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Energy 156 (2018) 181e195

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Energy

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Strategic spatial and temporal design of renewable diesel and biojetfuel supply chains: Case study of California, USA

Mohamed Leila a, *, Joann Whalen a, Jeffrey Bergthorson b

a Department of Natural Resources Sciences, McGill University, Montreal, Canadab Department of Mechanical Engineering, McGill University, Montreal, Canada

a r t i c l e i n f o

Article history:Received 1 February 2018Received in revised form20 April 2018Accepted 29 April 2018Available online 15 May 2018

Keywords:Mixed-integer linear programmingMilitary biofuelsSupply chain optimizationSpatio-temporal optimizationFischer-tropschHydrotreatment of esters and fatty acids

* Corresponding author.E-mail address: mohamed.laila@mail.mcgill.ca (M

https://doi.org/10.1016/j.energy.2018.04.1960360-5442/© 2018 Elsevier Ltd. All rights reserved.

a b s t r a c t

The United States (US) military plans to acquire drop-in biofuels (renewable diesel and biojet fuel) toreduce carbon emissions and diversify military energy portfolio. To expedite this endeavor, the militaryprovided direct financial incentives to offset investment costs of selected drop-in biofuel demonstrationfacilities. It is not known if investment incentives alone will stimulate the creation of a full-scaleadvanced biofuel supply chain capable of meeting US military demands, given limited availability oflow-cost sustainable biomass feedstocks in some areas and considering the uncertainty in global oilprices. The objective of this work is to determine 1) whether a state in the US can meet its share ofmilitary biofuel targets from local biomass resources, and 2) if direct financial incentives can expedite thedevelopment of the military biofuel supply chain, under two different oil price scenarios. The Biofuelsupply chain GeoSpatial and Temporal Optimizer (BioGeSTO), was developed for that purpose andapplied to the state of California, USA from 2020 to 2040. The BioGeSTO model determined that biomassresources in California can meet 12e19% of its annual military targets between 2020 and 2040 ofrenewable diesel and biojet fuel using the Fischer-Tropsch (FT) and Hydro-Treatment of Esters and FattyAcids (HEFA) conversion technologies. However, under the reference oil price scenario, only HEFA con-version facilities introduced at 2027 in Kings County were found feasible. Under the high oil price sce-nario, both the HEFA and FT technologies were financially feasible and the supply chain productionapproaches the theoretical production limit by 2032. In both scenarios, providing investment incentiveshas a modest impact on expediting the supply chain, as facilities are introduced only 1e3 years earlierwhen receiving direct investment incentives. Sensitivity analysis shows that biomass availability has thegreatest impact on the supply chain performance such that a 50% increase in the baseline amount ofbiomass feedstock results in a 150% surge in the total cumulative production. In conclusion, the referenceoil price scenario drastically limits the ability of California to meet its military drop-in biofuel targets.Assuming a high oil price scenario, the state may be able to meet military biofuel targets by subsidizinglocal biomass production and importing the rest of the biomass required for this purpose from thenorthwestern states of Washington and Oregon.

© 2018 Elsevier Ltd. All rights reserved.

1. Introduction

The United States Department of Defense seeks to replace aportion of its conventional fuels with renewable diesel and biojetfuel [1]. This initiative is expected to curb greenhouse gas emissionsand diversify the fuel supply of the military, reducing reliance onforeign oil. The United States Air Force (USAF) aims to replace 50%of its total jet fuel consumption with biojet fuel by 2025. The US

. Leila).

Navy aspires to the even more ambitious target of replacing 50% ofits diesel and jet fuel consumption on navy vessels with renewablediesel and biojet fuel by 2020 [1]. The production of military gradebiofuels is possible using two biomass conversion technologiesapproved by the American Society for Testing and Materials(ASTM): gasification followed by Fischer-Tropsch (FT) synthesis,and Hydrotreatment of Esters and Fatty Acids (HEFA) [1,2]. Thechallenge of meeting the military targets extends beyond thetechnical feasibility of synthesizing the biofuels, however, and re-quires the establishment of a supply chain that can deliver thenecessary amount of biofuels at a competitive price. In an effort to

M. Leila et al. / Energy 156 (2018) 181e195182

expedite the development of these supply chains, the US militaryprovided direct financial incentives amounting to $510 Million in2011 to offset the investment costs of drop-in biomass conversionfacilities [1]. However, amid these efforts, crude oil prices plum-meted from $110/Barrel in June 2014 to less than $50/Barrel inJanuary 2015 [3]. This drop in crude oil prices challenged thefinancial feasibility of military biofuel supply chains, especiallygiven the commitment of the military to purchase biofuels atcompetitive prices with conventional oil [1].

A strategic supply chain optimization model is an appropriatetool for determining the amount of renewable diesel and biojet fuelthat can be produced for the US military, and the cost associatedwith production of these biofuels. A strategic design of a biofuelsupply chain deals with long-term decisions such as selectingbiomass sources, determining biorefinery locations and capacities,defining modes of transportation, and choosing conversion tech-nologies [4e10].

The scientific literature is rich with studies focusing on one ormore aspect of the strategic design of biofuel supply chains. Thesestudies considered many types of biomass feedstocks such as forestresidues [5,11], Hardwood [10], agricultural residues [6,12], andmicroalgae [4,13] as well as several types of bioenergy and biofuelproducts such as [14,15], bioethanol [16e20], biodiesel [4,21,22]and drop-in diesel and biojet fuel [9,10,23,24]. The literature alsoconsiders several technological pathways for converting biomass tobiofuel and bioenergy products. Among these technologies arefermentation for converting sugars to alcohols (ethanol) [25],anaerobic digestion for converting agricultural residues to biogas[26], and lignocellulosic biomass to various liquid fuels usinggasification followed by the FT process [27e29]. The most commonquestion that the strategic optimization of biofuel supply chainsaddresses is finding an optimal location and capacity for conversionfacilities [30]. For example, researchers from Princeton Universityused strategic supply chain optimization to determine optimal lo-cations for biorefineries converting hardwood biomass to gasoline,diesel, and jet fuel [10]. Zhang and Hu (2013) used strategic supplychain design models to determine optimal facility location, capac-ity, and biofuel production levels in Iowa State [9]. Duarte, Sarache,and Cost (2014) located a second-generation bioethanol plant inColombia that uses coffee cut stems as feedstock [6]. Othersincorporated environmental objectives in their optimizationmodels to take into account the sustainability of the biofuel supplychain design [31]. The majority of these studies focused on spatialaspects supply chain design, but provided little emphasis on itsevolution in time. To test if a particular policy successfully expeditesintroduction of new conversion facilities, or if future technologicaladvancement renders them financially feasible [32], time-explicitoptimization models are required.

This paper introduces the Biofuel supply chain Geo-Spatial andTemporal Optimizer (BioGeSTO), an integrated modelling frame-work for optimizing and simulating biofuel supply chains in theUnited States. BioGeSTO estimates the amount of renewable dieseland biojet fuel that can be produced from biomass resources formilitary use at state to national scales. The main contribution ofBioGeSTO is its ability to capture time dependent effects such astemporal changes in crude oil prices, biomass costs and availabilityas well as improvements in technological performance. This allowsBioGeSTO users to determine the factors that can expedite thedevelopment of their biofuel supply chain and makes the modelideal for the military case study.

In this paper, the state of California was studied because 1) Cal-ifornia has military significance as the homeport of the Pacific Fleetof the US Navy, and 2) California leads US states in agriculturaloutput, with production amounting to approximately 13% of the UStotal [33], and is the third largest state in terms of forest land

availability [34]. The case study of Californiawas examined between2020 and 2040 to determine whether direct financial incentivesexpedited the military biofuel supply chain development underdifferent oil price scenarios. To overcome the hurdles of time-explicit computations, the model used the IBM Decision Optimiza-tion Cloud platform (DOCloud) to solve the case study [35].

2. The supply chain optimization problem

2.1. . Supply chain overview

The problem of interest in this manuscript is to optimize asupply chain of military biofuels. Such supply chain is similar to ageneric one except for the following two restrictions: Feedstocksmust be sourced United States based suppliers, and the final biofuelproducts must be sold at cost-parity with their fossil fuel com-petitors. More details about the envisioned US military biofuelsupply chain and its restrictions were given in previous work [36].

BioGeSTO models the biofuel supply chain as a network offeedstock production sites, preprocessing facilities, conversion fa-cilities, and markets (Fig. 1).

The first echelon of the supply chain model includes the activ-ities of growing, harvesting, and preprocessing the feedstock. Everyyear, biomass producers in a US county, whether they are farmersgenerating agricultural residues, such as wheat straw, or loggingfirms producing forest residues, will sell their feedstock to abiomass preprocessing facility. These facilities are assumed to belocated at the county Seat (administrative center). There, feed-stocks undergo a preprocessing treatment for the purpose of en-ergy densification. For example, a preprocessing technology forwheat straw is pelletization and for oilseed crops is seed crushing.In the second echelon, biomass conversion facilities receive speci-fied amounts and suitable types of feedstock depending on theircapacity and conversion technology. The feedstock is converted tobiofuel products based on a feedstock and technology specific massbalance and then shipped to markets. Depending on the capacityand the conversion technology, the model determines the invest-ment, operation and maintenance costs of each facility. In the lastechelon, markets purchase the biofuel products to satisfy a givendemand. Markets M are divided into two categories, militarymarketsmk 2MK , which in this study include all USAF and US Navyinstallations in California, and civilian markets ck2CK, which couldbe major cities (note that civilian markets were not considered inthe case study). Finally, BioGeSTO assumes unimodal trans-portation with freight trucks is used to transfer biomass and bio-fuels between different echelons.

2.2. The supply chain optimization problem

The optimization problem is to determine the optimal supplychain design that maximizes the Net Present Value (NPV) duringthe simulation period (i.e., from 2020 to 2040). The supply chaindesign includes 1) the sources, quantities and types of the biomassshipped to conversion facilities each year, 2) the location, capacity,and introduction year of conversion facilities, 3) the technologyselected for every conversion facility, and 4) the quantities andtypes of biofuel products shipped to the markets, each year.

3. Formulation of the mixed-integer linear program

The design problem described in the previous section lends it-self well to formulation as a Mixed-Integer Linear Programming(MILP) problem. This section describes the MILP constraints andobjective function of the supply chain problem.

Fig. 1. Supply Chain Superstructure as modeled in BioGeSTO. Biomass at each county, i, is transported to the administrative center (Seat) and then handled in a preprocessingfacility. Afterwards, freight trucks transport the preprocessed biomass to a conversion facility, j, to convert into biofuels. Finally, freight trucks transport the biofuels to their demandsites, major cities, ck, and military installations, mk.

M. Leila et al. / Energy 156 (2018) 181e195 183

3.1. Material flow

Every county, i in a given year, t, generates raw biomass of typef .Parameters biomamount*

f ;i;t and biomcost*f ;i;t represent the amount and the

cost of raw biomass at this county. The final biomassyieldbiomamount

f ;i;t , after accounting for the losses due to handling of

the biomass at the preprocessing facility is given by

biomamountf ;i;t ¼ preProcesslossf ;pq* biom

amount*f ;i;t (1)

where preProcesslossf ;pq is the loss fraction associated with technology

pq handling feedstock of type f. The total amount of feedstock fflowing from county i in year t, to all facilities (set J),FFf ;i;j;t , must be

less than or equal biomamountf ;i;t .

XJj

FFf ;i;j;t � biomamountf ;i;t c f2F; i2I; t2T (2)

The parameter distbiomMaxTrans specifies the maximum distancethat biomass could be shipped from a preprocessing to a conversionfacility. If distech1i;j is the distance between the seat of county i and

candidate facility location j, then

ði; jÞ2D c i2I; j2J��� distech1i;j >distbiomMaxTrans (3)

where set D contains all pairs of county seats and candidate facilitylocations ði; jÞ with distance greater thandistbiomMaxTrans. Equation(5) prevents feedstocks from flowing from county i to conversionfacility j if the pair (i,j) belongs to set D.

XFf

XTt

FFf ;i;j;t ¼ 0 cf2F; ði; jÞ2D; t2T (4)

The amount of feedstock f flowing from all counties to facility j,in year t, must equal the sum of feedstock amount available tomilitaryAAMf ;j;c;q;t, and civilianAACf ;j;c;q;t , products at this facility

XIi

FFf ;i;j;t ¼XQq

XCc

AAMf ;j;c;q;t þXQq

�XCc

AACf ;j;c;q;t cf 2F; j2J; t2T (5)

where subscripts c and q specify the capacity level and technologychoice of the conversion facilities. The total amount of militarybiofuel products of type mp, shipped to military market, mk, fromfacility j, with capacity level c, technology q in year t, MBFj;mp;mk;t ,toall military markets must equal to the amount of feedstock allo-cated to producing military-grade biofuels multiplied by the con-version efficiency parameteraf ;q;mp

XMK

mk

MBFj;mp;mk;t ¼XFf

XQq

XCcaf ;q;mpAAMf ;j;c;q;t

cmp2MP; j2J; t2T

(6)

A similar function is applied for civilian biofuel products:

XCKck

CBFj;cp;ck;t ¼XFf

XQq

XCc

af ;q;cpAACf ;j;c;q;t

c cp 2 CP; j2J; t2T

(7)

The amount of military biofuel products shipped from all facil-ities to military market mk in year t must be less than or equal thedemand of this market MilDem mp;mk;t

XJj

MBFj;mp;mk;t � MilDem mp;mk;t c mp2 MP; mk2MK; t2T

(8)

The same constraint applies to civilian biofuels

XJj

CBFj;cp;ck;t �CivDemcp;ck;t c cp2CP; ck2CK; t2T (9)

M. Leila et al. / Energy 156 (2018) 181e195184

3.2. Cash flows

The cost of preprocessed biomass, biomcostf ;i;t , is given by

biomcostf ;i;t ¼ transCostrawBiomass

f *distinterCounty þ preProcesscostf ;pq

þ biomcost*f ;i;t cf2F; i2I; t2T

(10)

Where transCostrawBiomassf is the cost of transporting 1 unit mass

of raw biomass of type f for 1 unit distance, distinterCounty is theaverage distance between a production site and the county seat,and preProcesscostf ;pq is the cost of preprocessing one unit mass of

biomass f using preprocessing technology pq.The total costs of facility j in year t are the sum of biomass

purchases, transportation, operations and maintenance, and in-vestment costs (equation (11))

TotalCostsj;t ¼ FeedstockPurchasesj;t þ FixedBiofTransCostj;t

þVariableBioFTransCostj;t

þVariableBiomTransCostj;t þFixedBiomTransCostj;t

þXQq

XCc

�InvcostAnnualizedj;c;q;t

þ OMCostj;c;q;t�

cj2J; t2T

(11)

Biomass feedstock purchased by facility j in year t is equal to thesum of feedstock flow from all counties multiplied by the biomasscost, in this year.

FeedstockPurchasesj;t ¼XIi

XFf

FFf ;i;j;t*biomcostf ;i;t

c j2J; t 2T

(12)

Transportation costs of biomass and biofuels are considered partof the total costs incurred by each facility. While in practice, theconversion facility is not responsible for the costs of transporting itsproducts to themarket, BioGeSTO adds this extra cost to account formarket locations in the supply chain design. Fixed costs cover thechargesof buyingor renting the freight trucks andpaying salaries fordrivers, while variable costs cover transportation expenses such asfuel andmaintenance. For example, FixedBiomTransCostj;t is the totalfixed transportation costs associated with transporting pre-processed biomass from all suppliers to conversion facility at j onyear t while FixedBiofTransCostj;t is the total fixed transportationcosts associated with transporting biofuel products (renewablediesel and biojet fuel) from conversion facility at j on year t to themarkets. All distances were calculated using the Vincenty formula[37].

FixedBiomTransCostj;t ¼XIi

XFf

biomdfcf ;t *FFf ;i;j;t cj2J; t 2T

(13)

VariableBiomTransCostj;t ¼XIi

XFf

biomdvcf ;t *FFf ;i;j;t*dist

ech1i;j

cj2J; t 2T

(14)

FixedBiofTransCostj;t ¼XCKck

XCPcp

biof dfccp;tCBFj;cp;ck;t þXMK

mk

�XCKck

biof dfcp;t *MBFj;mp;mk;t cj2J; t 2T

(15)

VariableBiofTransCostj;t ¼XCKck

XCPcp

biof dvccp;t*CBFj;cp;ck;t*distech2;civj;ck

þXMK

mk

XMP

mpbiof dvcmp;t*MBFj;mp;mk;t*dist

ech2;milj;mk cj2J; t 2T

(16)

The annualized investment costs are calculated over the lifespanof facility with technology q.

InvcostAnnualizedj;c;q;t ¼ InvCostj;c;q;tlifespanq

cj2J; c2C; q2Q ; t2T

(17)

BioGeSTO accounts for economies of scale and technologylearning while modelling the investment, operations and mainte-nance costs of conversion facilities. For every facility located at jwith technology q, the investment cost can be expressed as

InvCost**j;q ¼ InvCostbaselineq

CAP**j;q

CAPbaselineq

!b

c j2J; q2Q (18)

where CAPbaselineq and InvCostbaselineq are baseline capacity and in-

vestment cost of a benchmark facility, and CAP**j;q is the capacity of

facility located at j. The scaling factor, b, is typically between 0.6 and0.7 [38]. The two asterisks represent two levels of aggregation onthe investment cost and capacity variables. First, InvCost**j;qwill be

disaggregated to create time explicit investment cost variable byapplying a log-linear technology learning model given by

InvCost*j;q;t ¼�InvCost**j;q

�Mlog2ð1�LRÞ

t c j2J; q2Q ; t2T (19)

where LR is the learning rate and Mt is the cumulative industrycapacity. This approach follows the work of Daugaard, T., et al. onthe effect of learning rates on investment costs of biorefineries [32].The capacity variable is disaggregated to create new time explicitvariables

CAP*j;q;t ¼ CAP**j;q c j2J; q2Q ; t2T (20)

Fig. 2. Piecewise linearization of investment costs of a conversion facility as a functionof capacity. The departure of the curve from the dotted line (linear relationship) showsthe non-linear effect of economies of scale on reducing investment cost withincreasing capacity.

M. Leila et al. / Energy 156 (2018) 181e195 185

Solving the MILP requires piece-wise linearization of the in-vestment cost function. The set of capacity levels, C, divides theinvestment cost function into regions, inwhich investment cost is alinear function of capacity (Fig. 2). This is accomplished by dis-aggregatingCAP*j;q;t , and InvCost*j;q;t to create new capacity level

explicit variables using the convex hull technique [30].Since only one capacity level can be selected for each facility, the

problem is represented by the following logical disjunctions:

∨c

264

Bj;c;q;t

capminj;c;q;t � CAP*j;q;t � capmax

j;c;q;t

InvCost*j;q;t ¼ Interceptj;c;q;t þ Slopej;c;q;t*CAP*j;q;t

3775 c j2J; q2Q ; t2T (21)

where Bj;c;q;t is a boolean variable that is true for only one capacity

level c, capminj;c;q;t and capmax

j;c;q;t are lower and upper constraints on

CAP*j;q;t . Interceptj;c;q;tand Slopej;c;q;t are the linearization parameters.

To enforce the disjunction, the continuous variables CAP*j;q;t and

InvCost*j;q;t are first disaggregated.

CAP*j;q;t ¼XCc

CAPj;c;q;t c j2J; q2Q ; t2T (22)

InvCost*j;q;t ¼XCc

InvCostj;c;q;t c j2J; q2Q ; t2T (23)

The linearization parameters are then expressed as

Slopec;q;t ¼InvCostj;c;q;t � InvCostj;c�1;q;t

CAPj;c;q;t � CAPj;c�1;q;t

c j2J; c2C � cmin ; q2Q ; t2T(24)

and

Interceptc;q;t ¼ InvCostj;c�1;q;t c j2J; c2C � cmin; q2Q ; t2T

(25)

Binary variables are needed to express yes and no decisions in aMILP formulation. BioGeSTO uses two sets of binary variables:bj;c;q;t , Zj;t . The variable bj;c;q;t is 1 if a facility at location j, with ca-pacity level c and technology q exits in year t and Zero otherwise,while the variable Zj;t is 1 if a facility is introduced in location j inyear t and Zero otherwise. Zj;t can only assume the value 1 if bj;c;q;t is1 while bj;c;q;t�1 is zero, indicating that a facility at j existed in year tbut did not in year t-1 (equations (26) and (27)).

Zj;t ¼XQq

XCc

bj;c;q;t � bj;c;q;t�1 cj2J; t2T � ti (26)

and

Zj;t ¼XQq

XCc

bj;c;q;t¼ti cj2J (27)

The Boolean condition is implemented using the binary varia-blebj;c;q;t . Each facility will be allowed only one capacity level andone technology.

XQq

XCc

bj;c;q;t � 1 cj2J; t2T (28)

The constraints inside the disjunction can, therefore, be repre-sented in terms of the disaggregated and binary variables

bj;c;q;t*capc�1 � CAPj;c;q;t

� bj;c;q;t*capc cj2J; c2C � cmin; q2Q ; t2T

(29)

and

InvCostj;c;q;t ¼ Interceptj;c;q;t*bj;c;q;t þ Slopej;c;q;t* CAPj;c;q;tcj2J; c2C; q2Q ; t2T

(30)

where capc is maximum capacity at capacity level c.For example, if the optimal solution for a problem requires a

facility to be built with capacity level 2, this means that the Booleanvariable is false for all other values of c. Therefore, only the con-straints with c equals to 2 will be activated in the disjunction. Thebinary variable bj;c¼2;q;t is set to 1 and bj;cs2;q;t variables are set tozero. When the binary variable is set to 1, the continuous decisionvariable CAPj;c¼2;q;t in equation (29) is allowed to range betweencapmax

j;2;q;tand capmaxj;2;q;t(Fig. 2). All other CAPj;cs2;q;t are set to zero,

M. Leila et al. / Energy 156 (2018) 181e195186

which means the facilities cannot process any biomass and there-fore will not be constructed.

Operations and Maintenance costs are modeled as a fraction ofthe investment costs [31].

OMCostj;c;q;t ¼OM fraction*InvCostj;c;q;t cj2J; c2C; q2Q ; t2T

(31)

The capacity CAPj;c;q;t (in thousand barrels), is the total amountof fuel produced by facility j, at capacity level c, with technology q attime t

CAPj;c;q;t ¼XFf

XMP

mpaf ;q;mpAAMf ;j;c;q;t þ

XFf

�XCPcp

af ;q;cpAACf ;j;c;q;t cj2J; c2C; q2Q ; t 2T

(32)

To ensure that the capacity of a facility remains the same afterthe introduction year and for the rest of the simulation period, weadd the following constraints.

CAPj;c;q;tþ1 � CAPj;c;q;t� capmax

�1� bj;c;q;t

�cj2J; c2C; q2Q ; t2T � tf

(33)

and

CAPj;c;q;tf � CAPj;c;q;tf�1� capmax

�1� bj;c;q;tf

�cj2J; c2C; q2Q

(34)

where tf denotes the final year of the simulation. If bj;c;q;t is set to1 at time period t, then there cannot be a difference between thecapacity of the facility at this period and the next (tþ1). By induc-tion, it follows that the capacity of this facility will remain the samethroughout the simulation period. However, If bj;c;q;t is set to 0, theconstraint is relaxed, allowing the difference in capacities betweentime period t and tþ1 to range from 0 (no facility is introduced) tocapmax (a facility with the maximum possible capacity isintroduced).

Another constraint is needed to ensure that once a facility isintroduce at t, it remains there for the rest of the simulation period.

bj;c;q;tþ1 � bj;c;q;t cj2J; c2C; q2Q ; t2T � tf (35)

Revenues of facility j in year t are generated from selling civilianand military biofuels at a given market price in year t.

Revenuej;t ¼XCPcp

biofpricecp;t*XCKck

CBFj;cp;ck;t

þXMP

mpbiofpricemp;t*

XMK

mk

MBFj;mp;mk;t cj2J; t2T

(36)

BioGeSTO allows users to specify financial incentives that can bepaid directly to the conversion facilities. The incentives allocated toa facility at location j in year t is given by the decision variableINCj;t .

The parameter IncTechc;q specifies the fraction of investment costsprovided to a facility with capacity level c and technology q.Equation (36) shows the relationship between variable INCj;t and

parameter IncTechc;q

INCj;t �XQq

XCc

XCc

InvCostj;c;q;t IncTechc;q cj in J; t in T (37)

Incentives are provided on the introduction year of the facilitiesand are zero otherwise. This constraint is enforced by

INCj;t � Zj;t Incmax cj in J; t in T (38)

where Incmax is the maximum incentive provided to any facility.The profit of every facility j in year t is the difference between

revenues and total costs, as well as incentives (if provided).

Profitj;t ¼ Revenuej;t � TotalCostsj;t þ Incj;c;q;t cj2J; t2T

(39)

c. Objective FunctionThe Net Present Value (NPV) of facility at location j, is given by

NPVj ¼XTt

Profitj;tð1þ iÞt cj in J (40)

where i is the discount rate. The objective function is formulated asthe sum of the NPVs of all facilities.

maximizeXJj

NPVj (41)

The formulation of the objective function encourages the modelto introduce financially feasible facilities (NPV>0) within the periodof simulation.

4. Case study

There are two essential aspects that need to be considered whiledesigning a supply chain optimization study: scale and scope. Thefirst deals with the limitation on spatial and temporal boundaries ofthe problem, and the latter defines the pathways under investiga-tion such as conversion technologies, feedstocks, and markets. Thiscase study demonstrates how BioGeSTO can simulate a biofuelsupply chain for renewable diesel and biojet fuel in one state of theUnited States. The choices of the scale and scope were made tostrike a balance between the comprehensiveness of the case studyand its computational tractability.

The scale of the case study is bounded spatially by the state ofCalifornia and temporally by 20-year period from 2020 to 2040. Asstated in the introduction, Californiawas selected due to its militarysignificance and wealth of natural resources. The selected timeperiod is ideal because it covers the beginning of the USAF and Navymandates and spans the lifetime of a typical biomass conversionfacility [12].

The scope of the case studies limits the choices of feedstocks,preprocessing and conversion technologies considered. Feedstockswere chosen for their abundance in the state and compatibilitywith the selected conversion technologies. Literature was used todecide on the choice of preprocessing technologies to use with theselected feedstocks. Finally, the conversion technologies werechosen based on their ability to produce military-approved drop-inrenewable diesel and biojet fuels in compliance with ASTM stan-dard D7566 and MIL-DTL-5624 V [1]. The following sections pro-vide a detailed account of the data and parameter choices used thinthis case study.

Table 1Assumptionsof biomass preprocessing technologies used in the BioGeSTO model.

Biomass Preprocessing technology Mass losses (wt.%) Preprocessing costs ($/ton)

Wheat straw Pelletization 5% [42] 35 [42]Corn stover Pelletization 5% [42] 35 [42]Forest residues Torrefaction (following pelletization) 5% [44] 62 [44]Camelina Oil seed pressing 1% [46] a 53 [45]

a This is the mass loss associated solely with the pressing process, not to be confused with the mass balance for the extraction of camelina oil from the seed described indetails in section 8.1.2 of the supporting documents.

M. Leila et al. / Energy 156 (2018) 181e195 187

4.1. Feedstock availability and cost

This case study considered lignocellulosic and oilseed crops asbiomass feedstocks. Data for lignocellulosic feedstock availabilityand cost were retrieved from the Billion Tons Study (BTS-2011)update [39]. BTS is the Department of Energy's national assessmentof potential supply of biomass in the United States [40]. Lignocel-lulosic feedstock types under considerationwere 1) wheat straw, 2)corn stover, and 3) forest residues. BTS provides data up to year2030 and BioGeSTO linearly extrapolated the cost and availability toyear 2040. Oilseed crops are not part of the BTS data collection andwere estimated separately. Camelina, used as a proxy for oilseedcrops, is assumed to grow in rotation with wheat, barley and oats[41]. The biomass section in the supporting documents providedetails on the BTS scenarios associated with the lignocellulosicfeedstock data and explains how camelina availability and costwere estimated.

BioGeSTO adjusts the amount and cost of feedstocks available ineach county following the preprocessing step. The mass losses andcosts incurred of each preprocessing step are listed in Table 1.

Fig. 3. Spatial distribution and quantity (in tons) of feedstocks availab

Appropriate preprocessing technologies for each type of feedstockwere selected by reviewing the literature. Pelletization transformsraw agriculture residues such as wheat straw and corn stover intostandardized units (pellets) with uniform shape, moisture andenergy content [42]. Torrefaction technology heats biomass in theabsence of oxygen to release volatile compounds and break downhemicellulose structures which results in a homogeneous productwith higher energy and carbon content [43]. Torrefaction followingpelletizationwas shown to be a cost-effective preprocessing optionfor forest residues [44] despite costing almost twice as much assimple pelletization. Finally, oilseed crops such as camelina requiresimple and inexpensive seed pressing (crushing) to extract oil fromthe seeds [45,46].

Feedstock distribution in the state shows that wheat straw, cornstover and camelina are abundant in the central and southerncounties where agricultural activities occur, while forest residuesare concentrated in northern counties (Fig. 3).

Camelina oil is the most expensive feedstock, costing $563/ton,which is more than five times as expensive as the average cost oflignocellulosic feedstocks. However, due to the high calorific value

le in California in 2020 after accounting for preprocessing losses.

Table 2Average feedstock cost after adding preprocessing cost in 2020, based on BTS dataand the oilseed crop model described in the supporting documents.

Feedstock Calorific value(GJ/ton) Cost($/ton) ($/GJ)

Wheat straw 17.6 119 6.7Corn stover 17.6 108 6.13Forest residues 17.6 110 6.25Camelina oil 42 563 13.5

Table 3Mass balances and baseline capacities and investment costs of conversion facilities.

Technology Allowed Feedstock Mass Balance(Thousand Barrels/tonne)Renewable diesel Biojet

FT Wheat Straw 3.76� 10�4 [50] 5.01� 10�4

Corn Stover 3.76� 10�4 5.01� 10�4

Forest Residues 4.23� 10�4 5.64� 10�4

HEFA Camelina 1.698� 10�3 [48] 2.264� 10�3 [48]

M. Leila et al. / Energy 156 (2018) 181e195188

of camelina oil, its cost per gigajoule (GJ) is only roughly twice thatof lignocellulosic feedstocks (Table 2).

4.2. Facility locations, capacities, costs, and conversion technologies

Suggesting a set of candidate counties for introducing con-version facilities reduces the number of possible decision vari-ables and thus the solution time of the model. From the set ofcandidate locations, the model places conversion facilities suchthat it minimizes incoming biomass and outgoing biofuel trans-portation costs. Since biomass is significantly costlier to transportthan liquid biofuels (see section 4.4), the candidate facility loca-tions will be selected based on biomass availability. This usefulheuristic helps speed up the solution time. Out of 58 counties inCalifornia, the top 10 counties in lignocellulosic feedstock avail-ability (wheat straw, corn stover, forest residues) were consideredcandidates for hosting FT facilities and the top 10 counties incamelina production potential were considered candidates forhosting HEFA facilities.

The minimum and maximum allowed capacities of a conversionfacility, cmin andcmax, were set, respectively, at a 400 and 1400Thousand Barrels of renewable diesel and biojet fuel per year[47,48]. Investment costs are functions of capacity and introductionyear (Fig. 4), as described in equations (20)e(30). The scaling factor,b, was set to a value of 0.7 to account for economies of scalesassociated with biomass conversion facilities [38]. For example, aHEFA facility introduced in 2020 with capacity of 700 ThousandBarrels per year requires investment costs of approximately $88Million (Table 4). The investment cost per unit of products istherefore $125/Barrel. Using equation (20), the investment costs forthe facility with larger capacity can be calculated. For example, at acapacity of 1400 Thousand Barrels per year, the HEFA facility willcost $142 Million and the cost per unit drops to $101/Barrel.

Investment costs also depend on the introduction year torepresent reduction of costs due to technology learning. In this casestudy, technology learning was modeled using simple log-linear

Fig. 4. Investment costs as a function of facility capacity at the beginning, middle, and end othe whole curve shifts downwards as time progresses due to technology learning. Reductionsimulation (Following the log linear-model [32]).

model (equation (21)) as described by Daugaard et al. [32]. Thelog-linear model indicates that changes in X (cumulative industrialcapacity) exponentially diminishes change in Y (investment costs)i.e. reduction in investment costs due to technology learning slowsdown as the simulation years advance (Fig. 4). For simplicity, bothtechnologies were set to have the same technology learning pa-rameters. Mt¼0, the cumulative industry capacity at the base year ofsimulationwas set to 1000 Thousand Barrels and LR was set to 0.05[32]. For example, a 700 Thousand Barrels per year FT facility re-quires $230 Million in investment costs in 2020. If the same facilitywas introduced in 2030, it would require $192 Million in invest-ment costs (a reduction of 16%). After another decade has passed(2040), the facility will require $183 Million in investment costs(only 5% reduction). Section 8.2 in the supporting documentsprovide the estimates of investment costs of Fischer-Tropsch andHEFA conversion facilities used for different capacities and years.Operations and maintenance costs was calculated as % of invest-ment costs (equation (31) and the OM fractionwas set at 17% [49]. Adiscount rate, i, of 0.075 was used in NPV calculations.

Mass balances for the FT and HEFA conversion facilities wereestimated from the literature (Table 3) [48e50]. Both processesproduce renewable diesel and biojet fuel and it is assumed thatthey are set to maximize biojet fuel portion in their product slate.

4.3. Biofuel demand and prices

The Energy Information Administration (EIA) provides state-specific historical data for the demand and prices of differentcivilian and military transportation fuels through the State EnergyData System (SEDS) [51]. BioGeSTO linearly extrapolated historicalSEDS data to predict demand during the simulation period. Thedemand for biofuels (renewable diesel and biojet fuel) was the totaldemand for each fuel type multiplied by a target rate. In this casestudy, the military biofuel target rates of 50% for renewable dieseland biojet in California were applied [1]. Since the supply chain

f the 20 years simulation. The investment cost function follows economies of scale ands in costs are more significant at earlier years and tend to stabilize near the end of the

Fig. 5. Military demand for biofuels (diesel and drop-in biojet) in California, US in2020. Fuel requirements were estimated from the Defense Installations Spatial DataInfrastructure dataset [54].

M. Leila et al. / Energy 156 (2018) 181e195 189

network configuration is spatially explicit, the demand is alsodistributed spatially (Fig. 5). Military demand is distributed acrossall military installations in California based on their normalizedsurface areas, using the list of installations, their location, andsurface areas provided by the Defense Installations Spatial DataInfrastructure dataset [52]. BioGeSTO assumed that biofuels pro-duced in California were demanded by, and shipped to, militaryinstallations located within the state. Since this case study focuseson military biofuels, all civilian demand was set to zero. Section 8.3of the supporting documents provides more details on the pro-cedure used to estimate military biofuel demand.

4.4. Transportation

Freight trucks are the conventional method for transportingagricultural commodities such as biomass. In cases where theinfrastructure allows the biomass to be transported by train, or thebiofuel pumped in pipelines, it would be cheaper than freighttrucks. Therefore, choosing freight trucks serves as a good upperbound on transportation cost.

We experimented with different values for the parame-terdistbiomMaxTrans which specifies the maximum distance pre-processed biomass could be transported from preprocessingfacilities to conversion facilities parameter and decided to set thevalue to 800 km. As the value of distbiomMaxTransincreases, the modelbecomes more permissive but at the price of increasing computa-tional cost. On the other hand, setting the value too small would bedetrimental to the quality of the solution as it would pull thechoices of candidate facility locations towards the biomass

Table 4Fixed and variable distance cost parameters used in modelling biomass and biofu

Type of flow Fixed Distance Costs($/tonne)

Wheat Straw pellets 15 [44]Corn Stover pellets 15 [44]Forest Residues (wood pellets) 15 [44]Camelina Oil 3.86 [53]All Biofuels 3.86 ($/Thousand Bar

production centers. Our experiments have shown that given Cal-ifornia's geography, 800 km is the optimal value that strikes abalance between model permissiveness and computational cost.

Fixed and variable distance cost parameters were retrieved fromthe literature (Table 4) [44,53]. On average, transportation of solid,low energy density, lignocellulosic biomass costs five time more totransport than liquid material such as camelina oil and biofuelproducts. This justifies the heuristic explained in section 4.2regarding the candidate facility location. These baseline valuesare increased by 1% each year to account for increase in fuel costs.

5. Results and discussion

5.1. Theoretical production potential of biofuels in California

Theoretical production potential of biofuels in California is themaximum production limit achieved by converting all availablefeedstocks to biofuel. Generally, biomass availability retrieved fromthe BTS or estimated based on the oilseed crop tends to increaseover time. Therefore, the amounts of biomass available at the lastyear of the simulation (2040) are the greatest [39]. The maximumproduction potential of renewable diesel and biojet fuel is esti-mated bymultiplying the quantity of each biomass type consideredin the case study by the mass balance of an appropriate conversiontechnology. This shows that 1137 and 1518 thousand barrels ofrenewable diesel and biojet fuel, respectively, can be produced in2040 (Table 5). In the same year, however, the military re-quirements for biofuels are estimated at 14,646 thousand barrels ofbiojet fuel and 7561 thousand barrels of renewable diesel. There-fore, the maximum biofuel potential in California in this year meetsup to 12% of the military target for biofuels. Over the period of thesimulation, the percentage of fulfilled demand, ranged from 19%(2020) to 12% (2040) (see Supporting documents, section 8.4,Table 12). The percentage of fulfilled demand drops near the end ofthe simulation period because the rate of increase in estimateddemand for military biofuels is higher than the rate of increase inbiomass availability.

The modest production potential of biofuels in Californiacompared to its military requirements can be attributed to the largemilitary community in the state, which is home for more than160,000 active military personnel on duty (highest in the country)and to 63 military installations [52,55]. Of course, this case studyunderestimates the actual production potential of the State ofCalifornia as it does not explore all possible technological pathways.For example, other types of feedstocks (such as used cooking oil) orconversion technologies (Alcohol to Jet) may be considered. Addingmore conversion pathways to a case study increases its scope butcomes at the price of increased computational complexity.

5.2. Biofuel supply chain under reference oil scenario

The actual amount of biofuel produced in California is less thanthe maximum biofuel potential and is determined by solving the

el transportation costs using freight trucks in 2020.

Variable Distance Costs ($/tonne*km)

0.075 [44]0.075 [44]0.075 [44]0.05 [53]

rels) [53] 0.05 ($/Thousand Barrels.km) [53]

Table 5Annual biofuel maximum production potential in California. Forest residues, cornstover, and wheat straw estimates are based on BTS data for the year 2040, andCamelina oil estimates are based on the oil crop model described in the supportingdocument. The amount of resources available change throughout the simulationperiod.

Feedstock Amount(tonnes) Renewable dieselmaximum productionpotential (ThousandBarrels)

Biojet maximumproductionpotential(Thousand Barrels)

Forest Residues 1,728,843 731 975Wheat Straw 115,931 43 58Corn Stover 112,076 42 56Camelina Oil 189,371 321 429Total Potential - 1137 1518

M. Leila et al. / Energy 156 (2018) 181e195190

MILP, considering the logistical and economic constraints in thebiofuel supply chain. Using the case study parameters described insection 5, the MILP problem was solved under a reference oil pricescenario and no incentives. Oil price scenarios are discussed ingreater depth in the supporting documents. The MILP model con-sisted of 769,955 continuous and 10,962 binary variables and146,927 constraints and was solved in 83min using IBM DecisionOptimization Cloud (Virtual machine of 6 cores and 128 GB RAM)[35].

The solution of the MILP resulted in the introduction of a singleHEFA facility with a capacity of 697 Thousand Barrels per year at

Fig. 6. Spatiotemporal map of military biofuel supply chain in based on a 20 years simulationa HEFA facility in King's County (2027) was the only event to occur during the simulation permap.

Kings County in 2027 (Fig. 6). This was the only event to occurduring the simulation period and therefore no change in the supplychain structure is seen in the spatio-temporal map from 2027 to2040. Selecting the location of the conversion facilities aims tominimize the overall transportation costs. Since biomass is moreexpensive to transport than biofuels, BioGeSTO places the facilitiescloser to their feedstock supply than to military bases (see section5.2). Kings County ranks first in Camelina production potentialaccording to the oilseed crop model simulations, and it is expectedto produce an average of 25,000 tonnes (28 million liters) ofCamelina oil annually (Fig. 3). The county is also strategically sit-uated a few kilometers west of the highest demand point for mil-itary biofuels in the state, the Naval Air Weapons Station in ChinaLake.

BioGeSTO selects the introduction year of a facility such that itbalances the temporal tradeoff. Early introduction of profitable fa-cilities leads to higher NPV because of longer operation yearsthroughout the simulation. However, delays in introduction alsoreduces investment, operations and maintenance costs which alsoleads to higher NPV. The Minimum Selling Price (MSP) of HEFAproducts from the Kings County facility (average of renewablediesel and biojet) was $3.54/gallon and the market price of equiv-alent conventional oil products exceeded this barrier in 2025.BioGeSTO delayed the introduction of the conversion facility for 3years after the facility became profitable to capitalize on reductionsin the investment costs, amounting to $ 11.5 Million, due to tech-nological learning (Fig. 4).

(2020e2040) under reference oil price scenario and no incentives. This introduction ofiod and therefore no change in the supply chain structure is seen in the spatio-temporal

Table 6Supply chain characteristics under the reference oil price scenarios with no incentives.

Incentive level(% of capital cost) Incentives($M) NPV($M) Total Production(Thousand Barrels/year) Introduction year

0 None 47.6 697 Kings (2027)15 11 54.2 697 Kings (2027)30 22.7 61 697 Kings (2026)45 34.5 68.5 697 Kings (2025)

M. Leila et al. / Energy 156 (2018) 181e195 191

Providing direct financial incentives did not lead to the intro-duction of new facilities, since the HEFA facility already consumedapproximately all camelina resources available in the state(Table 5). However, incentives can expedite the introduction of theHEFA facility by offsetting investment costs, hence, neutralizing theeffect of technology learning. Incentives amounting to 30% and 45%of the facility's investment costs advanced the introduction year to2026 and 2025 respectively (Table 6).

5.3. Biofuel supply chain under high oil prices scenario

Under a high oil price scenario and no incentives, the military

Fig. 7. Spatiotemporal map of military biofuel supply chain in based on a 20 years sim

biofuel supply chain consisted of one HEFA and two FT facilities.The model introduced a HEFA facility (682 Thousand Barrels/year)at Kings County at the beginning of the simulation period, followedby an FT facility at Humboldt County (1284 Thousand Barrels/year)in 2030 and finally another FT facility at Alameda County (543Thousand Barrels/year) in 2032 (Fig. 7). The combined capacity ofthe supply chain after the introduction of the last facility in 2032approached the state's maximum production potential of renew-able diesel and biojet fuel in this year, amounting to 2509 ThousandBarrels. The selection of Kings County for the HEFA facility followsthe same rational described in the previous section. Themodel thenchose to build a large FT facility at Humboldt County to capitalize on

ulation (2020e2040) in California under high oil price scenario and no incentives.

Fig. 8. Cost breakdown of drop-in biofuels (average of renewable diesel and biojet fuel) produced from FT facility at Humboldt County and HEFA facility at Kings County inCalifornia, USA, and based on a 20 years simulation (2020e2040) under high oil price scenario and no incentives. Costs are divided between 1) biomass purchase costs (Biomass) 2)Operations and Maintenance costs (O&M), 3) Annualized Investment costs (Investment), and transportation costs (Transportation).

M. Leila et al. / Energy 156 (2018) 181e195192

economies of scale. The facility relied on the abundant forest resi-dues feedstocks in California's northern counties. The final facilityin Alameda County had limited capacity as there was no morelignocellulosic feedstock available to support a large FT facility. Itmostly relied on Wheat Straw available from central counties withhigh agricultural output (Fig. 3). The Humboldt facility deliveredrenewable diesel and biojet fuel to a cluster of military facilities inNorthern California including Beale and Travis Air Force Basis,while the Alameda facility delivered its production to the samecustomers of the HEFA facility.

The choice of introduction years depends on the same tradeoffdescribed in the previous section. BioGeSTO introduced the HEFAfacility as soon as the simulation started (7 years earlier than thecase of reference oil price scenario). This decision can be explainedby examining the cost structure of HEFA products (Fig. 8). Theaverage MSP of HEFA products (renewable diesel and biojet) was$3.46/gallon in 2020. Biomass purchases entailed the majority ofthe production costs ($2.6/gallon), while investment and opera-tions and maintenance costs contribution was minimal ($0.6/gallon). Therefore, reduction in investment costs related to tech-nology learning has very little effect on the HEFA production andthemodels introduces the facility as soon as it become profitable, inthis case, in 2020. The delay in the introduction of the FT facilitiesfollows the same tradeoff. The MSP of the Humboldt facility and theAlameda products amounted to $5.6/gallon, and $6.0/gallonrespectively. Conventional oil prices under this scenario broke the$5.6/gallon (average of conventional diesel and jet fuel) in 2030 andthe $6.0/gallon in 2032. By that time, most of the reductions ininvestment costs due to technology learning were already achieved(Fig. 4). This shows that technology learning effect on cost re-ductions was negligible at this point.

Similar to the reference oil price scenarios, providing directfinancial incentives to the conversion facilities had no effect on thesupply chain spatial design (number of facilities, their locations andcapacities) since the supply chain reached its maximum productionpotential in 2032. The only exceptionwas the results from incentivelevels reaching 45% of the investment costs (Table 7). The highincentives combined with high oil prices offset the investmentcosts component which led to the split of the HEFA productioncapacity between two facilities at Kings and Fresno Counties to

Table 7Supply chain characteristics under the high oil price scenarios with no incentives.

Incentives level(% of investment cost)

Incentives($M) NPV($M) Total installed(Thousand Bar

0 None 655 250915 81 697 250930 197 741 250945 260 783 2601

reduce transportation costs. Direct financial incentives greater thanor equal to 30% of facility investment costs expedited the supplychain development. At an incentives level of 30% of investmentcosts (amounting to $197 Million), the Alameda facility was intro-duced in 2029, 3 years earlier than its introduction under the 0%and 15% incentives level. The introduction year of the Humboldtfacility remained unchanged due to the large facility size, whichmeans it will incur greater losses if constructed before breaking the$5.6/gallon barrier.

5.4. Sensitivity analysis

Sensitivity analysis of the high oil price scenario with no in-centives was performed to determine the influence of a set ofcrucial parameters on the supply chain NPV and Total CumulativeProduction (TCP). The TCP metric measures both the total installedcapacity of the supply chain upon its completion and how fast itdevelops. Each of the parameters was varied over a ±50% range,while the others were kept at their baseline values, to obtain newsolutions (Fig. 9).

Biomass availability had the strongest impact on the results suchthat an increase of 50% in the parameter value corresponded to a100% and 150% increase in NPV and TCP respectively. However,when the available amount of biomass drops by 50%, NPV drops by50% while TCP drops by only 23%. This can be explained in terms ofthe non-linearity exhibited in the supply chain due to economies ofscale. An increase in biomass availability (for example by importingbiomass from other states) should enable the introduction of fa-cilities with larger capacities at Kings and Alameda counties andpossibly the introduction of new facilities. The cost of productionwill also drop for these facilities due to economies of scale andtherefore they can be introduced earlier and increase TCP. Variationin biomass costs did not cause any drastic changes to NPV and TCP.Only when the parameter was increase by 50%, it caused a 27% dropon TCP because a significant rise in biomass costs could shut downsmall facilities or at least delay their constructions. The discountrate was varied over a smaller range of ±25% of its baseline value, tomimic its realistic expectationwhich usually varies between 5% and10% [12,56]. The discount rate had an impact on the NPV but notenough to cause any notable changes to TCP, i.e. it only influenced

capacityrels/year)

Introduction years

Kings (2020), Humboldt (2030), Alameda (2032)Kings (2020), Humboldt (2030), Alameda (2032)Kings (2020), Humboldt (2030), Alameda (2029)Kings (2020), Humboldt (2030), Alameda (2029), Fresno(2037)

Fig. 9. Results of sensitivity analysis performed on BioGeSTO showing the influence of varying crucial parameters on the Net Present Value (NPV) and Total Cumulative Production(TCP) of the military biofuel supply chain in California. Each parameter was varied by ±50% (discount rate by ±25%) of its baseline value while other parameters remained constant.

M. Leila et al. / Energy 156 (2018) 181e195 193

the margin of profits the facilities made, rather than their capacitiesor introduction years. Finally, variation in biomass transportationcost parameters had very limited effect on both metrics. Sincetransportation contributes a small share to the final cost of pro-ducing FT and HEFA biofuels (Fig. 8), varying biomass trans-portation parameters merely influenced the supply chain.

6. Conclusion

BioGeSTO estimated that biomass resources in the state of Cal-ifornia can meet 12e19% of the annual state-wide military targetsof renewable diesel and biojet fuel produced with the FT and HEFAconversion technologies. This confirms that additional biomassresources will need to be purchased from outside the state to meetthe projected military biofuel targets. However, the drop-in biofuelsupply chain was subject to significant logistic and economic con-straints during the simulation period due to low oil prices and highinvestment costs. Under the reference oil price scenario, only oneHEFA facility was introduced at Kings County in 2027 and providingincentives expedited the supply chain introduction by 3 years.Under the high oil price scenario, two FT facilities were added inHumboldt County (2030) and Alameda County (2032) and the HEFAfacility at Kings County was introduced at the beginning of thesimulation. The combined capacity of the supply chain after theintroduction of the three facilities approached the theoretical limitof drop-in biofuel production that could be achieved with Cal-ifornia's biomass resources and providing incentives modestlyadvanced the introduction years of the FT facilities (1e3 years).Sensitivity analysis showed that an increase in biomass availabilityallowed for the introduction of larger facilities, with lower cost perunit production, earlier in the simulation. Hence, biomass avail-ability had themost impact on the supply chain's performance suchthat a 50% increase in biomass feedstocks corresponded to a 150%surge in TCP.

While providing direct financial incentives may benefitdemonstration facilities by lowering investment risks and signalingthe commitment of the military to its biofuel program, scaling thisstrategy is predicted to have little to no effect on the developmentof the supply chain in California. Crude oil prices will remain themain constraint to the financial feasibility of biofuels, especiallythose produced using FT technology. Biomass purchases areresponsible for the majority of drop-in biofuel production costs forboth technologies, and therefore biomass subsidies may beconsidered to expedite the military biofuel supply chain. Results ofsensitivity analysis implies that importing low-cost sustainablebiomass, for example from the northwestern states of Oregon and

Washington, might improve the economic performance and in-crease the output of the supply chain.

Acknowledgment

This research is funded by BioFuelNet Canada, a networkfocusing on the development of advanced biofuels. BioFuelNet is amember of the Networks of Centers of Excellence of Canada pro-gram. The authors thank Sierk de Jong, researcher at the CopernicusInstitute of Sustainable Development, Utrecht University,Netherlands for his consultations. The authors would also like toacknowledge the Office of the Assistant Secretary for Research andTechnology/Bureau of Transportation Statistics National Trans-portation Atlas Databases (NTAD) for developing the open accessDefense Installations Spatial Data Infrastructure dataset.

Nomenclature

IndicesF Biomass typesI Biomass sources (counties)J Candidate facility locationsMk Military marketsCk Civilian marketsT YearsC Capacity levelQ Conversion technologyPq Preprocessing technologyCp Civilian biofuel productsMp Military biofuel products

Parameters

distbiomMaxTrans Maximum distance preprocessed biomass could betransported from preprocessing facilities toconversion facilities (km)

D The set of pairs of county seats and candidate facilitylocations ði; jÞ with distance greater than distbiomMaxTrans

distinterCounty Average distance of raw biomass transportation fromlocal producer to the location of preprocessing facilityat county seat (km)

transCostrawBiomassf Transportation cost of raw biomass from source

to preprocessing facility ($/tonne)preProcesslossf ;pq Loss fraction in biomass due to preprocessing

M. Leila et al. / Energy 156 (2018) 181e195194

preProcesscostf ;pq Cost of preprocessing of biomass type f using

technology pq ($/tonne)biomamount*

f ;i;t Amount of raw biomass of type f at location i in year t

(tonnes)biomamount

f ;i;t Amount of preprocessed biomass of type f at location i

in year t (tonnes)biomcost*

f ;i;t The cost of raw biomass of type f at location i in year t

($/tonne)biomcost

f ;i;t The cost of preprocessed biomass of type f at location i

in year t ($/tonne)InvCostbaselineq Investment costs of the benchmark facility of

technology q ($)CAPbaselineq Capacity of the benchmark facility of technology q

(Thousand Barrels)Mt Cumulative Industry Capacity at time t (Thousand

Barrels)LRq Learning rate of technology qВ Scaling factor for the economies of scale modelcapmin Lower capacity limit on conversion facilities (Thousand

Barrels)capmax Upper capacity limit on conversion facilities (Thousand

Barrels)capmin

j;c;q;t Lower capacity limit on facility at j, with capacity level c,

technology q, at time period t (Thousand Barrels)capmax

j;c;q;t Upper capacity limit on facility at j, with capacity level c,

technology q, at time period t (Thousand Barrels)af ;q;p Yield of product p when converting biomass f with

technology q (Thousand Barrels/tonne)Slopesc;q;t Slope of straight line representing the investment costs

of installing a facility of technology q, at capacity level cand time t

Interceptsc;q;t y-intercept of straight line representing theinvestment costs of installing a facility of technologyq, at capacity level c and time t

lifespanq Lifespan of a facility with technology qOM fraction Operations and maintenance cost as a fraction of the

investment costsIncTechc;q The fraction of investment costs provided to a facility

with capacity level c and technology qIncmax Maximum incentives that any facility can get per year

($)I Discount ratebiofpricep;t Price of product p (either cp or mp) in year t ($)MilDem mp;mk;t Demand of military market mk on product p at time

t (Thousand barrels per year)CivDem cp;ck;t Demand of civilian market ck on product p at time t

(Thousand barrels per year)distech1i;j Distance in echelon 1 between county centroid i and

conversion facility j (km)

distech2;civj;ck Distance in echelon 2 between conversion facility j and

civilian market ck (km)

distech2;milj;mk Distance in echelon 2 between conversion facility j and

military market mk (km)biomdvc

f ;t Biomass distance variable transportation cost

($/tonne*km)

biomdfcf ;t Biomass fixed transportation cost ($/tonne)

biof dvcp;t Biofuel distance variable transportation cost($/thousand barrels.km)

biof dfcp;t Biofuel fixed transportation cost ($/thousand barrels)

Continuous Decision VariablesFFf ;i;j;t Feedstock Flow of type f from county I to facility at j in

year tAAMf ;j;c;q;t Available Amount of feedstock f for Military fuels

production at facility j of capacity c, using technology qin year t

AACf ;j;c;q;t Available Amount of feedstock f for Civilian fuelsproduction at facility j of capacity c, using technology qin year t

MBFj;mp;mk;t Military Biofuel Flow of type mp from facility at j, tomarket mk in year t

CBFj;p;ck;t Civilian Biofuel Flow of type cp from facility at j, tomarket mk in year t

CAPj;c;q;t Capacity of facility at j, with capacity level c, technologyq in year t

InvCostj;c;q;t Investment costs if facility at j, with capacity level c,technology q were to be constructed in year

InvcostAnnualizedj;c;q;t Annualized investment cost of constructing a

facility at location j, with capacity level c,technology q in year t. this is only has a nonzerovalue on the year of construction of selectedfacilities

OMCostj;c;q;t Operations andMaintenance costs for facility at j, withcapacity level c, technology q, in year t

FixedBiomTransCostj;t The Fixed Biomass Transportation Costs forfacility at j in year t

VariableBiomTransCostj;t The Variable Biomass TransportationCosts for facility at j in year t

FixedBiofTransCostj;t The Fixed Biofuel Transportation Costs for afacility at j in year t

VariableBiofTransCostj;t The Variable Biofuel Transportation Costsfor a facility at j in year t

FeedstockPurchasesj;t The costs of Biomass purchases for facility atlocation j in year t

TotalCostsj;t The total costs incurred by facility at location j in year tRevenuej;t Revenues of facility at location j in year tINCj;t The incentives allocated to a facility at location j in year tProfitj;t Profits of facility at location j in year t

Binary Decision Variablesbj;c;q;t Binary variable¼ 1 if facility at j, with capacity level c,

technology q in year t exists, and Zero otherwise.Zj;t Binary variable¼ 1 if facility at j, is constructed in year t,

and Zero otherwise.

Appendix A. Supplementary data

Supplementary data related to this article can be found athttps://doi.org/10.1016/j.energy.2018.04.196

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