exploratory data analysis) in order to find some insights related to the segregation within the groups of data. In the results section, several bi-plots are presented to show some of the insights found in the analysis.

Sometimes it is not possible to detect any pattern in the exploratory analysis (i.e., segregation in the data cannot be visually identified). For those occasions, a statistical analysis is needed to determine if there is a significant effect in the principal components due to the factors that were previously introduced. The statistical analysis in this work was performed with a t-test; the means for every group/level within a factor are compared to see if there is any significant difference between them, if so, it can be concluded that there is some evidence to claim that there is a significant effect in the data due to the factors. The statistical test has the following assumptions: unknown but equal population variances, known sample means and not equal sample variances. The following equations are defined for the t-distribution and the corresponding estimator is introduced with the expressions:

$$t = \frac{\overline{\mathbf{x}}\_1 - \overline{\mathbf{x}}\_2 - \left(\mu\_1 - \mu\_2\right)}{s\_p \sqrt{\frac{1}{n\_1} + \frac{1}{n\_2}}}\tag{1}$$

$$s\_p = \sqrt{\frac{(n\_1 - 1)s\_1^2 + (n\_2 - 1)s\_2^2}{n\_1 + n\_2 - 2}}\tag{2}$$

#### 2.3. Exploratory data analysis and statistical test results

therefore, it is possible to identify the principal components due to their share in the total variance. Figure 2 shows that the first two components contain almost 80% of the total variance; Table 3 presents the eigenvalues for all the components as well as their share in the total variance. As a rule of thumb, those components above the value of one in Figure 2 must be

Component Cellulose Hemicellulose Lignin Ash Extractives Cellulose 1.344 0.149 0.130 0.325 0.686 Hemicellulose 0.149 1.366 0.467 0.017 0.377 Lignin 0.130 0.467 0.541 0.198 0.064 Ash 0.325 0.017 0.198 0.334 0.226 Extractives 0.686 0.377 0.065 0.226 1.100

considered as the principal components of the analysis.

Table 2. Chemical components covariance.

Figure 1. Flow chart for PCA.

44 Advances in Biofuels and Bioenergy

Figure 2. Scree plot for PCA.

The following set of bi-plot graphs are introduced to show the relevant information about the groups/levels within each one of the factors under study. Figure 3 presents the data classification according to the wrap type that was utilized to wrap the switchgrass. As it can be


Table 4. Loadings in PCA.

observed, there is no distinguishable segregation within the groups to claim any possible effect due to this factor.

Like the wrap type, data information was also classified according to its particle size and was shown in a bi-plot graph presented in Figure 4. The visual representation of the data does not exhibit any clustering in the plotting area, and therefore, no significant findings can be concluded from the bi-plot. Same analysis occurs with the factor corresponding to the classification according to the weight of the bale that can be observed in Figure 5, no segregation is noticeable.

In the bi-plot that corresponds to the classification of the date with respect to the days of storage it is possible to identify a segregation in the data. Figure 6 exhibits this difference between the bales with more than 150 days of storage and those with less number of days. Figure 7 has another perspective to visually identify this division.

A t-test was applied for every group/level within every factor presented. The results are shown in Figure 8. The storage days is the most important factor since it is the only factor that shows a significant effect due to the statistical difference between the means in the groups. Based on the results, the storage days have repercussion in almost 80% of the variation within the data.

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47

PCA is a statistical tool that allows the analyst to introduce variance and covariance in the study. Adding the covariance or correlation between the variables could lead the analysis to find some insights that would not be visible with a univariate data analysis tool. Also, PCA allows to sort and classify in a more natural way the significance of every factor analyzed in

Hence, it is relevant in the design of operations that are time dependent.

Figure 5. Bi-plot chart for analysis of bale weight.

Figure 4. Bi-plot chart for analysis of particle size.

Figure 3. Bi-plot chart for analysis of wrap type.

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Figure 4. Bi-plot chart for analysis of particle size.

observed, there is no distinguishable segregation within the groups to claim any possible effect

Cellulose 0.64 0.48 0.30 0.52 0.09 Hemicellulose 0.33 0.83 0.05 0.33 0.32 Lignin 0.21 0.29 0.66 0.26 0.62 Ash 0.22 0.07 0.32 0.64 0.66 Extractives 0.63 0.02 0.61 0.39 0.29

12345

Principal component variables

Like the wrap type, data information was also classified according to its particle size and was shown in a bi-plot graph presented in Figure 4. The visual representation of the data does not exhibit any clustering in the plotting area, and therefore, no significant findings can be concluded from the bi-plot. Same analysis occurs with the factor corresponding to the classification according to the weight of the bale that can be observed in Figure 5, no segregation is

In the bi-plot that corresponds to the classification of the date with respect to the days of storage it is possible to identify a segregation in the data. Figure 6 exhibits this difference between the bales with more than 150 days of storage and those with less number of days. Figure 7 has

another perspective to visually identify this division.

Figure 3. Bi-plot chart for analysis of wrap type.

due to this factor.

Table 4. Loadings in PCA.

46 Advances in Biofuels and Bioenergy

noticeable.

Figure 5. Bi-plot chart for analysis of bale weight.

A t-test was applied for every group/level within every factor presented. The results are shown in Figure 8. The storage days is the most important factor since it is the only factor that shows a significant effect due to the statistical difference between the means in the groups. Based on the results, the storage days have repercussion in almost 80% of the variation within the data. Hence, it is relevant in the design of operations that are time dependent.

PCA is a statistical tool that allows the analyst to introduce variance and covariance in the study. Adding the covariance or correlation between the variables could lead the analysis to find some insights that would not be visible with a univariate data analysis tool. Also, PCA allows to sort and classify in a more natural way the significance of every factor analyzed in

Figure 6. Bi-plot chart for analysis of storage days.

product. Another approach considers genetic manipulation with different types of biomass to create hybrids with specific characteristics that suit better for a particular final product. Lastly, another alternative is the improvement of the logistics operations related to the production and

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49

SCs are being used widely in industry as a system of production and distribution due to the need of integrating processes from suppliers until reaching the end users of any good or service. SCs are presented in diverse scales, from local scale, regional scale up to global scale. Nowadays, large-scale are vastly utilized since they reduce operational costs due to the economies of scale. Large-scale SCs are more challenging since they are more difficult to analyze and solve, so they require the development of new algorithms in order to deal with the complexity of the problem. The introduction of models and algorithms to solve large-scale problems is fundamental in industry since real applications require big data, as well as a large set of constraints related to the problem. Bioenergy industry is a field where large-scale SCs are

The production and distribution of biofuels are a big challenge since their commercialization requires a competitive price in the market, and therefore, an efficient SC must be implemented to minimize the operational costs. The production of biofuels deals with the inherent variability in the physical and chemical properties within the biomass because of their impact in some key processes such as the conversion process. The second generation of biofuels (e.g., corn stover, miscanthus, and switchgrass) presents, in general, more variation in properties such as

distribution of the biofuel.

Figure 8. T-test results for all the factors.

being implemented.

Figure 7. Score plot analysis for PCA.

the database by identifying those factors that have an impact on the main principal components. PCA identifies those factors with a significant effect over the principal components. This information can be utilized to incorporate the relevant factors in stochastic programming models that use the insights found by the multivariate analysis in the optimization problem, and later on, in the decision process. A further discussion on this matter follows.

#### 3. Variable quality-related cost in SC design

The biofuel is an alternative energy resource for the fossil fuels. It is expected that biofuel production increases in the upcoming years due to the increase in the demand. There are some alternatives to approach a mature production of biofuel to support the demand satisfaction. One approach consists in developing new technologies with better conversion processes in order to get an efficient exploitation from the pre-processed biomass for a certain good or

Modeling and Optimization of Quality Variability for Decision Support Systems in Biofuel Production http://dx.doi.org/10.5772/intechopen.73111 49

Figure 8. T-test results for all the factors.

the database by identifying those factors that have an impact on the main principal components. PCA identifies those factors with a significant effect over the principal components. This information can be utilized to incorporate the relevant factors in stochastic programming models that use the insights found by the multivariate analysis in the optimization problem,

The biofuel is an alternative energy resource for the fossil fuels. It is expected that biofuel production increases in the upcoming years due to the increase in the demand. There are some alternatives to approach a mature production of biofuel to support the demand satisfaction. One approach consists in developing new technologies with better conversion processes in order to get an efficient exploitation from the pre-processed biomass for a certain good or

and later on, in the decision process. A further discussion on this matter follows.

3. Variable quality-related cost in SC design

Figure 6. Bi-plot chart for analysis of storage days.

48 Advances in Biofuels and Bioenergy

Figure 7. Score plot analysis for PCA.

product. Another approach considers genetic manipulation with different types of biomass to create hybrids with specific characteristics that suit better for a particular final product. Lastly, another alternative is the improvement of the logistics operations related to the production and distribution of the biofuel.

SCs are being used widely in industry as a system of production and distribution due to the need of integrating processes from suppliers until reaching the end users of any good or service. SCs are presented in diverse scales, from local scale, regional scale up to global scale. Nowadays, large-scale are vastly utilized since they reduce operational costs due to the economies of scale. Large-scale SCs are more challenging since they are more difficult to analyze and solve, so they require the development of new algorithms in order to deal with the complexity of the problem. The introduction of models and algorithms to solve large-scale problems is fundamental in industry since real applications require big data, as well as a large set of constraints related to the problem. Bioenergy industry is a field where large-scale SCs are being implemented.

The production and distribution of biofuels are a big challenge since their commercialization requires a competitive price in the market, and therefore, an efficient SC must be implemented to minimize the operational costs. The production of biofuels deals with the inherent variability in the physical and chemical properties within the biomass because of their impact in some key processes such as the conversion process. The second generation of biofuels (e.g., corn stover, miscanthus, and switchgrass) presents, in general, more variation in properties such as moisture and ash content than the first generation, and then, quality-related costs must be contemplated in the design and implementation of the SC. However, one of the advantages of using second-generation biomass for the production of biofuels is that local farmers are familiar with the techniques to cultivate and harvest the biomass. For example, harvesting techniques for forage, utilized to feed the livestock, and for the power grass have similar characteristics.

value <sup>t</sup>. A triangular distribution <sup>f</sup> <sup>ε</sup>ð Þ<sup>t</sup> has been defined for <sup>t</sup> in the range ½ � at; bt with a proba-

2ð Þ e � at

Modeling and Optimization of Quality Variability for Decision Support Systems in Biofuel Production

2ð Þ bt � e

The triangular distribution was proposed due to experimental results in the work of Boyer et al. [17]; in the experiment, a breed of Alamo switchgrass was utilized to test the effect of

Ash content was also represented with a random variable ϑ δð Þ and the corresponding function is a triangular distribution of the mean value δ. The triangular distribution is defined for the range ½ � cδ; dδ . Depending on the technology utilized for the conversion of biomass into biofuel, different requirements are necessary to accomplish the conversion. For example, the conversion of biomass using a thermochemical technology demands at most 10% of moisture content for an efficient process. The moisture target for technology k is defined as tk. Violating the target for the selected technology will lead to other necessary costs (\$q) to compensate not meeting the specifications. The cost of mechanically drying the biomass will be applied to the final good since the content of moisture needs to be reduced up to the target level for conversion purposes. The thermochemical technology also requires at most 10% of ash content for an efficient conversion. The target is defined as δk. Again, not meeting the target specification will

Stochastic programming introduces randomness into the models where the stochastic variables play a fundamental role in the decision processes. There are several types of stochastic models but probably the most utilized are the two-stage models. In the two-stage models, two types of variables arise, the here-and-now variables and the wait-and-see variables. The here-and-now variables are those that need to be solved in the first-stage because they represent the beginning of the decision and the rest of the decision variables will rely on this step. The wait-and-see variables are presented in the second-stage of the process and depend on the realization of each presented scenario as well as the first-decision stage. The randomness is presented by defining random parameters that will converge to a certain value depending on the scenario, an expected value function for these scenarios in the second-stage plus the value function of the first-stage form the objective function of the stochastic program. A stochastic programming assumes known

ð Þ bt � at ð Þ <sup>t</sup> � at (3)

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ð Þ bt � at ð Þ bt � <sup>t</sup> (4)

<sup>f</sup> <sup>∈</sup> ð Þ<sup>t</sup> ð Þ¼ <sup>e</sup>

<sup>f</sup> <sup>∈</sup>ð Þ<sup>t</sup> ð Þ¼ <sup>e</sup>

factors such as storage days, particle size, wrap type and weight of the bale.

lead to reprocessing of the biomass with an additional cost.

3.2. Two-stage stochastic model

bility density according to the following criteria:

if at ≤ e ≤ t then

if t < e ≤ bt then

Otherwise, 0.

One common objective of the optimization in SC of biofuels is the minimization of costs under the assumption that all types of biomass have similar properties. This assumption can derive in considering only purchasing, logistics and processing costs which is not adequate since every type of biomass possesses different physical and chemical properties that affect the way the SC works. Not including the aforementioned properties could lead companies to have a negative impact on their expected profit since these properties usually experience high levels of variability. Pilot scale biorefineries have experienced a significant difference between the expected and the actual input of biomass [11]. The randomness in the biomass is one of the challenges that biofuel producers must tackle in order to reach profitability and sustainability.

Biomass conversion technologies have their origins in laboratories where specifications of biomass are controlled. The technologies are designed to work under some specifications within the biomass such as the moisture, ash, and carbohydrates contents. When technologies are implemented in large- scale scenarios, it is very likely to receive biomass with specifications that do not meet the requirements, as a result, additional re-work must be done to utilize it. The quality of biofuel is associated with reaching the target levels of physical and chemical properties, for some specific technology, with a low variability.

A poor quality of the biomass results in higher total costs for companies. A quality-related cost can be defined as any cost derived from not meeting the required specifications for a specific conversion technology. The impact of these quality related costs is usually found after the biorefineries have begun operations. The optimization of biofuels [12, 13] considering randomness in the properties of biomass can be approached with stochastic programming [14, 15]. In literature, most of the supply chain models designed for biofuel production are deterministic; then, the stochastic programming is a novel approach to solve instances with variability in the feedstock.

Novel optimization models take into account inherent properties of biomass to lead better decisions that minimize the total cost. It is important to identify the factors that have an influence over the biomass and include those considerations in the optimization model. Castillo-Villar et al. [16] have proposed a stochastic programming model that includes the quality variability in order to make decisions about important aspects of the SC. The work of Castillo-Villar et al. [16] is revisited in this chapter since the authors present a seminal model that integrated biomass variability in the modeling of biofuel supply chains.
