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Sustainable Design and Operation of Cellulosic Bioelectricity Supply Chain Networks with Life Cycle Economic, Environmental, and Social Optimization Dajun Yue, Maxim Slivinsky, Jason Sumpter, and Fengqi You* Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, Illinois 60208, United States ABSTRACT: In this work, we propose a novel multiobjective optimization model for the sustainable design and operation of bioelectricity supply chain networks, which simultaneously accounts for the associated economic, environmental, and social impacts. The proposed model covers the cradle-to-gate life cycle of bioelectricity including biomass cultivation and harvesting, feedstock pretreatment, energy conversion, and biopower generation, as well as transportation and storage. We formulate the problem as a multiobjective mixed-integer linear fractional programming (MILFP) problem following the functional-unit-based life cycle optimization approach. The geographical dispersion and seasonality of biomass supply are captured and handled by the spatially explicit and multiperiod features of the model. The multiobjective optimization is accomplished via the ε-constraint method to obtain the approximate Pareto frontiers, which reveal the trade-off between economic performance and concerns about environmental and social impacts. Tailored solution methods are proposed for the effective global optimization of the resulting MILFP problem. An illustrative example and a county-level case study on the potential bioelectricity supply chain in the state of Illinois are provided to demonstrate the application of both the modeling framework and solution methods. regional economy.8 Hence, it is essential to simultaneously consider the economic performance as well as environmental and social impacts when addressing the design and operation of bioelectricity supply chains. There are a few works addressing the design and operation of bioelectricity supply chains in the existing literature, which will be reviewed below. Aksoy et al. proposed a supply chain optimization problem to study the feedstock allocation, optimum facility location, economic feasibility, and impacts of biorefinery plants in Alabama. A number of alternative biomassto-power technologies from woody biomass are considered in their work.9 Rentizelas and Tolis provided a decision support system for energy conversion supply chains involving multiple biomass types and three types of energy products, namely, electricity, heating, and cooling. The objective of their model was to maximize the financial yield of the investment.10 Keirstead et al. examined the ecologically sensitive and energyefficient construction of eco-towns in the U.K. Combined heat and power facilities using imported wood chips as feedstocks were considered along with other technologies to develop a low-cost energy supply chain system.11 Velazquez-Marti and Fernandez-Gonzalez studied the optimal logistics and best setup for biopower supply chains, where wood branches and straw are considered as the biomass feedstocks.12 Leduc et al. addressed the integration of ethanol production with combined heat and power plants and developed an optimization model to determine the optimal location of lignocellulosic ethanol refineries with polygeneration in Sweden.13 Gan and Smith developed a generic framework for determining the optimal

1. INTRODUCTION Currently, more than 90% of the electricity supply in the United States is generated from nonrenewable fuel sources, which are mainly based on coal, gas, and nuclear energy.1 With a large fleet of aging power plants and increasingly stringent environmental regulations and policies, the country is exploiting its energy portfolio and seeking potential sustainable alternatives for its electricity supply. Among the renewable power generation options, biopower offers the advantage of being dispatchable, that is, the biomass can be stored for the use of power plant operation to serve the load. This avoids many of the grid integration challenges associated with intermittent sources such as wind energy and solar energy.2,3 Among the various types of biomass resources, cellulosic biomass stands out as the most promising feedstock for biopower conversion, because it has minimum implications on food pricing and production, considerable potential for waste reduction, and abundant domestic availability across the country.4 A number of small- and medium-scale integrated biopower plants have been installed and in operation for years. Practical experiences show that a competitive levelized cost of electricity can be achieved and several biomass-to-electricity technologies are readily available for scale-up.5 Therefore, at the current stage, the major obstacle for large-scale implementation of biopower supply systems lies in the development of an efficient and robust supply chain network that links the biomass supply with biopower conversion facilities.6 Another perspective to note is that, although cellulosic biomass resources are considered carbon neutral, activities such as biomass collection, transportation, storage, and material processing would incur positive greenhouse gas (GHG) emissions, which can have implications on global warming and climate change.7 In addition, the development of bioelectricity projects can lead to significant social benefits and create considerable job opportunities for the © 2014 American Chemical Society

Received: Revised: Accepted: Published: 4008

November 15, 2013 January 24, 2014 February 19, 2014 February 19, 2014 dx.doi.org/10.1021/ie403882v | Ind. Eng. Chem. Res. 2014, 53, 4008−4029

Industrial & Engineering Chemistry Research

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Figure 1. Superstructure of the bioelectricity supply chain.

process cogeneration systems, which simultaneously considered economic, environmental, and social trade-offs.23 Recently, Gebreslassie et al.24 and Tong et al.25,26 addressed the uncertainties in hydrocarbon biorefinery supply chains using stochastic programming approaches. From the review of existing works in the field, we found a shortage of decision-support tools and methodologies dedicated to the sustainable design and operation of biomass-toelectricity supply chain systems, regardless of its practical importance. Therefore, it is the goal of this work to develop a generic optimization model for sustainable design and operation of biopower supply chains, which can simultaneously evaluate and optimize the economic, environmental, and social performances by achieving the optimal decisions in network design, technology selection, facility location and sizing, transportation and storage, etc. To address this challenge, we propose a multiobjective, multiperiod mixed-integer linear fractional programming (MILFP) model that captures critical features of the biopower supply chain, including geographically disperse distribution of biomass, seasonality in biomass supply, water content and degradation issues, etc. Levelized cost of electricity is chosen as the economic metric, which is extensively used as the major indicator for the projected economic performance of a renewable energy system. The environmental impact associated with the production of a unit amount of bioelectricity is chosen as the environmental metric, which is evaluated based on a cradle-to-gate life cycle assessment and would lead to a more environmentally sustainable way of manufacturing. The total number of local jobs generated throughout the lifetime of the biopower supply chain project is chosen as the social objective, which accounts for the employment impact to the regional economy in both the construction phase and operating years. We note that, due to the nonconvexity and combinatorial nature of the resulting MILFP problems, it can be challenging for the global optimization of large-scale supply chain problems. To tackle this issue, we further present two tailored MILFP solution approaches in this work, which tend to be much more efficient than conventional solution strategies in terms of both solution time and quality. Major novelties of this work are summarized as follows:

biopower plant size, the corresponding feedstock supply radius, and biopower generation costs.14 Cucek et al. presented a method for the synthesis of regional networks for the supply of electricity, heat, and bioproducts, where two metrics, profit and carbon footprint, were simultaneously considered.15 Frombo et al. provided a strategic decision model for the planning of woody biomass logistics for energy production. A number of thermochemical processes and specifically combustion, gasification, and pyrolysis processes were taken into account for the conversion from biomass to electricity, heat, and fuels.16 Besides the works reviewed above which directly incorporate biopower production in their optimal supply chain design, works on sustainable design and operation of biofuel supply chains are also relevant to this topic. Marvin et al. addressed the economic sustainability and feasibility of a biofuel supply chain in the Midwest considering both existing ethanol facilities and new candidate sites, where optimal biorefinery location and technology selection are determined through supply chain optimization.17 Liu et al. suggested using life cycle assessment methodology and incorporating GHG-related environmental objectives into the optimization framework for energy systems engineering.18 You and Wang proposed a life cycle optimization framework for the distributed−centralized design of biomassto-liquid supply chains. Minimization of total annualized cost and minimization of life cycle GHG emissions are simultaneously optimized using multiobjective optimization.19 Giarola et al. addressed the strategic design and planning of corn grain and stover based bioethanol supply chains through first and second generation technologies. Multiperiod, multiechelon, and spatially explicit features were embodied in their model, which optimized the environmental and financial performances simultaneously.20 Also, for the optimization of hybrid first/ second generation biofuel supply chains, Akgul et al. analyzed the potential GHG savings, impact of carbon tax, and trade-off between the economic and environmental performances.21 Compared to the economic and environmental performances, the social impact of supply chain design and operation is merely addressed by a limited number of works in the existing literature. You et al. explored three-dimensional sustainability perspectives in the optimal design and planning of cellulosic ethanol supply chains. The economic objective was measured by the total annualized cost; the environmental objective was measured by the total life cycle GHG emissions in a year; the social objective was measured by the number of accrued local jobs throughout the lifetime of the project.22 Bamufleh et al. presented another work on multiobjective optimization of

• novel multiobjective, multiperiod, spatial explicit model for the design and operation of cellulosic biomass to electric power supply chains 4009

dx.doi.org/10.1021/ie403882v | Ind. Eng. Chem. Res. 2014, 53, 4008−4029


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Figure 2. Flow sheet diagram of the biomass-to-electricity conversion pathway.

• consideration of three-dimensional sustainability, simultaneously optimizing the economic, environmental, and social impacts • application to a potential biopower supply chain in the state of Illinois The road map of this paper is given as follows. We first present an overview of the biopower technologies in section 2, followed by the discussion of three-dimensional sustainability in section 3. The problem statement and model formulation are presented in sections 4 and 5, followed by the solution strategies in section 6. To demonstrate the application of the proposed model and solution approaches, we provide an illustrative example in section 7 and a large-scale case study in section 8, with detailed discussion of the results.

2.1. Preprocessing System. The preprocessing system pretreats the raw biomass before sending it to the energy conversion process. Common steps in preprocessing include separation, sizing, removal of metals and other noncombustible materials, and grinding or other size-reducing methods.29 The preprocessing begins from the biomass receiving system, where the raw biomass resources are unloaded from trucks and then piled or stacked in the designated storage area. The most critical component in the preprocessing facility is the sizing equipment, which screens out the oversized biomass pieces and sizes them in order to meet boiler specifications. Specifically, the disk screener separates the oversized particles and bypasses the undersized feedstocks. The oversized particles are then sent to a tub grinder for size reduction, or in some cases a hammer hog (hogger) might be used. Dependent on the moisture content of the biomass received, drying might be needed after the sizing operation. It is reported that, for all biomass conversion technologies, the lower the moisture content in the biomass feedstock, the higher the energy efficiency of the conversion process, since part of the energy in the biomass is lost to heat and vaporizes the moisture. Another advantage of drying is that it helps to increase the energy density of biomass resources, thus facilitating their long-distance transportation. After coming out of the grinder/hogger and the potential drying process, the processed biomass is conveyed to the storage places (e.g., silo), waiting to be delivered to biopower plants for further energy conversion. 2.2. Boilers. We solely consider direct combustion system in this work, where the cellulosic biomass is burned in a boiler to produce high-pressure steam that is used in a steam-turbinedriven power generator. Specifically, stoker boilers and fluidized bed boilers are the two most commonly used types of boilers for biomass direct combustion.29 Stoker boilers directly fire solid biomass feedstocks with excess air, producing hot flue gases, which then produce steam in the heat exchanger section of the boiler. Cellulosic biomass feedstocks are fed by the stoker onto a grate where it burns with air passing up through it. Heat is transferred from the fire and combustion gases to water tubes on the walls of the boiler to produce steam.29 Fluidized bed boilers are the most recent type of boiler developed for solid fuel combustion. In this method of combustion, biomass is burned in a bed of hot inert, or

2. BACKGROUND ON BIOPOWER TECHNOLOGIES Cellulosic biomass can be converted to bioelectricity via various routes, including direct combustion, cofiring, gasification, and pyrolysis. Each route further involves numerous types of technologies which vary in cost, efficiency, technology maturity, and sustainability performance.27 In this work, we only consider the direct combustion system, which is the most common utilization of solid fuel biomass and has been commercialized at small and medium scales. Following this route of biomass-toelectricity conversion, the raw biomass collected from the field is first pretreated in the preprocessing facilities for size reduction, energy densification, and drying, and then shipped to the biopower plants, where the biomass is burned in the boiler to produce high-temperature high-pressure steam which drives the steam turbine to generate electricity. The superstructure of the bioelectricity supply chain is portrayed in Figure 1, which is composed of four echelons, namely harvesting sites, preprocessing facilities, biopower plants, and the grid. The cradle-to-gate life cycle boundary is also shown in Figure 1, which starts from biomass cultivation and harvesting through biomass processing and energy conversion to the point where bioelectricity is sold to the grid.28 Note that electricity transmission and end use are not considered in the life cycle boundary. Figure 2 presents the flow sheet diagram of the biomass-to-electricity conversion pathway showing a higher resolution of technical details about the critical physical and chemical processes involved in the supply chain, which will be covered in sections 2.1−2.3. 4010



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its outstanding environmental performance compared to that of coal-fueled power plants.31 However, although cellulosic biomass feedstocks are carbon neutral, the environmental impacts resulting from the various operations and activities along the biomass-to-electricity life cycle still need to be measured and optimized in order to minimize the implications of biopower supply chains to the ecosystem. In this work, we adopt the established life cycle optimization (LCO) framework,32−35 which is a generic methodology that organically integrates life cycle assessment (LCA) methodology with multiobjective optimization techniques. According to the principles and standards outlined by ISO 14040/14044,36,37 classical process-based LCA is composed of four phases, namely, goal and scope definition, analysis of life cycle inventory (LCI), life cycle impact assessment (LCIA), and results interpretation. Since classical LCA lacks the capability to automatically generate alternatives and further identify the optimal solution, the LCO framework complements LCA with multiobjective optimization to deal with the trade-off between economic and environmental performances and produce a series of Pareto-optimal solutions that constitute a Pareto frontier. Since bioelectricity is the only product of the supply chain system under study, we define “1 kWh of electricity produced” as the functional unit, which serves as the basis for calculation and comparison concerning the environmental impacts. The life cycle boundary is chosen to be cradle-to-gate as shown in Figure 2, which covers the life cycle stages of biomass cultivation and collection, feedstock preprocessing and storage, and material transportation, as well as biomass conversion and electricity generation. Greenhouse gas (GHG) emissions are the focus of this LCI analysis, including CO2, CH4, N2O, and NOx, of which the data are retrieved from the Argonne GREET Model,38 the Ecoinvent database,39 and a number of literature sources in the public domain. Global warming potential with respect to a 100-year time frame is chosen as the impact assessment model which specifies an impact factor to every GHG species and aggregates the environmental impacts of all GHGs in the LCI into a single indicator in terms of carbon dioxide equivalent (CO2-eq).40 On the basis of the inputs and tools mentioned above, we adopt the global warming impact in terms of CO2-eq associated with per kilowatt hour of bioelectricity generated as our environmental metric, which is a functional unit based objective function. We will also refer to this environmental metric as the unit environmental impact in the later presentation of the paper. Note that the levelized cost of electricity is in fact also a functional unit based objective function.32 3.2. Social Impact Quantification. The most critical concern in the social dimension of the bioelectricity supply chain might be the anticipated job opportunities brought about by the project. We note that this employment effect can be measured by the number of accrued local jobs in a regional economy. By definition, “job” refers to full time equivalent employment for a full year, which equals 2080 h. The more local jobs created, the higher social benefits generated to the regional economy. The Jobs and Economic Development Impact Model (JEDI) developed by National Renewable Energy Laboratory (NREL) can be employed and integrated with our multiobjective optimization framework to systematically evaluate the associated social impacts of bioelectricity supply chain systems.41 JEDI performs an input−output multiplier analysis to evaluate the number of local jobs accrued

incombustible, particles (e.g., sand) suspended by an upward flow of combustion air that is injected from the bottom of the combustor to keep the bed in a floating or “fluidized” state. This process allows oxygen to reach the combustible material more readily and increases the rate and efficiency of the combustion process. Boiler efficiency is an important indicator to evaluate the performance of a combustion process, which is defined as the percentage of the feedstock energy that is converted to steam energy. Typically, the efficiency of fluidized bed boilers compares favorably with that of stoker boilers due to low combustion losses. Stoker boilers can have 30−40% carbon in the ash and additional volatiles and CO in the flue gases, while fluidized bed boiler systems typically achieve almost 100% fuel combustion due to longer residence time and higher intensity of mass transfer. In addition, fluidized bed boilers are less sensitive to variation in biomass feedstocks because the inert materials provide a large inventory of heat in the furnace section, thus dampening the effect of brief fluctuations in the biomass supply or heating value on the boiler steam output. In terms of environmental aspects, fluidized bed boilers also exhibit advantages on emission control because cellulosic biomass can be efficiently burned in a fluidized bed combustor at temperatures considerably lower than in stoker boilers, which leads to less NOx emissions. Although fluidized bed boilers have a number of advantages over stoker boilers, the fluidized bed combustion system requires considerably higher installation and operation costs, which establishes the trade-off between cost and efficiency. 2.3. Steam Turbines. A steam turbine is a thermodynamic device that converts the energy in high-pressure, hightemperature steam into shaft power that can in turn be used to drive a generator and produce electric power.29 The bioelectricity generation process is accomplished via the thermodynamic cycle illustrated in Figure 2, called the Rankine cycle. Liquid water is converted to high-pressure steam in the boiler and fed into the steam turbine. The steam causes the turbine blades to rotate, creating power that is turned into electricity with a generator. A condenser and a pump are used to collect the steam exiting the turbine, feeding it into the boiler and completing the cycle. According to the fraction of heat and electric energy in the output, there exist different types of steam turbines. In this work, we only consider a condensing steam turbine which is for power-only applications and expands the pressurized steam to low pressure, at which point a steam/ liquid water mixture is exhausted to a condenser at vacuum conditions.

3. THREE-DIMENSIONAL SUSTAINABILITY FRAMEWORK Besides investigating the economic performance of the bioelectricity supply chain network, we also incorporate the consideration of environmental and social impacts into the optimal supply chain design and operation, thus leading to a three-dimensional sustainability framework. We employ the levelized cost of electricity as the measure of the economic performance of bioelectricity supply chains, which is an established indicator for energy generation systems.30 Regarding the environmental and social metrics, it is worth introducing the tools and methodologies used in this work for the integration of environmental and social dimensions. 3.1. Life Cycle Optimization. The motivation of using cellulosic biomass for electricity generation is primarily due to 4011



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assumption in this model. The distances between each pair of locations are given. In addition, a maximum transportation distance is also specified for biomass transportation. The lifetime of the bioelectricity supply chain project is given in terms of years. The capital costs at reference capacity levels are given for the preprocessing facilities and biopower plants. The cost data related to biomass harvesting, transportation, storage, and material processing are also given. In cases that government incentives may apply, construction and volumetric incentives are specified. The GHG emission data regarding the materials and operations involved in the life cycle of bioelectricity are obtained from relevant public databases and literature in the public domain. The multipliers of social impact associated with the activities in the bioelectricity supply chain are also given. The goal of this work is to maximize the economic, environmental, and social performances of the cellulosic bioelectricity supply chain by optimizing the following strategic and operational decisions: • number, location, size, and technology of the preprocessing facilities and biopower plants • timing and harvesting amount of raw biomass resources • storage level and material input/output of raw biomass resources and pretreated biomass feedstocks at preprocessing facilities • storage and material input of pretreated biomass feedstocks as well as electricity generation at biopower plants • intersite transportation loads for raw biomass resources and pretreated biomass feedstocks

to the regional economy, where the multipliers are derived from the IMPLAN professional model based on a large data matrix covering the various industry sectors in the regional economy.42 The social impacts are divided into three categories in the JEDI model, namely, direct, indirect, and induced effect. Direct effect corresponds to the immediate or on-site effect created by expenditure from the bioelectricity supply chain project. Indirect effect takes place when the contractors, vendors, or manufacturers who received their payments for goods or services in the bioelectricity supply chain project pay others who support their business. Induced effect reflects the change in wealth that occurs or is induced by the spending of those persons directly and indirectly employed in the bioelectricity supply chain. We note that the effect of a new production system on the creation of new jobs can be controversial, particularly when the new system is tightly connected and/or even alternative to other production systems (e.g., electricity production from fossil sources). However, the study of this effect is beyond the scope of this work.

4. PROBLEM STATEMENT The problem addressed in this work on the sustainable design and operation of bioelectricity supply chains is formally stated as follows. We are given a bioelectricity supply chain superstructure (Figure 1), including a set of harvesting sites (i ∈ I), a set of potential preprocessing facilities (j ∈ J), and a set of potential biopower plants (k ∈ K). A set of cellulosic biomass (b ∈ B) can be collected at the harvesting sites, including agricultural residues (e.g., corn stovers), wood residues (e.g., forest thinnings), and dedicated energy crops (e.g., switchgrass). A set of pretreated biomass feedstocks (p ∈ P) can be produced from the raw biomass resources at preprocessing facilities, where size reduction and drying are performed. The pretreated biomass feedstocks are then fed to biopower plants for electricity generation, where a set of conversion technologies (q ∈ Q) are available for choice. To account for the economy of scale on construction cost, we employ the piecewise linear cost function and specify a set of capacity levels (r ∈ R) for the preprocessing facilities and biopower plants. To capture the seasonal operations in the bioelectricity supply chain, a set of time periods (t ∈ T) is specified in order to improve the temporal resolution of the model. At the harvesting sites, we are given the amount of available biomass resources in each time period. At preprocessing facilities, we are given the storage capacities for both raw biomass resources and processed biomass feedstocks. The degradation nature of biomass is captured by the monthly deterioration rate given in the model. The density and moisture content of both raw biomass resources and processed biomass feedstocks are also given. The conversion ratio from raw biomass to pretreated biomass is given, which accounts for the material loss in preprocessing. At biopower plants, the storage capacity for pretreated biomass is specified. Furthermore, in order to maintain a continuous electricity output, we assume a minimum utilization rate of the process capacity and a safety period for the inventory of pretreated biomass feedstocks. The energy content of the biomass feedstocks is given, along with the biomass-to-steam efficiency of the boilers and steam-toelectricity efficiency of the steam turbine. At the end of the supply chain, upper and lower bounds of the electricity demand in each time period are given. Raw biomass resources and pretreated biomass feedstocks are shipped by truck, as an

5. MODEL FORMULATION A multiobjective, multiperiod model is developed to address the sustainable design and operation of bioelectricity supply chains. Constraints 1−3 model the upstream biomass supply system, which accounts for the seasonal feature in biomass availability. Constraints 4−16 model the preprocessing stage where raw biomass resources are pretreated. Constraints 17−29 model the conversion from biomass to electricity in biopower plants and the sales of bioelectricity to the grid. Equations 30−35 calculate the capital and operational costs, as well as incentives offered to the cellulosic bioelectricity supply chain, and the economic objective is given by eq 36. Equations 37−41 calculate the cradle-to-gate life cycle GHG emissions related to the operations in the supply chain, and the environmental objective is given by eq 42. Equations 43 and 44 calculate the employment effect brought about by the bioelectricity supply chain, and the social objective is given by eq 45. A list of indices, sets, parameters, and variables is given in the Nomenclature, where all the parameters are denoted in lower case or Greek letters and all the variables are denoted with an initial upper case letter. 5.1. Constraints. 5.1.1. Biomass Feedstock Supply System. The total amount of cellulosic biomass b collected from harvesting site i in time period t (Pbib,i,t) should not exceed its availability (avb,i,t) in terms of dry weight. Note that the seasonality, harvesting windows, and geographical availability of different biomass feedstocks can be taken into account through different values of the parameter Pbib,i,t in different biomass types b, harvesting sites i, and time period t. Pbib , i , t ≤ avb , i , t , 4012

∀ b ∈ B, i ∈ I , t ∈ T

(1)



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Based on the two constraints above, the capital cost for building preprocessing facility j is expressed as an interpolated piecewise linear cost curve and given by

The amount of biomass feedstocks collected in a certain time period are all sent to the adjacent preprocessing facilities for biomass pretreatment. This mass balance relationship is modeled by eq 2. Pbib , i , t =

∑ Fbijb ,i ,j ,t ,

⎡

Invjj =

∀ b ∈ B, i ∈ I , t ∈ T

r∈R

(2)

j∈J

where Fbijb,i,j,t stands for the amount of raw biomass b shipped from harvesting site i to preprocessing facility j in time period t. Due to the high moisture content and low energy density of biomass resources, it is not economically feasible for longdistance transportation of raw biomass feedstocks. Therefore, we impose a maximum transportation distance (mdbb,t), which prohibits the transportation of biomass feedstocks to remote preprocessing facilities. Fbijb , i , j , t = 0,

∀ (b , i , j , t )|(dsiji , j > mdbb , t )

+

∑ Fbijb ,i ,j ,t

(3)

+

(4)

Incjj ≤ incljj ∑ Xj , r ,

∀j∈J (9)

r∈R

∀j∈J

Incjj ≤ incfjj Invjj ,

(10)

As a facility can store multiple types of cellulosic biomass, the total amount of biomass feedstocks stored at a preprocessing facility cannot exceed its storage capacity, in terms of volume (vbjUj ). In addition, if the preprocessing facility is not built, the inventory level must be zero. This relationship is modeled by

∑ b∈B

(5)

Sbjb , j , t dbb(1 − mcbb)

≤ vbjUj ∑ Xj , r ,

∀ j ∈ J, t ∈ T

r∈R

(11)

where mcbb is the moisture content in biomass resource b. dbb is the density of wet biomass feedstock b. The processing amount of raw biomass feedstocks is constrained by the process capacity, as shown by eq 12. Again, note that the capacity of preprocessing facility is in terms of the weight of wet biomass processed.

where Xj,r is a binary 0−1 variable which equals 1 if a preprocessing facility with capacity level r at location j is built and otherwise equals 0. The annual processing capacity, in terms of the weight of wet biomass feedstocks processed, of the preprocessing facility is defined by the following constraint. ∀ j ∈ J, r ∈ R

∀j∈J

As a renewable power generation alternative, bioelectricity related facilities may be eligible for incentives from federal/local government. In most cases, the total incentives received for a project (Incjj) cannot exceed the allowable incentive cap (incljj) and cannot go beyond a certain percentage of the total construction cost (incfjj). Note that if the preprocessing facility is not installed, no incentives would be received, as modeled by the following constraints.

∀j∈J

prjj , r − 1Xj , r ≤ Cpjj , r ≤ prjj , r Xj , r ,

(Cpjj , r − prjj , r − 1Xj , r )(crjj , r − crjj , r − 1) ⎤ ⎥, ⎥⎦ prjj , r − prjj , r − 1

(8)

= Sbjb , j , t + Wbjb , j , t ,

r∈R

∀j∈J

⎡ Omcjj = cfjj ∑ ⎢crjj , r − 1Xj , r ⎢ r∈R ⎣

where ψb,j,t is the monthly deterioration rate of biomass b at preprocessing facility j in time period t. Sbjb,j,t stands for the inventory level of biomass b at preprocessing facility j at the end of time period t. Wbjb,j,t represents the amount of biomass b being pretreated at preprocessing facility j during time period t. Note that we assume cyclic planning in this model, indicating that if t = December, then t − −1 = November, and if t = January, then t − −1 = December. We employ piecewise linear functions to account for the economy of scale in the calculation of capital cost, which specifies a set of capacity levels r. The following constraint indicates that at most one capacity level can be chosen at each preprocessing facility.

∑ Xj ,r ≤ 1,

(Cpjj , r − prjj , r − 1Xj , r )(crjj , r − crjj , r − 1) ⎤ ⎥, ⎥⎦ prjj , r − prjj , r − 1

where Invjj is the investment cost of installing preprocessing facility j. crjj,r is the reference investment cost of installing preprocessing facility j with capacity equal to prjj,r. We note that alternative formulations for piecewise linear functions can also be employed, e.g., SOS2 formulation, delta-method, etc. The fixed operation and maintenance (O&M) cost, as a certain percentage (cfjj) of the capital investment, is given by

i∈I

∀ b ∈ B, j ∈ J , t ∈ T

⎣

(7)

where dsiji,j is the transportation distance from harvesting site i to preprocesing facility j. 5.1.2. Biomass Preprocessing Facilities. The raw biomass resources stored at preprocessing facilities are subject to deterioration during the storage period. The mass balance indicates that the total inflows of raw biomass b in preprocessing facility j in time period t plus the inventory at the end of the previous time period after taking into account the biomass deterioration should be equal to the total outflows plus the inventory level at the end of the current time period, which is given by (1 − ψb , j , t )Sbjb , j , t −−1 +

∑ ⎢⎢crjj ,r− 1Xj ,r

(6)

∑

where Cpjj,r is an auxiliary variable for the capacity of preprocessing facility j with capacity level r, which equals 0 if capacity level r is not chosen. prjj,r stands for the upper bound of the capacity of preprocessing facility with capacity level r.

b∈B

Wbjb , j , t 1 − mcbb

≤

ht rt

∑ Cpjj ,r ,

∀ j ∈ J, t ∈ T

r∈R

(12)

where ht is the length of time period t. rt is the effective operating time of the energy conversion facilities in a year. 4013



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During the pretreatment, the cellulosic biomass may go through size reduction, densification, and drying processes. We employ a conversion factor (αb,p,j) to model the relationship between the input biomass resources and the output of pretreated biomass p at preprocessing facility j in time period t (Wpjp,j,t). Note that Wpjp,j,t is also in terms of the weight of dry biomass and parameter αb,p,j can account for the material loss during preprocessing. Wpjp , j , t =

∑ αb ,p,j Wbjb ,j ,t ,

(1 − δp , k , t )Spk p , k , t −−1 +

j∈J

= Spk p , k , t +

∀ p ∈ P, k ∈ K , t ∈ T

(13)

Similar to the case of raw biomass storage at preprocessing facilities, the mass balance of processed biomass p at preprocessing facility j in time period t indicates that the inventory at the end of the previous time period after taking into account biomass deterioration plus the amount of pretreated biomass produced during the period should equal to the inventory at the end of the current time period plus the total amount shipped to biopower plants. This is given by,

∑ ∑ Yk ,q,r ≤ 1,

∑ p∈P

dpp(1 − mcpp)

≤

∑ Fpjk p,j ,k ,t , (14)

prk k , q , r − 1Yk , q , r ≤ Cpk k , q , r ≤ prk k , q , rYk , q , r ,

∑ Xj , r ,

∀ k ∈ K, q ∈ Q , r ∈ R

Invk k =

∀ j ∈ J, t ∈ T

∑ q∈Q

r∈R

+

where mcpp is the moisture content of pretreated biomass p and dpp is the density of wet biomass p. Since the energy density of the pretreated biomass is higher than that of the raw biomass feedstocks, the maximum transportation distance for processed biomass resources (mdpp,t) should also be larger than that for raw biomass resources. ∀ (p , j , k , t )|(dsjkj , k > mdpp , t )

(19)

where prkk,q,r is the upper bound of the biopower generation capacity with capacity level r. Cpkk,q,r is an auxiliary variable for the capacity of biopower plant k with technology q and capacity level r. The capital investment of installing a biopower plant (Invkk) is expressed by the interpolated piecewise linear function given by

(15)

Fpjk p , j , k , t = 0,

(18)

where Yk,q,r is a binary 0−1 variable which equals 1 if biopower plant k with technology q and capacity level r is built; otherwise it equals 0. The annual capacity of the biopower plant, in terms of the total amount of electricity generated in a year, is defined according to the upper and lower bounds for each capacity level.

where γp,j,t is the monthly deterioration rate of the pretreated biomass. Spjp,j,t stands for the inventory level of processed biomass p at preprocessing facility j at the end of time period t. Fpjkp,j,k,t represents the amount of pretreated biomass p shipped from preprocessing facility j to biopower plant k in time period t. The total amount of pretreated biomass cannot exceed the storage capacity (vpjUj ) in terms of volume, and the inventory level must be zero if the preprocessing facility is not built. vpjUj

∀k∈K

q∈Q r∈R

k

Spjp , j , t

(17)

where δp,k,t is the monthly deterioration rate. Spkp,k,t is the inventory level of processed biomass p at biopower plant k at the end of time period t. Wpkp,k,q,t stands for the amount of pretreated biomass p consumed by technology q at biopower plant k in time period t. The following constraint states that at most one technology and one capacity level can be chosen at a certain biopower plant.

∀ p ∈ P, j ∈ J , t ∈ T

∀ p ∈ P, j ∈ J , t ∈ T

∑ Wpk p, k , q,t , q∈Q

b∈B

(1 − γp , j , t )Spjp , j , t −−1 + Wpjp , j , t = Spjp , j , t +

∑ Fpjk p,j ,k ,t

⎡ ∑ ⎢⎢crk k ,q,r− 1Yk ,q,r r∈R ⎣

(Cpk k , q , r − prk k , q , r − 1Yk , q , r )(crk k , q , r − crk k , q , r − 1) ⎤ ⎥, ⎥⎦ prk k , q , r − prk k , q , r − 1 (20)

∀k∈K

where crkk,q,r stands for the reference capital investment for building a biopower plant with technology q at the capacity of prkk,q,r. The fixed O&M cost as a certain percentage (cfkk,q) of the construction investment is given by

(16)

Omck k =

where dsjkj,k stands for the transportation distance from preprocessing facility j to biopower plant k. 5.1.3. Bioelectricity Generation. The pretreated biomass resources are also stored at the biopower plant. The mass balance indicates that the inventory of pretreated biomass p at the end of the previous time period after taking into account the deterioration plus the inflows from preprocessing facilities should equal the inventory at the end of the current time period plus the amount consumed for biopower generation.

∑ q∈Q

+

⎡ cfk k , q∑ ⎢crk k , q , r − 1Yk , q , r ⎢ r∈R ⎣

(Cpk k , q , r − prk k , q , r − 1Yk , q , r )(crk k , q , r − crk k , q , r − 1) ⎤ ⎥, ⎥⎦ prk k , q , r − prk k , q , r − 1

∀k∈K

(21)

The total incentives received for the construction of a biopower plant (Inckk) cannot exceed the maximum allowable 4014



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directly sold to the grid. Therefore, explicit modeling of the electricity transmission and end-use phase is not considered. The total amount of bioelectricity generated from all the biopower plants in a certain time period should lie within the upper and lower bounds of the grid demand. This relationship is given by

amount (inclkk) and cannot be more than a certain percentage of the construction investment (incfkk).43 Inck k ≤ inclk k ∑

∑ Yk ,q,r ,

∀k∈K (22)

q∈Q r∈R

∀k∈K

Inck k ≤ incfk kInvk k ,

(23)

detL ≤

The total electricity throughput of the biopower plant cannot exceed its process capacity. At the same time, there is a minimum utilization rate (θk,q) of the biopower plant, which bounds the electricity throughput from below. θk , q

ht ∑ Cpk k ,q,r ≤ rt r ∈ R

∑ Wgk p, k , q,t ≤ p∈P

∑ p∈P

dpp(1 − mcpp)

(24)

≤ vpk kU ∑

C cap =

∑ Yk ,q,r , (25)

In order to guarantee continuous power generation at biopower plants, a certain amount of pretreated biomass is often kept in practice as safety inventory to hedge against a potential supply disruption. The level of the safety stock is usually empirically determined by the safety period (sfkk,t) and consumption rate, as given by Spk p , k , t ≥

sfk k , t ht

C acq =

1 − mcpp

+

∑ ∑ Wgk p, k , q,t ,

k∈K

∑ ∑ ∑ cmjb ,j ,t b∈B j∈J t∈T

+

Wbjb , j , t 1 − mcbb

∑ ∑ ∑ ∑ cmk k ,q,tWgk p,k ,q,t p∈P k∈K q∈Q t∈T

(32)

The transportation cost covers transportation of raw biomass feedstocks from harvesting sites to preprocessing facilities and that of processed biomass from preprocessing facilities to biopower plants. Both fixed and variable transportation costs associated with the shipping distance are considered. Note that the transportation costs are calculated based on the wet mass, thus reflecting the impact of different energy density.

(27)

where hhvp is the higher heating value (HHV) per unit of wet biomass p. βq,k is the biomass-to-steam efficiency of boiler technology q at biopower plant k. ηk is the steam-to-electricity efficiency of the condensing steam turbine at biopower plant k. The total amount of electricity generated at biopower plant k in time period t equals the sum of bioelectricity generated from different biomass resources and conversion technologies. Gek , t =

(31)

∑ Omcjj + ∑ Omckk j∈J

,

∀ p ∈ P, k ∈ K , q ∈ Q , t ∈ T

∑ ∑ ∑ pccb ,i ,t Pbib ,i ,t

C O&M =

(26)

As mentioned in section 2, the generation of electricity from biomass resources consists of two steps: biomass to steam and steam to electricity. The first step is accomplished in the boiler while the second step takes place in the steam turbine. Thus, the conversion to renewable electricity from the energy content within biomass resources can be expressed by eq 27. Wgk p , k , q , t = βq , k ηk

(30)

Besides the fixed O&M cost proportional to the capital investment, there is also a variable O&M cost proportional to the amount of biomass processed or the amount of bioelectricity generated, which accounts for expenses of utility, consumables, etc.

∑ Wpk p, k , q,t ,

hhvpWpk p , k , q , t

∑ Invk k) k∈K

b∈B i∈I t∈T

q∈Q

∀ p ∈ P, k ∈ K , t ∈ T

ir (∑ Invjj + 1 − (1 + ir)−lt j ∈ J

where ir is the discount rate and lt is the lifetime of the project in terms of years. The biomass acquisition cost covers the premium paid to farm/forest landowners as well as the machine and labor expenses for biomass collection.

q∈Q r∈R

∀ k ∈ K, t ∈ T

(29)

5.2. Economic Objectives: Minimizing Levelized Cost. The economic objective is to minimize the levelized cost of bioelectricity (Uc), accounting for the costs related to facility construction (capital; Ccap), biomass cultivation and harvesting (acquisition; Cacq), routine operation and equipment maintenance (CO&M), intersite transportation (Ctrans), inventory management (storage; Cstor), and financial credit from government incentives (Cinc). The capital investments for the construction of preprocessing facilities and biopower plants are annualized by multiplying the annuity.

where Wgkp,k,q,t stands for the amount of electricity generated from the consumption of processed biomass p through technology q at biopower plant k in time period t. Similar to the case in preprocessing facilities, the inventory level of the pretreated biomass cannot exceed the storage capacity at the biopower plant, in terms of volume (vpkUk ). Spk p , k , t

∀t∈T

k∈K

ht ∑ Cpk k ,q,r , rt r ∈ R

∀ k ∈ K, q ∈ Q , t ∈ T

∑ Gek ,t ≤ detU ,

C trans =

∑∑∑∑

(cvbbdsiji , j + cfbb)Fbijb , i , j , t

b∈B i∈I j∈J t∈T

+

∀ k ∈ K, t ∈ T

∑∑∑∑ p∈P j∈J k∈K t∈T

1 − mcbb (cvppdsjkj , k + cfpp)Fpjkp , j , k , t 1 − mcpp

(28)

(33)

We assume the biopower plants are located close to the connection point and the generated bioelectricity can be

Different inventory holding costs can be assumed for different biomass resources and different storage systems. The

p∈P q∈Q

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storage cost in this model covers the inventory of raw biomass in preprocessing facilities, as well as that of pretreated biomass in preprocessing facilities and biopower plants. C stor =

∑ ∑ ∑ epjj ,p Wpjp,j ,t

E O&M =

p∈P j∈J t∈T

+

∑ ∑ ∑ ht hbjb ,j ,t Sbjb ,j ,t

∑ ∑ ∑ ∑ epk p, q,kWgk p, k , q,t p∈P k∈K q∈Q t∈T

(39)

b∈B j∈J t∈T

The emission from transportation is largely due to the use of liquid transportation fuels, which relates both to the transportation distance and to the load of shipment.

∑ ∑ ∑ ht hpjp,j ,t Spjp,j ,t

+

p∈P j∈J t∈T

∑ ∑ ∑ ht hpk p,k ,tSpk p,k ,t

+

p∈P j∈K t∈T

Etrans =

(34)

The incentive is composed of the annualized incentive for the construction of preprocessing facilities and biopower plants, and tax credit from selling the electricity from renewable biomass resources. C inc =

ir (∑ Incjj + 1 − (1 + ir)−lt j ∈ J

∑ ∑ txc·Gek ,t

+

k∈K t∈T

∑ ∑ ∑ ∑ etbbdsiji ,j Fbijb ,i ,j ,t b∈B i∈I j∈J t∈T

+

∑ ∑ ∑ ∑ etppdsjkj ,kFpjkp,j ,k ,t p∈P j∈J k∈K t∈T

(40)

The emission from biomass storage may associate with the use of utility (e.g., electricity, hot air), which is dependent on the inventory level and the storage time.

∑ Inck k) k∈K

E stor =

(35)

∑ ∑ ∑ ht esbjb ,j ,t Sbjb ,j ,t b∈B j∈J t∈T

The levelized cost of electricity is a long-term cost concept, which represents a “break-even” value that a power provider would need to charge in order to justify the investment in a particular energy project. The levelized cost is often expressed as the total life cycle cost divided by the total lifetime energy production.44 Since we assume cyclic planning throughout the project lifetime, the levelized cost of electricity can be equivalently expressed as the annualized cost divided by the total amount of electricity generated in a year. This is given by min Uc =

+

p∈P j∈J t∈T

+

5.3. Environmental Objectives: Minimizing Unit GHG Emission. The environmental objective is to minimize the GHG footprint associated with per unit of bioelectricity (Ue), accounting for GHG emission from biomass cultivation and harvesting (acquisition; Eacq), soil carbon sequestration (Eseq), facility O&M (EO&M), transportation (Etrans), and storage (Estor). Global warming potential with respect to the 100-year time frame is employed here as the damage model for the life cycle impact assessment of GHG emissions. The emission during biomass cultivation and harvesting mainly stems from the use of fertilizers and utilities as well as operation of harvesting machines and vehicles, which is assumed to be proportional to the amount of biomass collected.

∑ ∑ ∑ eabb ,i ,t Pbib ,i ,t

min Ue =

∑ ∑ ∑ esq bPbib ,i ,t b∈B i∈I t∈T

Eacq + E O&M + Etrans + E stor − E seq ∑k ∈ K ∑t ∈ T Gek , t

(42)

5.4. Social Objective: Maximizing Local Job Opportunities. The social objective is to maximize the accrued local jobs (full-time equivalent for a year) in a regional economy throughout the lifetime of the biopower project. Jobs created during both the construction phase and operation phase are explicitly considered in our measurement. In this model, we employ several lumped multipliers derived from the IMPLAN professional model and the JEDI model in the formulation of the social objective. For clarification, we categorize the accrued local jobs into a fixed part (Jfix) and a variable part (Jvar). The fixed part of the accrued local jobs is proportional to the capital investment of the project, which includes total project development and on-site labor impacts, equipment and supply chain impacts, and induced impact during the construction period, as well as the on-site labor impacts during the operating years.

(37)

In addition, carbon sinks (such as soil carbon sequestration) should be taken into account as part of the emission credit in the life cycle analysis. E seq =

(41)

The life cycle boundary specified in this model is from cradle to gate, where electricity transmission and end use are not considered.28 Specifically, the life cycle stages include biomass cultivation and harvesting, biomass transportation and storage, biomass preprocessing, logistics of pretreated biomass, and biomass-to-electricity conversion in biopower plants. The environmental metric, unit environmental impact, is defined as the total environmental impact throughout the partial life cycle of the biopower supply chain divided by the total amount of bioelectricity generated.

C cap + C acq + C O&M + C trans + C stor − C inc ∑k ∈ K ∑t ∈ T Gek , t

b∈B i∈I t∈T

∑ ∑ ∑ ht espk p,k ,tSpk p,k ,t p∈P j∈K t∈T

(36)

Eacq =

∑ ∑ ∑ ht espjp,j ,t Spjp,j ,t

(38)

The emission during biomass conversion is dependent on the type of biomass resources, boiler technologies, and several other aspects of facility location and seasonality, as shown by eq 39. 4016


Industrial & Engineering Chemistry Research J

fix

Article

⎡ = ∑ (jcsjj + lt ·josjj ) ∑ ⎢crjj , r − 1Xj , r ⎢ j∈J r∈R ⎣ + +

(Cpjj , r − prjj , r − 1Xj , r )(crjj , r prjj , r − prjj , r − 1

this approach, a general model formulation of the subproblem in the ε-constraint method is given as follows and named (P0). (P0)

− crjj , r − 1) ⎤ ⎥ ⎥⎦

min

∑ ∑ (jcsk k ,q + lt·josk k ,q)

prk k , q , r − prk k , q , r − 1

(48)

cat

− crk k , q , r − 1) ⎤ ⎥ ⎥⎦

(and/or)

∑ J (cat) ≥ ε′ (49)

cat

The variable part of the accrued local jobs is dependent on the amount of bioelectricity generated, which covers local revenue and supply chain impacts and induced impacts during the operating years. Note that the utilization of different biomass feedstocks may have different impacts on the agricultural/forestry sector, thus resulting in different local revenue and supply chain impacts.

Co ∈ 9 n

and

Bi ∈ {0, 1}m

(50)

where C(cat), E(cat), and J(cat) stand for the cost, emission, and accrued local jobs related to the category (cat). Tg is the total amount of bioelectricity generated in a year. Co is the vector of continuous variables, and Bi is the vector of binary 0−1 variables. Note that C(cat), E(cat), J(cat), and Tg are included in Co. a, b, and c are parameters in the matrix form. Here eq 47 represents constraints 1−35, 37−41, 43, and 44. Without loss of generality, all the inequalities can be converted into equalities via the use of slack variables. Equation 46 corresponds to the economic objective function 36. Equations 48 and 49 correspond to the environmental objective (42) and social objective (45), respectively. We name the model with eqs 46−48 and 50 problem (P-CvE), which addresses the trade-off between economic and environmental performances, and we name the model with eqs 46, 47, 49, and 50 problem (P-CvJ), which addresses the trade-off between economic and social performances. As noted before, problems (P0), (P-CvE), and (P-CvJ) are formulated as MILFP problems, whose objective is a linear fractional function, and constraints are all linear.46 Although MILFPs can be dealt with using general-purpose MINLP solvers or global optimizers,47 the tailored MILFPs appear to be much more efficient in terms of both solution time and quality,48 because they can take advantage of the efficient mixed-integer linear programming (MILP) methods and require less memory resources. 6.2. Tailored MILFP Solution Methods. 6.2.1. Parametric Algorithm. Instead of solving the MILFP problem directly, the parametric algorithm solves a sequence of parametric MILP problems iteratively to obtain the global optimal solution.49,50 The parametric MILP problems are straightforward to formulate and given by (PD)

∑ ∑ ∑ (jlr p,k ,q + jii p,k ,q)Wgk p, k , q,t

p∈P k∈K q∈Q t∈T

(44)

The social objective, total accrued local jobs, equals the sum of the fixed part and variable part, representing the total number of local job opportunities created in both the construction and operating phases of the project.

max Tj = J fix + J var

(47)

∑ E(cat) ≤ ε·Tg

(43)

J var = lt ∑

(46)

a ·Co + b·Bi + c = 0

⎡ ∑ ⎢⎢crk k ,q,r− 1Yk ,q,r r∈R ⎣ (Cpk k , q , r − prk k , q , r − 1Yk , q , r )(crk k , q , r

Tg

s.t.

k∈K q∈Q

+

∑cat C(cat)

(45)

We note that, except for the fractional economic and environmental objective functions 36 and 42, all the other equations are linear. In addition, both the numerators and denominators of functions 36 and 42 are linear. Therefore, this model formulation represents a typical multiobjective MILFP problem. Since MILFP is a special class of mixed-integer nonlinear programming (MINLP) problem which is complicated due to the pseudoconvexity in the objective function and combinatorial nature, the global optimization of large-scale MILFP problems can be challenging. To tackle this issue, we introduce a number of tailored solution approaches for the efficient global optimization of MILFP problems in section 6.

6. SOLUTION STRATEGIES We employ the ε-constraint method to cope with the multiobjective optimization problem, which involves the solution of a series of single-objective MILFP optimization subproblems to obtain the Pareto frontier. The MILFPs can then be efficiently solved with the two tailored solution algorithms: the parametric algorithm and the reformulation− linearization method. 6.1. ε-Constraint Method. The ε-constraint method is very often used to obtain good approximations of the Paretooptimal solutions, due to its straightforward implementation.45 In this work, we consider the economic objective as the primary objective, while the environmental objective and social objective are transformed into the ε-constraints. Following

min ∑ C(cat) − q·Tg (51)

cat

s.t. a ·Co + b·Bi + c = 0

(52)

∑ E(cat) ≤ ε·Tg cat

(53)

(and/or) 4017



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Figure 3. Flowchart of the parametric algorithm.

∑ J (cat) ≥ ε′

∑ GJ(cat) ≥ ε′G (54)

cat

Co ∈ 9 n

and

Bi ∈ {0, 1}m

(55)

Comparing problems (PD) and (P0), we can see that the constraints remain unchanged. The only difference is that the objective function in problem (PD) becomes a parametric linear function, where q is a parameter. The parameter q will be updated in each iteration and eventually approach the optimal value of the original fractional objective function 46, as shown by the flowchart in Figure 3. We note that the optimal solution to problem (PD) would also be the optimal solution to problem (P0) if and only if the optimal value of eq 51 equals zero. The pros of the parametric algorithm include that (1) the MILP parametric problem is straightforward to formulate and (2) the size of the subproblem remains unchanged compared to that of the original MILFP problem. However, the cons of the parametric algorithm include that (1) the number of iterations is unpredictable and (2) gap information is not available during the solution. 6.2.2. Reformulation−Linearization Method. The reformulation−linearization method provides another alternative for the efficient global optimization of large-scale MILFP problems. The idea is to transform the original MILFP problem into its exact equivalent MILP problem via Charnes−Cooper transformation and Glover’s linearization techniques.51−53 The reformulated MILP problem of (P0) is given as follows and named (PR). (PR)

(59)

GTg = 1

(60)

GBi ≤ G

(61)

U

GBi ≤ g ·Bi

(62)

GBi ≥ G − g U (1 − Bi)

(63)

GCo, GBi, G ∈ 9 n

and

Bi ∈ {0, 1}m

(64)

Comparing problems (PR) and (P0), additional constraints and continuous variables are introduced in (PR), thus leading to a larger problem size. A one-to-one mapping correlation can be observed between the variables in the original MILFP problem and the reformulated MILP problem, as shown in Figure 4. Note that GC(cat), GE(cat), GJ(cat), and GTg are

min ∑ GC(cat) cat

cat

Figure 4. One-to-one mapping between variables in the original MILFP and reformulated MILP equivalent.

(56)

s.t. a ·GCo + b·GBi + c·G = 0

(57)

included in GCo, similar to the case in problem (P0). In order to obtain the global optimal solution for the original MILFP problem (P0), we can first solve the reformulated MILP problem (PR), and then convert the optimal solutions in the form of reformulated variables into solutions in the form of original variables following the one-to-one mapping.

∑ GE(cat) ≤ ε cat

(58)

(and/or) 4018



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The pros of the reformulation−linearization method include that (1) the equivalent MILP problem needs to be solved only once and (2) gap information is available during the entire solution process. The cons of the reformulation−linearization method include that (1) additional efforts are required to reformulate the problem and (2) the problem size increases due to the introduction of auxiliary variables and constraints for linearization.

We assume the capital cost increases as a power function of the facility capacity, with the power factor given in Table 3. The final capital investment is determined by multiplying the equipment cost by the cost factor in order to account for construction labor, balance of plant, spare parts, permitting, etc. We consider three capacity levels of preprocessing facilities, with ranges of 36−125, 125−250, and 250−500 kton of wet biomass per year. We also consider three capacity levels of biopower plants for both the stoker technology and the CFB technology, with ranges of 10−20, 20−30, and 30−50 MW. The effective operation time is assumed to be 24 h per day and 360 days per year. We consider different storage systems for biomass at different stages, which vary in inventory holding cost and biomass deterioration rate, as shown in Table 4. The degree of moisture content in biomass is a significant issue in the biopower supply chain problems. Here we assume that the moisture contents of raw corn stover, switchgrass, and forest residues are 0.3, 0.3, and 0.4, respectively. The moisture content of all pretreated biomass is assumed to be 0.1. The energy contents of bone-dry corn stover, switchgrass, and forest residues are 7560, 8670, and 8570 Btu/dry lb, respectively.29 Note that higher heating value (HHV) is used as the basis for energy calculation. The purchasing price paid to the farmers/ forest landowners for corn stover, switchgrass, and forest residues are 30.04, 47.82, and 10.42 USD/ton. The discount rate is assumed to be 0.1, and the lifetime of the project is expected to be 20 years. The GHG emissions data are obtained from the GREET model,38 the Ecoinvent database,39 and relevant literature,27,55−58 and the social impact multipliers are extracted from the JEDI model.41 By using the proposed model, we can determine the optimal facility locations, technology selection, production planning, transportation flows, and inventory management, simultaneously considering economic, environmental, and social performances of the supply chain. In this case study, we set the economic objective as the primary objective and transform the environmental and social objectives into two ε-constraints. We take 21 points for the environmental ε-parameter and 21 points for the social εparameter. By varying the respective environmental and social ε-parameters and solving a sequence of MILFP problems in the form of (P0), we obtain a total of 389 approximated Paretooptimal solutions, excluding the infeasible points. Based on these 389 scattered points, a Pareto surface is plotted using linear interpolation in MATLAB,59 as shown in Figure 6. The X-axis and Y-axis represent the environmental and social performances, respectively. The Z-axis stands for the economic performance of the bioelectricity supply chain. The levelized cost of bioelectricity increases as the color transits from blue to red. In Figure 6, the levelized cost of electricity ranges from 110 to 208 USD/MWh, the unit environmental impact ranges from 96.6 to 121.7 g of CO2-eq/kWh, and the employment effect ranges from 1614 to 7247 accrued local jobs. The solutions in the space above the Pareto surface are suboptimal, while the solutions in the space below the Pareto surface are infeasible. Trend 1 indicates that reducing the unit GHG emission will lead to the increase in levelized cost, while Trend 2 indicates that maximizing the job creation will also result in the sacrifice in economic performances. Note that problems with certain combinations of environmental and social ε-parameters are infeasible (e.g., minimum unit environmental impact and maximum jobs). These infeasible points are not plotted in Figure 6; thus we can see a nonsmooth (sawtooth shaped) boundary of the Pareto surface.

7. ILLUSTRATIVE EXAMPLE To demonstrate the application of the proposed modeling and solution framework, we present an illustrative example in this section, which involves three harvesting sites, three potential preprocessing facilities, and three potential biopower plants as shown in Figure 5. Three types of cellulosic biomass resources

Figure 5. Supply chain superstructure of the illustrative example. H, harvesting site; P, preprocessing facility; B, biopower plant.

are considered, namely, corn stover, forest residues, and switchgrass. We consider two alternative boiler technologies at the biopower plants, namely, stoker and circulating fluidized bed (CFB). For the temporal scale, we divide a year into 12 time periods, each representing 1 month. The locations and intersite transportation distances are given in Table 1. The maximum transportation distances for raw Table 1. Intersite Transportation Distances (km) location 1 location 2 location 3

location 1

location 2

location 3

15 40 150

40 20 50

150 50 10

biomass and pretreated biomass are set to 100 and 200 km, respectively. Hence the transportation links for raw biomass between location 1 and location 3 are dropped from the superstructure in Figure 5. The annual biomass availability of each type of biomass resources at each harvesting site are given in Table 2. Corn stover can only be harvested in October and November, while switchgrass and forest residues can be collected throughout the year. Some techno-economic details on the reference conversion facilities are given in Table 3.2,29,54 Table 2. Annual Biomass Availability (Dry kton/year)

corn stover forest residues switchgrass

harvesting site 1

harvesting site 2

harvesting site 3

200 20 10

50 100 70

10 10 150 4019



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Table 3. Techno-Economic Data of the Reference Conversion Facilities facility type

capacity

equipment cost

power factor

cost factor

fixed O&M percentage

variable O&M cost

preprocessing facility stoker-based biopower plant CFB-based biopower plant

324 kton/year 23.3 MW 24.3 MW

7,110 kUSD 30,835 kUSD 40,150 kUSD

0.85 0.7 0.7

2.6 2.6 2.6

2% 2% 2%

1.75 USD/wet ton 4 USD/MWh 4 USD/MWh

Table 4. Storage Systems storage phase

storage system

inventory holding cost (USD/(ton·month))

monthly deterioration rate (%)

raw biomass at preprocessing facility pretreated biomass at preprocessing facility pretreated biomass at biopower plant

outside atmosphere storage covered structure enclosed structure

3 4.5 6

1 0.5 0

Figure 6. Pareto surface showing the trade-off between economic and environmental and social performances.

biopower plant with a capacity of 26 MW and the stoker technology is built in location 2. The stoker boiler is chosen instead of the CFB boiler mainly because the stoker-based biopower plant requires much lower capital and operational costs. The primary biomass feedstock used in this solution is the forest residues, which are harvested in all three harvesting sites and shipped to the preprocessing facility in location 2. This is because the acquisition cost of forest residues is much lower than those of corn stover and switchgrass. The most environmentally sustainable solution has the levelized cost of bioelectricity of 208.3 USD/MWh, the unit environmental impact of 96.6 g of CO2-eq/kWh, and the social impact of 2178 accrued local jobs. The supply chain profile of this solution is shown in Figure 8. Three preprocessing facilities with capacity ranging from 93 to 500 kton/year are installed. Two biopower plants in locations 2 and 3 are installed with capacities of 17 and 10 MW, respectively. CFB boiler technology is chosen by both biopower plants instead of the stoker technology, because CFB has higher energy conversion efficiency, thus causing less material consumption and lower environmental impact. Corn stover is chosen as the only feedstock, because the acquisition and combustion of corn stover biomass leads to the lowest GHG footprint compared to the forest residues and switchgrass. Note that, in order to avoid the increase in GHG footprint from raw biomass transportation, the collected corn stover feedstocks are all preprocessed locally.

To further explore the results of this illustrative example, we select four representative Pareto-optimal solutions and investigate their supply chain profiles and operational features. These points are (1) the most cost-effective solution, (2) the most environmentally sustainable solution, (3) the most socially beneficial solution, and (4) a “good choice” solution that balances the economic, environmental, and social performances. The most cost-effective solution has the levelized cost of bioelectricity of 110.3 USD/MWh, the unit environmental impact of 121.7 g of CO2-eq/kWh, and the social impact of 1614 accrued local jobs. The supply chain profile of this solution is shown in Figure 7. One preprocessing facility at the capacity of 322 kton/year is installed in location 2. One

Figure 7. Supply chain profile of the most cost-effective solution. 4020



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capacities of 49 and 25 MW, respectively. Three types of biomass resources are all utilized, where forest residues contribute to lowering the levelized cost, corn stover contributes to lowering the unit environmental impact, and switchgrass contributes to additional job opportunities. All the approximated Pareto-optimal solutions are obtained using the reformulation−linearization method. To illustrate the application of different solution approaches, we apply them to the four representative problems and present the computational performances of the two proposed tailored MILFP methods and the general-purpose MINLP global optimizer in Table 5. All the computational experiments are performed on a PC with Intel Core i5-2400 CPU @ 3.10 GHz and 8.00 GB RAM. All models and solution procedures are coded in GAMS 24.1.3.60 The MILP problems associated with the parametric algorithm and reformulation−linearization method are solved with CPLEX 12. The global MINLP optimizer used in the computational experiments is BARON 12.61 The optimality tolerance is set to 0. From Table 5, we can see that the reformulation− linearization method, parametric algorithm, and BARON 12 all return the same global optimal solution, except that, in the case corresponding to the most environmentally sustainable point, BARON 12 fails to find a feasible solution within the specified 1 h computational time limit. Comparing the solution time of different solution methods, we can see that the reformulation−linearization method and the parametric algorithm are able to return the global optimal solutions for all four instances in seconds, while BARON 12 is much less efficient in terms of solution time. These results indicate that orders of magnitude reduction in computational time can be achieved by using the tailored MILFP methods instead of a general-purpose MINLP global optimizer.

Figure 8. Supply chain profile of the most environmentally sustainable solution.

The most socially beneficial solution has the levelized cost of bioelectricity of 152.9 USD/MWh, the unit environmental impact of 106.6 g of CO2-eq/kWh, and the social impact of 7247 accrued local jobs. The supply chain profile of this solution is shown in Figure 9. Three preprocessing facilities are

Figure 9. Supply chain profile of the most socially beneficial solution.

installed, all with the maximum capacity of 500 kton/year. Three biopower plants with the capacity ranging from 30 to 41 MW are installed. The CFB boiler technology is chosen by all the biopower plants, because the higher expenses of CFB-based biopower plants would result in more job opportunities. All the available three types of biomass resources are collected, because the more biomass converted, the higher the expenditure, and thus the more accrued local jobs generated in the regional economy. The “good choice” solution chosen by us has the levelized cost of electricity of 119.9 USD/MWh, the unit environmental impact of 109.1 g of CO2-eq/kWh, and the social impact of 5275 accrued local jobs. The supply chain profile of this solution is shown in Figure 10. Three preprocessing facilities are installed with capacity ranging from 93 to 500 kton/year. Two biopower plants are built in locations 1 and 3, with the

8. COUNTY-LEVEL CASE STUDY IN ILLINOIS In this section, we address a case study on the sustainable design and operation of a potential bioelectricity supply chain in the state of Illinois. In the past few years, the state has been making great efforts to develop a more sustainable and cleaner energy portfolio that protects consumers and creates jobs. A state law requires that 25% of Illinois’ energy must be renewable by the year 2025, where biomass-derived electricity provides a promising solution.62 The state of Illinois is abundant in cellulosic biomass resources, especially corn stover, which guarantees a sufficient feedstock supply for the biomassto-electricity energy conversion. Besides, direct combustion biopower plants at small and medium scales have already been commercialized and have been in operation for years with comprehensive supply chain experiences available. Therefore, it is now good timing for the large-scale implementation of a bioelectricity supply chain project in the state of Illinois.54 To formulate the mathematical model, we still consider 12 time periods in a year (i.e., 1 month per time period). Since the availability of forest residues and energy crops is trivial compared to that of corn stover in the state of Illinois, we solely consider one type of cellulosic biomass, corn stover, in this case study. The state of Illinois comprises 102 counties, and the spatial distribution of corn stover biomass in each county is shown in Figure 11. In order to eliminate unpromising candidate sites and facilitate the solution process, we further identify 60 harvesting sites, 29 potential preprocessing facilities, and 20 potential biopower plants through site screening. The transportation distance between each pair of counties is

Figure 10. Supply chain profile of the “good choice” solution. 4021



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Table 5. Computational Performances of Different Solution Methods instance

environ ε-param (g of CO2-eq/kWh)

social ε-param (accrued local jobs)

most cost effective

most environmentally sustainable

110.3 121.7

1614

96.6

2178

106.6

7247

109.1

5275

most socially beneficial

“good choice”

a

levelized cost (USD/MWh)

110.3 110.3 208.3 208.3 − 152.9 152.9 152.9 119.9 119.9 119.9

solution method reformulation− linearization parametric BARON 12 reformulation− linearization parametric BARON 12 reformulation− linearization parametric BARON 12 reformulation− linearization parametric BARON 12

solution time (CPU s) 1.8 3.6 105.1 0.6 1.1 3600a 0.5 0.7 4.5 1.0 3.2 148.4

No feasible solution returned within 1 h (3600 s).

variables, and 5742 equations. In order to globally optimize this large-scale MILFP problem efficiently, we employ the reformulation−linearization method for its solution. Although the parametric algorithm is also an efficient solution approach, it is difficult to achieve zero optimality tolerance within a reasonable amount of time for this large-scale NP-hard problem. In contrast, the reformulation−linearization method can solve the problem to a certain optimality tolerance and thus is the most suitable approach for this specific MILFP problem. The reformulated MILP problems in the form of (P-CvE) and (P-CvJ) are solved with CPLEX 12, where we address the trade-off between economic versus environmental performances and economic versus social impacts separately. Therefore, two Pareto curves will be presented and discussed in sections 8.1 and 8.2. 8.1. Economic vs Environmental Performances. The approximated Pareto curve showing the trade-off between economic and environmental performances of the potential bioelectricity supply chain in the state of Illinois is shown in Figure 12. The horizontal axis represents the unit environmental impact in terms of grams of CO2-eq per kilowatt hour bioelectricity generated from the supply chain system. The vertical axis represents the levelized cost of bioelectricity in terms of dollars per megawatt hour bioelectricity generated

Figure 11. Spatial distribution of corn stover in Illinois.

calculated using the haversine formula63 using the longitude and latitude information of the centroid of the counties, which takes into account the curvature of the earth and the area of the counties. The upper bound of the monthly bioelectricity demand in the state of Illinois is assumed based on the historical data of total electricity generated from all resources provided by the U.S. Energy Information Administration database.64 We assume the lower bound of the demand to be 5% of the upper bound, indicating that at least 5% of the electricity supply must come from the renewable biomass resources. We also specify three capacity levels for both preprocessing facilities and biopower plants. The capacity levels of preprocessing facilities are 36−250, 250−500, and 500−1000 kton of wet raw biomass processed per year, and the capacity levels of biopower plants are 10−75, 75−150, and 150−300 MW. The other input data associated with the cost, emission, and employment effect of the bioelectricity supply chains are the same as those under Illustrative Example. All the computational experiments are carried out on the same machine as that used in Illustrative Example. The resulting MILFP problem has 207 binary variables, 14 748 continuous

Figure 12. Pareto curve showing trade-off between economic and environmental performances. 4022



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large capacities (level 3), ranging from 242 to 300 MW. Though with a lower efficiency, the stoker boiler technology is chosen by all the biopower plants, because the capital and operational costs of stoker boiler are considerably lower than those of CFB. This indicates that a cost-effective bioelectricity supply chain design favors larger-size biopower plants and the stoker boiler technology. The total inventory levels of the raw biomass and pretreated biomass resources in each time period are shown in Figure 14. The total inventory equals the sum over all the preprocessing facilities or biopower plants. A strong seasonality can be observed in the inventory level of raw biomass in the preprocessing facilities. The inventory of raw biomass in the preprocessing facilities climbs in October and reaches its peak in November, because corn stover can only be harvested during October and November. The raw biomass is then stored in the preprocessing facilities for further energy conversion throughout the rest of the year. Figure 14 also shows that storage of pretreated biomass in preprocessing facilities is not required, since the pretreated biomass is shipped to biopower plants once produced in the preprocessing facilities. The inventory level of pretreated biomass in biopower plants is steady throughout the year in this most cost-effective solution, where safety inventory is kept to hedge against potential supply disruption. The reason for keeping most of the inventory of raw biomass in the preprocessing facilities, rather than in other storage phases, is mainly because of the lower inventory holding cost of atmosphere storage, though it also causes a higher deterioration rate. Figure 15 shows the cost breakdown of the most costeffective solution. Capital investment and biomass acquisition cost each account for slightly more than a quarter of the total cost. The fixed and variable O&M costs together take up 10% of the total cost. Due to the low energy density of biomass resources, transportation also contributes a considerable portion to the total cost, at 19%. Since corn stover is a type of cellulosic biomass resource with strong seasonality, and has merely a two-month harvesting window in a year, the storage cost is also significant, accounting for 18% of the total cost as shown in the chart. The solution on the upper left of the curve in Figure 12 has the lowest unit environmental impact of 96.2 g of CO2-eq/ kWh, and thus is the most environmentally sustainable design. The corresponding bioelectricity supply chain profile is given in Figure 16. In this most environmentally sustainable design, a total of 29 preprocessing facilities and 20 biopower plants are built. Most preprocessing facilities are at their largest capacity of 1000 kton/year, while the capacity of the preprocessing facility in Peoria County is 222 kton/year and that in Putnam County is 799 kton/year, mainly because of the lower biomass availability and longer distance to adjacent biopower plants. Compared to the most cost-effective solution, the most environmentally sustainable solution suggests building a larger number of biopower plants but with lower capacities, since all the installed biopower plants are of capacity level 1 or level 2, ranging from 13 to 120 MW. In the most environmentally sustainable design, the CFB boiler technology is chosen by all the biopower plants, because the higher energy conversion efficiency of the CFB boiler compared to thestoker boiler would lead to less biomass feedstock consumption, thus causing less GHG emissions during the transportation, storage, and collection activities along the bioelectricity life cycle.

from the supply chain system. The computational optimality tolerance is set to 2% for all instances. However, for some instances, the solution stops at a relatively larger gap because of the depletion of memory resources. Therefore, we specify an error bar for each point in Figure 12, ranging from 2 to 5%. It took a total of 38 303 CPU s to solve the 11 instances, of which the fastest took 174 CPU s and the slowest took 7344 CPU s. The 11 Pareto-optimal points are plotted, with unit environmental impact ranging from 96.2 to 109.9 g of CO2-eq/kWh and the levelized cost of bioelectricity ranging from 116 to 151 USD/MWh, corresponding to 11.6−15.1¢/kWh. We can see that, if we want to reduce the GHG footprint of bioelectricity, as a trade-off, the levelized cost of bioelectricity has to increase. Although all the solutions on the Pareto curve in Figure 12 are considered optimal, they have different emphases with respect to the economic and environmental performances. Points on the left emphasize on lowering the unit environmental impact and green manufacturing, while points on the right tend to pursue a more cost-effective supply chain. The solution on the lower right of the curve has the lowest levelized cost of 11.6¢/kWh, and it is therefore the most cost-effective supply chain design. The bioelectricity supply chain profile of the most cost-effective solution is given in Figure 13, showing

Figure 13. Pareto-optimal supply chain profile with the lowest levelized cost of bioelectricity.

the optimal location and capacity of conversion facilities. As can be observed, the preprocessing facilities and biopower plants are located in or close to the counties with higher biomass availability mainly in northern and central Illinois, indicating that the upstream is more significant than the downstream for the bioelectricity supply chain. This is because the product of the supply chain, electricity, can be sold to the grid for easily remote transmission, which is different from that of biofuel supply chains where liquid transportation fuel products need to be shipped to demand zones by truck, rail, barge, etc. In this supply chain profile which has the lowest levelized cost of bioelectricity, a total of 28 preprocessing facilities and five biopower plants are installed. The capacity of preprocessing facilities varies from 93 to 1000 kton/year. From the supply chain profile, we can see that the higher the biomass availability and the closer to the biopower plants, the larger the capacity of preprocessing facilities. The installed biopower plants are all at 4023



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Figure 14. Inventory level of biomass resources of the most cost-effective solution.

biopower plants. The inventory level of pretreated biomass in biopower plants climbs in October and reaches its peak in March, while the inventory level of raw biomass in preprocessing facilities climbs in October and reaches its peak in November. Storage of pretreated biomass in preprocessing facilities is still not desired. The trend in the inventory profile indicates that it is more environmentally favored to store the biomass resources in biopower plants, due to the lower material loss in inventory holding. However, the production of pretreated biomass is constrained by the maximum capacity of preprocessing facilities. Therefore, we can see the change in the inventory of both raw biomass in preprocessing facilities and pretreated biomass in biopower plants over the time periods. A breakdown of the GHG emission sources of the most environmentally sustainable solution is given in Figure 18. As can be seen, the GHG emission comes primarily (80%) from biomass acquisition, including cultivation and harvesting. This is because the cellulosic biomass resources are sparsely distributed and require extensive use of machines for collection and hauling, which are powered by electricity or fossil fuels, thus causing significant GHG footprints. The material processing stage accounts for 14% of the total emission, which is mainly from the use of utilities and consumables during O&M. The transportation contributes to 6% of the total GHG footprint, because in this most environmentally sustainable supply chain profile, most biomass resources are produced and consumed locally thus avoiding the potential GHG emission from long-distance transportation. 8.2. Economic vs Social Impacts. The approximated Pareto curve showing the trade-off between economic and social impacts of the potential bioelectricity supply chain in the state of Illinois is shown in Figure 19. The horizontal axis represents the total accrued local jobs created by the bioelectricity supply chain throughout the project lifetime, in terms of full-time equivalent for a year. The vertical axis represents the levelized cost of bioelectricity in terms of dollars per megawatt hour bioelectricity sold to the grid. The optimality tolerance is set to 1% for all the instances, which is represented by the error bars below each point. It took a total

Figure 15. Cost breakdown of the most cost-effective solution.

Figure 16. Pareto-optimal supply chain profile with the lowest unit environmental impact.

The inventory profile of biomass resources of the most environmentally sustainable solution is shown in Figure 17. In contrast to the inventory profile of the most cost-effective solution in Figure 14, more pretreated biomass is stored in the 4024



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Figure 17. Inventory level of biomass resources in the most environmentally sustainable solution.

the cost effectiveness of the bioelectricity supply chain. By observing the shape of the Pareto curve, we can see that the levelized cost climbs slowly below 12¢/kWh, when the total accrued jobs increase from less than 110 000 to about 150 000. However, the levelized cost soars rapidly when the total accrued jobs increase from about 150 000 to 160 000. Therefore, 12¢/ kWh might be an appropriate levelized cost of bioelectricity which balances the economic and social performances of the supply chain. Here we present in Figure 20 the supply chain profile of the Pareto-optimal solution at the upper right of the curve in Figure

Figure 18. GHG emission breakdown of the most environmentally sustainable solution.

Figure 20. Pareto-optimal supply chain profile with the highest employment effect.

Figure 19. Pareto curve showing trade-off between economic and social impacts.

19, which has the largest employment effect of 166 015 local jobs. This supply chain profile is similar to that of the most environmentally sustainable solution, where a total of 29 preprocessing facilities and 20 biopower plants are built. All the preprocessing facilities are at the maximum capacity of 1000 kton/year. All the biopower plants are at capacity level 2, ranging from 90 to 150 MW. The CFB boiler technology is chosen by all the biopower plants, mainly because of the higher

of 10 275 CPU s to solve the 11 instances, of which the fastest took 4 CPU s and the slowest took 3779 CPU s. The 11 points are plotted, with the employment effect ranging from 107 585 to 166 015 local jobs and levelized cost of bioelectricity ranging from 116 to 143 USD/MWh, or 11.6−14.3¢/kWh. This Pareto curve indicates that if we want to increase the number of local jobs generated by the supply chain project, we have to sacrifice 4025



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on the proposed superstructure, the minimum levelized cost of bioelectricity that can be achieved is 11.6¢/kWh, the minimum unit GHG footprint is 96.2 g of CO2-eq/kWh, and the maximum number of accrued local jobs created by the bioelectricity project is 166 015.

capital and operational expenses compared to a stoker boiler, which can bring out more direct, but more significantly, indirect and induced job creation. A breakdown of the job creation profile of the most socially beneficial solution is given in Figure 21. The employment effect generated during the construction

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (847) 467-2943. Fax: (847) 491-3728. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We gratefully acknowledge the financial support from the Institute for Sustainability and Energy at Northwestern University (ISEN).

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Figure 21. Breakdown of the job creation profile of the most socially beneficial solution.

NOMENCLATURE

Sets

I = set of harvesting sites indexed by i J = set of preprocessing facilities indexed by j K = set of biopower plants indexd by k B = set of raw biomass indexed by b P = set of preprocessed biomass indexed by p Q = set of power generation technologies indexed by q R = set of capacity levels indexed by r T = set of time periods indexed by t

phase accounts for 6% of the total accrued local jobs, while the 20-year operation phase accounts for the other 94%. As can be seen, the indirect impact during the operating years contributes the most to the bioelectricity supply chain, at 55%. This is mainly due to the local revenue and supply chain impacts to the agricultural sector, primarily in the upstream of the supply chain.

Parameters

avb,i,t = available amount of raw biomass b at harvesting site i in time period t cfbb = fixed transportation cost for raw biomass b cfjj = fixed annual O&M cost as a percentage of the capital investment for preprocessing facility j cfkk,q = fixed annual O&M cost as a percentage of the capital investment for biopower plant k with technology q cfpp = fixed transportation cost for processed biomass p cmjb,j,t = variable O&M cost for preprocessing biomass b at preprocessing facility j in time period t cmkk,q,t = variable O&M cost for power generation at biopower plant k with technology q in time period t crjj,r = reference capital investment for building preprocessing facility j with capacity level r crkk,q,r = reference capital investment for building biopower plant k with technology q and capacity level r cvbb = variable transportation cost for raw biomass b associated with transportation distance cvpp = variable transportation cost for processed biomass p associated with transportation distance dbb = density of raw biomass b deL(U) = lower or upper bound of biopower demand in time t period t dpp = density of processed biomass p dsiji,j = transportation distance from harvesting site i to preprocessing facility j dsjkj,k = transportation distance from preprocessing facility jto biopower plant k eabb,i,t = emission related to cultivation and collection of unit amount of raw biomass b at harvesting site i in time period t epjj,p = emission related to production of unit amount of processed biomass p at preprocessing facility j

9. CONCLUSION We proposed a novel multiobjective, multiperiod MILFP model for the sustainable design and operation of bioelectricity supply chains, simultaneously considering the economic, environmental, and social impacts. The objectives considered in this work are minimizing levelized cost of bioelectricity, minimizing unit environmental impact, and maximizing total accrued local jobs generated by the bioelectricity supply chain project. Critical features captured by the model include spatially explicit locations, seasonality in biomass supply, degradation of biomass resources, low transportation density, multistep biomass-to-electricity conversion, diverse conversion technology, government incentives, GHG emissions, employment effects to the regional economy, etc. Optimal decisions provided by the proposed model include supply chain network layout, facility location and sizing, technology selection, monthly production planning, inventory control, logistics management, etc. The multiobjective optimization problem was solved with the ε-constraint method. Two tailored solution approaches were applied for efficient global optimization of the resulting MILFP problems, of which the reformulation− linearization method is considered the better approach for this specific bioelectricity supply chain problem in terms of both solution time and quality. The proposed modeling and solution framework was demonstrated by an illustrative example and a county-level case study in Illinois. Pareto frontiers were obtained in both cases showing trade-offs between the economic, environmental, and social objectives. Supply chain profiles of selected Pareto-optimal solutions were also presented. Specifically for the latter case study, results showed that, for the potential bioelectricity supply chain based 4026



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prjj,r = upper bound of the capacity of preprocessing facility j with capacity level r prkk,q,r = upper bound of the capacity of biopower plant k with technology q and capacity level r rt = effective production time of a year sfkk,t = safety period for processed biomass storage at biopower plant kin time period t txc = tax credit for biopower vbjUj = volume capacity of storage place for raw biomass at preprocessing facility j vbjUj = volume capacity of storage for processed biomass at preprocessing facility j vpkUk = volume capacity of storage place for processed biomass at biopower plant k ψb,j,t = deterioration rate of raw biomass b at preprocessing facility j in time period t αb,p,j = conversion factor from raw biomass b to processed biomass p at preprocessing facility j βq,k = biomass-to-steam efficiency at biopower plant kwith technology q γp,j,t = deterioration rate of processed biomass p at preprocessing facility j in time period t δp,k,t = deterioration rate of processed biomass p at biopower plant k in time period t ηk = steam-to-electricity efficiency at biopower plant k θk,q = minimum utilization rate of biopower plant k with technology q

epkp,q,k = emission related to generation of unit amount of electricity from processed biomass p via technology q at biopower plant k esbib,i,t = emission related to storage of raw biomass b at harvesting site i in time period t esbjb,j,t = emission related to storage of raw biomass b at preprocessing facility j in time period t espjp,j,t = emission related to storage of processed biomass p at preprocessing facility j in time period t espkp,k,t = emission related to storage of processed biomass p at biopower plant k in time period t esqb = emission credit of soil carbon sequestration due to biomass b etbb = emission related to transportation of unit amount of raw biomass b etpp = emission related to transportation of unit amount of processed biomass p ht = duration of time period t hhvp = higher heating value of per unit of processed biomass p hbib,i,t = inventory holding cost for raw biomass b at harvesting site i in time period t hbjb,j,t = unit inventory holding cost for raw biomass b at preprocessing facility j in time period t hpjp,j,t = unit inventory holding cost for processed biomass p at preprocessing facility j in time period t hpkp,k,t = unit inventory holding cost for processed biomass p at biopower plant k in time period t incfjj = maximum percentage of the capital investment for building preprocessing facility jthat can be covered by incentive incfkk = maximum percentage of the capital investment for building biopower plant k that can be covered by incentive incljj = maximum incentive that can be provided for building preprocessing facility j inclkk = maximum incentive that can be provided for building biopower plant k ir = discount rate jcsjj = fixed job factor during construction of preprocessing facility j, covering direct, indirect, and induced impact during construction jcskk,q = fixed job factor during construction of biopower plant kwith technology q, covering direct, indirect, and induced impact during construction jiip,k,q = variable job factor for bioelectricity converted from biomass p at biopower plant k via technology q, covering induced impact during operation jlrp,k,q = variable job factor for bioelectricity converted from biomass p at biopower plant k via technology q, covering indirect impact during operation josjj = fixed job factor during operation of preprocessing facility j, covering direct impact during operation joskk,q = fixed job factor during operation of biopower plant kwith technology q, covering direct impact during operation lt = lifetime of the project mcbb = moisture content in raw biomass b mcpp = moisture content in processed biomass p mdbb,t = maximum transportation distance for raw biomass b in time period t mdpp,t = maximum transportation distance for processed biomass p in time period t pccb,i,t = acquisition cost for raw biomass b at harvesting site i in time period t

Continuous Variables

Pbib,i,t = purchasing amount of raw biomass b at harvesting site i in time period t Sbjb,j,t = storage level of raw biomass b at preprocessing facility j in time period t Spjp,j,t = storage level of processed biomass p at preprocessing facility j in time period t Spkp,k,t = storage level of processed biomass p at biopower plant k in time period t Fbijb,i,j,t = amount of raw biomass bshipped from harvesting site i to preprocessing facility j in time period t Fpjkp,j,k,t = amount of processed biomass p shipped from preprocessing facility j to biopower plant k in time period t Wbj b,j,t = amount of raw biomass b processed at preprocessing facility j in time period t Wpjp,j,t = amount of processed biomass p produced at preprocessing facility j in time period t Wpkp,k,q,t = amount of processed biomass p consumed at biopower plant k with technology q in time period t Wgkp,k,q,t = amount of electricity generated from biomass p at biopower plant k with technology q in time period t Cpjj,r = auxiliary variable for processing capacity of preprocessing facility j with capacity level r Cpkk,q,r = auxiliary variable for power generation capacity of biopower plant k with technology qand capacity level r Invjj = capital investment for building preprocessing facility j Invkk = capital investment for building biopower plant k Omcjj = annual O&M cost of preprocessing facility j Omckk = annual O&M cost of biopower plant k Incjj = incentive received for building preprocessing facility j Inckk = incentive received for building biopower plant k Gek,t = amount of bioelectricity generated at biopower plant k in time period t C(cat) = annualized cost associated with (category) E(cat) = total amount of life cycle emission associated with (category) 4027



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J(cat) = total accrued job creation associated with (category) Uc = levelized cost of bioelectricity Ue = unit environmental impact of bioelectricity Tj = total job creation throughout the biopower supply chain project lifetime

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Binary Variables

Xj,r = 1 if preprocessing facility j with capacity level r is built; 0 otherwise Yk,q,r = 1 if biopower plant k with technology q and capacity level r is built; 0 otherwise

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REFERENCES

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