Optimization-Based Approaches for Bioethanol Supply Chains

ARTICLE pubs.acs.org/IECR

Optimization-Based Approaches for Bioethanol Supply Chains Ozlem Akgul,† Andrea Zamboni,‡ Fabrizio Bezzo,‡ Nilay Shah,§ and Lazaros G. Papageorgiou*,† †

Centre for Process Systems Engineering, University College London (UCL), London WC1E 7JE, United Kingdom Dipartimento di Principi e Impianti di Ingegneria Chimica (DIPIC), Universita’ di Padova, via Marzolo 9, I-35131 Padova, Italy § Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ, United Kingdom ‡

ABSTRACT: The E.U. has adopted a target of 10% of energy for transportation coming from renewable sources, including biofuels, by 2020 to tackle the increasing greenhouse gas emissions problem and reduce dependency on fossil fuels. In this paper, mixed integer linear programming (MILP) models are presented for the optimal design of a bioethanol supply chain with the objective of minimizing the total supply chain cost. The models aim to optimize the locations and scales of the bioethanol production plants, biomass and bioethanol flows between regions, and the number of transport units required for the transfer of these products between regions as well as for local delivery. The optimal bioethanol production and biomass cultivation rates are also determined by the model. The applicability of the proposed models is demonstrated with a case study for Northern Italy.

1. INTRODUCTION Fossil fuels have been the dominant source of energy supply in the world for centuries. However, the burning of fossil fuels is known as the main contributor to the increase in global CO2 emissions, 25% of which currently result from the transportation sector.1 The negative impacts of greenhouse gas (GHG) emissions on the environment, with global climate change in particular, and declining fossil fuel resources have resulted in a growing interest in renewable sources recently. Biofuels are regarded to be among the best alternative solutions for reducing greenhouse gas emissions resulting from the transportation sector.2 This stems from the fact that carbon dioxide that is emitted to the atmosphere during burning of biofuels is considered to be offset by the amount that is absorbed during plant growth. Therefore, the “European Directive on the promotion of the use of biofuels or other renewable fuels for transport” has set a target of 10% of energy for transportation coming from renewable fuels, including biofuels, by 2020.1,3-8 Biofuels are commonly classified as “first-” or “second-” generation biofuels. First-generation biofuels are produced by well-established conversion technologies and use mainly food crops as feedstock, such as corn and sugar cane. The most common first-generation biofuels are bioethanol and biodiesel. On the other hand, second-generation biofuels, most of which are currently under development, use nonfood crops such as waste biomass or special energy crops. Second-generation biofuels are likely to replace first-generation biofuels in the future to avoid the controversies resulting from the use of food crops for transport fuel production.1,4,8 Therefore, it is important to assess the technological, social, or economic performance of wellestablished first-generation biofuel systems using suitable techniques or tools such as supply chain optimization, which will also give insight into the potential future use of second-generation technologies. Most of the research in the area of biofuel supply chains focuses on the economic aspect. Parker et al.9 developed a mixedinteger linear programming model for the assessment of potential biofuel production from different types of feedstock r 2010 American Chemical Society

resources such as agricultural, forest, urban, and energy crop biomass in the Western United States. Different types of biomass resources, their geographical distribution, and different conversion technologies are considered. The model aims at optimizing the locations and sizes of the biorefineries as well as allocation of biomass feedstock to those biorefineries by maximizing the profit over the entire supply chain, including the feedstock suppliers and fuel producers. They concluded that the model is capable of modeling different policy scenarios and can be used to test sensitivity against changes in several factors such as resource types, biomass production yield, and fuel type and quality. Kim et al.10 presented a mixed-integer linear programming model for the optimal design of biorefinery supply chains. The model aims to maximize the overall profit and takes into account different types of biomass, conversion technologies, and several feedstock and plant locations. In their work, they analyzed central and distributed systems. Gunnarsson et al.11 developed a mixedinteger linear programming model for a forest fuel supply chain to minimize the total supply chain cost consisting of transportation, chipping, purchasing, and terminal and storage terms. A heuristic solution approach was proposed to reduce the high computational times required to solve the resulting large-scale model. Dunnett et al.12 developed a multiperiod MILP modeling framework based on a state-task-network representation for the simultaneous design and operational scheduling of a biomass-toheat supply chain to minimize the total supply chain cost. Rentizelas et al.13 presented an optimization model for a multibiomass supply chain for a trigeneration energy supply including electricity, heating, and cooling applications to maximize the financial yield of the investment. Various technical, social, regulatory, and logical constraints were considered. Dyken et al.14 presented a mixed-integer linear programming approach Special Issue: Puigjaner Issue Received: June 30, 2010 Accepted: October 6, 2010 Revised: October 5, 2010 Published: November 02, 2010 4927

dx.doi.org/10.1021/ie101392y | Ind. Eng. Chem. Res. 2011, 50, 4927–4938

Industrial & Engineering Chemistry Research for biomass supply chains including the supply, transport, and storage and processing of biomass. Eksioglu et al.15 proposed a dynamic mathematical model for the design and management of a biomass-to-biorefinery supply chain. The model determines the optimal number, size, and location of biorefineries to produce biofuel from a range of available biomass feedstocks as well as the amount of biomass to be processed and shipped and biomass inventory levels during a time period. Huang et al.16 developed a mixed linear integer programming model for the multistage optimization of biofuel supply chains with the objective of evaluating the economic potential and infrastructure requirements of biofuel systems. Transportation comprises an important part of the total biofuel supply chain cost. Morrow et al.17 used a linear optimization model to determine the cost of distributing various ethanol fuel blends to all metropolitan areas in the Unites States. The results have shown that transportation cost is a significant contributor to the overall cost, and the transport infrastructure has to be improved to increase the competitiveness of ethanol as a fuel in the longer term. Yu et al.18 proposed a discrete mathematical model for a mallee biomass supply chain in Western Australia that takes into account biomass production, harvest, on-farm haulage, and road transport to a central bioenergy plant with the objective of minimizing the total delivered cost of biomass. They concluded that transportation was a significant cost component for the supply chain and proposed some strategies for reducing the total cost such as locating the biomass processing plant near areas with high biomass cultivation density. In addition to the financial criteria, environmental emissions and uncertainty in market conditions are key issues to be addressed for the determination of the performance of bioethanol supply chains. Lam et al.19 developed a new method for the minimization of the carbon footprint of regional biomass supply chains by dividing the region under consideration into clusters through a developed regional energy clustering algorithm. Zamboni et al.20 presented a static MILP model with spatially explicit characteristics for the strategic design of a biofuel supply chain to minimize the overall supply chain cost and the environmental impact in terms of GHG emissions. They tried to capture the varying nature of the demand using a scenario approach. Dal Mas et al.21 developed a dynamic mixed-integer linear programming model for the optimal design and planning of biomassbased fuel supply networks according to financial criteria, taking into account uncertainty in market conditions. Supply chain models can be classified as mathematical programming and simulation-based models. Mathematical programming models are suitable for optimization under the existence of an unknown configuration by applying an aggregate view approach into the dynamics and detail of operation. On the other hand, simulation-based models can be used to identify the detailed dynamic performance of a supply chain under operational uncertainty. The expected performance for the fixed configuration can be evaluated with a high level of accuracy.22,23 Work related to the area of biofuel supply chains in the literature is limited, most of which focuses on a particular aspect of the overall chain. However, the development of an approach focusing on the whole chain is essential for the evaluation of the environmental and economical performance of such systems. The goal of this paper is to introduce an optimization-based approach for the optimal design of bioethanol supply chains by minimizing the overall supply chain cost. This work is based on the application of a neighborhood flow approach that overcomes

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Figure 1. A biofuel supply chain network.

Figure 2. Neighborhood flow representation with 4N and 8N configurations.

the problem of long computational times required when solving network problems of large scale. This paper is organized as follows: The problem statement is presented in section 2, and the mathematical formulation is described in detail in section 3. A case study with the computational results is presented in section 4. Finally, some concluding remarks are drawn in section 5.

2. PROBLEM STATEMENT There is a wide range of decisions to be made during the optimal design of a biofuel supply chain, including the locations of biomass cultivation sites, transport system characteristics, and capacity assignment of production facilities. A biofuel supply chain network is represented in Figure 1. The network under consideration includes the following components: biomass cultivation and delivery to production facilities, biofuel production, and distribution to demand centers. The overall problem can be stated as follows. Given are: • locations of biofuel demand centers and their biofuel demand • geographical biomass availability • unit biomass cultivation and biofuel production costs • transport logistics characteristics (cost, modes, distances, and availabilities) • capital investment costs for the biofuel production facilities to determine optimal • biomass cultivation and biofuel production rates • locations and scales of biofuel production facilities • flows of biomass and biofuel between regions • modes of transport for delivery of biomass and biofuel so as to minimize the total supply chain network cost. The model introduced in this paper assumes steady-state conditions and adopts a “neighborhood” flow representation. Two different configurations are considered in this context: 4N and 8N, namely, von Neumann and Moore neighborhoods, as 4928

dx.doi.org/10.1021/ie101392y |Ind. Eng. Chem. Res. 2011, 50, 4927–4938

Industrial & Engineering Chemistry Research

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NTUImax = maximum number of units for local biomass transfer (units/day) PCappmin/PCappmax = minimum/maximum biofuel production capacity of a plant of size p (tons/day) Qilmin/Qilmax = minimum/maximum flow rate of product i via mode l (tons/day) SusF = maximum fraction of domestic biomass allowed for biofuel production TCapil = capacity of transport mode l for product i (tons/unit) TCap* = capacity for local biomass transfer (tons/unit) UCCg = unit biomass cultivation cost in region g (euros/ ton) UPCp = unit biofuel production cost for a plant of size p (euros/ton) UTCil = unit transport cost of product i via mode l (euros ton-1 km-1) UTC* = unit transport cost for local biomass transfer (euros ton-1 km-1)

Figure 3. Illustration of alternative delivery routes using the neighborhood flow representation.

seen in geosimulation studies. These two configurations differ in the flow directions to and from a region, as illustrated in Figure 2. In the 4N and 8N configurations, the material (biomass or biofuel) flow directions to and from a region (cell) are mutual with the four and eight neighboring regions (cells), respectively. Material is delivered to its destination by the addition of such flows one after another, as illustrated in Figure 3, where alternative delivery routes between two points are given according to the 4N and 8N flow representations.

3. MATHEMATICAL FORMULATION The proposed model for the design of bioethanol supply chains is described in this section. The biofuel supply chain optimization problem is formulated as a mixed integer linear programming (MILP) model with the following notation: Indices gg0 = square cells (regions) i = product (biomass, biofuel) l = transport mode p = plant size Sets G = set of square cells (regions) I = set of products (biomass, biofuel) L = set of transport modes P = set of plant size intervals Totaligg0 l = set of total transport links allowed for each product i via mode l between regions g and g0 nigg0 l = subset of Totaligg0 l including all regions g0 in the neighborhood of region g for each product i and mode l Parameters ADg = arable land density of region g (km2 arable land/km2 region surface) ADDgg0 l = actual delivery distance between regions g and g0 via model l (km) ALDg = average local biomass delivery distance (km) R = operating period in a year (days/year) BCDgmin/BCDgmax = minimum/maximum biomass cultivation density in region g (km2 cultivation/km2 arable land) CCF = capital charge factor (year-1) CFg = binary parameter for domestic biomass cultivation sites CYg = cultivation yield within region g (tons biomass day-1 km-2) GSg = surface area of region g (km2) γ = biomass-to-biofuel conversion factor (tons biofuel/tons biomass) ICp = investment cost of a plant of size p (euros) LDDgg0 = linear delivery distance between regions g and g0 (km)

Binary Variables Epg = 1 if a biofuel production plant of size p is to be established in region g Integer Variables NTUigg0 l = number of transport units of mode l required to transfer product i between regions g and g0 (units/day) Continuous Variables Dig = demand for product i in region g (tons/day) NTUIg = number of transfer units required for local biomass transfer within region g (units/day) Pfpg = biofuel production rate at a plant of size p located in region g (tons/day) Pig = production rate of product i in region g (tons/day) Qigg0 l = flow rate of product i via mode l from region g to g0 (tons/day) TDC = total daily cost of a biofuel supply chain network (euros/day) TIC = total investment cost of biofuel production facilities (euros) TPC = total production cost (euros/day) TTC = total transportation cost (euros/day) Neighborhood flow representation is introduced to the mathematical formulation through a set, nigg0 l, which is a subset of the set of total feasible links between two cells denoted by Totaligg0 l and covers only the neighboring cells of each cell g. Mathematically, this can be represented as nigg 0 l ⊂ Totaligg 0 l f or LDgg 0 e LDlimit

ð1Þ

where LDlimit is a distance limit whose value depends on the type of neighborhood configuration. This distance limit represents the longest linear distance between the centers of a cell and its neighboring cells. For 4N, the distance between a cell and its neighbors is the same in all directions. For the 8N configuration, the longest distance is between a cell and its neighbors located along the four diagonal directions, as shown in Figure 4. Hence, for a square cell of dimensions 50 50 km, as used in the illustrative example described in section 4, LDlimit is calculated as 50 and 70.7 km, for 4N and 8N representations, respectively. 4929



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average local delivery distance, and NTUIg is the number of transport units required for local biomass transfer within region g. The actual delivery distance, ADDgg0 l, is calculated by the multiplication of the linear delivery distance, LDDgg0 l, and tortuosity factor for that transport mode. 3.2. Demand Constraints. The biomass demand in region g is related to the local biofuel production rate by the conversion factor, γ: Pbiof uel, g ¼ γDbiomass, g " g ∈ G

Figure 4. Representation of LDlimit for 4N and 8N configurations.

3.1. Objective Function. The objective function is based on

the minimization of the total daily cost and is formulated as follows: TDC ¼

TIC CCF þ TPC þ TTC R

ð2Þ

As seen in eq 2, the total daily cost function consists of three main terms: • TIC: total investment cost of the biofuel production facilities converted to daily basis using the capital charge factor, CCF (year-1) and the operating period in a year R (days/ year) • TPC: total production cost including the biomass cultivation and biofuel production costs • TTC: total transportation cost The term TIC accounts for the total capital investment required for the establishment of new conversion facilities and is calculated by adding up the capital investment cost of each conversion plant of size p established in region g: TIC ¼

∑ ∑ ICp Epg

ð3Þ

p∈P g ∈G

where Epg represents the binary variable for establishing a conversion plant of size p in region g and ICp is the investment cost for that plant. The term TPC accounts for the biomass cultivation and biofuel production costs and is calculated by TPC ¼

∑ UCCg Pbiomass, g þ g∈G ∑ p∈P ∑ UPCp Pf pg

Pig þ ¼ Di , g þ

þ

∑ ðUTCTCapALDg NTUIg Þ

g ∈G

0

∑ ∑

l∈L g0 ∈nigg 0 l

Qig 0 gl

Qigg 0 l " i ∈ I, g ∈ G

Pbiof uel, g ¼

∑ Pf pg

p∈P

"g∈G

max PCapmin p Epg e Pf pg e PCapp Epg " p ∈ P, g ∈ G

ð9Þ

A constraint can be added to allow up to one production facility to be established in region g:

∑ Epg e 1

"g∈G

ð10Þ

The local biomass cultivation rate is also limited by the minimum and maximum local biomass availability. The local biomass availability is defined by the product of the terms: cultivation yield CYg, arable land density ADg, surface area GSg and cultivation density BCDg. e Pbiomass, g GSg CY g ADg BCDmin g e GSg CYg ADg BCDmax "g∈G g

where UTCil is the unit transportation cost of product i via mode l, TCapil is the transport capacity of mode l for product i, ADDgg0 l is the actual delivery distance between regions g and g0 via mode l, NTUigg0 l is the number of transport units of mode l required to transfer product i between cells g and g0 , UTC* is the unit transport cost for local biomass transfer within region g, TCap* is the transport capacity for local biomass transfer, ALDg is the

ð8Þ

The biofuel production rate at a plant in region g is limited by the minimum and maximum production capacities if that plant is to be established in that region; otherwise it should be forced to zero:

0

ð5Þ

ð7Þ

The biofuel production in region g is equal to the sum of the biofuel production rates at the plants located within that region:

∑ ∑ ∑ ∑ ðUTCilTCapilADDgg l NTUigg l Þ

i∈I l∈L g ∈Gg 0 ∈nigg 0 l

∑ ∑

l∈L g 0∈nig 0 gl

p∈P

where UCCg is the unit biomass cultivation cost in region g, Pbiomass,g is the local biomass production rate, UPCp is the unit biofuel production cost for a plant of size p, and Pfpg is the biofuel production rate at a plant of size p located in region g. The total transportation cost, TTC, is calculated by the sum of the transportation cost for delivery of products between regions and that for local biomass transfer: TTC ¼

It should be noted that the demand is considered as a single variable in this work instead of partitioning it into “local” and “imported” demand as in the model introduced by Zamboni et al.24 (see Appendix A for a brief description). This eliminates the need to take into account the related constraints in their model (eqs A.2-A.4 in Appendix A). 3.2. Production Constraints. The mass balance for each product i and region g states that the production of that product in region g plus the total flow from other regions should be equal to the demand in that region plus the total flow from that region to other regions:

ð4Þ

g ∈G

ð6Þ

ð11Þ

A sustainability constraint is also introduced so that only a fraction of the total potential biomass resources is used for biofuel production to prevent the negative impact on food production: !

∑ Pbiomass, g e SusF ∑g CFg GSg CYg ADg BCDmax g

g∈G

ð12Þ

The left-hand side of constaint 12 represents the total biomass production, whereas the right-hand side represents the product 4930



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of the sustainability factor, SusF, and the total potential biomass availability from domestic resources, which are defined by the binary parameter CFg. If the sustainability concept is also required for local production (per cell), constraint 11 can be replaced by

where Qilmax is the maximum flow rate of product i via mode l between regions g and g0 . 3.4. Non-Negativity Constraints. The following non-negativity constraints are introduced to represent the physical meaning of some variables:

e Pbiomass, g SusF GSg CY g ADg BCDmin g

Dig , Pig g 0 " i ∈ I, g ∈ G

ð17aÞ

Pf pg g 0 " p ∈ P, g ∈ G

ð17bÞ

NTUIg g 0 " g ∈ G

ð17cÞ

Qigg 0 l g 0 " i, g, g 0 , l ∈ nigg 0 l

ð17dÞ

e

SusF GSg CY g ADg BCDmax g

"g∈G

ð12aÞ

3.3. Transportation Constraints. The number of transfer

units for product transport between regions must satisfy the minimum number of units required: NTUigg 0 l g

Qigg 0 l " i, l, g, g 0 ∈ nigg 0 l TCapil

ð13Þ

Similarly to constraint 13, the number of transfer units required for local biomass transport within region g must meet the minimum requirement: NTUIg g

Pbiomass, g "g∈G TCap

Table 1. Bioethanol Demand Data for the Demand Centres in Northern Italy Dbioethanol,g (tons/day)

ð14Þ demand center

scenario 2011

scenario 2020

An upper limit on the number of transport units required for the local transfer of biomass can also be introduced:

22

129.71

203.70

25

193.02

303.10

NTUIg e NTUImax "g∈G g

27

374.54

588.15

32 37

193.33 61.56

303.59 96.67

39

192.51

302.31

41

132.62

208.26

46

121.28

190.45

52

160.20

251.57

ð15Þ

max

where NTUIg is simply an upper bound. Similarly for NTUigg0 l NTUigg 0 l e

Qilmax " i, l, g, g 0 ∈ nigg 0 l TCapil

ð16Þ

Figure 5. Optimal network configuration for scenario 2011 according to 8N flow representation with global sustainability constraint. 4931



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Figure 6. (a) Optimal network configuration (biomass flows) for scenario 2011 according to 8N flow representation with local sustainability constraint. (b) Optimal network configuration (bioethanol flows) for scenario 2011 according to 8N flow representation with local sustainability constraint.

4. COMPUTATIONAL RESULTS Corn-based bioethanol production in Northern Italy from the work of Zamboni et al.24 was chosen as the case study with appropriate soil conditions, biomass yields, and a wide range of transfer modes available to highlight the model applicability. Northern Italy was discretized into 59 homogeneous square regions of equal size (50 km of length) to represent the geographical dependency of biomass production. The choice of the cell size depends on the tradeoff between computational time and resolution. In addition, most data were available on territorial (administrative) units with sizes ranging between 2000 and 5000 km2. One additional cell, g = 60 was added to account for the option of biomass import (Eastern Europe as the potential

foreign biomass supplier). It should be noted that ethanol import from foreign suppliers was not considered as an option in this work due to the national policy that aims to encourage local biofuel production for energy security. Two different demand scenarios are considered on the basis of the renewable fuel targets set by the European Directive. Lower heating values of fuels are used when applying the EU biofuel targets.25 They are converted to mass fraction as explained in Appendix B. The target for 2011 has been calculated on the basis of the assumption of a smooth transition from 2010 (5.75%) to 2020 (10%). Local and global sustainability constraints have been applied separately to both scenarios. In scenario 2020, it is also assumed that the domestic biomass resources are doubled in 4932



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year 2020 with improved cultivation practices, yields, and soil conditions. The internal depots used for conventional fuel storage are assumed to be the actual demand centers for biofuel, as bioethanol has to be blended with gasoline just before the final distribution stage to the customers due to stability problems.24 The resulting demand data for both scenarios is given in Table 1. The operating period in a year is taken to be 365 days. All other data related to the case study is given in the Appendices B-E for biothenol demand, transportation, biomass cultivation, and biofuel production, respectively. The proposed models were solved in GAMS 22.8 using CPLEX 11.1 solver on a 3.4 GHz, 1 GB of RAM machine. Figures 5 and 6 show the optimal configurations according to 8N with global and local sustainability constraints, respectively, for scenario 2011. For convenience, biomass and bioethanol flows have been presented in Figure 6a and b separately. With the global sustainability constraint, there are

Table 3. Comparison of Results for the Supply Chain Network Costs for Scenario 2020 with Global and Local Sustainability Constraints According to 8N (Optimality Gap: 1%)

Table 2. Comparison of Results for the Supply Chain Network Costs for Scenario 2011 with Global and Local Sustainability Constraints According to 8N (Optimality Gap: 1%)

Table 4. Comparison of Computational Statistics for Scenarios 2011 and 2020 with Global Sustainability

proposed model: 8N objective function and components

global

local

(euros/day)

sustainability

sustainability

1 892 273

1 985 121

total daily cost total investment cost

444 304

461 638

total production cost

1 357 356

1 364 933

biomass cultivation cost biofuel production cost

989 216 368 141

991 383 373 550

total transportation cost

90 613

158 550

biomass transport cost

55 288

126 194

biofuel transport cost

35 324

32 356

model statistics

proposed model: 8N

Zamboni et al.24

4N

8N

no. of constraints

167 653

1520

1970

no. of integer variables

72 300

914

1364

no. of continuous variables

36 789

1222

1674

objective function and components

global

local

(euros/day)

sustainability

sustainability

1 225 166

1 317 733

total investment cost

292 858

295 595

total production cost biomass cultivation cost

867 188 630 670

872 559 635 822

biofuel production cost

236 488

236 737

total transportation cost

65 120

149 579

total cost (keuros/day)

1899

1896

1894

biomass transport cost

35 426

118 033

optimality gap

1%

1%

1%

biofuel transport cost

29 694

31 546

CPU time (s)

989

1

2

total daily cost

scenario 2011 total cost (keuros/day)

1231

1229

1225

optimality gap

1%

1%

1%

CPU time (s)

285

12

12

scenario 2020

Figure 7. Optimal network configuration for scenario 2020 according to 8N flow representation with global sustainability constraint. 4933



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Figure 8. (a) Optimal network configuration (biomass flows) for scenario 2020 according to 8N flow representation with local sustainability constraint. (b) Optimal network configuration (bioethanol flows) for scenario 2020 according to 8N flow representation with local sustainability constraint.

three biofuel production plants located in cells 26, 32, and 40 with capacities of 250, 150, and 150 ktons/year, respectively. The location of the plant in grid 32 is in accordance with one of the potential Italian industrial plans.24 In addition, biomass cultivation sites are mostly located within the same cell as the biofuel production plants. On the other hand, when sustainability is considered locally, these three plants are located in cells 22, 27, and 42 with capacities of 110, 250, and 200 ktons/ year, respectively. In both optimal configurations in Figures 5 and 6, rail is the preferred transport mode due to its higher capacity and lower unit cost. Table 2 shows the breakdown of the total cost for the bioethanol supply chain for scenario 2011 with global and local

sustainability constraints according to 8N representation. As can be concluded from the table, local sustainability results in higher overall supply chain cost mainly due to the increase in biomass transport cost, as more cultivation areas are activated in this case and the biomass cultivated on these sites needs to be transported to the biofuel plants. Figures 7 and 8 show the optimal configurations for scenario 2020, when global and local sustainability constraints are considered separately. With the global sustainability constraint, there are four production plants located in cells 25, 27, 33, and 41 with capacities of 250, 250, 110, and 250 ktons/year, respectively. On the other hand, with local sustainability, there are five production plants located in cells 22, 25, 27, 40, and 42 4934



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summarized below. The symbols used for indices, sets, and parameters are the same as those introduced in section 3.

Table 5. Comparison of Computational Statistics for Scenarios 2011 and 2020 with Local Sustainability model

Zamboni et al.24

4N

8N

∑ PCCp Ypg ðCCF=RÞ

min TDC ¼

p, g


1349

1325

1318

optimality gap CPU time (s)

1% 2185

1% 244

1% 168

þ þ


1991

1985

optimality gap

1%

1%

1%

CPU time (s)

1152

34

42

T ∑g ðUPCbg Pbiomass UPCf p Pf pg Þ ,g þ ∑ p

∑i, l ðUTCilTCapilADDgg l NTUigg l Þ 0

1989

þ UTC

0

∑g TCapALDg NTUIg

ðA.1Þ

Subject to: Demand Constraints:

with capacities of 200, 110, 250, 150, and 150, respectively. In Figure 8a, all of the biomass produced in cell 28 is not transferred directly to cell 27; instead, some of it is transferred to 39 and then to 27. This stems from transport capacity limitations. Table 3 shows the optimal results for the bioethanol supply chain cost for scenario 2020 with global and local sustainability constraints according to 8N representation. Similarly to the results for scenario 2011, local sustainability results in higher overall supply chain cost compared to global sustainability. Table 4 shows the comparison of computational statistics for scenarios 2011 and 2020 with the global sustainability constraint according to the models: Zamboni et al.,24 4N, and 8N. As seen from the table, the proposed neighborhood approaches provide a reduction in the problem size by a factor of 100 and achieve time savings of 20-30 when compared to the model of Zamboni et al.24 Table 5 shows the computational statistics for both scenarios with local sustainability according to 8N and 4N representations. Similar to the case of global sustainability, the computational savings are high.

DTig ¼ DLig þ DIig " i, g

ðA.2Þ

DLig e PigT " i, g

ðA.3Þ

∑ Qig gl

ðA.4Þ

DIig e

0

l, g 0

" i, g

T T Pbiof uel, g ¼ γDbiomass, g " g

ðA.5Þ

TDi ¼

∑g DTig

"i

ðA.6Þ

TPi ¼

∑g PigT

"i

ðA.7Þ

Production Constraints:

∑ðQigg l - Qig glÞ

PigT ¼ DTig þ

5. CONCLUDING REMARKS In this paper, two new modeling approaches, 4N and 8N neighborhood representations, have been introduced for the optimal design of bioethanol supply chains. Corn-based bioethanol production in Northern Italy has been chosen as an illustrative case study. Two different demand scenarios have been investigated for years 2011 and 2020 on the basis of the EU biofuels target. The optimal configurations for both scenarios have been presented. Considering sustainability per region results in a more complex network with more cultivation sites being active. A comparison has also been made with the model introduced by Zamboni et al.24 The results for both scenarios show that the two neighborhood flow representations proposed provide significant reductions in problem size and computational requirements. Current work considers extension of the proposed approaches to second-generation technologies and uncertainty aspects.

0

l, g 0

T Pbiof uel, g ¼

0

∑p Pf pg

" i, g

"g

max PCapmin p Ypg e Pf pg e PCapp Ypg " p, g

∑p Yp, g e 1

"g

ðA.8Þ

ðA.9Þ ðA.10Þ ðA.11Þ

T GSg CYg ADg BCDmin e Pbiomass ,g g

e GSg CY g ADg BCDmax "g g TPbiomass e SusFTPot

ðA.12Þ ðA.13Þ

Transportation Constraints: Qilmin Xigg 0 l e Qigg 0 l e Qilmax Xigg 0 l " i, g, g 0 , l

’ APPENDIX A: SUMMARY OF ZAMBONI ET AL.24 MODEL The mathematical formulation for the bioethanol supply chain optimization model introduced by Zamboni et al.24 is

∑l Xigg l þ ∑l Xig gl e 1 0

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0

" i, g, g 0 6¼ g

ðA.14Þ ðA.15Þ



∑i ∑i Xigg l ¼ 0 0

∑ i, g , g , lˇTotal 0

igg 0 l

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" g, g 0 ¼ g

ðA.16Þ

Xigg 0 l ¼ 0

ðA.17Þ

Table C2. Maximum Cultivation Density in Each Cell of Northern Italy

’ APPENDIX B: BIOETHANOL DEMAND The biofuel targets are converted to a mass fraction for the gasoline-bioethanol fuel mixture using the following formula: e ¼ Xbioethanol

m LHV bioethanol Xbioethanol m m LHV bioethanol Xbioethanol þ LHV gasoline Xgasoline

ðB.1Þ where Xe and Xm represent the fraction of a component in the mixture on the basis of energy and mass contents, respectively, whereas LHV is the lower heating value of each component.

’ APPENDIX C: BIOMASS CULTIVATION PARAMETERS The input data for biomass cultivation is given in Tables C1C5, including the following parameters specific to each region respectively: cultivation yield (CYg), maximum cultivation density (BCDgmax), surface area (GSg), biomass production cost (UCCg), and arable land density (ADg). The value of the binary parameter CFg was set to 1 for domestic cultivation sites and 0 for the foreign cultivation sites. The minimum cultivation density, BCDgmin, was set to 0 for all regions. Table C1. Cultivation Yield in Each Cell of Northern Italy region (g) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

CYg (tons day 1.9 1.9 1.9 2.0 2.2 2.3 2.2 1.2 1.4 2.1 2.9 2.9 1.8 2.1 2.5 2.4 4.0 2.8 1.4 2.5 2.5 2.9 2.7 3.4 3.0 2.7 3.1 3.7 3.3 2.6

-1

-2

km )

region (g) 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

CYg (tons day

-1

region (g)

BCDgmax (km2cultivation/ km2arable land)

region (g)

BCDgmax (km2cultivation/ km2arable land)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

0.00 0.00 0.00 0.00 0.05 0.00 0.07 0.00 0.01 0.18 0.56 0.55 0.00 0.04 0.12 0.12 0.15 0.19 0.08 0.25 0.39 0.56 0.37 0.24 0.34 0.45 0.31 0.32 0.28 0.31

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.44 0.50 0.54 0.00 0.22 0.23 0.23 0.21 0.19 0.24 0.27 0.46 0.46 0.17 0.17 0.10 0.10 0.05 0.07 0.11 0.17 0.20 0.00 0.01 0.02 0.08 0.08 0.06 0.06 1.00

Table C3. Surface Area of Each Cell of Northern Italy

-2

km )

3.0 2.7 2.9 2.4 3.1 2.3 1.7 2.6 3.2 3.1 2.9 2.4 2.4 2.3 2.0 1.8 2.2 2.9 2.9 2.7 2.3 2.2 0.0 0.5 1.8 2.8 2.5 2 2 3 4936

region (g)

GSg (km2)

region (g)

GSg (km2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1875 2500 1500 1250 1000 1250 2000 2500 2500 2500 2500 1250 2000 2250 2500 2000 2500 2500 2500 2500 2500 2500 1250 2000 2500 2500 2500 2500 2500 2500

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2500 1500 750 250 2500 2500 2500 2500 2500 2500 2500 2500 1500 2500 2500 1750 2000 2500 2500 2500 2500 1000 1000 1500 1500 2500 2500 2500 1750 210000



ARTICLE

Table C4. Unit Biomass Cultivation Cost in Each Cell of Northern Italy region (g)

UCCg (euros/ton)

region (g)

UCCg (euros/ton)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

145.6 145.6 145.6 141.6 137.2 136.2 137.1 195.2 174.4 141.3 130.4 130.4 151.3 140.0 132.7 134.7 134.8 130.8 170.1 133.1 133.4 130.4 131.1 130.7 130.3 131.5 130.2 132.0 130.4 131.8

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

130.2 131.3 130.5 135.1 130.2 135.3 152.8 132.3 130.3 130.2 130.5 134.0 133.8 135.5 142.7 151.4 138.4 130.4 130.6 131.7 135.8 138.6 195.2 197.3 151.3 131.1 133.0 142.4 142.4 114.6

Table C5. Arable Land Density of Each Cell in Northern Italy

a

region (g)

ADg (km2/km2)a

region (g)

ADg(km2/km2)a

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

0.10 0.10 0.10 0.10 0.10 0.10 0.15 0.20 0.20 0.20 0.25 0.10 0.10 0.10 0.15 0.25 0.25 0.20 0.20 0.32 0.45 0.74 0.33 0.10 0.43 0.80 0.72 0.88 0.60 0.50

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.70 0.65 0.75 0.10 0.38 0.42 0.58 0.39 0.67 0.89 0.73 0.81 0.73 0.29 0.28 0.13 0.15 0.15 0.50 0.60 0.72 0.75 0.20 0.10 0.15 0.15 0.20 0.25 0.40 1.00

’ APPENDIX D: TRANSPORTATION SYSTEM PARAMETERS The available modes of transport are trucks, rail, barge, and ships. In addition, small trucks are used for local transfer of biomass within each cell element, and trans-ships can be used for biomass and ethanol import from foreign suppliers. However, as mentioned previously, ethanol import is not considered in this work; hence the capacity for trans-shipping of bioethanol is set to 0. The input parameters for these modes of transport are given in Table D1. The tortuosity factors for road and rail are taken as 1.4 and 1.2, respectively. Local roads are assumed to exist between all elements. Trans-shipping is considered for biomass import from foreign suppliers (region g = 60). The data for other transport modes are given in Table D2. The average local delivery distance, ALDg, is assumed to be proportional to the actual surface area of each region g, GSg. Table D1. Unit Transport Costs and Transportation Capacities for Each Transfer Mode UTCil (euros ton-1 km-1) transport mode

ethanol

corn

small truck

TCapil (tons) ethanol

0.27 (UTC*)

corn 5 (TCAP*)

truck rail

0.500 0.210

0.540 0.200

23.3 59.5

21.5 55

barge

0.090

0.120

3247

3000

ship

0.059

0.064

8658

trans-ship

0.005

8000 10000

Table D2. Tortousity Factor for Barge and Ship Transport Modes element linkages

transport mode

tortuosity factor

38-39

barge

1.9

39-40

barge

1.0

40-42 42-43

barge barge

1.4 1.8

32-34

ship

0.85

32-43

ship

1.18

32-52

ship

1.06

34-43

ship

0.66

34-52

ship

0.68

43-52

ship

1.54

’ APPENDIX E: BIOETHANOL PRODUCTION PARAMETERS The input data related to ethanol production is given in Table E1. The biomass-to-bioethanol conversion factor (γ) is taken as 0.324 tons bioethanol/tons biomass. Table E1. Input Parameters for Ethanol Production plant

PCapp

PCappmax

PCappmin

size, p (ktons/year) (ktons/year) (ktons/year)

km2 arable land/km2 regional surface. 4937

PCC (million euros)

UPCp (euros/ ton)

1

110

120

80

70

160

2

150

160

140

91

154

3

200

210

190

115

151

4

250

260

240

139

149



’ AUTHOR INFORMATION Corresponding Author

*Tel.: þ44 (0) 20 7679 2563. E-mail: [email protected].

’ ACKNOWLEDGMENT O.A. gratefully acknowledges financial support from Centre for Process Systems Engineering (CPSE). ’ NOMENCLATURE Binary Variables

Xigg0 l = 1 if product i is to be shipped via mode l from region g to region g0 Yg = 1 if a biofuel production plant of size p is to be established in region g Integer Variables

NTUigg0 l = number of transport units of mode l to transfer product i between regions g and g0 NTUIg = number of transfer units for local biomass transfer within region g Continuous Variables

DigL = local demand for product i in region g (tons/day) Digi = imported demand for product i in region g (tons/day) DigT = total demand for product i in region g (tons/day) FCC = total capital costs of facilities (euros) PC = total production cost (euros/day) Pfpg = biofuel production rate of a plant of size p located in region g (tons/day) PigT = production rate of product i in region g (tons/day) Qigg0 l = flow rate of product i via mode l from region g to g0 (tons/ day) TC = total transportation cost (euros/day) TDC = total daily cost for the biofuel supply chain network (euros/day) TDi = total demand for product i (tons/day) TPi = total production rate of product i (tons/day) TPot = total potential domestic biomass production rate (tons/day)

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Optimization-Based Approaches for Bioethanol Supply Chains

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