A Multi-Objective Approach toward Optimal Design of Sustainable Integrated Biodiesel/Diesel Supply Chain Based on First- and Second-Generation Feedstock with Solid Waste Use

: This study proposes a multi-objective approach for the optimal design of a sustainable Integrated Biodiesel/Diesel Supply Chain (IBDSC) based on first- (sunflower and rapeseed) and sec-ond-generation (waste cooking oil and animal fat) feedstocks with solid waste use. It includes mixed-integer linear programming (MILP) models of the economic, environmental and social impact of IBDSC, and respective criteria defined in terms of costs. The purpose is to obtain the optimal number, sizes and locations of bio-refineries and solid waste plants; the areas and amounts of feedstocks needed for biodiesel production; and the transportation mode. The approach is applied on a real case study in which the territory of Bulgaria with its 27 districts is considered. Optimization problems are formulated for a 5-year period using either environmental or economic criteria and the remainder are defined as constraints. The obtained results show that in the case of the economic criterion, 14% of the agricultural land should be used for sunflower and 2% for rapeseed cultivation, while for the environmental case, 12% should be used for rapeseed and 3% for sunflower. In this case, the price of biodiesel is 14% higher, and the generated pollutants are 6.6% lower. The optimal transport for both cases is rail.


Introduction
The global trend for energy consumption shows a steady increase until 2030, with liquid fuels accounting for the largest share of fuel demand in the transport sector. Biodiesel is one of the most commercially available biofuels, which has many advantages, such as reducing harmful emissions of SOx, CO, CO2, soot and NOx [1], a higher cetane number, improved engine performance, increased power, and reduced fuel consumption, as well as the production of glycerol as a by-product, which is applicable in medicine, cosmetics and others [2]. The biodiesel production has resulted in the adoption of Directive 2003/30/EC on the promotion of the use of biofuels for transport, which aims to gradually integrate biofuels into diesel and petrol fuels in the countries of the European Union [3]. However, the high production costs of biodiesel are one of the main drawbacks to achieving the commercial viability of biodiesel. This is due to the price of used feedstock, which accounts for 70-95% of the total production costs. modern communication technologies provide a large number of opportunities to improve SC efficiency. Therefore, the integrated overall optimization of operations and activities throughout the enterprise is key to the competitiveness of a company [16]. To this end, an approach for optimal design of integrated biodiesel/diesel supply chain using first generation feedstock was developed [17].
However, full sustainability can be achieved by taking into account the three aspects of sustainability-economic, environmental and social sustainability [18]. The main issues related to achieving environmental sustainability are reducing greenhouse gas emissions, improving the quality of water resources, reducing soil degradation and biodiversity loss [19]. The main aspects of economic sustainability are related to the price of the biofuel produced, achieving energy balance by reducing energy for production [20], and increasing budget programs to stimulate biofuel production [21]. Some of the issues involved in the concept of social sustainability are related to reduction: such as poverty [22], indirect effects on soil and plants [23], and the impact on social resources, such as water supply systems.
Many of the studies in the available literature related to the production of biodiesel from various feedstocks are related to the investigation of some of the economic and technical parameters of the process and how they affect the performance of the engine in terms of fuel consumption, ignition and reduction of CO, HC and NOx. Some studies are related to the investigation of the process parameters that affect the yield of biodiesel. There are studies that are based on the optimization of all activities across the network or the optimal design of biodiesel supply chains using only of one feedstock, where economic environmental and/or social criteria are taken into consideration. There are no approaches for the design of integrated biodiesel/diesel supply chain using different feedstocks and while accounting for all aspects of sustainability.
This study proposes an approach for the optimal design of an IBDSC based on 1G and 2G feedstocks with solid waste use. Sunflower and rapeseed are used as 1G feedstocks, while the 2G feedstocks used are waste cooking oil, animal fats and sunflower husk. The approach is applied in the territory of Bulgaria and its corresponding 27 districts. The approach includes mathematical models of the economic, environmental and social impact of considered supply chain which are defined in terms of mixed integer linear programming (MILP). The aim is to develop a strategy, methods and software for optimal use of resources in the biodiesel production. The approach applies the principle of life cycle analysis, which considers all stages of biodiesel production. The latter includes feedstock cultivation, transport of feedstocks to the plant, production of biodiesel, and its transport to the blending centers. Three optimization criteria are defined-economic, environmental and social-in terms of costs. The economic criterion is related to the price of the produced biodiesel, the environmental criterion is related to the amount of greenhouse gas emissions generated during SC operation, and the social criterion determines the number of new jobs related to the design and operation of the considered SC. Optimization problems are formulated and solved for one criterion at a time-economic or environmental-while the others, including the social one, are defined as constraints.

Problem Description
The proposed approach is developed in order to plan the activities in an integrated biodiesel/diesel supply chain using as feedstocks cereals such as sunflower, rapeseed and others within a 5-year horizon, including government regulations, production, construction and a carbon tax. The supply chain includes a set of collection sites and a set of search areas, as well as potential locations for individual facilities and biorefineries as the feed materials are transported to biorefineries for further processing. Data about the costs of cultivation and harvesting energy crops are available. For each potential collection facility, the fixed and variable costs of building the facilities are defined, as well as the production costs and the capacity for each potential biorefinery. For each search area, the respective biofuel is defined, as well as its environmental impact. For each transport connection, the transport capacity, the available transport modes, the transport costs per unit distance, as well as the transport distances and emissions for each type of transport are defined.
The superstructure of IBDSC represented in Figure 1 includes the following: 1. A set of biomass production areas where different types of feedstocks are used for biorefineries. 2. A set of adopted initiatives for the implementation of plants for the production of biodiesel with different capacities. 3. A set of blending and sales areas where final products meeting certain requirements are sold. 4. A set of existing refineries for petroleum diesel fuel. The aim is to determine the number, location and the capacity of biodiesel refineries, as well as the bioresources to be transported between the different sites of designed supply chain with minimal costs while satisfying product demand constraints. It is planned that the biodiesel refineries will operate in the determined time interval with the possibility of upgrades related to increasing the production capacity.
The 5-year planning horizon H is divided into a set of discrete time intervals t. This time interval is divided into several equal time intervals = {0,1,2, … , }, each of which lasts ∇ . Within the planning horizon, it is assumed that diesel consumption will change by an estimated value. At the same time, it is assumed that the annual growth of biodiesel consumption is known, in order to meet the requirements of the directives adopted by the government.
Generally, the problem for each time interval t is to determine: 1. Potential locations of the centers for realization of biofuels; 2. Diesel demand for each of the fuel search centers; 3. Relevant requirements for the percentage of biodiesel as a constituent of diesel fuel during the considered period of time; 4. Types of biomass and their geographical availability; 5. Costs for the cultivation of a unit of biomass for each type of raw material; 6. Unit cost of biodiesel according to the type of raw material; 7. Characteristics of the transport logistics (costs, modes); 8. Capital investment costs of biodiesel production facilities; 9. Specific emission factors of greenhouse gases during the life cycle stages of biodiesel production; 10. Carbon tax; 11. Government incentives for the production and the use of biodiesel.
The aim of the study is to find values of variables that optimize the economic, environmental and social performance of IBDSC in the interval t of the time horizon H: 1. Supply chain (SC) structure; 2. Time for biomass cultivation for each type of biomass and biodiesel production; 3. Locations of biodiesel production facilities and locations of biomass cultivation sites; 4. Biomass and biodiesel flows of each type between regions; 5. Type of transport for the supply of biomass, biodiesel and petroleum diesel; 6. GHG emissions at each stage of the life cycle of the products; 7. Amounts transported for each transport connection and transport mode; 8. Strategy for biomass supply of the production facilities; 9. Processes of distribution of biofuels and diesel fuel, delivered in the demand areas.

Formulation of the Optimization Problem
The optimal design of IBDSC is related to solving three key problems, namely finding: (1) the number, sizes and locations of biorefineries and solid waste plants; (2) the sites and amount of 1G feedstocks and 2G feedstocks; (3) the transportation plans of 1G and 2G feedstocks, solid waste, fossil diesel, glycerin and biodiesel.
This leads to the formulation and solution of optimization problems in terms of Mixed Integer Linear Programming (MILP). The problems involve mathematical models for description of economic, environmental and social performance of the IBDSC, economic, environmental and social optimization criteria and constraints. The social criterion is related to the equality of work, health and safety. It depends on government policies and cultural norms as well as input parameters, decision variables, sets, subsets and indices (Appendix A). At first, the set of time intervals on the planning horizon is defined = {0,1,2, … , }. The index t indicates the variable or parameter corresponding to the t-th scheduling interval.

Mathematical Modeling of the Environmental Impact Performance of IBDSC
The environmental impact of IBDSC is assessed on the basis of total annual GHG emissions, such as carbon dioxide (CO ), methane (CH ) and nitrogen oxide (NO ), resulting from supply chain activities. The greenhouse gases are grouped in a common indicator in terms of equivalent carbon dioxide emissions [CO eq./ y] using their respective global warming potentials (GWPs) based on the recommendation of the Intergovernmental Panel on Climate Change (IPCC, 2007) [23] for a 100-year time horizon as follows: 1 for CO , 25 for CH and 298 for NO . The total GHG emissions are converted into carbon credits [kg . ] multiplied by the price of carbon on the market. A Life Cycle Analysis (LCA) approach was applied to assess the overall impact of IBDSC, which takes into account the following stages of the life cycle of liquid fuels for transport based on biomass: 1. Stage of biomass production. This consists of different sub-stages depending on the type of bioresource and subsequent use. 2. Stage of biomass transportation. This refers to the delivery of biomass to the processing facility. 3. Stage of biomass conversion into biodiesel. 4. Stage of transportation of biodiesel (B100) and petroleum diesel fuel to blending areas for diesel fuel and customers. 5. Stage of final biofuel consumption-a stage in which the biofuel is introduced into the engine of the vehicle and is burned to provide mechanical energy for mobility.
The environmental criterion represents the total environmental impact during the operation of the IBDSC through the resulting GHG emissions at each time interval ∈ . These emissions are equal to the sum of the environmental impacts of each stage of the life cycle. GHG emissions are usually determined as follows for each time interval ∈ : • Environmental impact of biomass cultivation , kg . d GHG emissions as a result of biomass production depend on the specifics of the crops grown as well as the geographical region in which the biomass is cultivated [24]. In particular, the environmental impact is influenced by the use of fertilizers and pesticides, the type of irrigation techniques used, and soil characteristics. It has different values for different production areas. The stage of biomass cultivation can be defined as follows: where is the total environmental impact of the biomass cultivation, which represents the rate of production of bioresource ∈ in region ∈ , kg . d .

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Environmental impact of biodiesel production , kg . d The environmental impact of the biodiesel (B100) production stage is related to the feedstocks and biodiesel production technology used. GHG emissions related to this stage will be assumed in proportion to the specific amount of biomass in the biodiesel production: where, = ∈ , ∀ , ∀ ∈ = ∈ , ∀ ℎ , ∀ ∈ where is the overall environmental impact of biodiesel (В100) production kg . d .

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Environmental impact of petroleum diesel production , where is the environmental impact of petroleum diesel production, kg . d .

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Environmental impact of transportation , kg . d The environmental impact of both biomass supply and fuel distribution depends on the type of the used vehicles. The resulting GHG emissions depend on both the distance and payload capacity of the used vehicles. As a result, the emission factor represents the corresponding carbon dioxide emissions: where is the environmental impact of transportation of all resources, kg . d = ∈ ∈ ∈ ∈ + ∈ ∈ ∈ ∈ , ∀ is the environmental impact of biomass and WCO transportation is the environmental impact of biodiesel (B100) transportation from areas ∈ to ∈ ; is the environmental impact of petroleum diesel transportation from areas ∈ to ∈ . = ∈ , ∀ ∈ ∈ is the environmental impact of solid waste transportation from areas ∈ to ∈ , [kg_{CO eq} d ]; is the environmental impact of straw transportation from areas ∈ to ∈ , kg . d ; is the environmental impact of the transportation of sunflower/rapeseed to provide food security from the areas ∈ to ∈ , kg . d . where are the GHG emissions that should have been generated if part of the solid waste had not been treated in the areas determined for this purpose, kg . d , is the amount of solid waste generated during the operation of each of the plants ∈ for the time interval ∈ , and is the amount of solid waste generated by ∈ that is processed in all plants ∈ .
= ∈ ∈ ∈ ∈ , ∀ , = ∈ ∈ , ∀ represents GHG emissions generated by solid waste use when it takes place at one of the plants ∈ and it is determined as follows: where are GHG emissions related to straw use, kg . d .
• Environmental impact of the use of biodiesel (B100) and petroleum diesel during transportation , are the GHG emissions from the use of biodiesel (B100) and petroleum diesel in vehicles, kg . d .

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Environmental impact of WCO use if not used for biodiesel (В100) production , kg . d where are the GHG emissions released during the WCO use in case it is not used for biodiesel (В100) production, kg . d .

Mathematical Modeling of Economic Performance of IBDSC
The economic assessment of IBDSC includes all types of costs related to its operation. Annual operating costs include biomass acquisition costs, local final product costs, final product production costs and transportation costs for the biomass and final products. The production costs take into account both the fixed annual operating costs, which are given as a percentage of the total capital investment concerned, and the net variable price, which is proportional to the amount to be processed. For transportation costs, both the fixed distances and distances with variable costs are taken into account. The economic assessments are the costs related to the plant, which include the total investment costs for biodiesel production capacity (B100) and the operation of the IBDSC. They are expressed as follows for each time interval [25] ∈ : where Government incentives for biodiesel production and consumption (B100), Total value of by-products (glycerol, cake), [$ y ]; Price of the unused portion of WCO in the production of biodiesel (B100), which is considered to be a penalty function. (This unused portion of the WCO is considered to be a pollutant, the amount of which should be minimized).

Investment costs for biorefineries , [$ y ]
The planning of the design of the facilities at IBDSC is carried out for a certain time period, ensuring that after their creation, they will work during the remaining period: where is the discount factor defined by [26], which is calculated as follows: where is the interest rate [%] for the time interval ∈ . The refinery's capital costs consist of fixed and variable costs. Fixed capital costs vary depending on the location of the refineries. The variable capital value of plants from biomass to biodiesel (В100) is mainly influenced by the size of the plantations. Variable capital costs are scaled using a common relationship [27]: where pt CostB is a variable capital cost and is the investment costs and production capacity of new plant, is the known investment costs for a certain pland capacity , and is the scaling factor varying usually between 0.6 and 0.8.
The capital costs of the biorefinery for each region are determined by the following equation: where is the correction factor in the price of biorefineries in the region ∈ according to the built biorafineries ≥ 1.
• Investment costs for solid waste use plants , [$ y ] The total value of solid waste processing facilities is determined as follows: and is the correction factor in the price of the solid waste plant in the region ∈ according to the built solid waste plants ≥ 1. •

Total production costs of IBDSC , [$ y ]
Total production costs include the costs of biomass cultivation (sunflower/rapeseed) , costs for used WCO , costs for biodiesel (B100) production ( , ), production costs for petroleum diesel for each time interval ∈ as follows: where = + ∈ ∈ , ∀ ; Total costs of solid waste processing ,[$ y ] The total costs of solid waste use are calculated as follows: Only one of the sizes ∈ can be selected for the region ∈ (this is provided by satisfying the system of inequalities ∑ ≤ 1.0 ∀ , ∈ ), and is "0" for all sizes except the selected one ∈ . This is provided by satisfying inequalities ≥ , ∀ , , , , where is a large enough number. is the total amount of solid waste [$ y ], which are generated by each biorefinery ∈ , and is the total amount of solid waste that is treated in each of the plants ∈ : •

Total transportation costs , [$ y ]
The transportation, supply of biomass to processing plants as well as the distribution and transportation of biodiesel (B100) to blending facilities are treated as an ancillary service, provided by those already working within the industrial/transport infrastructure. As a result, is calculated as follows: where = ∈ ∈ ∈ ∈ , ∀ are the transportation costs of energy crops (sunflower and rapeseed) for the biodiesel (B100) production, are the transportation costs of WCO for the biodiesel (B100) production, where ( , ) are fixed or variable costs for transportation of biomass of type ∈ , , are fixed or variable costs for transportation of WCO of type ∈ , ( , ) are fixed or variable costs for transportation of biodiesel (B100), and ( , ) are fixed or variable costs for transportation of petroleum diesel, and ( , ) are fixed or variable costs for transportation of solid waste, and ( , ) are fixed or variable costs for transportation of straw, and are fixed or variable costs for transportation of biomass of type ∈ . The costs of biomass transportation are described in [28], using tractor, truck and train as vehicles . These include fixed costs ( , ) and variable costs ( , ). Fixed costs include loading and unloading costs. They do not depend on the transportation distance. Variable costs include fuel costs, vehicle maintenance costs, driver salary, etc. They depend on the transportation distance [27].
Many countries have different mechanisms in place to reduce GHG emissions by imposing a carbon tax or government incentives to produce biofuels. Carbon taxes and carbon markets (emissions trading) are recognized as the most cost-effective mechanisms. The main idea is to set a price value for carbon emissions and to create new investment opportunities to generate a fund for the development of green technologies. There are several active markets for carbon trading [29].
The introduced carbon tax is determined as follows: is the IBDSC operating period for one year, [d/y].
The total emissions are converted into carbon credits by multiplying by the carbon price C on the market, where it has a value 0.149 $/kg .

Government incentives costs for biodiesel (B100) production, [$ y ]
The government incentives for biodiesel (B100) production and their use determines as follows: • Total costs of selling straw for other purposes, •

Total costs for by-products (glycerin and cake), [$ y ]
By-products (glycerol and cake) are used as a substitute for related products [30]. The use of by-products can effectively reduce the environmental impact. Biomass sludge was used to replace organic fertilizers, and glycerol from biodiesel production is used in cosmetics. The price of by-products (glycerol, cake and pellets) is determined as follows: where 1. Price, obtained from the sale of glycerol obtained from the i-th raw material (glycerol in the production of soap) = , ∈ ∀ ∈ , ∀ ∈ = ∈ , ∈ ∈ ∀ ∈ , ∀ ∈ 2. Price, obtained from the sale of cake obtained from the i-th raw material (animal feed cake) Price of unused WCO for biodiesel (В100) production.
The price of unused WCO for (В100) production, which is a penalty function determined as follows:

Mathematical Modeling of Social Performance of IBDSC, , [ / ]
The social assessment model for the IBDSC operation determines the expected total number of jobs created ( ) as a result of the action of all elements of the network during its operation: where the terms of Equation (26) are determined according to the ratios at each time interval ∈ , [Number of Jobs/y]: 1 -the number of jobs created during the building biodiesel (B100) and solid waste plants; 2 -the number of jobs created during the operation of the biodiesel (B100) and solid waste plants; 3 -the number of jobs created during the bioresources cultivation for the biodiesel (B100) production. They determine as follows: Equations (26) and (27) represent a simplified model of the social criterion [31].

Constraints
The optimization problem includes constraints in terms of: balance of all products, plant capacity, demand satisfaction.

Plants Capacity Constraints
The capacities of the plants are limited by lower and upper boundaries. These boundaries for each region are determined by implementing the system of inequalities: where = ∈ ∈ + ∈ ∈ , ∀ , , , .

Balance of Biodiesel (B100) to be Produced from Biomass Available in the Regions
Equation (37) provides the admissibility of solid waste flows to the places where they are generated: Equation (38) provides keeping the admissible rates of biodiesel (B100) flows from each region for their production: Constraint on the balance of biodiesel (B100) produced from available biomass in the regions: Equation (41) provides the permissible values of petroleum diesel flows from each of the regions for their production:

Constraints on the Facilities for Use of Solid Waste
The condition ensuring that the total amount of solid waste generated by all biorefineries can be processed in plants built for this purpose is satisfied by implementing the system of inequalities:

Logical Constraints
• Constriants providing that in a given region ∈ a plant can be built ∈ for biodiesel (В100) production.
Equation (48) providing the ability to select only one size ∈ for each facility: • Constraints providing that in a given region ∈ only one plant will be built with size ∈ for solid waste use: The equations (48) provide that only one size can be selected ∈ for each solid waste use plant.

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Constraints providing a possible connection between regions producing raw materials only in a certain region: • Constraints providing that petroleum diesel produced in region ∈ is transported from region ∈ to ∈ using transport ∈ for the given interval ∈ when petroleum diesel is currently being produced in the region ∈ during the same time interval: • Constraints providing that each region producing bioreasource ∈ will be connected to at least one biodiesel (В100) plant: Constraints providing that each plant ∈ for biodiesel (В100) production will be connected to at least one area ∈ for blending and consumption: Constraints providing that each plant ∈ for solid waste processing will be connected to at least one plant ∈ for biodiesel (В100) production: Constraints providing that solid waste produced from a given biorefinary will be processed in only one of the plants for use:

Constraints for Design of IBDSC
These constraints represent material balances between the various echelons in the SC. Biomass productivity regional constraint: 3.4.10. Constraints on the Overall Environmental Impact of All Regions where are the maximum values of the total environmental impact of the SC for biodiesel (B100) and the SC for fossil fuels in the regions kg . d .

Constraints on Arable Land
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Constraints on cereal yields for food security
This type of constraint is intended to comply with the requirements regarding the amounts of cereals produced to ensure food security. The idea is to avoid competition with other sectors and to maintain sustainable land use. The model introduces a constraint to prevent competition between "used biomass for food" and "used biomass for fuel": Arable land used for cultivation of bioresources for food security and biofuel production should not exceed the available arable land for each region:

Constraints on Crop Rotation
Crop selection makes it possible to control pests, improve soil fertility, maintain longterm soil productivity and increase yields and profitability on rotation [32]. The planning of crop rotation with energy crops depends on the environmental and economic conditions in the different regions. In addition, the application of rotation in crop production is a common practice that is applied for environmental benefits and helps to reduce dependence on additional resources. The crop rotation in a given region is carried out according to a certain scheme of replacement of the crops ∈ cultivation on areas and .

Constraints on Energy Balances
• Constraints providing the overall energy balance in the region.
Constraint on the applicability of the energy balance: The energy equivalent diesel fuel needed to meet the energy needs of all customer areas where biodiesel (B100) is not used is determined as follows: where is the annual consumption of energy (petroleum diesel) from all regions [GJ y ].
The energy equivalent of petroleum diesel, which should be added to balance the energy required for all customer areas, is determined as follows: where is the annual energy added to petroleum diesel to balance the energy required for all regions [GJ y ].
The energy equivalent of biodiesel (B100) obtained per year is determined as follows: where is the annual energy derived from biodiesel (B100) supply chain for the whole consumer area [GJ y ].
The total value of fuel used by the regions [$/y] is: Constraints providing the overall energy balance in each consumer area Constraint on the applicability of the energy balance for each region: • Constraints providing the required amount of fuel is provided for each region 3.4.14. Constraints on Total Costs of IBDSC where is maximal total value of considered supply chain [$].

Economic Objective Function
The economic objective function represents the annual costs related to cultivation and collection of biomass, its transportation to the collection facilities, storage and conversion, storage of biodiesel and its transportation to the blending facilities. It also includes the investment costs for the building of biorefineries and facilities for use of solid waste. The economic criterion is an object of minimization and is defined as follows: In addition, as the objective function, the price of the used fuel (petroleum diesel and biodiesel) can also be used. This applies to the whole time interval, provided that the needs of the regions for this energy carrier are met.

Environmental Objective Function
As an environmental optimization criterion, Eco-Indicator 99 is used [33]. It is an object of minimization. Eco-Indicator 99 is a standard method for assessing the global impact of a process, product and/or activity. This method can be applied either as a standalone tool or in combination with an optimization model. The proposed environmental impact model uses the Eco-Indicator 99, which assesses the environmental impact of all activities in the network expressed in terms of the amount of carbon dioxide equivalent generated throughout the life cycle of the products.

Formulation of the Optimization Problem
The purpose of optimization is to find the solution of the problem-the values of the decision (binary and continuous) variables-in which the optimization criterion has a minimum value. They are the following: 1. Structure of the SC network, which includes number, size and location of the biorefineries; 2. Localization of the areas for biomass cultivation and biodiesel (В100) production; 3. Mass flows of biomass and biodiesel between different areas; 4. Type of transport for delivery of biomass and biodiesel; 5. Amounts of GHG emissions generated at each stage of the life cycle of the biodiesel production; 6. Amounts of transport for each transport connection and mode of transportation; 7. Distribution of the biodiesel in blending areas.
The optimization problem includes the following criteria: The optimization problem for optimal design of IBDSC is defined as a single-objective one in terms of MILP, at one optimization criterion-environmental or economic-as the rest are considered as constraints. The strategic design of the supply chain combines two levels of decision making: decisions related to the creation of a superstructure of the supply chain, and those related to distribution of the material flows of biomass and biodiesel between different units.

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Minimization of GHG emissions, [kg . /d] When the optimization problems include an environmental criterion, then the aim is to minimize the total annual equivalent GHG emissions resulting from the IBDSC operation. Formulation of this objective function is based on total GHG emissions in SC and other fuels, which are assessed on the basis of the LCA approach, where emissions are added to each life cycle stage.
The optimization problem for determining the optimal location of the facilities in the regions and their parameters is formulated as follows: The objective equations (72) and the equations (28)-(69) are linear functions with respect to all decision variables. •

Minimization of total annual costs, [$/y]
When the optimization problems include an economic criterion, then the aim is to minimize the total annual costs. The latter include: the total annual capital costs, the annual operating costs, the annual government incentives and the emission costs of CO .
The optimization problem for determining the optimal location of the facilities in the regions and their parameters is formulated as follows: The objective equations (70) and the equations (28)-(69) are linear functions with respect to all decision variables.

Case Study
The optimization problem is formulated and solved either with an economic criterion-the total annual costs for design of the IBDSC-or using environmental ones, such as the total GHG emissions related to its operation and an integrated economic and environmental criterion. The other criteria are defined as constraints. The purpose is to determine the optimal locations of biodiesel facilities in the regions and their parameters.
Two types of feedstocks, first generation-sunflower and rapeseed-and second generation-waste cooking oil (WCO) and animal fats-were used for biodiesel production.

Input Data
The proposed optimization approach is applied on a real case study from Bulgaria. For this purpose, the territory of the Republic of Bulgaria with its 27 districts is considered. The problem of optimal design of IBDSC is defined for the 5-year planning horizon (2016-2020). To calculate the amount of biodiesel needed for these regions, real data on the amounts of fossil diesel fuels taken from the National Statistical Institute of Bulgaria were used. For the considered period 2016-2020, these are: 2016 → 2,050,000 t, 2017 → 2,219,000 t, 2018 → 2,401,000 t, 2019 → 2,583,000 t, 2020 → 2,775,500 t. As a result of implementation of the proposed approach, the obtained solutions propose building solid waste use facilities in four districts of Bulgaria, as well as use of glycerin obtained as a by-product in another four districts of Bulgaria. The search areas are equipped with the necessary diesel from three refineries or combined warehouses.
The total GHG emissions for the whole life cycle of the growing energy crops vary significantly depending on the soil, meteorological conditions, the technology for growing the crops, as well as the fertilization to increase the yields for the different regions of Bulgaria. Table 1 presents the GHG in the agronomic phase of rapeseed and sunflower and the cultivation of the harvest for the different regions of Bulgaria. The costs for growing biomass and the maximum amount of biomass that can be produced in the regions of Bulgaria are listed in Table 2. The most suitable possible locations for biorefineries in the regions were selected on the basis of accessibility to transport infrastructure, urban planning and zoning. All 27 regions were selected as potential sites for biorefineries that are scattered throughout Bulgaria. The refineries for oil diesel production are located in the regions of Burgas, Ruse and Sofia.
The classical esterification technology for production of biodiesel (B100) from raw sunflower and rapeseed is taken into consideration [36].
The average price of glycerin is 1.088 $/kg [37]. Another by-product is the sludge from processed oilseeds, which are rich in protein and used for animal feed. According to [36], per ton of biodiesel (B100), approximately 1.575 t oil cake is generated. The average price of sunflower seeds is 115 $/t [38].
The efficiency of biodiesel (B100) conversion from rapeseed and sunflower varies from 389 L/t to 454 L/t. For the purpose of modeling, we used 422 L/t, which represents the average of the lowest and highest conversion efficiencies found in the literature [39]. Table 3 shows the values of the conversion factor for sunflower and rapeseed, applicable to the conditions in Bulgaria by the most popular technology for extraction of biodiesel (B100). In this study, the value of the conversion factor used is 371 kg/t of biomass for sunflower and 303 kg/t of plant biomass, applicable to the conditions in Bulgaria by the most popular technology of biodiesel production (B100). When determining the optimal number of biorefineries to be built on the territory of the Republic of Bulgaria, it should be borne in mind that they are four types that have different maximum capacities. The capital costs, minimum and maximum capacities of biodiesel (В100) plants are given in Table 4. It is assumed that the consumption of vegetable oil in a given region should be proportional to its population, and the amount of generated WCO is 30% of this.
Production costs per unit of biodiesel (B100) in a biorefinery built in a given region depend on the total costs for: chemicals and catalysts, gas, electricity, water supply, wastewater treatment, administrative and operational costs and labor. The average costs are, respectively, 125 $/t for each region in which biodiesel is produced (B100) (excluding raw material costs) [35].
The emission factors of petroleum diesel and biodiesel and their corresponding energy equivalents are presented in Table 5. The transportation costs for biomass (sunflower and rapeseed) and biodiesel (B100) related with the used vehicles -tractor, truck and train and loading and unloading costs are listed in Table 6 and Table 7. Table 6. Transport costs for different modes of transport for biomass [16].  Table 7. Transport costs for the different vehicles for biodiesel (B100) and petroleum diesel [16]. The GHG emissions from road and rail transport assess based on the carbon content of the respective fuel, the fuel consumption per km and the amount of biomass and biodiesel transported. The respective assessments are listed in Table 8. The rest data related with the population, cultivated and free cultivated areas used for crops production are taken from [45].

Computational Results and Analysis
The proposed MILP optimization model is coded and run in the GAMS optimization software, GAMS Release: 22.8 [46] using CPLEX 11.1 solver with WEX-WEI x86 64bit/MS Windows on Intel Core 2 Duo P8600 2.4 GHz CPU with 4GB RAM on a 32-bit platform. The optimization problem was calculated in 3:8:25:297 h. The MILP model includes 222,790 binary variables, 1,029,580 positive continuous variables and 1,512,846 constraints. The latter represent the investment possible decisions and required management.
The solution obtained in the case of optimal design of IBDSC using the optimization criteriа (A) Minimum total GHG emissions and (B) Minimum annual costs shows that the GHG emissions are 6.6% lower for criterion (A) than for criterion (B), while the price of biodiesel is 14% higher for criterion (A). This is due to the increased capital and operating costs in the case of criterion (A). In the case of IBDSC design using the minimum GHG emissions optimization criterion, the best parameters are obtained if the used feedstocks for the Bulgarian conditions are sunflower, rapeseed, animal fats and waste oils.
In Figures 2-4 the structure of the obtained optimal IBDSC with corresponding logistics in terms of biodiesel, petroleum diesel and solid waste (Figure 2), as well as the raw materials used (Figures 3 and 4) is shown.   Figure 5 shows that the GHG emissions with the highest values are generated from the processes related to biodiesel production. These are followed by emissions from its burning, as well as emissions from the cultivation of biomass as feedstock for biodiesel production. The GHG emissions due to transport of raw materials and products have the lowest values. The lower emission values under the criterion (A) Minimum total GHG emissions compared to (B) Minimum total annual costs are due to the fact that according to criterion (A), the preferred transport is rail, while criterion (B) relies on short-distance auto transport.  Table 9 and Table 10 represent the optimal size, capacity and location of biorefineries and solid waste disposal facilities, using the two main criteria: (A) Minimum total greenhouse gas emissions and (B) Minimum total annual costs.  Table 11 and Table 12 represent the obtained results using the two main criteria: (A) Minimum total greenhouse gas emissions and (B) Minimum total annual costs.

Conclusions
Based on the analysis conducted, the following conclusions can be drawn: 1. The available agricultural land in Bulgaria meets the needs for production of a sufficient amount of first-generation feedstock for the production of the required amount of biodiesel (B100) in order to meet Bulgarian needs and reach the required quota of 10% for liquid biofuel by 2020. 2. The optimal land required for sunflower and rapeseed cultivation is concentrated in a small number of regions of the country, selected independently of the optimization criteria for the optimal design of IBDSC. 3. The optimal mix of first-generation bioresources, applying the approach based on the "Minimum total annual costs" criterion for the design of IBDSC for 2020, requires 14% of the agricultural land to be used for sunflower cultivation and 2% to be used for rapeseed cultivation. Applying the approach based on the "Minimum total GHG emissions" criterion requires 12% of the agricultural land to be used for rapeseed cultivation and 3% for sunflower cultivation. Applying the approach based on using both criteria, second-generation bioresources (waste cooking oils and animal fats) are used as the main raw material to meet the requirements of the required quota of 10% for biodiesel by 2020. 4. An important conclusion for transportation is that rail is the optimal mode of transport to use for both types of bioresources (sunflower and rapeseed; animal fats and waste oils) and fuels (biodiesel (B100) and petroleum diesel). 5. The average price of biodiesel (B100) for the period (2016-2020) applying the approach based on the "Minimum total annual costs" criterion is 378 $/ , while applying the approach based on the "Minimum total GHG emissions" criterion in the same circumstances gives a price of 428 $/ , i.e., 14% higher. 6. Applying the approach based on the "Minimum total GHG emissions" criterion showed that GHG emissions have a 6.6% lower value compared to the use of the criterion "Minimum total annual costs", while the price of biodiesel is 14% higher. 7. The estimated value of capital investment for the entire period (2016-2020) is $ 96.779 million, applying the approach based on the "Minimum Total Annual Costs" criterion, and $ 127.257 million for the solution obtained when the "Minimum Total GHG Emissions" criterion is used based on the same input data.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Appendix A
•

Sets/Indexes
Set of first-generation feedstock (sunflower and rapeseed), ; Set of second-generation feedstock (waste cooking oil and animal fat), ; Set of type of vehicles for transportation, ; Set of type of plants for biodiesel (В100) production and thier capacities, = 1, ; Set of type of facilities for solid waste use and thier capacities, = 1, ; Set of the regions into which the territory of Republic of Bulgaria is divided, ; Set of proportions biodiesel (В100) and diesel, subject to blending for each of the customer areas, ; Set of time intervals . •

Subsets/Indexes
Set of types of vehicles for transportation of biodiesel (В100) and diesel, which is subset of ( ⊂ ), ; Set of types of vehicles for transportation of biomass, which is subset of ( ⊂ ), ; Set of types of vehicles for transportation of WCO and animal fat, which is subset of ( ⊂ ), ; Set of types of vehicles for transportation of solid waste, which is subset of ( ⊂ ), ; Set of types of vehicles for transportation of waste biomass, which is subset of ( ⊂ ), ; Set of types of vehicles for transportation of sunflower and rapeseed for food, which is subset of ( ⊂ ), ; Set of regions for biodiesel (В100) production, which is subset of ( ⊂ ), f; Set of areas for blending and use of biodiesel, which is subset of ( ⊂ ), ; Sets for the supply and production of petroleum diesel, which are subsets of ( ⊂ ), ; Set of regions for collection and treatment of solid waste, which is subset ( ⊂ ), ; Set of regions for treatment and use of glycerol, which is subset of (К ⊂ ), ; Set of regions for treatment and use of sunflower husk, which is subset of ( ⊂ ), ; Set of regions for collection and treatment of waste biomass, which is subset of ( ⊂ ), ; Set of regions for using sunflower and rapeseed for food, which is subset of ( ⊂ ), ; Set of regions for collection of WCO and animal fat, which is subset of ( ⊂ ), h; G Set of regions for bioresources cultivation (sunflower, rapeseed, etc.) (G ⊂ GF), g;

Input parameters
• Constant parameters or those that can change very slowly over time:

Environmental parameters
Emission factor for biodiesel (B100) production from biomass ∈ according to technology ∈ , [kg . eq}/t biofuel]; Emission factor for biodiesel (B100) production from WCO and animal fat ∈ according to technology ∈ , [kg . /t ]; Fixed costs for transportation of WCO ∈ using vehicles of type ∈ , [$/t]; Variable costs for transportation of WCO ∈ using vehicles of type ∈ , [$/t]; Fixed costs for transportation of biodiesel (B100) using vehicles of type ∈ , [$/t] ; Variable costs for transportation of biodiesel (B100) using vehicles of type ∈ , [$/t km]; Fixed costs for transportation of petroleum diesel using vehicles of type ∈ , [$/t]; Variable costs for transportation of petroleum diesel using vehicles of type ∈ , [$/t km]; Fixed costs for transportation of solid waste using vehicles of type ∈ , [$/t]; Variable costs for transportation of solid waste using vehicles of type ∈ , [$/t km]; Fixed costs for transportation of biomass using vehicles of type ∈ , [$/t]; Variable costs for transportation of biomass using vehicles of type ∈ , [$/t km]; Fixed costs for transportation of sunflower and rapeseed for food using vehicles of type ∈ , [$/t]; Variable costs for transportation of sunflower and rapeseed for food using vehicles of type ∈ , [$/t km].

Technical parameters
Minimum transport capacity l, used for transportation of biomass i, [t]; Minimum transport capacity ∈ used for transportation of biodiesel, [t]; Amount of glycerol obtained in the process of processing feedstock in the production of biodiesel, [t/t]; Amount of glycerol obtained in the process of processing WCO in the production of biodiesel, [t/t]; Amount of cake obtained in the process of processing 1 ton feedstock in the f biodiesel, [t/t]; Amount of grist obtained in the process of processing of 1 ton WCO in the production of biodiesel, [t/t]; Maximum annual capacity of plant of type ∈ for the production of biodiesel (B100), using sunflower and rapeseed of type ∈ and WCO of type ∈ , [t/y]; Minimum annual capacity of plant of type ∈ for the production of biodiesel (B100), using sunflower and rapeseed of type ∈ and WCO of ∈ , [t/y]; Maximum annual capacity of plant of type ∈ for the production of biodiesel (B100), using sunflower and rapeseed of type ∈ , [t/y]; Minimum annual capacity of plant of type ∈ or the production of biodiesel (B100), using sunflower and rapeseed of type ∈ , [t/y]; Maximum annual capacity of plant of type ∈ for the production of biodiesel (B100), using WCO of type ∈ , [t/y]; Minimum annual capacity of plant of type ∈ for the production of biodiesel (B100), using WCO of type ∈ , [t/y]; Minimum annual capacity of the type facility ∈ for solid waste processing, [t/y] Maximum annual capacity of the type facility ∈ for solid waste processing, [t/y] Energy equivalent per unit of petroleum diesel, [GJ/t]; Energy equivalent per unit of biodiesel (B100), [GJ/t]; Delivery distance between regions ∈ and ∈ using vehicles of type ∈ , [km]; Delivery distance between regions ∈ and ∈ using vehicles of type ∈ , [km]; Delivery distance between regions ∈ and ∈ using vehicles of type ∈ , [km]; Delivery distance between regions ∈ and ∈ using vehicles of type ∈ , [km]; Delivery distance between regions ∈ and ∈ using vehicles of type ∈ , [km]; Delivery distance between regions ∈ and ∈ using vehicles of type ∈ , [km]; Delivery distance between regions ℎ ∈ and ∈ using vehicles of type ∈ , [km]; Minimum capacity of vehicles of type ∈ used for transportation of sunflower and rapeseed ∈ , [t]; Minimum capacity of vehicles of type ∈ used for transportation of WCO ∈ , [t]; Minimum capacity of vehicles of type ∈ used for transportation of biodiesel (B100), [t]; Necessary jobs for building biodiesel refinery of size ∈ ; Necessary jobs for operation of biodiesel refinery of size ∈ per year; Necessary jobs for cultivation of feedstock of type ∈ in region ∈ per year; Necessary jobs for building solid waste use facilities of size ∈ ; Necessary jobs for operation of the solid waste use facilities of size ∈ per year; Factor for changing the employment assessment depending on the region ∈ in which the plant is built; Factor for changing the employment assessment depending on the region ∈ in which the plant is built. •

Parameters depending on time interval
These parameters are influenced by market fluctuations and other external factors and have a different value for each time interval ∈ , but do not change in it.

Environmental parameters depending on the time interval
Emission factor for cultivation of biomass ∈ in region ∈ , [kg . / t ]; Maximum overall environmental impact, [kg . ]

Economic parameters depending on the time interval
Production costs per unit of biodiesel (В100) from biomass of type ∈ in a biorefinery of size ∈ , built in region ∈ for each time interval ∈ , [$/t]; Production costs per unit of biodiesel (В100) from WCO of type ∈ in a biorefinery of size ∈ , built in region ∈ for each time interval ∈ , [$/t]; Production costs per unit of petroleum diesel in refinery, built in region ∈ for each time interval ∈ , [$/t]; The price paid for use of a unit of solid waste in a solid waste facility of size ∈ , built in region ∈ , for each time interval ∈ , [$/t]; The price paid for use of a unit of solid waste, if this is realized in the plants ∈ for the production of biodiesel (B100)for each time interval ∈ , [$/t]; The price paid for use of a unit of WCO of type ∈ in region ℎ ∈ for each time interval ∈ .

Technical parameters depending on the time interval
Proportion of biodiesel (В100) and petroleum diesel during blending for each of the customer's areas. The ratio of biodiesel (B100) and petroleum diesel has a higher energy equivalent for both fuels for each time interval ∈ , [Dimensionless]; Biomass to biodiesel conversion factor depending on the type of biomass ∈ , [t /t ]; Consumption of petroleum diesel in different years in customer areas ∈ , [t/y]; Maximum amount of biomass of type ∈ , which can be cultivated in a region ∈ per year, [t/y]; Minimum amount of biomass of type ∈ which can be cultivated in a region ∈ per year, [t/y];

Maximum amount of biomass for region ∈ , [t/d];
Maximum amount of biodiesel from the region ∈ , [t/d]; Maximum amount of petroleum diesel from the region d, [ / ]; The total amount of feedstock of type ∈ , which should be provided for all regions ∈ for food security, [t]; Optimal transport capacity ∈ used to transport biomass, [t],; Optimal transport capacity ∈ used to transport biodiesel, [t]; Free arable land in the region ∈ for cultivation of biomass for each time interval ∈ , [ha]; Free arable land in region ∈ for cultivation of sunflower/rapeseed for food security for each time interval ∈ , [ha]; Production rate of biomass ∈ cultivated in region ∈ for each time interval ∈ , [t/ha]; Duration of time intervals ∈ , [y]; Period of operation of IBDSC for a year, [d/y]; Biomass to biodiesel (B100) conversion factor for biomass of type ∈ , according to ∈ for each time interval ∈ ,[t /t ]; WCO to biodiesel (B100) conversion factor for WCO of type ∈ , according to ∈ for each time interval ∈ ,[t /t ]; Amount of solid waste generated during the production of one tonne of biodiesel (B100), using biomass of type ∈ and technology ot type ∈ during time interval ∈ , ; Demand for petroleum diesel in customer areas over the years ∈ for each time interval ∈ , [t/ y]; Maximum amount of biomass of type ∈ , which can be cultivated in region ∈ per year for each time interval ∈ , [t/y]; Minimum amount of biomass of type ∈ , which can be cultivated in region ∈ per year for each time interval ∈ , [t/y]; Maximum amount of WCO of type ∈ , which can be provided in region ℎ ∈ per year for each time interval ∈ , [t/y]; Minimum amount of WCO of type ∈ , which can be provided in region ℎ ∈ per year for each time interval ∈ , [t/y]; Maximum permissible flow rate of feedstock of type ∈ from region ∈ for each time interval ∈ , [t/d]; Maximum permissible flow rate of WCO of type ∈ from region ℎ ∈ for each time interval ∈ , [t/d]; Maximum amount of WCO and animal fat h∈ , [t/d]; Maximum permissible flow rate of biodiesel (В100) from region ∈ for each time interval ∈ , [t/d]; Maximum permissible flow rate of petroleum diesel from region ∈ for each time interval ∈ , [t/d]; Maximum permissible flow rate of solid waste from region ∈ for each time interval ∈ , [t/d]; Maximum permissible flow rate of waste biomass from region ∈ for each time interval ∈ , [t/d]; Maximum permissible flow rate of sunflower/rapeseed for food security from region ∈ for each time interval ∈ , [t/d]; total amount of bioresources of type ∈ , which should be provided by the regions ∈ to provide food security for each time interval ∈ , [t/y]; Optimal capacity of vehicles of type ∈ , used to transport biomass of type ∈ for each time interval ∈ , [t]; Optimal capacity of vehicles of type ∈ , used to transport biodiesel (В100) and petroleum diesel for each time interval ∈ , [t]; Optimal capacity of vehicles of type ∈ , used to transport waste biomass for each time interval ∈ , [t]; Optimal capacity of vehicles of type ∈ , used to transport sunflower/rapeseed for food security for each time interval ∈ , [t]; Optimal capacity of vehicles of type ∈ , used to transport solid waste for each time interval ∈ , [t]; Optimal capacity of vehicles of type ∈ , used to transport WCO of type ∈ for each time interval ∈ , [t].

Decision variables
•

Positive continuous variables
Biodiesel flow rate produced from feedstock of type ∈ transported by vehicles of type ∈ from region ∈ to ∈ in each time interval ∈ , [t/d]; Petroleum diesel flow rate transported by vehicles of type ∈ from region ∈ to ∈ , in each time interval ∈ , [t/d]; Amount of petroleum diesel that will be delivered to meet the energy needs of a region ∈ , for each time interval ∈ ,[t/y]; Amount of biodiesel produced from biomass that will be delivered to meet the energy region ∈ , for each time interval ∈ , [t/y]; Land occupied by sunflower/rapeseed in region , for each time interval t, [ha]; Land occupied by sunflower/rapeseed ∈ needed for food security in region ∈ , for each time interval ∈ , [ha]; Price of transport, for each time interval ∈ , [$]; Total capital investment, for each time interval ∈ , [$]; Total environmental impact, for each time interval ∈ , [kg . ]; Total impact of GHG emissions, for each time interval ∈ , [kg . ]; Crop biomass of type ∈ , which should be provided from region ∈ in the time interval ∈ ; Flow rate of crop biomass of type ∈ , transported by vehicles of type ∈ from region ∈ to ∈ , for each time interval ∈ , [t/d]; Flow rate of crop biomass of type ∈ , transported by vehicles of type ∈ from region ∈ to ∈ , according to technology ∈ , for each time interval ∈ , [t/d]; Flow rate of WCO biomass of type ∈ , transported by vehicles of type ∈ from region ℎ ∈ to ∈ , for each time interval ∈ , [t/d]; Flow rate of WCO biomass of type ∈ , transported by vehicles of type ∈ from region ℎ ∈ to ∈ according to technology ∈ , for each time interval ∈ , [t/d]; Flow rate of biodiesel (В100), produced from biomass of type ∈ and ∈ , transported by vehicles of type ∈ and ∈ from region ∈ to ∈ , for each time interval ∈ , [t/d]; Flow rate of biodiesel (В100), produced from crop biomass of type ∈ and transported by vehicles of type ∈ from region ∈ to ∈ , according to technology ∈ , for each time interval ∈ , [t/d]; Flow rate of biodiesel (В100), produced from WCO biomass of type ∈ and transported by vehicles of type ∈ from region ∈ to ∈ , according to technology ∈ , for each time interval ∈ , [t/d]; Flow rate of petroleum diesel, transported by vehicles of type ∈ from region ∈ to ∈ , for each time interval ∈ , [t/d]; Flow rate of solid waste, transported by vehicles of type m ∈ M from region ∈ to ∈ , for each time interval ∈ , [t/d]; Flow rate of solid waste, transported by vehicles of type ∈ from region ∈ to ∈ , in plant with size ∈ , for each time interval ∈ , [t/d]; Flow rate of straw collected from crop biomass of type ∈ and transported for processing by vehicles of type ∈ from region ∈ to ∈ , for each time interval ∈ , [t/d]; Flow rate of sunflower/rapeseed to provide food security transported by vehicles of type ∈ from region ∈ to ∈ , for each time interval ∈ , [t/d]; Amount of diesel that should be provided to meet the energy needs of the region ∈ , for each time interval ∈ , [t/y]; Amount of biodiesel (B100) produced from WCO biomass, which is provided to meet the energy needs of the region ∈ , for each time interval ∈ , [t/y]; Free arable land for cultivation of crop biomass of type ∈ , for the production of biodiesel (B100) in the region ∈ , for each time interval ∈ , [ha]; Free arable land for cultivation of crop biomass of type ∈ , needed to meet the food security in the region ∈ , for each time interval ∈ , [ha]; • Binary variables 0-1 variable, takes value "1", if crop biomass of type ∈ is transported from region ∈ to ∈ by vehicles of type ∈ for production according to technology ∈ , and takes "0" otherwise in time interval ∈ ; 0-1 variable, takes value "1", if WCO biomass of type ∈ is transported from region ℎ ∈ to ∈ by vehicles of type ∈ for production according to technology ∈ , and takes "0" otherwise in time interval ∈ ; 0-1 variable, takes value "1", if biodiesel(В100) is transported from region ∈ to ∈ by vehicles of type ∈ , and takes "0" otherwise in time interval ∈ ; 0-1 variable, takes value "1", if solid waste is transported from region ∈ to ∈ by vehicles of type ∈ , and takes "0" otherwise in time interval ∈ ; 0-1 variable, takes value "1", if straw is transported from region ∈ to ∈ by vehicles of type ∈ , and takes "0" otherwise in time interval ∈ ; 0-1 variable, takes value "1", if crop biomass of type ∈ for food security is transported from region ∈ to ∈ by vehicles of type ∈ , and takes "0" otherwise in time interval ∈ ; 0-1 variable, takes value "1", if solid waste use facility with size s ∈ S is built in region w ∈ W, and takes "0" otherwise in time interval t ∈ T; 0-1 variable, takes value "1", if solid waste use facility with size ∈ should operate in the region ∈ , and takes "0" otherwise in time interval ∈ , which includes the facilities built in the previous time interval and the new ones built during this interval, calculated by an equation ZWF = ZWF ( ) + ZW for the first year (t = 1) the configuration is set by initialization ZWF = ZW ; 0-1 variable, takes value "1", if plant for biodiesel(В100) production with size ∈ should be built in the region ∈ , and takes "0" otherwise in time interval ∈ ; 0-1 variable, takes value "1", if plant for biodiesel(В100) production with size ∈ should operate in the region ∈ , and takes "0" otherwise in time interval t ∈ T, which includes the plants built in the previous time interval and the new ones built during this interval, calculated by following recursive equation ZF = ZF ( ) + Z for the first year (t = 1) the configuration is set by initialization ZF = Z ; 0-1 variable, takes value "1", if diesel is produced in the region ∈ , and takes "0" otherwise in time interval ∈ ; 0-1 variable, takes value "1", if diesel is transported from region ∈ to ∈ by vehicles of type ∈ , and takes "0" otherwise in time interval ∈ .