Optimization and analysis of a bioelectricity generation supply chain under routine and disruptive uncertainty and carbon mitigation policies

Increasing greenhouse gas emissions and negative environmental consequences have raised worldwide attention to ecological issues. The development of carbon regulations (CRs) beside carbon capture and storage (CCS) systems is part of carbon mitigation policies (CMPs), which are following in recent years to control and manage carbon liberation. Along with environemtal policies, the utilization of renewable energy resources have been promoted significantly. However, the economic opportunities for renewable energy development considering CMPs have not addressed extensively. In this study, a stochastic mathematical programming model has been presented to minimize cost and downside risk (DSR) of the bioelectricity generation supply chain considering the pre‐ and postdisaster conditions. The role of several CMPs on the economic behavior of the system has been analyzed by investigating the potential uncertainties on material availability, material quality, and consumer demand. To consider disruption effects, the postdisaster stage has been classified into several substages including damage, recovery, and back to the sustainability stages. Mississippi State after the Katrina Hurricane is addressed as a case study to examine the performance of the proposed model. The results demonstrated that the occurrence of disruptive uncertainties creates 8,978,502 $, 8,864,335 $ and 8,884,055 $ as the DSR, under carbon tax policy (CTP), carbon offset policy (COP), and CCS, respectively. The effect of disruptive scenario 1 with a 15% reduction of resource has led to the greatest postdisaster supply chain costs in comparison with other scenarios. Although the financial analysis showed CTP has the greatest DSR after the occurrence of disaster, this policy has the most investment attractions, as well as COP, with the internal rate of return (IRR) of 9%. While implementing the CCS policy with the IRR of 2% creates 7% missed opportunity costs compared with other CMPs.


| INTRODUCTION
Increasing global carbon emissions and the negative environmental consequences have led to greater adoption and commitment to environmental policies to reduce CO 2 emissions. At the same time, the use of renewable energy resources and cleaner fuels is being pursued with greater speed and enthusiasm. [1][2][3] Among different types of renewable resources, forest biomass has characteristics that make it one of the viable options for biofuel or bioenergy production. 4,5 Variations in type, availability throughout the year, ability to store and improve its quality with changes in chemical or physical properties are the most important indicators of forest biomass to use for bioenergy production. [6][7][8][9][10] However, there are several problems with using forest biomass in energy applications. In particular, the rate of carbon emission during woody biomass combustion is significantly higher than the rate of carbon absorption over its growth cycle. This phenomenon, on a large scale, can affect the balance between the amounts of released and absorbed carbon in the atmosphere. Hence, this challenge causes a barrier for utilizing the forest biomass for energy production. 11,12 Due to environmental concerns, the carbon mitigation policies (CMPs) are seriously implemented for controlling and reducing CO 2 emission over the recent years. [13][14][15][16] CMP adoption gains rapid attention due to their direct effects on the economic, social, and environmental feasibility of future renewable energy resources. 17,18 In this regard, several carbon regulations (CRs) have been developed with prevention and control (PC) mechanisms to include limitations, financial penalties or subsidies on the volumes of liberated or captured CO 2 . Despite their benefits, there are various issues for implementing CMPs. Variability in energy intensity and utilization by consumers, incompatibility with elasticity in energy demand over time, and lack of financial attractiveness for private investors make shortages in CR implementation. 19,20 To deal with these problems, alternative CMP strategies such as carbon capture and storage (CCS) have been introduced as a more sustainable option for many industrial communities. 21,22 Contrary to CRs, which impose specific monitoring and limitations on industrial activities, CCS focuses on capturing the exhaust gas of production units and transferring to the storage site. 23,24 In other words, CRs are based on a PC approach, while CCS is an option to treat and improve (TI) postrelease carbon liberation. Although there are various CCS technologies such as precombustion, postcombustion, and oxyfuel can be selected regarding social, economic, and environmental targets, 25,26 the configuration of the CCS system is a challenge, particularly by considering the existence of uncertain factors.
Generally, the bioenergy supply chain is subject to routine and disruptive uncertainties. Routine uncertainties are diverse but predictable, such as normal fluctuation in material availability, consumer demand, and weather conditions. 27,28 While predicting and controlling routine uncertainties are more manageable, disruptive events could have detrimental effects on systems performance through damaging impacts on various elements of bioenergy supply chains. These damages can cause financial loss and investment risk besides stakeholder's reluctance to invest in bioenergy projects.
Given the effects of uncertainties on the economic efficiency of the bioenergy supply chain, this research aims to measure bioenergy supply chain cost under disruptive scenarios, considering the acceptable level of downside risk (DSR) for investors. Along with uncertainty and risk effects, the impacts of implementing different CMPs such as carbon offset policy (COP) and carbon tax policy (CTP) as PC-based approaches, and CCS approach as a TI-based concept are employed to measure the economic feasibility of a bioelectricity generation supply chain.
To incorporate uncertain factors into the model (eg variability in the availability and quality of materials, and diversification of consumer demand), a two-stage stochastic programming model is provided. In this model, the strategic decisions are made in the first-stage and tactical decisions such as resource allocation, carbon capturing, energy generation, material storing, and electrical distribution are structured in the second stage.
For the effective presentation of uncertainty impacts, the postdisaster decision-making space is classified into the damage, recovery, and back to suitability substages, so that the uncertain parametric behavior of the system during these substages is different. The validity of the proposed model is then tested based on data and parameters obtained for the state of Mississippi in the face of Hurricane Katrina. Accordingly, the financial analysis is performed to determine the investment payback period and system profitability under each CMPs.
The remainder of this paper is organized as follows. Section 2 provides a brief review of the related work on modeling uncertainty in bioenergy supply chains and CMP applications. The model is formulated in Sections 3 and 4. The case study, computational results, and economic analysis are presented in Sections 5 and 6. Finally, conclusions and directions for future research are provided in Section 7.

| LITERATURE REVIEW
In this section, a brief review of measuring and modeling uncertainty in bioenergy supply chains with a focus on nondeterministic mathematical programming models has been discussed. Then, relevant studies of implementing CMPs on the supply chain structures are reviewed. Accordingly, the research gap and contributions of this research are highlighted at the end of this chapter.
Generally, the bioenergy supply chain is contained a wide range of activities from material cultivation and harvesting, material processing, storage, transportation, and conversion to transform biomass to bioenergy. [29][30][31] While the existing literature covers economic, environmental, and social aspects of biomass utilization for energy generation, 32,33 the majority of literature focuses on the optimization of economic objectives using mathematical programming. 34 In this context, optimization models for supplier selection, 35 network configuration, [36][37][38] logistical decisions, conversion technology selection, 39 vehicle routing, 40 and supply chain uncertainty coverage 29,41,42 are the most popular issues, which are discussed by vast of researchers recently.
Stochastic, fuzzy, and robust optimization models are the most nondeterministic modeling approaches that have been employed widely in recent researches. In this regard, the concepts of the energy life cycle and carbon emission were assessed in a study by Ref. [43. In this research, a biobjective mixed integer programming (MIP) model was developed to cover uncertainties of feedstock availability, transportation capacity, yield, and downside demand. Fattahi and Govadian 44 addressed a multistage stochastic programming model to mitigate greenhouse gas emissions and optimize the social impacts of a biomass-based supply chain under material supply uncertainty.
By presenting a robust optimization model, Babazadeh 45 optimized the total economic performance of the supply chain considering cost minimization and growth of carbon trade under uncertainties. A robust multiobjective model addressed by Ref. [46] to highlight the effects of uncertain factors on the sustainability and risk attitudes of decision-makers in a biofuel supply chain. Saghaei et al. formulated a two-stage stochastic programming model combined with chance constraint and storage limitations to consider the uncertainty of material availability, material quality, and consumer demand in a bioelectricity supply chain. The authors presented the model in both small and large scales and provided basic and improved cross-entropy algorithms to solve them.
In addition to the external uncertainties, the adoption of CMPs imposes new constraints or environmental costs to the system that complicates the decision-making. To indicate the effects of CMPs, Ortiz-Gutiérrez et al. 47 proposed a mixed integer linear programming (MILP) model to develop a bioethanol supply chain under demand uncertainty and GHG savings. They showed that the increment of CO 2 allowance price leads to a reduction in the economic profitability of the system. 48,49 provided a mathematical model to analyze the impacts of several CRs, including carbon cap, carbon tax, carbon cap and trade, and carbon offset schemes on the performance of a biofuel supply chain. In another paper, 50 introduced a MILP model considering carbon tax and carbon trading (cap-and-trade) regulations in a bioenergy supply chain. Their results demonstrated that change of the carbon price has led to fluctuated emission rend that had not steady behavior.
Along with CR effects, the impacts of CCS technologies on the mitigation of carbon and performance of the supply chain have been attention recently. In this regard, the roles of CCS implementation on the emission level, electricity, price and system's financial behavior have been highlighted by recent researches. [51][52][53] According to reviewed literature, uncertainty plays a key role in the performance of the bioelectricity supply chains. On another side, environmental considerations such as the CMPs increase the complexity of decision-making and reduce the economic profitability of bioenergy production. Therefore, studying the effects of uncertainty and environmental considerations on the attraction of investment for stakeholders in the bioenergy projects is necessary.
In this regard, this study presents a two-stage stochastic programming model to minimize the costs of a bioenergy generation supply chain under uncertainty and several CMPs. In our presented model, investment and technical cost elements are formulates in the postdisaster conditions, so that the facility establishment decisions are made as to the first (strategic) stage, and decisions related to the material flow, material storage, and level of generated electricity are formed in the second (tactical) stages under disruption scenarios.
To better incorporate uncertainty effects, the second decision-making stage has classified into three substages after the disaster, to show the effects of damage, recovery, and back to sustainability phases on the tactical decisions.
Our presented model not only focuses on the minimization of supply chain cost but also it is following the reduction of DSR as a variable dependent on the gap of optimal decision costs between pre-and postdisaster conditions. In this way, to consider risk concepts, we have defined DSR constraints in our model.
All formulations are performed in a case study in the southeast area of the Mississippi State to analyze the effects of Katrina hurricane disruptions on the construction of a bioelectricity production project. Finally, due to the net present value (NPV) concepts, a financial analysis is provided to evaluate economic feasibility and missed opportunity of the project regarding several CMPs.

| MODEL FORMULATION
In this study, a bioenergy supply chain is configured considering supply areas, material storage locations, power plant locations, and electrical consumer sectors. Firstly, a two-stage stochastic programming model is formulated to minimize the postdisaster supply chain costs (PoSCC) with attention to the | 2979 SAGHAEI Et Al. uncertainty of material availability, material quality, and consumer demand under DSR considerations.
DSR variable is calculated simultaneously with PoSCC, regarding defined upper and lower bounds of risk, where the upper bound is the maximum acceptable level of DSR, and lower bound is the gap between PoSCC and an Ideal target for investors. One of the innovations of this study is suggesting the calculating of predisaster supply chain cost (PrSCC) as the ideal target for investors under routine uncertainties.
In this regard, Figure 1 demonstrates the schematic view of the bioenergy generation network. According to this figure, flows of the harvested materials move from supply areas to the storage locations as the green or salvaged woods.
In the storage, air-drying operations use to reduce about 50% of moisture content (MC) of woody materials. In each period, some amounts of dried materials are maintained in the storage as the safety stock to coping with the material shortage in the future. In the next step, the dried feedstocks are sent from storage to the power plant to convert to the electricity and then distributing in the power network.
Affecting by routine uncertainties such as fluctuations of weather conditions, forest resource availability usually is changing. On the other side, the quality of green woods is determined regarding the rate of MC and higher heating value (HHV) that are constantly changeable proportional to the weather indicators such as humidity and temperature. Although supply chain parametric behavior is predictable under routine uncertain conditions, the occurrence of a sudden event such as natural disasters can significantly influence its performance. In this regard, Figure 2 demonstrates the three separate substages after the disaster.
After the occurrence of catastrophe, time interval a 1 is known as the damage substage, when the large part of the green materials is destroyed in the following the disaster. Therefore, salvaged materials with lower quality will replace in the supply areas. During the recovery stage (a 2 ), natural or artificial recovery processes will start. In this stage, due to a reduction of the salvaged wood, the stored or new harvested green materials will resupply. Gradually with the regrowing of green materials, the balance between supply and demand will form and system behavior returns to the sustainable level before the disaster (a 3 ).
Changes in the parametric behavior of the system after the disaster can affect the supply chain decision-making process. In another word, the costs of the optimal decisions over the postdisaster phase are different in comparison with the routine conditions.
In general, supply chain decisions are made in three strategic (long-term), tactical (midterm), and operational (shortterm) levels. Strategic decisions are those types of decisions that will be considered prior to observe uncertainty in the system. For example, in the bioelectricity production supply chain, the location and size of power plants and storages are decisions that prospective investors make them, here and now, without considering occurrence the probable uncertainty in the future.

Consumers Suppliers Storage
On the other hand, tactical decisions such as the amount of material harvested and transported, the amount of stored material and produced electricity are time-dependent decisions that can be affected by disruption scenarios in the future. For instance, uncertainty can influence the level of available biomass resources and the quality of them.
Therefore, in this study, we have employed a two-stage stochastic programming model to optimize the PoSCC. In this way, strategic decisions (size and location of facilities) will be made in the first stage, and tactical decisions (material flows, the level of stored material, and the level of electricity generation and distribution) will be offered proportional to the uncertain scenarios in the second stage.
In this regard, a model is developed to minimize PoSCC, where SC is the cost of first stage (strategic decisions), pr s is the probability of occurrence of disruptive scenario s, and TC s is the second-stage decisions (technical decisions) costs (Equation 1).
According to Equation 1, SC are the first-stage decision costs including investment and fixed operation and maintenance (O&M) costs to construct a power plant and ∑ s (pr s * TC s ) is the second-stage decisions (weighted tactical decisions) costs including harvesting, holding, and transportation costs of materials as well as the variable O&M cost of the power plant to generate electricity.

Subject to
According to Equations 4 to 6, the constraints of the problem are classified into the first stage, second stage, and DSR constraint groups. In continue, the constraints of each class are presented.
First-stage strategic constraints are including.
(4) First − stage sterategic constraints Equation 15 demonstrates the storage should maintain the safety stock in each period to deal with the uncertainty of available material in the future.
Equation 16 explains that total distributed electricity should satisfy the demand of consumers.
Equations 17 and 18 describe the upper and lower bound of DSR. The parameter R is the maximum acceptable level of DSR that is the highest risk level for investors. is an ideal target that investors are willing to the realization of it, after the disaster.
As before discussed, we have assumed is the optimal PrSCC under routine uncertainties. It is known as the ideal value for stakeholders that it justifies the investment. In another word, investors will be satisfied if the costs of the supply chain after the occurrence of disaster has the minimum gap with the costs over the predisaster stage (under routine uncertainties). Accordingly, to calculate , we should optimize the PrSCC. In this regard, a nondeterministic mathematical model is developed under routine uncertainties to calculate decision costs without considering scenario and substage sets.
Equation (19) describes PrSCC objective function as bellow: where SC follows Equation 5 and TC is

Subject to:
The configuration of the PrSCC model under routine conditions is completely similar to the PoSCC model with this difference that disruption scenarios, separated main, and substages do not exist in the structure of formulas. In another word, the space of decision-making is integrated and it is not decomposed.
It means the behaviors of uncertain parameters (material availability, material quality, and electrical demand) are proportional to defined statistical distribution functions and disruption scenarios do not affect their probability function's characteristics. Therefore, we can consider Equations 7 to 18 as the constraints of the PrSCC model with ignoring indexes s and a and considering an integrated time set, t = {1 … .T} . After calculating the optimal costs of the PrSCC model, it will be replaced as the ω in Equation  17 of the PoSCC model. The presented two-stage model in this chapter is the main configuration of a cost minimization model for constructing a bioenergy supply chain under disruptive uncertainties and DSR considerations. In the following, the effect of CMPs on the model structures has been discussed.

| CMP FORMULATIONS
In this part, different CMPs approaches according to the CTP, COP, and CCS add to the body of the PoSCC model. Due to introduced parameters, first, the CR models are formulated (PoSCC-CTP, PoSCC-COP), and then, the CCSbased model is presented (PoSCC-CCS).

| PoSCC-CTP model
Carbon tax as an environmental policy imposes the financial penalty for the released CO 2 to different layers of the supply chain. The penalty costs add to the objective function as new cost elements. This policy does not allocate any capacity limitation on carbon emission. The formulated objective function of this policy is as below: where SC and TC s follow the Equations 5 and 6 and

| PoSCC-COP model
Carbon offset as an environmental regulation allocates a limited capacity to CO 2 emission through supply chain operations. However, purchasing the additional carbon capacity from the market is permitted. In another word, the required surplus capacity can be supplied; nevertheless, unused carbon capacity cannot be sold.
If spc s t a would be a variable to show the amounts of surpluses purchased carbon capacity and Cap t a would be the permitted emission capacity in the stage a and time t a , the objective function and related constraint to this policy are presented as below: where SC and TC s follow the Equations 5 and 6 and (21) Equations 7 to 18 (without indexes s and a).

| PCC-CCS model
CSS technology is one of the options to implement the TI approach for dealing with carbon emission. To impose CCS regulation on the model, the main structure othe supply chain should be connected to the set of facilities and operations which are involved in capturing, transportation, and store the carbon underground. The related mathematical elements to connect CCS structure to the main model are described in continue.
The presented objective function under CCS regulation is a combination of two supply chain elements related to the bioenergy generation and CCS network structures. Therefore, the investment and operational costs of both are considered in the model. All the strategic and tactical decisions of structuring a CCS network are considered and added to the model. Decisions for selecting the best locations and sizes to establish capture unit, geological storage, and pipeline facility between capture unit and storage are considered as the strategic decisions and tactical decisions considering flows of transformed and stored CO 2 through the CCS network. In this regard, the PoSCC-CCS model is formulated as below: where SC. and TC s follow the Equations 5 and 6 and And According to Equations 27-29, the objective function of the PoSCC-CCS model has several new components depending on the investment and fixed O&M costs to establish a capture unit, pipeline, and geological storage. The added tactical costs are including carbon capturing, transferring, and storage costs through the CCS operations. The PoSCC-CCS model not only includes the previous constraints (Equations [7][8][9][10][11][12][13][14][15][16][17][18] but also contains new limitations as below: Equation 30 shows the amount of captured CO 2 is dependent on the generated electricity, emission rate, and efficiency of the capture unit.
Total CCS establishment costs describes that the amounts of captured CO 2 should be less or equal to the capacity of the capture unit. Equations 36 emphasizes that the amounts of stored carbon in geological storage should be equaled to the defined target value to mitigate and store carbon underground.
Equations 37 and 38 describe that the established capturing units and geological storages should be less or equal to the permitted numbers (B 1 and B 2 ). Equation 39 emphasizes that between every two points of the capture unit and geological storage just one size of the pipeline facility could be selected.
All provided CPM-based models are trying to describe the changes in the basic PoSCC model under environmental considerations. With ignore of scenario set s, and substage set a, as well as integrating the time horizon of the problem in the form of t = {1 … .T}, the PrSCC-CTP, PrSCC-COP, and PrSCC-CCS models can be formulated similarly.
To analyze the performance of the formulated models and CMP scenarios, in the next chapter, the Mississippi case study is presented and discussed.

| Case study
Mississippi, as one of the southern states of the United States, due to 305,010,178 hectares of forests, is known as a high potential area for forest wood extraction and utilization in bioenergy and biofuel generation. Opportunities for biofuel and bioelectricity generation in this state have been subjects of several studies in recent years. 54 The majority of forestlands in this state are covered with pine and hardwood, which often found in two shapes of pulpwood and saw timber. 54 Although this state has great access to forest resources, natural disasters have always been serious threats to forest conservation, availability of wood resources, the stability of the timber market, and the quality of wood materials. For instance, the Katrina hurricane in August 2005 led to intensive damages to the forests in the forms of lean or blowdown. 55,56 Although this destructive cyclone affected a large part of the Mississippi State, the 15 counties in the southeast area suffered the most. Figure 3 shows the level of damage in the 6 most destructed southeast counties of Mississippi after the Katrina hurricane.
Details of pine pulpwood, pine saw timber, hardwood pulpwood, and hardwood saw timber types for all 15 counties in the southeast of Mississippi are in Appendix A. These volumes are the monthly average materials that are available in the routine condition.
To perform the effects of routine uncertainty, for instance, seasonal changes and climatic variations, ±10% fluctuations are considered in the average available forest biomass in each county. It is assumed that the monthly average volumes for each county in the routine condition are distributed by Uniform distribution function in an interval with minimum and maximum boundaries as below.
After the natural disaster, the Katrina hurricane, the fluctuations in the forest availability are changed significantly. According to the reports, 57 the consequences of the Katrina hurricane caused 15-30% fluctuations in the blowdown factor, as the most prevalent factor, in several counties.
Hence, to consider the impact of disruption in the availability of the forest, four scenarios with −15, −20, −25, and −30% reductions of greenwood resources are applied to the model. The loss of material is assumed to be zero, hence during the damage substage, the amount of salvaged resources after the disaster are equal to initial resources minus reduced green material under each scenario.
Obviously, the quality of green and salvaged woods is wieldy depend on the weather conditions and levels of the damage. Shabani 58 presented an equation to measure the energy value (EV) of green materials regarding the MC and HHV values (Equation 43). We have generalized this formula to each time, type, and form of green resources.
According to the Haliwood and Horrobin's theory, the MC of woody material can be calculated depending on several indicators such as air temperature, humidity, and molecular weight of polymer unit that forms a hydrate in each time period. 59 In another study, the humidity factor is addressed as a parameter-dependent to the dew point and normal temperatures. The temperature is not a fixed parameter and it is usually fluctuating over time. 60 Therefore, the mentioned effective indicators obtain various values in each month.
In this way, Saghaei et al 61  Proportional HHV values are measured according to a general classification presented in Table 1 and employing the linear interpolation technique. Appendix C addresses the lower and upper boundaries of the MC, HHV, and EV in each month. The final EV value is chosen using a random selection in the uniform distributed intervals, with attention to the lower and upper bounds of EV.
In another side measuring the quality of the salvaged woods is a challenge, since it depends on different features such as the severity of the damage, timber decay, and environmental condition after a disaster. 62 To simplify it, Equation 44 is proposed to convert the quantities of green resources to salvaged type by multiplying to the specific parameter. 63 where the Q s G and Q s Sl are quantities of green and salvaged woods respectively, and K is a translate factor to convert the salvaged wood value to green type. In another word, the translate factor K explains the equivalent green quantitates of salvaged wood. Using this factor, we convert the salvaged resources to green type and then use the measured green EV values for them. The average values for K after Hugo hurricane are reported as K = 4.5 and K = 6.6 for saw timber and pulpwood forms of pine, respectively. 64 Due to the lake of knowledge about relevant hardwood translate factors in these two forms (pulpwood and saw timber); in this study, reported values are generalized to hardwood forms too.
To consider postdisaster substages in our study, the first year after the disaster is introduced as damage stage when salvaged woods are available to supply instead of greenwoods.
The second year addresses the recovery stage, when the green woods are recovered but it does not completely. In this regard, a random value between 10 and 15 percent is considered as the rate of greenwood unavailability over the recovery stage, in comparison with the predisaster phase. Finally, the last stage, as the back to sustainability, is performed with 0 to 10% material fluctuation.
The distribution of electrical demand for the southeast area of Mississippi after the Katrina hurricane is not exactly available. Generally, when the actual data are not available, the normal distribution function can be used to cover many information deficiencies of the system. 65 In this study, we have employed simulated data of monthly electricity consumption in the southeast area of Mississippi that is provided by 61 (Table 2).
Investment and fixed annual costs to establish facilities such as power plant and capture units are relevant to the size of these facilities. On the other side, the variable cost of the system is directly dependent on the electrical demand and stored materials. In this regard, the provided data by 61 are employed to consider efficiency, investment, fixed, and variable O&M costs and suggested sizes including 116, 119, and 122 MW to establish a power plant.
The storage capacity should be proportional to the electrical consumer demand (suggested sizes for power plant) and the quality of materials. The storage capacity is proportional to the volumes of safety stock and required materials during routine conditions. It also should be as much as enough, for supporting of sudden increment in the material volumes, when the green resources are scarce and salvaged types with lower quality (higher quantities) should be replaced. In this regard, the storage capacity is suggested to be in proportion to the volumes of the dry material considering average EV of 4.5 (MWh/ Dry ton (Dt)), and average translate factor K of 5.5, with attention to all types and forms of materials. The storage capacity should be enough to run the power plant's operations for 20 days, 66 regarding the three mentioned sizes (Table 3).
Appendixes B and D address some of the other supply chain parameters and distance between locations. Given that, the location of the power plant in each county is defined as the distance from the forest resources. As we do not know the accurate amount of that, a numerical interval is proposed to calculate each county's distance from itself as a range between zero and root square mile of surface (S) in that county (0, √S/2).
The CO 2 capturing unit size calculates in the proportion to the size of the power plant and electricity net generation. Appendix B introduces the costs and emission parameters of the CCS system, as the average values of the three

Residential
Commercial Industrial implementable technologies for CCS including oxyfuel, precombustion, and postcombustion. 26 The provided information by Appendix B is converted data, proportional to the three suggested sizes for the power plant considering the scale factor 0.7 and US $ cost per unit. 67 The total CCS variable cost includes the CO 2 avoiding cost in the capture unit plus 10$ for transportation and storage. 68 Fixed O&M costs for total facilities of the CCS are assumed 3.5% of investment costs, similar to the power plant. 61 The amount of CO 2 released during the CCS operations mainly depends on the emission of capturing unit, pipeline transferring process, and the associated underground carbon storage operations. To reduce carbon dioxide emissions and the cost of pipeline construction and decrease the risk of line failure, it is assumed that the CCS system is built in the same county where the power plant is established. The supply chain performance under CCS policy faces challenges such as the geographical conditions of the route between carbon storage and capture unit, and embedded facilities over carbon transferring and storage that may change the rate of carbon emissions. Thus, a random value between 5% and 10% is assumed for the CO 2 emission increment rate through transportation and storage operations. The CCS costs and emission are presented in Appendix B. The numerical results of the proposed model for the mentioned case study are widely presented in the next section.

| COMPUTATIONAL RESULTS
This section presents the computational results of the proposed models under several CMPs. GAMS software with a CPLEX solver has used to optimize mathematical models. Table 4 and Table 5 demonstrate the binary decisions and supplier counties under routine and disruptive uncertainties. The summation of realized monthly electricity consumption for three residential, commercial, and industrial sectors is provided in Figure 4. According to Figure 4, the most consumption rate refers to January with 85.9 thousand MWh. Among the three suggested sizes to establish power plants, 122 MW has been the best size to cover the electricity demand completely in both routine and disruptive conditions.
Over the predisaster stage, county 4 (Wayne) has been selected as the best place to establish the power plant. Regarding the transportation cost concept, the same county is proposed as the best location to establish the material storage and CCS facility.
*Appendix A. Figure 5 shows the total supplied materials in two forms of green and salvage over both pre-and postdisaster stages. The salvaged materials are available exclusively in the postdisaster stage. The total supplied green material under routine (ru) and disruptive uncertainties (DU) is 887,634 and 787,566 Green ton (Gt), respectively. At the same time, the volumes of salvaged material under disruption have been 122,371.9 Gt. According to Figure 5, there is not any considerable gap in the total supplied green materials between RU and DU. However, the contribution of material based on their types and forms is different. In this way, Figures 6, 7,and demonstrate the proportions of pine pulpwood, pine saw timber, hardwood pulpwood, and hardwood saw timber for both forms of green and salvaged woods. Over the routine conditions (predisaster stage), pine pulpwood with the 48% contribution has the most share regarding the higher resource availability in comparison with others ( Figure 6). Due to the significant depletion of resources under disruptive conditions, the percentage of resource utilization has been adjusted and the participation of other types of resources is increased. However, the 24% reduction in the volume of pine pulpwood under disruption (Figure 7) leads to the 80% contribution of salvaged wood (Figure 8).
The difference in the numbers and locations of suppliers and the volumes of supplied materials under RU and DU affect the operational and environmental performance of the supply chain considering CMPs. Figure 9 shows the costs of  implementing a bioelectricity supply chain under CMPs for both routine and disruptive conditions. The presented costs in Figure 9 are the first-year PoSCC results including investment costs, fixed and variable O&M costs, and operational and environmental costs under CMPs. Tables 6-9 present details of them. As before discussed, to run the PoSCC model, we need to determine the parameter as the optimal PrSCC. In this regard firstly, we have calculated the optimal costs of the bioenergy supply chain under RU considering CMPs. The detailed cost elements for the predisaster model are presented in Table 6.
In continue, the cost elements of the supply chain in the postdisaster stage are presented under each CMPs separately considering disruption scenarios (Tables 7-9). Finally, Figure 10 demonstrates the amounts of DSR for each CMP with attention to the provided information.
Tables 7-9 illustrate supply chain cost items under disruption scenarios including 15, 20, 25, and 30% reduction in primary resources (chapter 5). According to refers to the ratios of available salvaged wood compared with greenwood.
In scenario 1, the availability of salvaged material is not considerable, as results, due to the shortage of salvaged wood and the needs of the system to be fed; some cost elements have increased to supply green resources from a wider range of counties. In scenarios 2 and 3 although green wood reduction rate is higher than scenario 1; however, rate of replacing salvaged wood is more than it; consequently, the system can reduce the needs of harvesting material from farther counties. As discussed, increasing and decreasing costs of the supply chain in exchange for parametric volatility have been achieved by efforts to minimize costs and maximize DSR reduction. In this regard, Figure, 10 shows the amounts of DSR under CMPs separately.
As in Figure 10, the highest DSR belongs to CTP, which has the most cost increment over the postdisaster stage. It is because of the allocated carbon tax to the whole operations of the supply chain. It means the role of disruption on the material availability rate has more effect on the rate of emission that is deserving to penalty costs, in comparison with the shortage of carbon capacity (COP) or volumes of transferred carbon (CCS).
Another important issue is the green material proportion in comparison with the salvaged type in each scenario and its effects on the DSR. As it is observable, all three CPMs have experienced the highest DSR under scenario 1. This scenario assumes the least amount of destruction in the primary sources. However, the reduced availability of green materials, along with limit accessory to salvaged resources (compared to other scenarios), has made the supply chain obliged to supply green materials from farther counties. It has led to an increase in the cost of material shipping.
To evaluate the level of problem complexity under routine and disruptive conditions, considering CMPs, we have analyzed the solving time for different sizes of the problem. The analyzed sizes and results are presented in Table 10.   The size 1 refers to the presented case study, which includes 15 counties and indexes such as potential locations of forestlands (l), material storages (i) , power plants (k), capture units (q) , geological storages (h). The solving time of the predisaster model under CTP, COP, and CCS for size 1 has been 71, 54, and 112 seconds. Similarly, for the postdisaster model under disruptive scenarios, 90, 61, and 144 seconds are recorded, respectively.

Two-stage model
By increasing the size of the problem from case 1 to 4, the gap of solving time between pre-and postdisaster is evaluated considering CMPs. The results show that by increasing the size of the problem, the solving time is increased. Noticeably, significant growth in solving time is observed in the CCS scenario with attention to the existence of more viables and parameters.

| Fancial analysis
Regarding DSR results and a considerable gap between CMP's economic performances in the pre-and postdisaster stages, financial analysis is employed based on the NPV concept to evaluate economical attractions of CMPs under disruptive conditions. Net present value (NPV) in engineering economics is one of the standard methods of evaluating economic plans. In this way, the cash flow (income and expense) is discounted based on the time of occurrence (income or expense). Present net value is widely used in economic calculations, engineering economics, countries' budgets, microeconomics, macroeconomics, commerce, and industry. In this way, the NPV formulation is presented below:  where t is the period index, i is the internal rate of return (IRR), and R t is the net cash outflow in the period. Obviously, at the beginning of the project, there is no revenue, and investment and fixed O&M costs are only the financial flow at the start point. Economic comparison of projects is one of the important approaches that can affect investment attractiveness. Many investors face different conditions and investment options that can lead them to profitability or in contrast losing the opportunity.herefore, evaluating and comparing the economic performance of different projects would have a key role to justify stakeholders. There are various methods for economic comparinof p. However, IRR method offers a comprehensive approach to determining the interest rate of investment over time. The other advantage of using IRR is the opportunity of comparing it with the minimum attractive return rate (MARR). This comparison can result in selecting the best alternatives for investment. In addition, this method helps to find out how much opportunity is lost after investment in each project. To perform the IRR. approach, an equal investment payback period should be considered for all projects. Then, by using Equation 46, the IRR. is calculated for each plan where P. is the initial investment value, N. is the investment payback period, and a. is the net profit in each period.
If IRR ≥ MARR, the plan has economic feasibility. Otherwise, it wod not be an attractive option for investment.
To compare plans, multiple cases are introduc.onsidering plans A. and B., three situations will be occurred as below: Ading to what was discussed, various CMPs are compared in terms oeconomic for determining the IRR of the project for each CMPs and its investment attractions. Compared projects are considered for after disaster conditions. To calculate NPV, t average electricity sale rate is considered 90.9 $ per MWh. 69 The time horizon after the disaster, as is discussed earlier, is divided into three stages including the first yr (damage stage), second year after the disaster (recovery stage), and the third year as the back to sustainability stage. The MARR is considered equal to the bank discount rate in the Mississippi (1.25% per annum). 70 In addition, the investment payback period is considered 40 years for each CMP. Table 11 shows the cost, revenue, and profit values. Items reported in Table 11 include investment costs, annual fixed O&M costs, and variable costs of each CPM (total costs of harvesting, transportation, storage, electricity generation, and environmental costs), which are listed in Tables 7, 8,9 and with details. These tables report only the costs associated with the first year. The costs of the system in the second and third years are then calculated based (46)  on the parametric behavior of the system in the recovery and back to sustainability stages described in chapter 4. The system revenue is also determined based on the sum of electricity generated per year ( Figure 4) and its supply price. 69 Obviously, first-year costs will be higher than other years due to widespread depletion of resources, which will lead to increment of costs and reduced profits from electricity sales.
According to the data of Table 11, the calculated IRR for each CMP is presented in Table 12.
Due to Table 12, IRR of the project under CTP and COP scenarios are equal (9%) while CCS experiences lower IRR (2%). It means, although the project under all CMPs is feasible, the CCS scenario leads to missing 7% annual profit rather than CTP and COP. In other words, considering the equal investment payback period, the attraction of investment on the project under CTP and COP is 7% higher than the CCS scenario. Regarding the IRR approach, CTP-and COP-based scenarios are equally the same, due to equal investment cost and equal IRR after 40 years. However, both CTP and COP models create the same long-term attraction of investment for stakeholders.

| CONCLUSION
This study is an optimization platform to minimize costs and DSR of implementing a bioenergy supply chain considering pre-and postdisaster conditions, disruptive scenarios, and various CMPs. To consider uncertainty of material availability, material quality, and consumer demand, a two-stage stochastic programming model has been provided in which the strategic and tactical decisions are made in the first and second stages, respectively.
We have considered the performance of a natural disaster (Katrina hurricane), as the start point of disruptions, in a real-world case study in the Mississippi State. Our research has categorized the decision-making space after the disaster into three substages including damage, recovery, and back to sustainability. To evaluate environmental considerations in the design and planning of the bioelectricity supply chain, two groups of CMPs including CTP and COP, as the PC-based regulations, and CCS, as the TI-based approach, have been added to the model. The computational results showed the model under disruptive conditions and the CTP scenario experiences the highest DSR value (8,978,502 $).
Additionally, a financial analysis has performed to show economic feasibility and missed opportunities of different CMPs in the postdisaster condition. The results of the financial analysis showed that although the impact of uncertainty on the system under the influence of the CTP scenario results in the highest unexpected cost (DSR) equals to 8,978,502 $; however, the COP and CTP are the most cost-effective scenarios, respectively. They created the 9% as the IRR in the equal comparative terms (payback periods and MARR) while applying a CSS policy with 2% IRR created a 7% missed opportunity costs in comparison with them.
As future research opportunities in this field, we suggest considering a wider range of CMPs and analyzing their impacts on biomass supply chain performance. The ability to sell the captured or unused carbon in the market to improve the economic attractions of the bioenergy projects can be another interesting topic for investigation. It should be noted the future cash flows in this study have been considered as static values. As a result, considering the fluctuation of cost and profit elements with attention to the changes in electricity price and MARR in the future could be helpful to more accurate financial analysis. The cost per unit of holding material type m in form n in the storage i ftli mnli The fixed cost of transportation material type m in form n between forestland l to storage i vtli mnli The variable cost of transportation one unit of material type m in form n per each unit of distance between forestland l to storage i ftik mnik The fixed cost of transportation material type m in form n between storage i and power plant k. vtik mnik The variable cost of transportation one unit of material type m in form n per each unit of distance between storage i and power plant k ic kb The investment cost of construction a power plant with size b in location k fc kb The annually fixed operation and maintenance (O&M) cost of a power plant with size b in location k vc kb The variable (O&M) cost of electricity generation per unit in the power plant with size b in location k eff kb The The moisture content of material type m, in form n and period t a and stage a d li The distance between forestland l and storage i d ik

NOMENCLATURE
The distance between storage i and power plant k d qh The distance between capture unit q and geological storage h fsc yq The annually fixed O&M cost of the capture facility with size y in the location q cc yq The carbon capture cost per unit, for a capture facility with size y in the location q isc yq The investment cost to construct carbon capture facility with size y in the location q igs uh The investment cost to construct a geological storage with size u in the location h fgs uh The annually fixed O&M cost of the geological storage with size u in the location h hg t a uh The cost of holding carbon in geological storage with size u in location h, at time t a and stage a tcs t a uh The target of capturing carbon in the geological storage with size u in location h, at time t a and stage a vtp jqh The variable cost of transportation one unit of carbon by pipeline with size j between capture unit q and geological storage h ipj jqh The investment cost of construction the pipeline with size j between locations q and h ftp jqh The fixed cost of carbon transportation by pipeline with size j between capture unit q and geological storage h fpj jqh The annually fixed O&M costs of construct pipeline with size j between locations q and h cap cap yq The capacity of capture unit with size y in location q cap gs uh The capacity of geological storage with size u in location h cap pip j The capacity of the pipeline transportation with size j eff yq The efficiency to absorption of CO 2 from the exhaust gas of power plant by capture unit with size y and in location q eff jqh The efficiency of the pipeline with size j to transfer carbon from capture unit in location q to geological storage in location h eff uh The efficiency of the geological storage with size u in the location h Cap t a The permitted emission capacity of carbon at time t a and stage a ehrv mnl The CO 2 emission for harvesting one unit of material in type m in form n at forestland l esrt mni The CO 2 emission for holding one unit of material type m in form n at storage i feli mnli The fixed CO 2 emission for transporting material type m in form n, between forestland l and storage i veli mnli The variable CO 2 emission for transporting one unit of material type m in form n per each unit of distance, between forestland l and storage i P 1 The permitted numbers of locations to open storages P 2 The permitted numbers of locations to establish power plants x ir Binary variable that is 1 if storage has been opened in location i with size r and 0 otherwise | 2995 SAGHAEI Et Al.
x bk Binary variable, which is 1 if power plant has been established in location k with size b and 0 otherwise x jqh Binary variable, which is 1 if the pipeline transportation facility with size j has been constructed between locations q and h and 0 otherwise. The CO 2 emission tax for a unit liberated carbon cp

Continues (Non-negative) Variables
The price of purchasing one unit of surplus carbon The ideal target (cost of supply chain) that investors are willing to the realization of it R The maximum acceptable rate of downside risk for investors B 1 The permitted numbers of locations to establish capture unit B 2 The permitted numbers of locations to establish geological storage Binary Variables x yq Binary variable, which is 1 if the capture unit has been established in location q with size y and 0 otherwise x uh Binary variable, which is 1 if the geological storage has been established in location h with size u and 0 otherwise