*4.1. Constraints*

period *t*

The demand for energy is applied in Equation (1). The amount of biomass and coal that undergo combustion multiplied by the combustion efficiency and the lower heating value of the feedstock must be greater than or equal to demand. Equation (2) enforces the processing capacity of the power plants. Equations (3) and (4) ensure that the amount of biomass and coal delivered from their corresponding source locations are limited by the amount that is available in each period:

$$\sum\_{l} \lambda\_{lt} q\_{lt} \left(\sum\_{j} x\_{jlt} \left(1 - b\_{jl}^{tp}\right) + \sum\_{k} y\_{klt}\right) \ge D\_t \quad \forall t \tag{1}$$

$$\sum\_{j} \mathbf{x}\_{jlt} \left( \mathbf{1} - b\_{jl}^{tp} \right) + \sum\_{kl} y\_{klt} \le c\_{lt}^{c} A\_{lt} \qquad \forall lt \tag{2}$$

$$\sum\_{j} w\_{ijt} \le s\_{it}^{b} \qquad \forall it \tag{3}$$

$$\sum\_{l} y\_{klt} \le s\_{kt}^{\varepsilon} \qquad \forall kt \tag{4}$$

The amount of biomass brought to the pre-treatment facilities should be less than or equal to the processing capacity of each facility, shown in Equation (5). The inventory of biomass kept in the pre-treatment facilities is defined by Equation (6). This amount is equal to the amount of biomass carried from the previous period, plus the amount of biomass that were delivered from sources and have undergone pre-treatment, less the biomass transported to the coal power plants in the current period. Equation (7) makes sure that the amount of biomass held each period is restricted by the facility's storage capacity:

$$\sum\_{i} w\_{ijt} \left(1 - b\_{ij}^{tr}\right) \le c\_{jt}^p F\_{jt} \qquad \forall jt \tag{5}$$

$$I\_{jt+1} = I\_{jt} \left(1 - b\_j^\epsilon \right) + n\_{jt+1} - \sum\_{l \ge 1} x\_{jlt+1} \qquad \forall jt \tag{6}$$

$$I\_{jt} \le c\_{jt}^s S\_{jt} \qquad \forall jt \tag{7}$$

The capacity of the pre-treatment facilities and the coal power plants may be expanded. Equations (8) and (9) show how the capacities of each facility and power plant in a given period are increased according to the expansion in the previous period. Binary variables for expanding the capacities of the pre-treatment facilities and coal power plants are switched on in Equations (10) and (11):

$$
\sigma\_{jt}^p P\_{jt} + c\_{jt}^p = c\_{jt+1}^p \qquad \forall jt \tag{8}
$$

$$f\_{lt}^{\varepsilon} \mathbf{C}\_{lt} + \mathfrak{c}\_{lt}^{\varepsilon} = \mathfrak{c}\_{lt+1}^{\varepsilon} \qquad \forall lt \tag{9}$$

$$f\_{jt}^p \le MP\_{jt} \qquad \forall jt \tag{10}$$

$$f\_{lt}^c \le \text{MC}\_{lt} \qquad \forall lt \tag{11}$$

Equation (12) requires an existing power plant to first undergo retrofitting before the biomass co-firing option can be used. Meanwhile, Equation (13) sets upper and lower limits to the amount of biomass to displace coal in the power plants if the biomass co-firing option is activated:

$$R\_l \ge O\_{lt} \qquad \forall lt \tag{12}$$

$$\mathbf{L}\_{I}^{I}\mathbf{O}\_{\mathrm{lt}} \le \frac{\sum\_{j} \mathbf{x}\_{j\mathrm{lt}} \Big(\mathbf{1} - \mathbf{b}\_{j\mathrm{l}}^{tp}\Big)}{\sum\_{j} \mathbf{x}\_{j\mathrm{lt}} \Big(\mathbf{1} - \mathbf{b}\_{j\mathrm{l}}^{tp}\Big) + \sum\_{k} \mathbf{y}\_{k\mathrm{lt}}} \le \mathbf{L}\_{I}^{\mathrm{u}}\mathbf{O}\_{\mathrm{lt}} \qquad \forall \mathrm{l}\mathbf{t} \tag{13}$$

The weight of the biomass in a pre-treatment facility after pre-treatment is given in Equation (14). This is computed for by adding the dry (moisture and ash-free) biomass weight (first term) and the remaining amount of moisture and ash in mass units after completing treatment (second and third term, respectively). This is dependent on the e ffectiveness of the pretreatment process:

$$\sum\_{i} w\_{ijt} \Big( \mathbf{1} - b\_{ij}^{tr} \Big) \Big[ \left( \mathbf{1} - m\_{it}^{r} - a\_{it}^{r} \right) + \left( m\_{it}^{r} \right) \left( \mathbf{1} - m c\_{j} \right) + \left( a\_{it}^{r} \right) \left( \mathbf{1} - a c\_{j} \right) \Big] = n\_{jt} \qquad \forall jt \tag{14}$$

Equation (15) computes for the moisture content of the biomass that has just completed pre-treatment. This biomass is mixed with the existing biomass in stock. The moisture content of the biomass from inventory was determined in the previous period; however, this is increased by a certain factor as an effect of storage. The moisture content of all the biomass in each pre-treatment facility is shown in Equation (16). Equation (17) defined the average moisture content of all the biomass received by a coal power plant in each period, while Equation (18) computes for the moisture content of the feedstock mix received by each power plant each period. Equations (19)–(22) compute for the ash content of the feedstock as it flows through the supply chain in the same manner. Equations (15)–(22) are conceptually similar to the generating function methodology, which are intensively discussed and applied by Shang on his works on the robustness of complex networks against failure [23,24]:

$$m\_{jt}^t = \frac{\sum\_{\substack{i}} w\_{ijt} \Big(1 - b\_{ij}^{tr}\Big) \binom{m\_{it}^r}{i} \Big(1 - mc\_j\Big)}}{n\_{jt}} \qquad \forall jt \tag{15}$$

$$m\_{jt+1}^p = \frac{m\_{jt+1}^t n\_{jt+1} + I\_{jt} m\_{jt}^p (1 + z\_{jt})}{n\_{jt+1} + I\_{jt} (1 - m\_{jt}^p) + I\_{jt} m\_{jt}^p (1 + z\_{jt})} \qquad \forall jt \tag{16}$$

$$m\_{lt}^{ppb} = \frac{\sum\_{j} m\_{jt}^p x\_{jlt} \left(1 - b\_{jl}^{tp}\right)}{\sum\_{j} x\_{jlt} \left(1 - b\_{jl}^{tp}\right)} \qquad \forall lt \tag{17}$$

$$m\_{lt}^{pp} = \frac{\sum\_{j} m\_{jt}^{p} \mathbf{x}\_{jlt} \left(\mathbf{1} - b\_{jl}^{tp}\right) + \sum\_{k} m\_{}^{c} y\_{klt}}{\sum\_{j} \mathbf{x}\_{jlt} \left(\mathbf{1} - b\_{jl}^{tp}\right) + \sum\_{k} y\_{klt}} \qquad \forall lt \tag{18}$$

$$a\_{jt}^{t} = \frac{\sum\_{i} w\_{ijt} \Big(1 - b\_{ij}^{tr}\Big) \Big(a\_{it}^{r}\Big) \Big(1 - a e\_{j}\Big)}{n\_{jt}} \qquad \forall jt \tag{19}$$

$$a\_{jt+1}^p = \frac{a\_{jt+1}^t n\_{jt+1} + I\_{jt} a\_{jt}^p}{n\_{jt+1} + I\_{jt}} \qquad \forall jt \tag{20}$$

$$d\_{lt}^{ppb} = \frac{\sum\_{j} d\_{jt}^{p} \mathbf{x}\_{jlt} \left(1 - b\_{jl}^{tp}\right)}{\sum\_{j} \mathbf{x}\_{jlt} \left(1 - b\_{jl}^{tp}\right)} \qquad \forall lt \tag{21}$$

$$a\_{lt}^{pp} = \frac{\sum\_{j} a\_{jt}^{p} \mathbf{x}\_{jlt} \left(\mathbf{1} - b\_{jl}^{tp}\right) + \sum\_{k} a^{c} y\_{klt}}{\sum\_{j} \mathbf{x}\_{jlt} \left(\mathbf{1} - b\_{jl}^{tp}\right) + \sum\_{k} y\_{klt}} \qquad \forall lt \tag{22}$$

Equation (23) determines the lower heating value of the biomass in each power plant. This equation is adapted from Hernández et al. [25]. The average lower heating value of the feedstock mix considering the biomass and coal blend is given in Equation (24):

$$q\_{lt}^{b} = \mathcal{g} \left( 1 - m\_{lt}^{ppb} \right) \left( 1 - d\_{lt}^{ppb} \right) - 2.4443 m\_{lt}^{ppb} \qquad \forall lt \tag{23}$$

$$q\_{lt} = \frac{\sum\_{j} q\_{lt}^{b} \mathbf{x}\_{jlt} + \sum\_{k} q^{c} y\_{klt}}{\sum\_{j} \mathbf{x}\_{jlt} + \sum\_{k} y\_{klt}} \qquad \forall lt \tag{24}$$

The efficiency in each power plant is defined in Equation (25). This is a function of the excess and lacking moisture content of the feedstock, excess ash content, and the total amount of feedstock processed by the plant, as these values increase, the efficiency will decrease. Equation (26) describes excess moisture content to be equal to the maximum between zero and the difference between the actual moisture content of the feedstock and the upper limit, while Equation (27) defines shortage in moisture. Similarly, Equation (28) computes for the excess ash content based on its maximum allowable amount. With this approach, there will be no amount stored if the difference returned is negative. Equation (29) sums up the biomass and coal processed in a coal power plant each period to ge<sup>t</sup> the total feedstock handled by the equipment:

$$
\lambda\_{\rm It} = f(m\_{\rm It}^+, m\_{\rm It}^-, a\_{\rm It}^+, \mathcal{Q}\_{\rm It}) \qquad \forall \rm lt \tag{25}
$$

$$m\_{lt+1}^{+} = \max\{m\_{lt+1}^{pp} - m\_{l}^{ll}, 0\} + m\_{lt}^{+} \qquad \forall lt \tag{26}$$

$$m\_{lt+1}^{-}=\max\{m\_l^L-m\_{lt+1'}^{pp},0\}+m\_{lt}^{-}\qquad\forall lt\tag{27}$$

$$a\_{lt+1}^{+} = \max\{a\_{lt+1}^{pp} - a\_{l}^{ll}, 0\} + a\_{lt}^{+} \qquad \forall lt \tag{28}$$

$$Q\_{lt+1} = \sum\_{j} \mathbf{x}\_{jlt+1} + \sum\_{k} y\_{klt+1} + Q\_{lt} \qquad \forall lt \tag{29}$$

Equations (30) and (31) compute for the number of trips needed to transport biomass from source to pre-treatment facilities and from pre-treatment facilities to coal power plants based on weight and volume capacities. Likewise, Equation (32) defines the number of trips required to deliver coal from source locations to coal power plants. Lastly, non-negativity, binary, and integer constraints apply to relevant variables:

$$t\_{ijt}^r \ge \max\left\{ \frac{w\_{ijt}}{u\_{ijt}^r}, \frac{w\_{ijt}}{\rho\_{it}^r v\_{ijt}^r} \right\} \qquad \forall ijt \tag{30}$$

$$\mathbf{r}\_{jlt}^p \ge \max \left\{ \frac{\mathbf{x}\_{jlt}}{\mathbf{u}\_{jlt}^p}, \frac{\mathbf{x}\_{jlt}}{\rho\_{jt}^p \mathbf{v}\_{jlt}^p} \right\} \qquad \forall \text{ jlt} \tag{31}$$

$$t\_{klt}^c \ge \max\left\{ \frac{\mathcal{Y}\_{klt}}{\mathcal{U}\_{klt}^c}, \frac{\mathcal{Y}\_{klt}}{\rho^c \mathcal{U}\_{klt}^c} \right\} \qquad \forall klt \tag{32}$$

#### *4.2. Objective Function*

The model seeks to maximize the performance of both objectives, which are to minimize total cost and emissions; a balance is achieved by maximizing the smaller desirability value to prevent optimizing one objective at the expense of the other as shown in Equation (33). Dimensionless efficiency values (not to be confused with thermodynamic efficiency) are obtained by dividing the improvement achieved (difference between worst and actual values) and the potential improvement (difference between worst and potential values). Potential objective values are obtained by minimizing each corresponding objective as single objective optimization models. The worst value that the cost objective may take is its value when the environmental objective is optimized, and vice-versa. Note that this max-min aggregation approach always optimizes the less satisfied objective:

$$\text{Max } Z = \min \left[ \left( \frac{\text{Cost}\_{\text{max}} - \text{Cost}}{\text{Cost}\_{\text{max}} - \text{Cost}\_{\text{pot}}} \right) \left( \frac{Env\_{\text{max}} - Env}{Env\_{\text{max}} - Env\_{\text{pot}}} \right) \right] \tag{33}$$

#### 4.2.1. Cost Component

The first sub-objective of the model is to minimize total costs incurred by the system as indicated in Equations (34)–(36). The total fixed cost (Equation (35)), includes costs obtained from retrofitting existing coal power plants, from operating and expanding coal power plants and pre-treatment facilities, from using the biomass option in modified power plants and using storage areas in pre-treatment facilities. Variable costs, shown in Equation (36), include costs to purchase feedstock, convert biomass and coal to energy, pretreat biomass, keep biomass in inventory, transport biomass and coal, and expand the capacities of power plants and pretreatment facilities. Transportation costs are based on the average cost (which may include fuel and labor costs, loading and unloading costs, insurance, taxes, etc.) per distance travelled, which is the applied convention in industry [26]:

$$\text{Cost} = \sum\_{t} \text{Fixed Cost}\_{t} + \sum\_{t} \text{Variable Cost}\_{t} \tag{34}$$

$$\begin{aligned} \text{Fixed Cost}\_{l} &= \sum\_{l} \text{ic}\_{l} \text{R}\_{l} + \sum\_{l} \alpha \text{c}\_{ll} A\_{ll} + \sum\_{l} \text{lc}\_{ll} O\_{ll} + \sum\_{j} \alpha \text{c}\_{jt}^{p} F\_{jt} + \sum\_{j} \text{sc}\_{jt} S\_{jt} + \sum\_{l} \text{rc}\_{ll} N\_{ll} + \\ &\quad \sum\_{j} \alpha \text{c}\_{jt}^{p} P\_{jt} + \sum\_{l} \alpha \text{c}\_{ll}^{c} C\_{lt} \qquad \forall t \end{aligned} \tag{35}$$

$$\begin{array}{c}\text{Variable Cost}\_{l} = \sum\_{j} \sum\_{l} r\_{l\mathbf{\bar{t}}}^{h} \mathbf{x}\_{j\mathbf{\bar{t}}l} + \sum\_{k} \sum\_{l} \Big( r\_{l\mathbf{\bar{t}}}^{c} + p\_{k\mathbf{\bar{t}}}^{c} \Big) y\_{k\mathbf{\bar{t}}} + \sum\_{i} \sum\_{j} \Big( p c\_{j\mathbf{\bar{t}}} + p\_{i\mathbf{\bar{t}}}^{b} \Big) w\_{i\mathbf{\bar{t}}} + \sum\_{j} \mathbf{h}\_{j\mathbf{\bar{t}}} \mathbf{l}\_{j\mathbf{\bar{t}}} + \\ \sum\_{i} \sum\_{j} \mathbf{t}\_{i\mathbf{\bar{t}}}^{r} \mathbf{t}\_{i\mathbf{\bar{t}}}^{r} \mathbf{t}\_{i\mathbf{\bar{t}}}^{r} \mathbf{d}\_{i\mathbf{\bar{j}}}^{r} + \sum\_{j} \sum\_{l} \mathbf{t}\_{j\mathbf{l}}^{p} \mathbf{t}\_{j\mathbf{l}}^{p} \mathbf{d}\_{j\mathbf{l}}^{p} + \sum\_{k} \sum\_{l} \mathbf{t}\_{k\mathbf{l}}^{c} \mathbf{t}\_{k\mathbf{\bar{t}}}^{c} \mathbf{d}\_{k\mathbf{l}}^{c} + \sum\_{j} \mathbf{e}\_{j\mathbf{\bar{t}}}^{p} \mathbf{f}\_{j\mathbf{\bar{t}}}^{p} + \sum\_{l} \mathbf{e}\_{l\mathbf{\bar{t}}}^{c} \mathbf{f}\_{l\mathbf{\bar{t}}}^{c} \qquad \forall \mathbf{t} \end{array} \tag{36}$$

#### 4.2.2. Emissions Component

Another sub-objective of the model is to minimize the system's emissions, which includes emissions from pre-treatment, combustion, and transport processes. The environmental objective is shown in Equation (37). Similarly, the amount of carbon footprint attributed to transportation is based on emissions per unit distance and total distance travelled:

$$En\boldsymbol{\nu} = \sum\_{i} \sum\_{j} \sum\_{t} p c\_{jt} w\_{ijt} + \sum\_{k} \sum\_{l} \sum\_{t} c c\_{lt} y\_{klt} + \sum\_{i} \sum\_{j} \sum\_{t} t\_{ijt}^{r} t c\_{ijt}^{r} d\_{ij}^{r} + \sum\_{j} \sum\_{l} \sum\_{t} t\_{jlt}^{p} t c\_{jt}^{p} d\_{jl}^{p} + \mathbf{c} \tag{37}$$
 
$$\sum\_{k} \sum\_{l} \sum\_{t} t\_{kl}^{c} t c\_{kl}^{c} d\_{kl}^{c}$$

#### **5. Model Implementation**

The model was implemented in General Algebraic Modelling System (GAMS) and solved using the nonlinear solver Convex Over and Under Envelopes for Nonlinear Estimation (COUENNE), with a solution time of 285.66 s and integer gap of 0.0523 on a MacBook Pro with a 3.1 GHz Intel Core i5 processor and 8 GB 2133 MHz LPDDR3 RAM. The case study considers three potential locations each for biomass sources, coal sources, pre-treatment/storage facilities, and coal power plants considered over three time periods. The biomass considered is rice straw. The resulting model has 656 continuous variables, 164 integer variables, and 425 constraints. Figure 2 illustrates the exponential increase in solution times (expressed in seconds) as the number of potential locations in each echelon is increased from 2 to 5. As the number of nodes in each echelon is increased even further, it is expected that the computation times will also increase following the same trend. Although the model seems complex, it can be easily implemented with most commercially available solvers. The data inputs required to run the model are also typically available to the user. Parameter values were used based on various literature sources.

The electricity demand and supply of biomass and coal are given in Table 2. The bulk density, moisture content, and ash content of raw biomass, particularly rice straw, from each source are summarized in Table 3. The higher heating value of rice straw is 18 MJ/kg. Data on rice straw properties were adapted from Liu et al. [27] and Kargbo et al. [28]. The improvement effectiveness for ash and moisture content, and resulting bulk density of each pretreatment facility are shown in Table 4. Table 4 also gives the amount of damage in biomass when it is stored, and the storage capacity in each pretreatment facility. The damage factor for transporting raw and pretreated biomass are 0.10 and 0.05, respectively, while moisture content increases by 0.10 due to storage. Additionally, the initial processing capacity of the pretreatment facilities is 500 kt. The displacement, ash content, and moisture content limits of each power plant are given in Table 5. Upper and lower coal displacement limits are strictly enforced in the power plants. On the other hand, the feedstock may violate the maximum preferred ash content and allowable range for moisture content, but this would lead to negative consequences on equipment efficiency; thus, they act only as soft constraints. Input parameters for coal composition are summarized in Table 6 and were adapted from Bains et al. [29]. The distances between biomass sources and pretreatment facilities, pretreatment facilities to power plants, and coal sources to power plants are shown in Tables A1–A3 of the Appendix A. The weight and volume capacities are 450 kt and 75 m<sup>3</sup> respectively. Costs to purchase biomass and coal, and to retrofit each coal power plant for co-firing are given in Table A4. Power plant associated costs are summarized in Table A5, while costs associated with processing and storing biomass in pretreatment facilities are given in Table A6. Transportation costs are assumed to be US\$ 18/km-kg. Lastly, Table A7 summarizes the emissions from biomass pretreatment, transporting biomass, and the combustion of biomass and coal. Cost and emissions parameters were adapted from the studies of Griffin et al. [14] and Mohd Idris et al. [13] respectively.

**Figure 2.** Solution Time of Varying Model Sizes.


**Table 2.** Supply and Demand Parameters.

**Table 3.** Biomass Quality Parameters.


**Table 4.** Pretreatment Facility Characteristics.



**Table 5.** Power Plant Facility Characteristics.

**Table 6.** Coal Quality Parameters.


The relationship between conversion equipment efficiency, feedstock property violations and total feedstock processed is modeled with an arbitrary function for the model validation. An exponential decay function is used as in Equation (38):

$$
\lambda\_{lt} = \text{constant}^{-(m\_{lt}^+ + m\_{lt}^- + a\_{lt}^+ + Q\_{lt})} \tag{38}
$$

Statistical experiments support that the negative exponential function may be used to describe the performance degradation of equipment. The specific behavior of degradation differs between each unit of equipment and, as a result, would have a unique combination of input parameters to accurately predict behavior. These parameters may be obtained through exponential regression [30]. An exponential decay function with a base that is between 0 to 1 will return decreasing values as the exponent variables increase. Efficiency will begin at 1 when the exponent is 0 or when no feedstock property violations have been made and/or no feedstock has been handled by the power plant yet. The efficiency value will then decrease, approaching 0 as the exponent increases. The constant dictates the rate of decrease per unit increase in the exponent variables. The higher the constant is, the faster the rate of decrease will be. As shown in Figure 3, the decrease in efficiency is more significant when the constant used is 4 compared to when the constant is equal to 2. For the purpose of validating the model, a hypothetical system is captured, and the constant for the negative exponential function was set to 2.

**Figure 3.** Conversion Efficiency Function Graphs.

The results are presented in three parts, namely where each sub-objective is optimized separately, followed by the complete model run. Running the model wherein each objective is minimized

individually is necessary to obtain the potential and worst values for cost and emissions needed in the full model run.

#### *5.1. Base Case*

## 5.1.1. Minimizing Cost

In minimizing the cost component separately, model results show a bias towards using only coal to satisfy the demand for energy as presented in Figure 4. This is because coal is relatively cheap compared to biomass, especially when considering transportation and storage requirements, pre-treatment costs, and investment costs for retrofitting existing coal power plants. Furthermore, using biomass, which are not within machine specifications, decreases conversion e fficiency which then requires more feedstock to satisfy demand. However, optimizing the network based solely on minimizing costs sacrifices the environmental objective as shown in Table 7.

**Figure 4.** Minimum Cost Network.

**Table 7.** Comparison of costs and emissions objective performances.


### 5.1.2. Minimizing Emissions

On the other hand, when the environmental objective is optimized solely, more biomass is purchased and used in all existing coal power plants to prevent incurring the much larger emissions from coal firing as shown in Figure 5. However, cost inflates significantly (Table 7) because of several reasons. Transporting biomass is relatively more expensive because of its inherent properties, in addition pre-treatment will also have associated fixed and operating costs. Without regard for costs, all the pre-treatment facilities are opened depending on the pre-treatment process and e ffectiveness of each facility most suited to the initial quality of the biomass. In addition, the use of more biomass results in e fficiency loss in the equipment leading to the purchase of more fuel to reach demand. This is why significant increases are seen in fuel use in the second and third periods.

**Figure 5.** Minimum Environmental Emissions Network.

Optimizing each objective as single optimization models reiterate that a compromise must be found between the two conflicting objectives. One objective should not be minimized too much that no attention is given to the other. Considering only economic costs in optimizing the network result to a scheme where crucial investments and processes are disregarded to reduce costs, significantly compromising environmental sustainability. Similarly, when the system is optimized solely on environmental performance, costs are dramatically increased which may make the solution impractically expensive.

A goal programming approach is used to address this and achieve a solution that balances the two objectives. Each sub-objective–the economic and environmental–are optimized as single objective models and the results are recorded. The desirability levels of the objectives are computed for by dividing the actual improvement achieved by the potential improvement. In this case, the potential improvements for cost and environmental emissions are Million US\$ 314,960.03 and 1367.1058 kt CO2, respectively, based on the values shown in Table 7. The minimum between two efficiencies are maximized to obtain a solution that balances the minimization of costs and emissions.

#### 5.1.3. Full Model Run

As shown in Table 7, simultaneously optimizing both objectives allow the system to reach efficiency ratings closer to each other, both objectives getting 0.8892 desirability levels. Figure 6 also show a more manageable network configuration. In an effort to control both costs and emissions, biomass is used by the system and only two pre-treatment facilities are opened. Less biomass is used compared to when only the emissions were minimized. Only two of the three coal power plants are retrofitted for co-firing. Because less biomass is used, the decrease in boiler efficiency is slower. As a result, when comparing the fuel usage of the optimal network and the network which optimized the environmental aspect only, the increase across periods is not as dramatic. Aside from this, overall fuel usage is also less because a lower biomass-to-coal blend ratio means that the lower heating value of the feedstock is higher, resulting in a higher electricity yield. In addition, only two pre-treatment facilities are chosen to avoid the additional costs needed to operate more pre-treatment facilities. This required the model to choose the facility which costs the least to operate but resulted in the best improvements in biomass properties.

**Figure 6.** Optimal Biomass Co-firing Network.

#### **6. Scenario Analysis**

#### *6.1. Impact of Feedstock Properties Consideration*

The model was optimized without considering feedstock properties and compared to the results of the proposed model to demonstrate the impact of these considerations on a biomass co-firing supply chain, particularly on storage, transportation, and pretreatment decisions, and conversion yield. The resulting network is presented in Figure 6.

The optimized network without quality considerations (Figure 7) is compared to the optimal network obtained from the model proposed in this work (Figure 6). Without the consideration of biomass and coal properties in the network, biomass is sourced only from two locations and only two coal power plants are activated. Less fuel is used by the network because no damage occurs to the fuel during storage and transport and coal power plant conversion equipment does not experience any changes in yield or capacity. Thus, the supply and capacity of two biomass sources and two coal power plants are already enough to satisfy the demand for power in each period. Selecting where to source biomass is based only on distance and costs, unlike in the proposed model where the properties of the biomass from each source is also a factor in this decision. Similarly, pretreatment facilities/processes are chosen based on distance and pretreatment costs instead of their effectiveness in improving the qualities of the biomass. The amount of inventory held across periods is reduced also because the cost of purchasing and pretreating biomass remains relatively stable, so there is no need to keep inventory. On the other hand, the proposed model chooses to hold inventory on certain periods to avoid periods where the quality of the biomass is worse. In addition, only one of the two active coal power plants are retrofitted for co-firing. The system becomes less careful with distributing the amount of biomass usage among coal power plants, as it no longer has to avoid possible deterioration in conversion equipment and variations in the lower heating value of the mixed fuel. As such, in an effort to reduce transport and retrofitting costs, as well as transport emissions, biomass is only transported and used in one of the two active coal power plants. The model which overlooks quality related issues also has significantly lower costs (Million US\$ 40,150.17) and emissions (2209.40 kt CO2). The graphs in Figure 8a,b illustrate the components of costs and emissions for both optimized models.

Without considering biomass quality, costs are lowered in all of its components–purchase, transport, pretreatment, combustion, holding, and capital costs. As explained earlier, this is because of the significantly decreased fuel that flows through the system. Transportation costs are also decreased because the bulk density of the biomass and coal are not accounted for, which entail difficulties in transporting material (e.g., requiring additional trips). Similarly, emissions are considerably lower in this scenario because of the same reasons.

**Figure 7.** Optimal Biomass Co-firing Network without Quality Considerations.

**Figure 8.** Breakdown of (**a**) costs and (**b**) environmental with and without Quality Considerations.

Although this scenario achieved better performance for the financial and environmental objectives, it is an inaccurate and unreliable model of a biomass co-firing network, and will not be useful as a planning or managemen<sup>t</sup> tool.

## *6.2. Biomass Properties*

Biomass properties show to be a significant consideration in the modelling of biomass supply chains because it influenced network decisions across all activities in the supply chain. Changes in the properties of the biomass may cause an impact in the way the biomass co-firing network is constructed, consequently affecting the network's financial and environmental sustainability.

The biomass properties were improved and worsened across all periods in two different scenarios and are compared with the base scenario. In the improved properties scenario, moisture content and ash content are decreased by 20%, while bulk density is increased by 20%. On the other hand, biomass properties are worsened by increasing moisture content and ash content by 20%, and reducing bulk density by 20%. The cost and environmental emissions performance for the two scenarios and the baseline scenario are shown in Figure 9.

**Figure 9.** Breakdown of (**a**) costs and (**b**) environmental when Biomass Properties are Varied.

It can be observed that costs and emissions increase as the properties of biomass worsen. The improved properties scenario yielded the least cost and environmental emissions, while the worsened properties scenario resulted in higher costs and emissions.

The breakdown of costs is analysed in Figure 9a to understand why costs increased as properties worsened. With worse biomass quality, efficiency loss experienced by the conversion equipment in coal power plants also worsen, requiring the system to purchase and use more fuel. This increases all cost components, such as fuel purchase costs, transport, pre-treatment, and combustion costs. Transportation costs also increase because of the worse bulk density of the biomass, requiring multiple deliveries. On the other hand, as properties improved, the system would have to rely on less fuel overall because the power plants experience less loss in efficiency. Thus, less biomass and coal are used to reach the required amount of electricity. However, it is noticeable that when properties are worsened, biomass purchase increases only slightly, while the increase in coal purchase is more pronounced. This is because the model attempts to control the damage biomass causes on the conversion equipment and the additional costs needed to handle biomass by diluting biomass properties with more desirable coal properties.

Likewise, Figure 9b also shows an overall increase in environmental emissions as biomass properties worsen. For similar reasons, all components of environmental emissions increase due to the need to process more fuel. Combustion emissions due to coal increases because the model chooses between the corrosion in boiler equipment, which will require additional fuel and cause harmful emissions, and the emissions from burning coal.

Another set of scenarios are analysed. Particularly, a scenario wherein biomass properties are worsened only in the second period and where properties are improved only in the second period. The properties are enhanced and worsened by 50% from their original value.

When biomass properties are relatively stable across periods, storage of the biomass is avoided because it damages the biomass. However, when biomass properties experience increased moisture content, for example during wet season, and increased ash content, purchases are done during earlier periods with sufficient quantity and appropriate quality and stored for future use. When moisture content and ash content were higher and bulk density was lower in the second period, purchase during this period decreased significantly. Instead, the biomass to be used on the second period were purchased during the first and stored. The additional amount purchased in period 1 allotted an extra amount to account for deterioration and loss due to transport and storage. As a result, purchase, transport, and pre-treatment costs and emissions increase because of the additional biomass purchased in period 1, holding costs also increase to store biomass. Changes to combustion costs and emissions, as well as the efficiency loss experienced by the equipment are negligible because the original properties in period 2 are only slightly different from period 1. The optimal network for this scenario is shown in Figure 10. In the same way, when the properties in period 2 are made significantly better relative to period 3, the model chooses to purchase biomass for period 3 during the second period (Figure 11).


**Figure 10.** Optimal Network for Worse Biomass Properties in Period 2.

**Figure 11.** Optimal Network for Improved Biomass Properties in Period 2.
