A sustainable network design of a hybrid biomass supply chain by considering the water–energy–carbon nexus

Nowadays, with population growth, rising global energy demand, increasing water consumption, carbon emissions, and excessive use of fossil fuels, the world faces a major challenge. Biomass is one of the most attractive sources of energy production, with positive effects on the economy, environment, and society, which can decrease the world's reliance on fossil fuels and deal with this universal challenge. Consequently, the biomass supply chain network design has received more attention in recent decades. Since energy and water are two significant sources for society's sustainable development and carbon emissions are essential for environmental health, the study of the water–energy–carbon (WEC) nexus is essential. In this study, a multiobjective multiperiod model for designing a sustainable supply chain network based on hybrid second‐generation (i.e., Jatropha, agricultural waste, and animal waste) and third‐generation (i.e., microalgae) biomasses is presented. The proposed multiobjective model consists of five objective functions that maximize the total energy produced and the number of jobs created and minimize the total water consumed, carbon emitted, and total costs. Case study results demonstrate the performance of the model utilizing the MINMAX goal programming approach. Based on the results, energy production from Jatropha is more appropriate in comparison with energy production from microalgae, agriculture waste, and animal waste. The findings also show that the proposed model in this research considering the WEC nexus performs significantly better than the classical model without considering the WEC nexus.


| INTRODUCTION
Contemporary human society is highly dependent on the use of various forms of energy. The significance of energy in human society is highlighted by cases where adequate energy supply is disrupted. For example, the power outages in New York City on July 13, 1977, and in the entire eastern United States on August 14, 2003, led to two catastrophic blackouts. In both cases, power outages in several US cities led to civil unrest, looting, and widespread municipal unrest. 1 On the other hand, due to environmental effects and reduced dependence on fossil fuels, it is one of the most significant reasons to consider and turn to renewable energy sources. Among the numerous renewable energy sources, biomass is very attractive because of the wide range of sources. 2 Therefore, it can be concluded that bioenergy as a neutral source of carbon 3 has solved two important human problems, which include environmental and social problems by reducing Greenhouse Gases and creating jobs. 4,5 From a social point of view, biomass is relatively cheap. 6 Biomass can be converted into liquid and gas, and it can be affected by surrounding environmental situations. 5 To the best of our knowledge, biomass can be classified into three categories. In this study, a unique biomass classification is presented which can be seen in Figure 1.
Achieving energy production is very important due to population growth; it is also essential to pay attention to other issues in this area. One of these issues is the issue of pollutant emissions. Air pollution is one of the significant causes of death. Pollution-related deaths are projected to increase from 3 to 4.5 million by 2020. That number includes premature deaths, a loss of $225 billion in labor income, and $5.11 trillion in welfare income. 7 On the other hand, there is a need for water consumption in different parts of biomass energy and fuel supply networks. Subsequently, for first-generation (i.e., corn and soybeans), second-generation (i.e., Jatropha, agricultural waste, and animal waste), and third-generation (i.e., algae and microalgae) plant biomasses, conversion procedures such as anaerobic digestion, cooling of other pyrolysis reactors, and gas sector conversion, water plays a prominent role. Furthermore, the management of the water subsystem requires both water and energy. 8 Most of the articles focus on two aspects from three aspects, and the relationship between water and energy (water-energy nexus) represents the main issue. Therefore, the study of the WEC nexus needs evaluation. 9 Also, there is a complex trade-off between the water-energy F I G U R E 1 Biomass classification nexus and the environment, 10 and discovering the tradeoff between water use, energy consumption, and carbon emissions are crucial. 11 The primary contribution of this research is the use of second-generation (Jatropha, agricultural waste, and animal waste) and the third-generation (microalgae) biomass types as renewable energy sources by considering the interaction of water, energy, and carbon (WEC nexus). According to our best knowledge, the presented model is the first to consider the WEC nexus in this context.
The following are the contributions of this paper in general: (1) Proposing a mathematical model for designing a combined bioenergy network (simultaneous combination of second-and third-generation biomass as a WEC nexus) with sustainability considerations in the model. (2) To design a multiobjective sustainable network, environmental concerns such as carbon emissions are considered in the objective function, and to consider social aspects of the problem, job creation is considered in the objective function. This research is divided into five sections. In Section 2, an up-to-date and systematic literature review of secondgeneration biomass, third-generation biomass, and a combination of two generations is presented. The problem definition and formulation are presented in Section 3. The case study and numerical results are discussed and conducted in Section 4. Finally, conclusions and future research suggestions are described in Section 5.

| LITERATURE REVIEW
In the present study, unprocessed materials such as wheat straw, Jatropha, and microalgae from biomass have been used. In this section, several articles on the fuel supply network and bioenergy field from secondand third-generation biomasses have been reviewed. Finally, a selection of the articles reviewed based on the indicators extracted from the relevant articles is presented in the literature review tables, categorization, and the existing research gaps.

| Second-generation biomass
Given that animal husbandry and agriculture are within the most significant economic activities in Izmir, Turkey, animal waste and agricultural waste as unprocessed materials for biogas production by anaerobic fermentation in a three-tier supply chain considering primary sources, biomass storage, and electricity supply sites is taken into consideration. For this result, a mathematical model is presented, and during the process, a by-product can be produced which can be utilized as fertilizer, which also considers the reverse logistics issue and the return of these fertilizers to the main biomass resources production. 12 Then a two-objective model was presented with the first objective function of cost minimization and the second objective function of carbon dioxide emissions minimization. In the presented study, two processes of anaerobic digestion and gasification are utilized together, and the biogas generated by them is finally converted into electricity in the simultaneous production units of electricity and heat, and fuzzy programming is used to cope with the uncertainty in the problem. 13 An uncertain model for designing a supply network with the same biomass and final product combination was introduced a year later. This model placed great emphasis on different types of uncertainties, and to deal with them, including random, cognitive, and deep uncertainties, a hybrid robust model was used. Technology uncertainty is modeled as inaccurate conversion rates using possible scenarios, uncertainty in biomass access is expressed using fuzzy numbers, and it is assumed that demand changes over a period of time. In addition, the fixed costs of the biorefinery are defined as linear functions in terms of capacity levels. 14 In the same year, the biodiesel supply chain of the Jatropha energy plant was designed, and a two-objective mathematical model (economic and environmental objective function) was proposed using possibilistic programming to cope with uncertainties. The mathematical model presented in the paper was initially nonlinear complex integer programming and has been transformed into the mixed-integer linear model by linearization techniques. A combined method of augmenting ε-constraint and an optimization method has been used to solve the twoobjective model. 15 One year later, the same team of authors designed the biodiesel and glycerin supply chain from Jatropha. The proposed model is a MILP to reduce construction costs, transportation, shortages, and maintenance, and increase carbon and glycerin revenue. The robust optimization method has been used to address the lack of historical information on some parameters, and it is a case study in Iran. SimaPro software is also utilized to calculate the amount of carbon emitted. 16 In connection with the bioethanol supply chain network design, an uncertain model was presented in which different types of second-generation biomass such as switchgrass and agricultural and wood waste were considered. Benders decomposition was used to solve the model. 17 Petridis et al. 18 presented a sustainable multiobjective model for biomass supply chain design focusing on second-generation biomass production, transportation, and storage. This multiobjective model has been solved utilizing the weighted goal programming approach. According to results, weight gain due to environmental function causes a sharp decrease in CO 2 emissions from biomass transport. Economic and environmental functions are in the same direction, and the social goal function moves in the opposite direction, which is one of the results of this article. Ahranjani et al. 19 designed a sustainable multicycle biofuel supply chain network from second-generation biomass by presenting a MILP model. The model uses robust optimization to cope with the uncertainty of some parameters (supply, demand, biomass price, cost, import and export, and social parameters). Sarker et al. 20 Proposed a multistage multifacilitation model with several unprocessed materials for biogas production. Objectives of the problem include purely economic. To solve it, according to the coordinates of the locations of some places (unprocessed material collection centers), a genetic algorithm has been used.

| Third-generation biomass
Mohseni and Pishvaee 21 have developed a model for designing the supply network of biodiesel production from microalgae, and uncertainty in production and transportation costs has been considered. Finally, it has been used to deal with uncertain parameters with deep uncertainty. In the same year, Mohseni et al. 22 Continued the previous work, discussing the competition among customers and distributors and the competition among distributors. A geographic information system (GIS) method was utilized to locate the facility in the developed model. Then, by presenting a network design model, additionally finding network decisions, including the location of facilities and flow between facilities, utilizing game theory and the concept of competition, they have also discussed the pricing of this type of fuel.

| Combination of two generations
Recently Mahjoub and Sahebi 23 proposed a model of a bioenergy supply network of second-generation biomass including Jatropha, agricultural waste, animal waste, and third-generation biomass (i.e., microalgae), taking into account the water-energy relationship and carbon emissions. The model selected the best energy production option considering geographical, climatic conditions and economic goals, energy production, water consumption, and CO 2 emissions. Determining microalgae cultivation sites, location, and the land area allocated for Jatropha planting, agricultural waste and animal waste disposal sites, construction sites of storehouses, and production facilities are some of the choices made by the model.

| WEC nexus
Because of the complexities of the WEC nexus, it has received little attention in the literature. 24 In addition, the bioenergy industry has significant evaluation capacity regarding WEC and greenhouse gas impact. 25 Chhipi et al. 26 presented a WEC model from the standpoints of systems dynamics. Fajardy and Dowell 27 presented a study on CO 2 absorption and storage in the bioenergy industry, along with analyzing the whole supply chain of planting, harvesting, and transformation in dedicated biomass power plants. Zahraee et al. 10 proposed a dynamic simulation model under uncertainty to investigate the WEC nexus in the bioenergy industry. In another study, they also provided a comprehensive review of studies on the water-energy nexus and greenhouse gases. 25 Hiloidhari et al. 28 presented the WEC life cycle for producing sugar, ethanol, and electricity from sugarcane. Recent studies have placed little emphasis on the implementation of the WEC nexus in the bioenergy industry, and some have missed doing so despite investigating this nexus to several important concepts such as sustainability, examining multiple generations of biomass, or demonstrating the multiproduct model as a viable option. Some studies have a multiproduct model, others have a sustainability model, still others have a WEC nexus or examine these three goals without the concept of nexus, still others have presented a study of several generations of biomass, but this study investigated all of the components mentioned above at the same time.
According to the literature review, the gaps observed in the literature are as follows: (1) Ignoring the sustainability aspect of the problem in articles involving a combination of several biomass generations.  Therefore, the classification for the design of biomass supply chain network models can be seen in Table 1. According to the literature, the WEC nexus and the simultaneous analysis of several generations of biomass have received less attention in this biomass industry, and this study addresses the importance of studying this relationship. On the other hand, in this study, related gaps are supported by considering the multigeneration biomass combination, WEC nexus, and sustainability aspects of the problem.

| PROBLEM DEFINITION AND FORMULATION
The goal of this study is to design a sustainable biomass supply network model which includes second-generation biomass (jatropha, wheat straw, and animal waste) and third-generation biomass (microalgae) considering the WEC nexus. The model is capable to select the best energy supply network according to geographical and climatic conditions and considers economic, social, and environmental goals of energy production, water consumption, and carbon emissions. Determining the location of microalgae cultivation, the place, and area of land allocated for planting Jatropha, the location of supply of agricultural waste and animal waste, and the location of the construction of storehouses and production facilities are the decisions that the model makes.
Since geographical factors play an essential role in determining suitable locations for biomass production, to reduce the response space, in determining appropriate locations for growing microalgae and potential points for planting Jatropha, the existing literature of previous research has been used, which is one of the model inputs ( Figure 2).

| Sustainable supply chain
The sustainable supply chain can be investigated in economic, environmental, and social dimensions. 36 The following is a description of each section.

| Economic aspect
Due to the immaturity of bioenergy production technologies and the fact that the biofuels industry is still in its early development stages, 37 biofuels costs (especially second-and third-generation biofuels) is noticeably higher than the conventional fossil fuel prices. In fact, the economical aspect is primarily focused on designing a supply chain that manages the various activities of the supply chain from farms to the production of biofuels in biorefineries and their distribution in a cost-effective manner, to improve the competitiveness of biofuels. Therefore, efficient use of resources and reduction of costs is the main concern of bio-economic supply chains. 5 This research considers the costs of constructing production sites, constructing storehouses, constructing pipelines, storing unprocessed materials, transporting unprocessed materials, and cost of product distribution in the cost objective function.

| Environmental aspect
With population growth and increasing demand for nonrenewable energy sources and their use, environmental pollution is increasing day by day, and the amount of these sources is also decreasing. 38 In this case, the possible alternatives are fossil fuels, lignocellulosic biomass, and microalgae. Biofuels produced from these sources are very suitable for reducing environmental pollution (e.g., The use of these biofuels has the potential to reduce 1983 kg of CO 2 emissions 39 ). This study considers objectives such as reducing water and energy consumption, emissions of CO 2 released during jatropha planting and conversion to biodiesel, CO 2 released during microalgae cultivation and conversion to biodiesel, CO 2 released to generate electricity from waste in anaerobic power plants and CO 2 released During the transport operation in the environmental objective function

| Social aspect
One of the most significant dimensions in the sustainable supply chain is the social dimension. Heidari et al. 5 considered the most important advantage of bioenergy as its social effects and showed that if bioenergy accounts for 23% of the total amount of electricity produced in a developing country, it will result in an annual increase of 79% in employment. In general, measuring social aspects is challenging due to the complex nature of social issues  and only a few studies have focused on designing and planning social metrics to provide biofuels. 40 This research focuses on labor-related issues (number of jobs created) to optimize the social objective function.

| Sources of bioenergy production
As shown in Figure 2, the intended three-echelon supply chain consists of the supply of unprocessed materials, the use of different biomass types (explained below), storage, and production sites.

| Jatropha
Jatropha is an important tropical biofuel product known for its drought resistance. 41 Jatropha seedlings need watering in their first 2 or 3 years and then much less. The maximum height of the Jatropha tree is 3 m, its longevity is 50 years, and it is resistant to salinity. 42 Other characteristics of this plant are as follows [41][42][43][44] : (1) High resistance to pests and diseases.
(2) Opportunities for poor rural areas and help reduce poverty.

| Agriculture and animal waste
The anaerobic digestion process has been utilized to generate energy from plant and animal waste. Anaerobic digestion is the breakdown and fermentation of microorganisms' organic matter without oxygen. This process results in biogas production, which is a combination of methane and CO 2 . 45 In this study, the considered agricultural waste is wheat straw.

| Microalgae
Microalgae have a short growth period, and their biomass almost doubles in about 24 h. Microalgae store large amounts of oil which can be utilized to produce biodiesel. 46 In general, the common stages of fuel production from microalgae are 42 : (1) cultivation and F I G U R E 2 Three-echelon bioenergy supply chain of different biomass types. g s and go s are related to unprocessed material delivering, g J and go J are related to Jatropha delivering, and eg is related to productions (for more detail about symbols see Section 3.4). Biofuel production processes in the refinery Biofuel production processes in the refinery CO 2 emissions through production processes multiplication of microalgae, (2) harvesting and drying, (3) oil extraction, and (4) conversion to biodiesel.

| WEC nexus
Water plays a significant role in energy production, as the water footprint in biomass is 70-400 times more than other primary energy carriers. 47 Also, in the bioenergy industry, the transmission, distribution, collection, water refinery, and reuse processes require an energy system. On the other hand, fossil fuels are the main energy sources, and their production emits significant amounts of CO 2 . 9 To the best of our knowledge, the relationship between water and energy has been studied in various studies, whereas the trade-off between water, energy, and CO 2 has received less attention. 48 Analyzing the relationship between water use, energy consumption, and CO 2 emissions is crucial. 49 In fact, the three components of water, energy, and CO 2 are the most significant factors affecting environmental sustainability. 50 According to Li and Zhao, 51 there are different methods for WEC analysis, including life cycle analysis (LCA), computable general equilibrium (CGE), input-output analysis, system dynamics models, optimization models, and material flow analysis. In this research, optimization models have been used.
Defining the system boundaries is the first step in analyzing the WEC nexus because the definition of boundaries can more precisely influence the characteristics of the WEC nexus and the outcomes of the relevant evaluation. 51 Figure 3 indicates the general boundaries of the WEC nexus in the bioenergy industry, while Table 2 shows the system boundaries in more detail. In fact, Table 2 shows water consumption for energy production, energy consumption for water-related matters, and consequently CO 2 emissions. Cost of production of each unit of electricity at production location p in period t EXP pt A Cost of production of each unit of microalgae-based biodiesel in production location p in period t EXP pt J Cost of production of each unit of Jatropha-based biodiesel at production location p in period t EXPJ st Cost of production of each unit of Jatropha at location s in period t e pt n Cost of each unit of nitrogen supplied from the market to production location p in period t e pt p Cost of each unit of phosphorus supplied from the marketplace to production location p in period t TE pt S Product distribution cost of each unit of electricity at production location p in period t  distribution at production location p in period t coe pt A CO 2 emissions related to product (microalgae) distribution at production location p in period t coe pt J CO 2 emissions related to product (jatropha) distribution at production location p in period t coe sk S CO 2 emissions for biomass unit delivered from source s to storehouse k by truck (waste) coe kp S CO 2 emissions for biomass unit delivered from storehouse k to production location p by truck (waste) coe sk J CO 2 emissions for biomass unit delivered from source s to storehouse k by truck (Jatropha) coe kp J CO 2 emissions for biomass unit delivered from storehouse k to production location p by truck (Jatropha) coe A CO 2 emissions for biodiesel produced unit from microalgae coe J CO 2 emissions for Jatropha land unit coe S CO 2 emissions for electricity generated unit in biogas plant wrf st Minimum rainfall needed for Jatropha cultivation in location s in period t wrf ′ st Quantity of rainfall in location s in period t enw J Energy needed for irrigation of Jatropha lands for water unit enw A Energy needed for transfer water to microalgae pools and circulate it for unit of pool area enw S Energy needed for continuous mixing and stirring of water and biomass within the anaerobic digester for generated electricity unit μ st Yield rate of the land in site s for Jatropha cultivation in period t As mentioned, the model has five objective functions. The first objective function (1) maximizes the total energy produced, including electricity generated, biodiesel energy produced from microalgae, and biodiesel energy produced from Jatropha.

  
The second objective function (4) minimizes the total water consumed, including water used in Jatropha planting lands, regulation of anaerobic digestion biomass concentration, and microalgae cultivation.
The third objective function (5) minimizes the total CO 2 emitted, including the amount of gas emitted during Jatropha cultivation and conversion to biodiesel, during microalgae cultivation and conversion to biodiesel, and during electricity generation from waste in anaerobic power plants. The next four terms of the environmental objective function represent the CO 2 emitted when transporting unprocessed materials from storehouses and then from storehouses to production sites using trucks and also product distributions at production locations in related periods. The link between CO 2 emissions and energy consumption in the form of diesel used by each truck between the two nodes (ψ) is given here. 52 The fourth objective function (6) maximizes the number of jobs created, including those created during the Jatropha cultivation and conversion to biodiesel, during microalgae cultivation and conversion to biodiesel, and during electricity generation from waste in anaerobic power plants. The following four terms of the social objective function represents the number of jobs created during transporting unprocessed materials from resources to storehouses and then from storehouses to production sites using trucks.
The fifth objective function (7) minimizes the present value of total costs over all time periods. To evaluate the present value of cost, α 1 (1 + ) t−1 has been used in which t is the period and α is the discount rate. All terms of this objective function are defined.
TIC presents the fixed investment cost that includes the cost of constructing production sites, constructing storehouses, constructing pipelines for the transfer of algae cultivation resources, and investing in the cost of planting Jatropha (8). TPC t shows the production cost of final products (electricity and biodiesel) and the Jatropha production cost in each period (9). THC t shows the storing unprocessed materials cost in storage during period t (10). TSC t shows the supplying unprocessed materials cost in each period (11). TTC t shows the transporting cost of unprocessed materials and the cost of product distribution from resources to the storehouse and then from the storehouse to the production sites by truck or transporting some unprocessed materials in the pipeline to the production sites (12). TFC t is the annual fixed cost as a proportion of initial investment (13 Equations (14)- (16) indicate the unprocessed material supply source capacities. Equation (14) shows the quantity of chicken excreta, cow excreta, and wheat straw in supply areas in each period. Equation (15) relates to the microalgae biomass capacity cultivation sources, including the quantity of saline water, raw water, wastewater, and CO 2 from energy plants in each period. Equation (17) indicates the land area available for Jatropha cultivation.
s s (16) Equations (17)- (19) related to storehouse storage capacity. Equations (18) and (19) indicate the capacity of the storehouses to hold the waste resources and the capacity of the Jatropha storehouses, respectively, to ensure that the total input flow to the storehouse in each period and remaining inventory from the previous period must be less than or equal to the storehouse capacity. Equation (20) states that among the sources of cow excreta, chicken excreta, and straw, it is possible to keep more than one period only for straw, and the other two substances should be utilized within the same period relevant to putrescence.
Equations (20) and (21) refer to the balance of input and output flows of the holding storehouse. These equations ensure in each period, the total input flow to the storehouse and the remaining inventory from the previous period should be similar to the sum of the output flow and inventory remaining at the end of the period.
Equations (26)-(28) refer to anaerobic digester processes. Equations (27) and (28) demonstrate the composition ratio of unprocessed materials in an anaerobic digester: one ratio of chicken excreta, one ratio of straw, and three ratios of cow excreta. Equation (28) indicates the appropriate mixture concentration of substances in an anaerobic digester.
Equations (29)- (31) relate to the amount of energy produced. Equation (30) indicates the amount of electricity generated in the biogas plant, Equation (31) indicates the amount of biodiesel produced from algae, and Equation (32) indicates the amount of biodiesel produced from Jatropha.
Equations (32)-(37) refer to microalgae production conditions. Equation (32) shows that the water supply required for microalgae production makes it viable to use only one of the two types of raw or saline water. 21 Equation (33) shows the water supply required for algae cultivation, which can be provided from raw water, saline, or wastewater. Equations (34) and (35) indicate the supply of phosphorus and nitrogen required for microalgae cultivation, respectively, obtained from wastewater or can be bought from local markets. Equation (36) is similarly relevant to the supply of carbon dioxide required from power plants. Equation (37) indicates the amount of raw water used to cultivate microalgae.
Equations (38) and (39) refer to Jatropha production conditions. Equation (38) demonstrates the amount of Jatropha cultivated in each period, and Equation (39) demonstrates the amount of water required to irrigate Jatropha fields.
Equations (40)- (45) show that every facility can have a maximum one capacity level.

| MINMAX goal programming approach
There are generally three methods for multiobjective optimization in the literature. These methods include priori, interactive and posteriori approaches. Goal programming, which is one of the priori methods that was first proposed in the application of single-objective linear programming problem by Charnes et al. 53 For this purpose, the goal programming method has been used to solve the proposed model. In priori methods, the decision-maker determines expectations and preferences in advance. The basic idea of goal planning is to find answers that meet pre-determined aspirations for one or more goals. Otherwise, in the absence of any solution to the stated conditions, looking for solutions that minimize deviation from aspirations is essential. Target functions may have different scales, so normalization is needed.
One of the normalized models is the MINMAX goal programming model or Chebyshev, which is as follows 54 : In the MINMAX model, the goal is to minimize the maximum amount of deviation from the aspiration. The value of k i , which is added to equalize the scale of objective functions, is defined as It should be noted that the MINMAX approach satisfies all goals, and so the decision point is the closest to positive ideal solutions. 55 Goal programming solutions are regarded as good feasible compromises and viable solutions instead of true optimal solutions. 56 The variation of the presented approach differs from other goal programming variants such as weighted goal programming or lexicographic goal programming in that it assists in identifying balanced solutions between the target functions rather than extreme solutions. Moreover, the Chebyshev variant can assist goal programming solutions in avoiding extreme values of high-priority objective functions. 57 On the other hand, considering predetermined aspiration levels allows the decision-makers to make a choice without weighing all the alternatives. It should be considered that obtaining the necessary knowledge may conflict with goals such as making a quick decision, in which case using pre-determined aspiration levels can be extremely beneficial. 58

| Model parameters values
The WEC nexus parameters are listed in Table 3, and the production conditions parameters are listed in Table 4. According to Table 5, four capacity levels are assumed for biodiesel power plants from Jatropha, biodiesel production from microalgae, anaerobic digestion, and power generation capacity in biogas plants. Finally, economic parameters relevant to energy production from Jatropha have been extracted from Babazadeh and colleagues, 15,44,64 economic parameters relevant to energy production from microalgae from Mohseni and Pishvaee, 21,22 economic parameters relevant to energy production from agricultural and livestock waste from Maleki-Ghelichi and colleagues, 66,67 and social parameters relevant to the job from Heidari et al. 5 4 | CASE STUDY AND NUMERICAL RESULTS

| Case study
In this study, a model for designing a bioenergy supply chain network of different types of second-generation biomasses (i.e., Jatropha, wheat straw, and animal waste) and thirdgeneration biomasses (i.e., microalgae) with WEC nexus is developed (Figure 2). The main purpose of this study is to find suitable biomass for cultivation and harvesting in Iran. Candidate locations for production sites of all three types of biomasses are presented in Figure 4. 22,64 Since all Iranian provinces cultivate wheat and raise cattle and chicken, all of them are recognized as potential locations for the construction of biogas power plants (Figure 4). Iran's Ministry of Agriculture website provides data on annual wheat cultivation, poultry, and cattle numbers in Iran's provinces.

| Numerical results
The formulated model has been solved by the GAMS 24.1.2 software using a COREi7 PC with 8 GB RAM. The target values, the weights associated with deviation from the target values, and the results are presented in Table 6.
Regarding population growth and increase in energy demand, 40 the energy objective function is the most significant with the highest deviation weight. The cost, CO 2 emission, and water consumption objective function with same-weight stand second, and the job creation objective function stand third. Based on the model results, 1 GJ energy will cost $16.73, absorb 35.80 kg of CO 2, consume 8.48 m 3 of water and create 0.01 jobs. After the breakdown of the cost objective function, the highest costs of the bioenergy industry are production and F I G U R E 4 Candidate locations for biogas power plants, biodiesel production site from Jatropha, and biodiesel production site from microalgae investment costs, respectively, and fixed annual costs are in third place ( Figure 5). Optimal biomass production sites are shown in Figure 6. It can be seen that seven provinces have been selected as optimal places for constructing biodiesel production sites from Jatropha. Based on the results, no biodiesel production site from microalgae and no biogas plants (wheat straw and animal waste productions sites) are constructed for three reasons: (1) As shown in Table 4, Each kilogram of Jatropha, microalgae (the product of these two types of biomasses is biodiesel), animal waste, and wheat straw (the product is electricity) produces 0.0425, 0.0412, and 0.0036 gigajoules of energy, respectively. On the other hand, each one gigajoule of energy is approximately equivalent to 0.277-MWh. At first, the amount of energy in gigajoules is converted to megawatt hours. For instance, for Jatropha, the product of 0.425 × 0.277 is 0.0118-MWh, and similarly, 0.0114 and 0.001 are obtained for algae, animal waste, and wheat straw. Now, dividing the value of 0.0118 × 0.001 yields 11.8, and dividing the value of 0.0114 × 0.001 yields 11.4, which indicates that Jatropha is more cost-effective. (2) The amount of net CO 2 emissions during Jatropha production, considering the supply chain structure in this paper, is lower than wheat straw and animal waste. Several studies 23,59,62,68,69 have also emphasized the priority of Jatropha and (3) not only is Jatropha socially and economically superior to microalgae, but it also has an advantage in terms of water and energy consumption. From a social perspective, considering that for Jatropha F I G U R E 5 Cost objective function breakdown F I G U R E 6 Production sites built in different provinces based on the developed model there are agricultural lands, transportation, and storage, and each part requires manpower, but for algae biomass, there is only pipeline transportation, and the number of jobs created for Jatropha biomass is 4,048,517, and for microalgae, it is nearly 337,000. The total cost of microalgae biomass is $21,320,000, while jatropha biomass costs $5,330,000. Therefore, from an economic point of view, jatropha is superior to algae. Several studies 70,71 have also emphasized the priority of Jatropha.

| Sensitivity analysis
To investigate the trade-off between the water consumption and energy production objective functions, a constant value of 0.5 was assumed for the sum of the weights relevant to them (see Table 6), and other weights associated with the CO 2 emission, cost, and job objective functions' deviations from target values kept constant. Afterward, the weight of the water and energy objective functions were modified in the range of 0.05-0.45 at 0.05 intervals, and their values were determined. It is important to note that the ordered pair corresponding to each point displays the objective function deviation weights, where the first value belongs to the water consumption objective function and the second value belongs to the energy production objective function. As seen in Figure 7, a reduction in the weight of the water objective function and an increase in the weight of the energy objective function will lead to an increase in both objective function values. In conclusion, the diagram shows the trade-off between these two objective functions in such a way that more energy is produced along with increased water consumption (because with the decrease of the water function importance and the increase of the energy function importance, the model decides to produce more energy, and the water consumption also increases). Likewise, to investigate the trade-off between energy production and CO 2 emission objective functions, a constant value of 0.5 was assumed for the sum of the objective functions' weights. Finally, the weight of energy production and CO 2 emission objective functions were modified in the range of 0.05-0.45 at 0.5 intervals. Each point displays the objective function deviation weights, where the first value belongs to the CO 2 emission objective function and the second value belongs to the energy production objective function. As seen in Figure 8, a reduction in the weight of the CO 2 emission objective function and an increase in the weight of the energy objective function will cause an increase in both objective function values.
In conclusion, the diagram shows the trade-off between these two objective functions in such a way that more energy is produced along with increased CO 2 absorption.
Likewise, to investigate the trade-off between the cost and energy production objective functions as well as job and cost objective functions, as shown in Figures 9  and 10, values of 0.5 and 0.3 were assumed to be constant for the sum of the objective functions' weights, F I G U R E 7 Water consumption and energy production objective functions trade-off F I G U R E 8 CO 2 emission and energy production objective functions trade-off F I G U R E 9 Cost and energy production objective functions trade-off respectively. The weights of objective functions were modified at 0.05 intervals, and their value was determined. In Figures 9 and 10, the first point value belongs to the cost objective function, and the second value belongs to the energy production and job objective function, respectively. As seen in Figure 9, an increase in the weight of energy objective functions and a reduction in the weight of the cost objective function will lead to an increase in both objective functions. In Figure 10, an increase in the weight of the job objective function and a reduction in the weight of the cost objective function will cause an increase in both objective functions. Actually, improving job objective function increases the cost of the supply chain. Finally, Figure 11 shows the trade-off between cost and CO 2 emission. To reduce the environmental impact of all biodiesel supply chain network processes, more costs must be incurred and also Babazadeh 72 demonstrate this.
For analyzing the parameters' effects on the objective functions, the parameters of each category were calculated with an increase of 5-30%. The model was solved for each parameter change case, and hybrid diagrams are presented after reporting each objective function's results. Parameter changes' effect is reported simultaneously for the energy and cost objective functions, and by comparing these two objective functions, the decisionmaker can reach a more informed conclusion. Figure 12A-D shows the trend of changes in energy and cost objective functions with changes in variable cost, investment cost, conversion rate, and sources capacity. All diagrams demonstrate the appropriate behavior of the model. In Figure 12A,B, an increase in the variable cost and investment cost parameters causes an incremental trend in the total cost objective function. For example, a 10% increase in the variable cost and investment cost parameters causes a 5.12% and 2.34% increase in total cost, respectively. Figure 12C shows the change in the trend of total cost and energy production in the face of an increase in the conversion rate parameter (assuming that it is technologically possible to increase the conversion rate of biomass to energy). Conversion of raw materials into biofuels is one of the most significant steps in the bioenergy supply chain, which usually occurs in biorefinery. 74 As expected, a higher conversion rate increases the amount of energy produced. On the other hand, improvement in the conversion process has reduced costs; for example, a 5% increase in conversion rate causes a 4% reduction in total cost. In Figure 12D, an increase in the value of the capacity parameter up to 20% has reduced costs but has remained constant after this point. These changes also indicate the correct behavior of the model and can have two reasons: (1) the model uses cheaper sources until it reaches the amount of energy required to produce and, (2) increasing the capacity of sources will be usable as long as the capacity of other facilities responds to this increase, it means that the facility's capacity may not be sufficient to use the additional sources after a specific point.
Decision-makers commonly need a single solution, and the Pareto front is helpful in assisting individuals in selecting the preferred solution. 73 Since multiobjective optimization problems are being investigated, the concept of Pareto has been utilized so that the decisionmaker can finally choose the best decision based on the objective and Pareto charts. Due to the importance of economic and environmental issues in the bioenergy industry, Pareto analyzes have been done 2 × 2 between the goals of water, energy, cost, and carbon ( Figure 13).
To evaluate the performance of the model presented in this study under the assumption of a 10-period and a 10-year time horizon, the cost of this model is compared to the cost of a classical model without considering the WEC nexus in its objective function. After solving the model, the proposed model's costs in all periods are lower than the classical model (see Figure 14). The cost in the y-axis includes production, investment, fixed annual, transportation, and purchasing costs. Another reason for the importance of examining the proposed model compared to the classical model is a comparison of these two models in terms of energy production and water consumption. According to the results, the difference between the two models can be seen not only in costs but also in water consumption and energy production. In the proposed model, there was a 25.6%, 28.4%, and 25.1% improvement in water consumption, energy production, and CO 2 emissions, respectively, which was followed by a 22.3% reduction in costs.
The insights obtained from this study demonstrate the utility and effectiveness of the proposed approach in assisting policymakers in making appropriate strategic and tactical decisions regarding bioenergy supply chain F I G U R E 12 Trend of changes in energy and cost objective functions with changes in (A) variable cost, (B) investment cost, (C) conversion rate, and (D) sources capacity management. To achieve optimal solutions in optimizing the biofuel supply chain, all supply chain echelons should be considered and evaluated in multiperiod conditions. Besides, results show that Jatropha has a high potential for solving crises related to climate change, global warming, and population growth, which is one of the primary concerns of policymakers. In addition to economic factors, the echelons of the supply chain should be investigated through significant environmental and social aspects. Furthermore, this study considered several types of biomasses, including animal waste, wheat straw, Jatropha, and microalgae. Finally, it should be noted that the structure proposed in this article can be used to optimize the design of the different biodiesel supply chain networks.

| CONCLUSIONS
This research considers the sustainable development concept in biomass supply chain network design with a combination of second-generation and third-generation biomass. For increasing the model flexibility, a threeechelon model was proposed. Then, by adding the concepts of the WEC nexus, a developed model with five objective functions is presented, which can be used in future research. Finally, the mathematical model with the MINMAX goal programming method has been solved by GAMS Win64 24.1.2 software for the provinces of Iran as a case study. After solving the model, the obtained results led to the Jatropha construction in seven provinces of Iran to generate energy.
The achievements of this research, which distinguishes it from other studies in the area of hybrid biomass supply chain, can be summarized as follows: (1) Present a model for developing a biomass supply chain network by proposing a combination of second-and third-generation biomass as an energy source with the objectives of maximizing the total energy produced and the number of jobs created and minimizing the total water consumed, CO 2 emitted, and total costs. (2) Promote a sustainable network design of a hybrid biomass supply chain model by incorporating the WEC nexus. (3) Considering CO 2 emission and related nexuses due to environmental problems and considering water consumption and job creation and related nexuses due to the problem of water shortage and employment situation in the country.
Some managerial and future research suggestions are described below: (1) Allocate more budget and investment to expand power plants and employment. (2) Addressing the issue of water consumption in the supply chain, as well as the substitution of salt water or wastewater instead of fresh water. (3) Utilizing approaches such as systems dynamics and life cycle analysis to consider the concept of reverse logistics or closed-loop supply chain, as well as the concept of the WEC nexus. (4) Studying uncertainties in parameters such as capacities, conversion rates, number of jobs created, CO 2 emissions, and related costs. (5) Considering a more comprehensive combination of biomass types and conversion processes to increase the model's flexibility in selecting the most appropriate energy source under geographical conditions and other facilities. (6) Addressing international logistics issues such as importing equipment and unprocessed materials and exporting products and prioritizing the areas with more rainfall for Jatropha's growth.