Analysis of an imperfectly competitive cellulosic biofuel supply chain

Transportation Research Part E 72 (2014) 1–14

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Transportation Research Part E journal homepage: www.elsevier.com/locate/tre

Analysis of an imperfectly competitive cellulosic biofuel supply chain Yongxi Huang a,⇑, Yihsu Chen b,c a

Glenn Department of Civil Engineering, Clemson University, Clemson, SC 29634, United States School of Social Sciences, Humilities and Arts, School of Engineering, University of California Merced, 95340, United States c National Graduate Institute for Policy Studies (GRIPS), Tokyo 106-8677, Japan b

a r t i c l e

i n f o

Article history: Received 14 April 2014 Received in revised form 21 August 2014 Accepted 19 September 2014

Keywords: Biofuel Supply chain Cournot Complementarity

a b s t r a c t We study the strategic behavior in an imperfectly competitive cellulosic biofuel supply chain. An optimization-based supply chain model is used to obtain long-run planning outcomes, based on which we develop market models considering both perfect and imperfect competitions. The equilibrium among stakeholders in the multi-echelon supply chain can be obtained by solving a collection of first-order conditions associated with their profit-maximization problems. For the imperfect competition, the model, additionally, allows firms with significant market share at different segment of the supply chain to exercise market power. We apply the models to an illustrative case study of California. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Biofuels are liquid fuels that are used in a combination with fossil fuels such as gasoline and diesel. Currently, ethanol blend wall, which is defined as a technical barrier to accommodating additional ethanol supply (Energy Information Administration, 2010), is limited to E10, i.e., gasoline mixed with 10% ethanol. To promote biofuel, the Renewable Fuel Standard (RFS) in the Energy Independence and Security Act of 2007 requires an increase of the minimum annual level of renewable fuels used in U.S. transportation fuel from 9 billion gallons in 2008 to 36 in 2022, of which 21 billion gallons are cellulosic-based biofuel produced from agricultural residues, forest residues, wastes, or energy crops (EISA, 2007). Reaching the 2022 goal requires almost all new infrastructures in support of supply chain of cellulosic biofuels. One emerging issue that has received limited attention so far is the implications of firms’ strategic behavior along the supply chain of biofuel markets, including the cellulosic biofuel. In the current content, the strategic behavior refers to a situation in which the participants in the market possess ability to raise price above the marginal cost.1 The consequences of strategic behaviors include price distortions, productive and allocative inefficiencies, and redistribution of income among entities in the market. There are a few reasons why the strategic behavior possibly could be present in the biofuel supply chain. First, the facilities’ siting and operational permitting process is typically lengthy, and could involve delays due to compliance ⇑ Corresponding author. Tel: +1 864 656 3661; fax: +1 864 656 2670. E-mail addresses: [email protected] (Y. Huang), [email protected] (Y. Chen). ‘‘Raising price above the marginal cost’’ or ‘‘raising price above the cost of marginal unit’’ is a generic concept that describes the economic purpose when a firm engages in any sort of strategic behavior. By doing so, a firm can increase its gross margin, thereby increasing its profit. In a centralized market in which a firm needs to submit a bid to supply goods, it can bid above its marginal cost to inflate the price if the bid is accepted. In this paper, we applied a quantity-based or Cournot assumption in modeling strategic behavior. That is, a firm recognizes that demand is price responsive and therefore could withhold its output level in order to elevate the biofuel prices in equilibrium. Please also see footnote 7 for discussion on various ways to model strategic behavior. 1

http://dx.doi.org/10.1016/j.tre.2014.09.008 1366-5545/Ó 2014 Elsevier Ltd. All rights reserved.

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Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14

with environmental regulation, opposition from local communities and competing interest groups (White, 2010).2 Second, a multi-echelon biofuel supply chain network is capital intensive, including multiple layers such as feedstock logistics, fuel production and distribution. New entries might find it difficult to access to low-cost capital to finance new projects (Solecki et al., 2013). Also related, the economies of scale of infrastructure imply that excessive capacity could be used by incumbent producers to deter small investors from entering biofuel markets, resulting in local demand to be satisfied by only a few biofuel producers or blenders (Tirole, 1988). Third, coordination of logistics among entities in the supply chain is daunting, at least in the early stage of its development prior to the formation of centralized markets (EPA, 2011). Thus, new entries need adequate time to retain sufficient knowledge in order to be successful in the markets. Fourth, existing transportation system might not be sufficient to support the increasing transportation demand of procuring biomass (Solecki et al., 2013). This suggests that isolated local markets would emerge, in which supply and demand is controlled by a few local entities, before long-distance procurement options become economically viable. Finally, historically, several network industries, such as railroad, electricity, and airlines, have experienced some degree of local market manipulation, leading to less competitive market outcomes.3 With biofuel markets sharing some of the similar traits of these network industries (e.g., both involve multi-echelon network structure), it is reasonable to believe that local market power could be a concern. Therefore, analyses of biofuel supply chain markets need to explicitly account for strategic behaviors. Despite the implications of strategic behaviors in the biofuel supply chain and the associated economic consequences, most of research so far has been concerted on developing a cost-effective biofuel infrastructure system by solving an optimization-based supply chain design model that is based on social-surplus-maximization or cost-minimization principles (Beamon, 1998; Geunes and Pardalos, 2003; Meixell and Gargeya, 2005; Melo et al., 2009; Min and Zhou, 2002). The related studies in biofuel supply chain design can be broadly classified into three general categories: (1) deterministic biofuel supply chain optimization (Bai et al., 2011; Eksßiog˘lu et al., 2010; Eksßiog˘lu et al., 2009; Parker, 2007), (2) biofuel supply chain design under uncertainty (Chen and Fan, 2012; Cundiff et al., 1997), and (3) multistage biofuel supply chain expansions (Acharya et al., 2008; Gunnarsson et al., 2004; Huang et al., 2010; Walther et al., 2012). For a comprehensive reviews on biofuel supply chain design, please refer to An et al. (2011) and Awudu and Zhang (2012). On the other hand, modeling firms’ strategic behavior is methodically challenging. It typically requires explicitly solving individual firms’ or entities’ profit-maximization problems simultaneously. A common approach is to solve a collection of first-order conditions derived from each individual’s optimization problem.4 When considering non-interior or corner solutions of those optimization problems, the resulting model is a complementarity problem. Examples of studies using this approach include following references (Hobbs, 2001; Jing-Yuan and Smeers, 1999; Limpaitoon et al., 2011). Nagurney et al. (2002) was the first paper that developed a supply chain network equilibrium model as a variational inequality formulation. That model was later analyzed for the similarities and difference between transportation network equilibrium and supply chain network equilibrium problems. Variants of the model have been developed in subsequent years to adapt different market structures (Nagurney, 2006; Nagurney et al., 2002; Zhang, 2006; Zhang et al., 2003). More recently, a general supply chain design in an oligopolistic setting has been conducted in Nagurney (2010), in which a general supply chain network design problem under oligopoly competition was considered and formulated as a variational inequality problem based on a NashCournot equilibrium condition. With the regard to the biofuel market, however, few recent papers have addressed the impacts of strategic behaviors. For example, Chen et al. (2011a) developed a dynamic, spatial, and multi-market equilibrium model to estimate the effects of public policies on cropland allocation, food and fuel prices, and the mix of biofuels from corn and cellulosic feedstocks. Bai et al. (2012) developed Stackelberg game models to integrate strategic behaviors of farmers and biofuel manufactures in determining locations and capacities of biorefineries as well as supply chain operations. Wang et al. (in press), also based on Stackelberg game models, considered the influence of renewable identification number (RIN) trading market in the biofuel supply chain design. Our contribution is to use long-run planning outcomes to analyze imperfect competitive cellulosic biofuel sector. Our approach is to examine the market equilibrium as if entities in the supply chain are allowed to behave strategically in market models. The market models are built on individual’s optimization problems by treating the location and capacity from a cost-minimization planning model5 as given and solve for biomass/biofuel transportation, biofuel production, and biofuel blending activities. The biofuel prices in the market are determined endogenously by supply and demand conditions. We consider two scenarios in the market models, one under perfect competition and the other under imperfect competition when

2 For example, New Source Review (NSR) under the Clean Air Act (CAA) is a pre-construction permitting process that requires that the operator of a large new (or modified) stationary source controls its air pollution using advanced pollution-control technologies (EPA, 2013; Evans et al., 2007). The owner or operator also needs to show that the construction would neither exacerbate the attainment of national ambient air quality standards nor worsen the air quality in clean air areas. Other related legislations include New source Performance Standards (NSPS) under the CAA section 111 (EPA, 2013). 3 For example, a well-known situation in the power sector is that when transmission line connecting a load center (e.g., a city) to the rest of the power grid is congested, creating so-called a ‘‘load pocket.’’ The local power supplier, facing an inelastic demand, can theoretically possess significant market power (as a monopoly) and increase its profit substantially when reducing its sales to the locally isolated markets (Stoft, 2002). 4 As an example, a duopoly game involves a production decision qi and qj of two entities. The standard technique for solving the equilibrium is, first, to find each firm’s best-response function by representing each firm’s decision as a function of its rival’s decision qi(qj) or qj(qi) using the first-order condition of each entity’s profit-maximization problem. The equilibrium can then be identified as the intersection of the two best-response functions. Mathematically, this is equivalent to solving for a system of two equations or two first-order conditions. 5 The planning model presented in Section 2.1, similar to other existing studies examining cost-effective biofuel supply chain design, yields a least-cost cellulosic biofuel infrastructure system.

Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14

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firms with significant market share and allowed to raise prices above marginal cost.6 For both scenarios, the equilibrium among stakeholders in the multi-echelon supply chain can be obtained by solving a collection of first-order conditions associated with the profit-maximization problems of the stakeholders. In particular, we deploy a quantity-based (or Nash-Cournot) setting to model the imperfect competitions in the market models.7 We argue that our results provide a reasonable bound of outcomes from a full-fledged model under imperfectly competition.8 The remaining of the paper is organized as follows. In Section 2, we will present our biofuel supply chain planning model and profit maximization problems for each market stakeholder, followed by the market equilibrium model. We illustrate the model using an illustrative case study of cellulosic biofuel market in California and the model results are presented in Section 3, together with further analysis on economic and emission inefficiencies in comparisons with imperfect competition runs. We draw conclusions and outline future research in Section 4. 2. Models A multi-echelon biofuel supply chain system consists of multiple infrastructure layers to support commodity flows from feedstock fields to consumer markets. In particular, fuel producers procure feedstock to biorefineries, produced biofuels are transported to terminals for blending with gasoline and possible storage, and the mixed fuels are distributed to markets. For completeness purpose, we will first introduce the biofuel supply chain planning model, followed by the market models for the cellulosic biofuel market participants. The cost-minimization planning model results in locations and capacity of biorefineries and terminals that the market models will treat as existing cellulosic biofuel infrastructure. In market models, we explicitly formulate the problems faced by consumers, biofuel producers, and blenders. The ‘‘joint’’ market equilibrium model is then derived by the collection of the first-order conditions for each of the market participant. The indices, parameters, and variables used in the paper are summarized in Table 1. We use lower-case letters for variables, upper-case letters for parameters, and Greek letters for dual variables. 2.1. Cellulosic biofuel supply chain planning model The cellulosic biofuel supply chain planning model, (1)–(8), is formulated as a deterministic mixed-integer linear program. The model minimizes the total costs, which include capital costs of refineries and terminals as well as operational costs in feedstock procurement, fuel production, and transportation. The output from the model is a geographic identification of optimal locations and capacities of refineries and terminals (where biofuel blending activities occur). Minimize

F RCost þ F FCost þ F FSProcureCost þ F RpCost þ

X il 2Il ;l2L;j2J

F RCost ¼

X

Rv R R ðC Rf j zj þ C j qj Þ

TC iFSl j R f il j þ

X j2J;k2K

TC Rjk F xjk þ

X

F C TC km skm

ð1Þ

k2K;m2M

ð1:aÞ

j2J

F FCost ¼

X Frb F ðC k þ C Ft k Þzk

ð1:bÞ

k2K

F FSProcureCost ¼

X

C FSpr f il j l

ð1:cÞ

il 2Il ;l2L;j2J

6 From an individual’s perspective, the perfect competition is equivalent to the price-taking assumption. That is, an individual, a firm for example, will take a price as given and decide its output by comparing the price to its marginal production cost. The same equilibrium can be found by solving a social surplus maximization problem (Mas-Colell et al., 1995). 7 There is a long history of debates in electricity and other network industries concerning whether a quantity-based (Cournot), a price-based (Bertrand) or a supply function equilibrium (SFE) competition is more correct to describe the competition among producers in the sectors. There are at least two reasons why a quantity-based Nash-Cournot assumption is more appropriate for market modeling. First, theoretically, as shown in the paper (Kreps and Scheinkman, 1983), quantity pre-commitment followed by a Bertrand competition yield Cournot outcomes. That is, a quantity competition in capacity investment (or Cournot) in first stage followed by a price-based (Bertrand) competition in second stage will produce equivalent outcomes as a pure Cournot competition. Second, empirically, Bushnell et al. (2007) show that the results of quantity-based or Cournot competition better describe the market data in PJM (Pennsylvania–New Jersey–Maryland) and NYISO (New York Independent System Operator) power markets. While we cannot rule out the possibility that the future biofuel supply chain and market might evolve into an entirely different situation other than what we have considered in the paper, we believe that a quantity-based assumption will be a good starting point. 8 The full-fledged model under imperfect competition would theoretically predict a supply chain with lower production capacity. More specifically, higher biofuel prices under a full-fledged imperfect competition model would suppress quantities demanded by consumers owing to price-responsive demand, thereby leading to lower capacity than the perfect competitive case. We note that to study future cellulosic biofuel supply chain when firms compete strategically, a full-fledged imperfect competition supply chain long run model based on solution concept of the Sub-game Perfect Equilibrium (SPE) with a closed-loop formulation is desired. That is, when making early decisions (e.g., facility locations and capacities), a firm would optimize its overall payoff or profit by rationally anticipating how its early decisions could impact its particular position in the latter market stage. These models are typically not easy to come by due to methodological challenges.

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Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14

Table 1 Notation. Indices L Il J K M

Index Index Index Index Index

l, set of feedstock types il, set of feedstock fields of type l j, set of refineries k, set of terminals m, set of demand cities

Parameters C Rf Refinery (denoted by ‘‘R’’) annualized fixed (‘‘f’’) capital cost ($) at location j j C Rj v

Refinery variable (‘‘v’’) capital cost ($/gallon) at location j;

C Rj

Maximum allowable refinery capacity (gallon) at refinery j

C Rj

Receiving facility and blending system (‘‘rb’’) cost ($) at terminal (‘‘F’’) k

C Ft k

Capital cost ($) of fuel tank (‘‘t’’) at terminal k

C FSpr l C RP Rl

Inelastic average procurement (‘‘pr’’) cost ($/dry ton) of feedstock (‘‘FS’’) type l Biofuel production (‘‘p’’) cost at refineries ($/gallon) Conversion rate (gallon/dry ton), measuring amount of biofuel converted from one unit of feedstock of type l

TC FS il j

R

Unit cost of delivering feedstocks from fields (‘‘FS’’) to refineries (‘‘R’’), based on time spent and distance traveled, and feedstock moisture content, also incorporating loading and unloading cost and labor cost

TC Rjk F

Unit cost of shipping produced biofuels from refineries (‘‘R’’) to terminals (‘‘F’’) for blending

TC FkmC Dm

Unit cost of distributing blended fuels from terminals (‘‘F’’) to cities (‘‘C’’) Biofuel demand by city m under perfect competition

P 0m Q 0m Y il

Price and quantity intercepts of inverse demand function Feedstock availability (dry ton) at location il

Decision variables zRj := 1 if refinery (‘‘R’’) is opened at location j; =0 otherwise zFk qRj f il j xjk yjk skm pm pjk hk kj

:= 1 if blender is placed at terminal (‘‘F’’) k; =0 otherwise Design capacity of refinery at j The amount of harvested feedstock (dry ton) of type l from il to producer j Sales of biofuel (gallon) from producer j to blender k Amount of biofuel (gallon) purchased from producer j by blender k Sales of biofuel (gallon) from blender k to city m Sale price ($/gallon) at city m Sale price ($/gallon) of biofuel from producer j to blender k Dual variable associated with flow conservation constraint at terminals ($/gallon) Dual variable associated with production flow constraint for producers ($/gallon) Dual variable associated with production capacity constraint ($/gallon) Dual variable associated with feedstock procurement constraint ($/dry ton)

lj jil

X

F RpCost ¼

C Rp xjk

ð1:dÞ

j2J;k2K

Subject to:

X f il j  Y il ;

8il 2 Il ;

l2L

ð2Þ

8j 2 J

ð3Þ

j2J

XX X R l f il j ¼ xjk ; il 2Il l2L

k2K

X xjk  qRj ;

8j 2 J

ð4Þ

k2K

qRj  C Rj zRj ; X

8j 2 J

skm  MzFk ;

ð5Þ

8k 2 K

ð6Þ

m2M

X m2M

skm ¼

X xjk ;

X skm  Dm ; k2K

8k 2 K

ð7Þ

j2J

8m 2 M

ð8Þ

Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14

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The objective function (1) minimizes the total of planning and operational costs, in which the planning cost accounts for capital costs of refineries and terminals.9 The operational costs include feedstock procurement, fuel production, and transportation costs. Mathematically, the planning cost equals the summation of capital costs of refineries and terminals in Eqs. (1.a) and (1.b); and the operational cost equals the summation of feedstock procurement cost10 given in Eq. (1.c), and fuel production cost given in Eq. (1.d). Transportation cost consists of the costs associated with shipping feedstocks from feedstock fields to refineries, produced biofuels from refineries to terminals, and blended fuels from terminals to cities. These costs are based on quantities of feedstock or biofuel shipped and distance and time traveled, with consideration of the loading and unloading costs and the labor cost. For a detailed description of how the transportation costs are modeled, including their data sources and assumptions, please refer to Huang et al. (2010). Turning to the constraints, inequalities (2) state that the amount of feedstock procured cannot exceed its availability. Eq. (3) is a production function that equates the amount of biofuel produced (right-hand-side) to the amount of converted biomass (left-hand-side) by relating them to conversion rates. Constraints (4) assure that the biofuel production does not exceed the designed refinery capacity. Constraint set (5) is a logic constraint, stating that there is no capacity needed unless a refinery is open at that location. Similar explanation is applied to constraints (6) with respect to the blender terminals, where M is a sufficiently large positive number. Eq. (7) are a mass-balance condition, indicating that total sales are equal to the total blended. Finally, constraints (8) ensure that biofuel demand at each city is satisfied by the aggregate sales from all blenders k. This mixed-integer linear program can be solved using commercial solver CPLEX programed in AMPL (Fourer et al., 2003). As discussed earlier that the cellulosic biofuel market is not commercialized yet, the solutions from the cellulosic biofuel supply chain planning model (1)–(8), i.e., refineries capacity and location, will be treated as the default layout of the cellulosic biofuel supply chain in the biofuel market models in the next section. 2.2. Cellulosic biofuel market models The major difference between a planning model and a market model is that a planning model assumes that all individual entities achieve a cost minimization of an entire system while in a market model, the individual entity seeks their own optimizations (e.g., profit maximization for their own) and a market equilibrium is solved when all the individual optimization problems are considered simultaneously. In this section, we first develop the profit maximization models for each of the market entities (i.e., biofuel blenders and producers) in Section 2.2.1, and then derive the first-order conditions of their profit maximization problems. The collection of the first-order conditions, with market clearing conditions, forms our cellulosic biofuel market models under both perfect and imperfect competitions in Section 2.2.2. 2.2.1. Profit maximization models for cellulosic biofuel market players (1) Consumers: Consumers’ willingness to pay for biofuel in city m is represented by the price-responsive inverse demand function in (9):

pm ¼ P0m 

! P0m X Skm ; Q 0m k2K

ð9Þ

where the sale price in city m, pm , is a function of total biofuel sale quantity to city m, in which parameter P0m is the choke price, above which the consumption quantity will be zero. The Q 0m is horizontal intercept of the inverse demand function. Beyond this point, the prices will drop below zero. The P0m and Q 0m were calibrated by the pair of price and quantity from the planning model with a demand elasticity of 0.08. This level of elasticity is consistent with studies of consumers’ price elasticity of demand for gasoline with which ethanol is blended (Lin and Prince, 2013). (2) Blenders: A blender k maximizes its profits and its profit-maximization problem is in (10):

X

Maximize

skm pm 

m2M

X X FC pjk yjk  TC km skm j2J

ð10Þ

m2M

Subject to:

X m2M

skm ¼

X

xjk ; ðhk Þ

ð7Þ

j2J

9 The capital costs of refineries and terminals are annualized or levelized fixed costs of refineries and terminals as well as variable capital costs. The annualized fixed cost depends on the locations where these facilities are built at while the variable capital cost is a function of capacities, i.e., gallon. The facilities in terminals include fuel tanks, facilities for receiving product by delivery trucks, and gasoline blending systems. 10 The procurement cost in this study refers to the average expense of purchasing biomasses (in a transportable form) from a field’s central biomass storage location, which varies with feedstock types (Huang et al., 2010; Parker et al., 2007). The associated transportation cost of delivering biomass from fields to refineries is captured separately by transportation cost in this model. We acknowledge that the ‘‘collection cost’’ from field to its central location (including harvesting costs) could be nonlinear (Gan and Smith, 2011; Sun et al., 2011). In a way, our approach represents the procurement cost by taking the average of distance-depended nonlinear collection cost over a crop-field.

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Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14

A blender k maximizes its profits by deciding the sales of biofuel to city m, skm, as well as the amount of biofuel purchased from producers yjk. Variable pjk is the biofuel sale price from producer j to blender k, which is endogenously determined by the market model. For each gallon of biofuel sold by the blender k to city m, it receives pm. When the blenders are pricetakers under perfect competition, we treat pm as a variable. When the blenders are allowed to exercise market power in imperfectly competitive market, we then replace the term pm with the inverse demand function in (9). In a sense, the blenders realize that by reducing their sale quantities, they can effectively raise the prices above their marginal costs, thereby making more profits. We make assumptions for the blender’s profit maximization problem as follows: (i) the cost of blending biofuel (e.g., ethanol) with gasoline is insignificant and incorporated in the capital cost of receiving and blending facility; (ii) the terminals have sufficiently large capacities, and thus there is no capacity limitation associated with blenders. Therefore, F C in equilibrium under perfect competition, blenders will earn zero profit;11 (iii) the transportation costs TC km for delivering biofuel from terminal k to city m will be paid by the blender k; and (iv) a blender enters the market at each chosen terminal from the planning model. We later analyze and address the results when this assumption is relaxed in Section 3.3. The only constraint associated with the blenders’ problem is a mass-balance condition (7), duplicated from the planning model. (3) Biofuel producers: Producers are located in the immediate upper stream of the blenders in the supply chain. Their profit maximization model is shown in (11) and it stats for each producer j.

X XX FSp X Rp XX FS R X RF Maximize pjk xjk  C l f il j þ C xjk þ TC il j f il j þ TC jk xjk k2K

il 2Il l2L

k2K

il 2Il l2L

! ð11Þ

k2K

Subject to:

X

f il j  Y il ;

8il 2 Il ;

l 2 Lðjil Þ

ð2Þ

j2J

XX il 2Il l2L

Rl f il j ¼

X xjk ; ðkj Þ

ð3Þ

k2K

X xjk  qRj ; ðlj Þ

ð4Þ

k2K

We assume that biofuel producers are price-takers in the market. They take the pjk as given and decide the amount of biofuel that they are willing to sell by considering the incurred costs, including production cost C Rp , feedstock procurement FS R cost C FSp and fuel deliveries TC Rjk F . Three constraints (2)–(4) associated with the blender are l , and costs on feedstock TC il j duplicated from the planning model: feedstock procurement constraint in (2), mass-balance constraint on the sales and procurements in (3), and the refineries’ capacity constraint in (4). Note that the term qRj in (4) is the result of the supply chain planning model and now treated as a parameter in the market model here. With the profit-maximization models for the blenders and producers in place, we derive their first-order or Karush–Kuhn–Tucker (KKT) conditions to form our market equilibrium models in Section 2.2.2. Due to the possibility of binding constraints, all the KKT conditions will be presented in complementarity forms. With market clearing conditions, we form the mixed linear complementarity problems (LCPs) (Cottle et al., 1992). Market clearing conditions are conditions that are necessarily to hold to define market equilibrium. Those conditions are essentially equivalent to the concept of ‘‘no excessive supply’’12 and implicitly define market product prices. 2.2.2. Market equilibrium models The market equilibrium models are defined by the collection of KKT conditions in (k1–k3 and j1–j5) and market clearing conditions defined in (mk1). Note that the only difference in the modeling under perfect and imperfect competitions is in constraint (k2). The models are solved with the complementarity solver PATH (Dirkse and Ferris, 1994) in AMPL (Fourer et al., 2003). In the following expression, the sign ‘‘0  x ? y  0’’ indicates that hx; yi ¼ 0, and x  0; y  013. Note that we duplicate the variable of the sales of biofuel from producer j to blender k (i.e., xjk and yjk) in order to identify pjk in equality (mk1). For every blender k, its set of KKT is as follows:

11 This also will be seen by substituting condition (k1) into (k2) when the variables yjk and skm are positive. From (k1), as yjk > 0, then hk ¼ pjk . Substituting this equation to (k2) under perfect competition, as skm > 0, then pm  TC FkmC  pj k ¼ 0. Thus, the profit is zero. 12 In case when demand is fixed, ‘‘no excess supply’’ implies supply is less than or equal to demand. However, when demand is price responsive, the shortage of supply implies a ration of consumption among consumers with a rise of commodity price, reflecting its scarcity rent. Consumers with a lower willingness to pay would forgo the opportunity to consume the commodity as net benefit of consuming it will be negative. In equilibrium, supply will then be equal to demand. 13 The resulting LCP is a square system in a sense that the number of equations is equal to the number of variables. Theoretical properties of LCPs, such as existence and uniqueness of the solution, can be found in (Cottle et al, 1992). With consumers represented by linear demand or equivalently quadratic utility functions, if producers’ optimization is well behaved (i.e., strictly concave profit function and convex feasible set), it has been shown elsewhere that the resulting LCPs will be solvable with a unique solution to the total sales variables, and therefore, the market prices, when applying them to modeling electricity markets (Chen et al., 2011b; Metzler et al., 2003). However, the theoretical proof of the model properties is beyond the scope of our paper.

Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14

8j 2 J; 0  yjk ? pjk þ hk  0

For yjk ;

ðk1Þ

F C 8m 2 M; 0  skm ? pm  TC km  hk  0 under imperfect competition

For skm ;

0  skm ? pm  skm

For hk ;

7

P 0m Q 0m

! F C  hk  0 under imperfect competition  TC km

X X skm ¼ yjk m

ðk2Þ

ðk3Þ

j

For every producer j, the set of KKT is as follows:

For f ij j ;

8il 2 Il ; l 2 L; 0  f il j ? C FSp  TC iFSl j R  kj Rl þ jil  0 l

ðj1Þ

For xjk ;

8k 2 K; 0  xjk ? pjk  C Rp  TC Rjk F þ kj  lj  0

ðj2Þ

For kj ;

XX X R l f il j ¼ xjk il 2Il l2L

For

lj ; 0  lj ?

ðj3Þ

k2K

X xjk  C Rj  0

ðj4Þ

k

Market clearing conditions: This condition is essential to calculating a market equilibrium and serves two purposes: first, ensuring balance of the physical system and, second, implicitly yielding prices for products based on demand and supply. We incorporate here the demand and supply of biofuel between pair of blenders and producers:

For pjk ;

8j 2 J; k 2 K; xjk ¼ yjk

ðmk1Þ

3. A case study of California We apply our models to an illustrative case study of cellulosic biofuel market in California. California serves as a good case study for two primary reasons. First, the government of California has been aggressively promoting de-carbonating the transportation sector through several legislations, e.g., AB32 (Global Warming Solution Act), AB1493 and Low Carbon Fuel Standards (California Energy Commission, 2013). In particular, California’s Bioenergy Action Plan targets the in-state ethanol production at 40% of the total state’s biofuel consumption by 2020 and 75% by 2050, which are equivalent to 350 and 590 million gallons per year (MGY), respectively (Jenkins et al., 2007). Secondly, with advanced biofuel conversion technologies that use lignocellulosic biomass are anticipated to be ready for commercialization by 2020 (Parker et al., 2007). Given that there are abundant biomass residues from the San Joaquin Valley, i.e., corn stover, and the surrounding Sierra forest, i.e., forest residues, California is in a good position to utilize its resources and promote the cellulosic biofuel industry. In this study, biofuel refers only to ethanol, and its demand for in-state production by year 2020 of 350 MGY (Jenkins et al., 2007) is set as the demand target. There are 28 candidate refinery locations and 29 candidate terminal locations across the state. A set of 143 cities are considered as demand centers, which are mainly clustered in the populated areas, such as the San Francisco Bay area and the Los Angeles area. The details on the data used for this study are referred to (Huang and Pang, 2014). We first present the results from the cellulosic biofuel supply chain planning model in Section 3.1, which give us the configuration of the cellulosic biofuel supply chain. We then report the results under perfect and imperfect competitions when using the configuration as the existing cellulosic biofuel market for the market model analyses in Section 3.2. We present results of additional analyses in Section 3.3. 3.1. Planning model results The outcomes of the planning model are shown in Fig. 1, in which the locations for refineries and terminals are denoted by letters P and T, respectively. The respective capacities of refineries are presented in Table 2. As shown in Fig. 1, there appears to be pair-wise relationships between refineries and terminals. For example, the refinery P27 is paired with the terminal T18 to meet the demand in the Central Valley area. The two pairs of refineries and terminals in Southern California are necessary to satisfy the high demand. This output is a result of tradeoffs between the proximity to biomass procurement location and distance to demand centers. We then assume that those four biofuel producers and four blenders are owned by separate entities, and each enters the market at a chosen location. (We also consider a case that a single firm owns all the blending facilities and will discuss it in Section 3.3.) The layout of refineries and terminals in Table 2 and Fig. 1 forms the back-bone of the cellulosic biofuel supply chain of the market model in next section.

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Fig. 1. Map of the selected refinery (P) and terminal (T) locations by the planning model.

Table 2 Results from the supply chain planning model. Refinery locations

Refinery capacity (MGY)

Terminal locations

P4 P7 P21 P27

60 60 63 89

T4 T7 T11 T18

3.2. Market model results This section reports the outcomes of our market model analyses. The social surplus analysis is presented in Section 3.2.1, followed by detailed market outcomes in Section 3.2.2. 3.2.1. Social surplus analysis Tables 3 and 4, respectively, report the biofuel prices at cities weighted by sales, surpluses earned by consumers, and producers and blenders under perfect and imperfect competitions. The social welfare is the summation over the three measurements of the surpluses. Several observations emerge from comparing Table 3 with Table 4, as a result of the blenders’ exercise market power. First, the sales-weighted biofuel price at cities increases by 237%, from 1.87 in Table 3 to 6.30 $/gallon in Table 4, which suppresses the biofuel consumption, leading to a sizeable reduction of sales from 272 to 221 MGY or by 18.75%. Secondly, the blenders’ profit increases to $1043M from $0, which is at the expenses of other price-taking entities in the market. For instance, the consumer surplus drops by $1092M (=$3178M  $2086M), and the producer surplus declines by $87M (=$101M  $14M). Note that the blender’s zero profit is due to the assumptions of constant marginal cost and unlimited capacity under perfect competition. Finally, the overall social surplus is shrunk by $137M (=$3143M  $3280M), suggesting that possessing market power by the blenders will lead to an economically less desirable outcome. We further decompose

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Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14 Table 3 Results from perfect competition. Sales-weighted average price ($/gallon) 1.87 Consumer surplus ($M) 3178 Producer surplus (profit) ($M) 101 Blender surplus (profit) ($M) 0 Social welfare ($M) 3280 Blenders

Profit ($M)

Total sales to city (million gallons)

Producers

Profit ($M)

T4 T7 T11 T18 Total

0 0 0 0 0

60 60 77 75 272

P4 P14 P21 P27

23 23 26 29 101

Table 4 Results from imperfect competition. Sales-weighted average price ($/gallon) 6.3 Consumer surplus ($M) 2086 Producer surplus ($M) 14 Blender surplus ($M) 1043 Social welfare ($M) 3143 Blenders

Profit ($M)

Total sales to city (million gallons)

Producers

Profit ($M)

T4 T7 T11 T18 Total

259 257 265 263 1,043

55 55 56 55 221

P4 P14 P21 P27

6 5 3 0 14

Table 5 Results of biofuel sale prices from producers (P) to blenders (T) in ($/gallon). Blenders

T4 T7 T11 T18

Perfect competition

Imperfect competition

P4

P7

P21

P27

P4

P7

P21

P27

1.86 1.85 1.81 1.80

1.86 1.85 1.81 1.80

1.86 1.85 1.81 1.80

1.86 1.85 1.81 1.80

1.56 1.54 1.64 1.61

1.53 1.54 1.62 1.59

1.53 1.54 1.44 1.48

1.53 1.54 1.49 1.47

profits by each blender and biofuel producer in the same tables. The blenders’ profits increase by $259M, $259M, $265M, and $263M, respectively for blenders at T4, T7, T11, and T18 while the producers’ profits drop by $17M, $18M, $23M, and $29M, respectively for producers at P4, P7, P21, and P27. 3.2.2. Market outcomes Biofuel selling prices at the equilibria from producers to blenders are presented in Table 5 under both perfect (left panel) and imperfect competition (right panel). The reported prices correspond to the variables pjk in the models and can be viewed as the resulting prices between producers and blenders through bi-lateral contracts. Under perfect competition, those prices are necessarily identical for the ‘‘positive’’ sales (see Table 6) designated to the same blenders regardless of biofuel producers. For instance, the sale price to the blender T11 in Table 5 under perfect competition is $1.81/gallon for all producers despite the fact that their distances to the blender are different. This is mainly due to endogenous arbitrage by blenders when purchasing biofuel. Had a lower price been provided by one of the producers, blenders would prefer to

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Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14

Table 6 Results of biofuel sales from producers (P) to blenders (T) in (million gallons). Blenders

Perfect competition P4

T4 T7 T11 T18 Total

P7

Imperfect competition P21

P27

P4

60 60

51 63

60

P7

60

P21

P27

2 56

1

55

63

14 75 89

51

55

58

55 56

purchase biofuel exclusively from this lower-price producer, which incentivizes the producer to raise its price until its offer price becomes slightly lower than the prices offered by the other producers. Under imperfect competition, blenders would procure biofuel from one (or more producers) that provides lowest offer prices. As an instance, the blender T11 purchases its biofuel from the producer P21 with the lowest price of $1.44/gallon. On the other hand, different prices across rows for each producer in Table 5 reflect the difference in transportation cost (owing to travel distance) when delivering biofuel to blenders. Overall, producers (blenders) would sell (purchase) biofuel from the facilities located in their close proximity when considering transportation costs, which can be seen from Fig. 1. The sale quantities at the equilibria from producers to blenders are presented in Table 6. Overall, quantities demanded by the blenders are less under imperfect competition than that under perfect competition because the total biofuel sales dropped from 272 to 221 MGY at equilibria (as reported in Tables 3 and 4). The breakdowns of the total cost are reported in Table 7, which include the costs in transportation (from feedstock to refineries, from refineries to blenders, and from blenders to cities), fuel production, and feedstock procurement. Several observations can be made from the table. The average production costs are compatible between the cases of perfect and imperfect competitions: $0.919/gallon (=$250M/272 MGY) and $0.918/gallon (=$203M/221 MGY), respectively and so are the average feedstock procurement costs: $0.334/gallon (=$91M/271 MGY) and $0.330/gallon (=$73M/221 MGY). However, the average transportation costs are notably different, especially between blenders and cities. In particular, such cost is almost doubled under the imperfect competition, $0.07gallon (=$16M/221MGY), compared with the perfect competition, $0.04/gallon (=$11M/272 MGY). A further investigation on the trucking trips between blenders and cities reveal that a city is supplied by one or at most two blenders under perfect competition, but the same city is met by all four blenders under imperfect competition. This implies the profits earned by blenders under imperfect competition outweigh the incurring transportation cost. Thus, blenders find it economically desirable to sell biofuel even to distant cities, to which they would not supply in the perfect competition. 3.3. Further analyses We conduct further analyses to quantify the magnitude of economic inefficiencies, the effects of price-taking blenders, and implications on air pollution emissions. The economic inefficacies are defined as the additional costs to serve the same level of demand at different locations arising from an imperfect competition. In particular, we conduct a companion run that solves a market model under perfect competition by fixing biofuel demand at the solutions of imperfect competition. That is, the companion run finds the perfect-competition solution to meet the same level of demand from the imperfect-competition solution. We also conduct an additional analysis focusing on the strategic assumption associated with blenders. More specifically, we alternate one of the four blenders to be a price-taker in order to quantify the ability of blenders in manipulating markets in the presence of price-taking blenders.14 Finally, we analyze the implications of air pollution emissions. The results of economic inefficiencies are reported in Section 3.3.1, the results of runs of price-taking blenders are reported in Section 3.3.2, and the emission inefficiencies are quantified in Section 3.3.3. 3.3.1. Analysis of economic inefficiencies Table 8, with a similar layout as Table 7, reports the breakdown of the total cost of the companion run. Except for the cost of shipping biofuels from blenders to cities and from producers to blenders, which respectively drops by $7M (=$16M$9M) and by $1M (=$7M$6M), all other costs remain unchanged in the companion run. It indicates that imperfect competition causes an increase in transportation cost by $8M. In other words, blenders’ seeking profits under imperfect competition distorts their sales decisions and cause an economic inefficiency. 14 We also conducted another run that assumes all the blenders are owned by the same parent firm. (The detailed results of this run are not reported here for the reasons explained below.) In particular, we allow the biofuel purchased by one blender to be shipped and processed by the other blenders with additional transportation costs. Accordingly, we altered the blender’s profit maximization model in two ways. First, we modified the objective function (10) to account for the profits earned by all the blenders as well as the incurred costs related to the inter-blenders deliveries. Second, we changed the mass-balance in Eq. (7) to account for the possibility of inter-blender deliveries. To our surprise, with such monopoly assumption in the market model, the model yields the same equilibria as the imperfect competition. Thus, with a sparse geographic distribution of the blenders in the market, it becomes economically undesirable to undertake inter-blender deliveries. In a sense, the ability of a monopoly to exercise market power is limited by the physical distance among blenders in the supply-chain network.

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Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14 Table 7 Breakdown of the total costs under perfect and imperfect competition. Cost Elements Transportation costs

From feedstock to refinery ($M) From refinery to blender ($M) From blender to city ($M)

Production cost ($M) Feedstock procurement cost ($M)

Perfect competition

Imperfect competition

47 8 11 250 91

34 7 16 203 73

Table 8 Breakdown of the total cost of the companion run. Transportation costs

From feedstock to refinery ($M) From refinery to blender ($M) From blender to city ($M)

34 6 9 203 73

Production cost ($M) Feedstock procurement cost ($M)

Table 9 Biofuel sales (million gallons) from blenders to cities under price-taking competitive fringe runs. Blenders

Blenders as price takers T4

T7

T11

T18

T4 T7 T11 T18

270 0 1 0

0 270 1 1

1 1 267 1

1 1 0 268

Table 10 Economic surpluses of price-taking competitive fringe runs. Economic surpluses

Sales-weighted average price ($/gallon) Consumer surplus ($M) Producer surplus ($M) Blender surplus ($M) Social welfare ($M)

Blenders as price takers T4

T7

T11

T18

1.92 3164 99.79 0.16 3263

1.92 3165 94.91 0.22 3260

2.04 3131 122.74 0.53 3255

2.00 3143 116.74 0.23 3260

3.3.2. Analyses of economic inefficiencies of runs with a price-taking competitive fringe We alternate one of four blenders (i.e., T4, T7, T11, and T18) as a price-taker, each as a scenario, while keeping the other blenders possessing the market power. The demand function still depends on the total biofuel sale to the cities, including the blender being a price-taker. The motivation of this analysis is that, in reality, small competitive fringes, behaving as pricetakers, typically co-exist with incumbent or large firms. The resulting blenders’ sales, social surpluses, and the breakdown of the systems costs are presented in Tables 9–11, respectively. In each table, the columns with headings of T4-T18 correspond to the scenarios when a blender at terminals T4-T18 is designated as a price-taker. When compared to perfect competition, a price-taking blender under imperfect competition would find in its favor to expand its output when other strategic blenders restrict their output to push up prices. This is because a price-taking fringe takes prices as given and adjusts its sale decision until its marginal cost equals the price. As imperfectly competitive market yields a higher price in comparison with perfect competition, it implies that a price-taking fringe would increase its sales accordingly. As alluded in Table 9, blenders who are designated as price-takers expand their sales to satisfy the demand while other blenders reduce their outputs dramatically, even to zero in some cases. Thus, the presence of a price-taking blender would mitigate the effect of market power by other blenders and significantly improve the overall economic efficiency. This is indicated by the decreased sales-weighted average prices and the increased economic surpluses in Table 10, which are compatible to their counterparts under perfect competition in Table 3. Interestingly, the four blenders have almost identical effects on the social surpluses as indicated in Table 10, and the resulting total costs reported in Table 11 are nearly equivalent to the imperfect-competition counterparts reported in Table 4. This is due to our assumption concerning their identical production cost, and no limit on their blending capacity. Had their capacity been derived from a full dynamic or full-fledged model, there could be asymmetry in the production cost and capacity, thereby leading to different outcomes.

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Table 11 Breakdowns of the total costs of price-taking competitive fringe runs. Cost Elements

Transportation costs

Blenders as price takers

From feedstock to refinery ($M) From refinery to blender ($M) From blender to city ($M)

Production cost ($M) Feedstock procurement cost ($M)

T4

T7

T11

T18

46 20 16 250 91

46 21 17 250 91

46 20 24 248 90

46 18 21 249 90

Table 12 Breakdowns of the total costs of companion runs of price-taking competitive fringe runs. Cost elements

Transportation costs

Blenders as price takers

From feedstock to refinery ($M) From refinery to blender ($M) From blender to city ($M)

Production cost ($M) Feedstock procurement cost ($M)

T4

T7

T11

T18

46 8 11 250 91

46 8 11 250 91

46 8 11 248 90

46 8 11 249 90

Table 13 Assumptions concerning the GHG pollutants in biofuel life-cycle analysis. GHG pollutants Global warming potentials (GWP) Procurementa a,b

Production

Transportationc a b c

Corn stover Forest residues Corn stover Forest residues Truck

CO2 1

CH4 25

N2O 298

CO2-eq

18.045 21.537 1005 229 2437

28.35 33.84 6.76 2.12 3.34

0.22 0.26 0.87 0.89 0.06

18,819 22,461 1433 548 2538

The units of GHG pollutants associated with procurement and production are grams/dry ton. Excludes emissions of electricity byproducts. The units of GHG pollutants associated with transportation are grams/mile/truck load.

Economic inefficiencies due to strategic behaviors of blenders when considering price-taking competitive fringes are substantially more significant than the companion run reported in Section 3.3.1. For example, comparisons between Tables 11 and 12 indicate that the total transportation cost increases by $17M (=20 + 16–8–11), $19M $25M and $20M, respectively when each of blenders T4, T7, T11 and T18 is alternately designated as a price-taker, which is much higher than $8M reported in Section 3.3.1. As one of the four blenders becomes a price-taker, the reduction of the sales by the three other blenders is made up by the increase in sales from this price-taking blender. To satisfy the demand in different cities, the price-taking blender needs to procure biofuel from distant producers and deliver biofuel to cities in distance, thereby leading to significant transportation costs. 3.3.3. Implications on air pollution emissions One of direct consequences from economic inefficiencies in transportation is the additional air pollution emitted when delivering biofuel from blenders to cities and from producers to blenders. We estimate the extent that imperfect competition may result in additional emissions compared with the resulted emissions by the companion-run solutions. We limit our attention to GHG (greenhouse gas) emissions, considering three GHG species: CO2, CH4, and NO2. (There could be implications for local pollutants such as PM10, SO2, and etc.) We break up the emissions along the supply chain of biofuel into three phases in our analysis: feedstock procurement, production, and transportation. We base our analysis on the emission intensities of three GHG species from the GREET (Greenhouse gases, Regulated emissions, and Energy use in transportation model) (Wang et al., 2005). We further aggregate their emission intensities into an environmental performance indicator CO2-eq by applying the concept of 100 year global warming potentials (GWP) (BSI Group, 2011). The emissions in ethanol production are low, because large amount of CO2 emitted from burnt biomass is considered to offset the absorbed CO2 in the biomass growing phase (Raphael et al., 2009; Wang et al., 2005). Furthermore, the emissions from electricity generation as a by-product are out of the scope of the study and thus not considered here. The transportation emissions are dependent on the distance traveled and number of truckloads. Table 13 details the assumptions we use in the analysis.

Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14

13

Our results indicate that the total GHG emission is equal to 0.23 (Mton CO2-eq) under the imperfect competition (Table 4). The three phases of the biofuel life-cycle we consider, feedstock procurement, production and transportation, respectively account for 23% (0.053), 48% (0.11) and 29% (0.068) of the total GWP impact, where the numbers within the parentheses are the emission in Mton CO2-eq. When compared with the emissions resulted from the companion run in Section 3.3.1, the total GHG emission of the imperfect-competition run is only marginally higher by 8%. However, all of the increased emissions occur in the transportation phase, increased by a margin of 28% (from 0.049 to 0.068 Mton CO2-eq) while the emissions from the other two phases remain unchanged. This suggests that the distortion of economic inefficiencies under an imperfectly competitive market could lead to additional air pollutions, mainly during the transportation phase. 4. Conclusions In this study, we develop market models to examine the implications of strategic behavior in the cellulosic supply chain under both perfect and imperfect competitions. We treat the biofuel supply chain infrastructure as existing and the system layout is obtained through solving a cost-minimization supply chain planning model. The market models are comprised of a collection of first order conditions of each entity’s profit maximization optimization problems. The strength of the developed models lies on its flexibility to incorporate policy designs, and assumptions about asymmetric behaviors of different entities in the market to evaluate supply chain operations and market outcomes. We demonstrate the application of the approach by using an illustrative case study in California. In particular, we examine several imperfect-competition scenarios that allow the blenders in the supply chain to behave strategically. The companion runs that solve for perfect-competition solutions with retained solution of equilibrium demand quantities under imperfect competition are used to quantify the magnitude of the economic and emission inefficiencies. The results indicate that blenders’ strategic behavior could distort market outcomes, leads to sizable allocative inefficiencies, and increases emissions associated with the transportation phase along the life-cycle of biofuel distributions. Consistent with economic theory, the blenders can benefit greatly at the expenses of the other entities in the supply chain. To our surprise, even all the blenders are owned by the same firm, its ability to manipulate the market is limited by the spatial distributions of the facilities of the blenders in the supply-chain network. We had also shown that strategic behavior along the supply chain of the biofuel could be a serious concern, not only with regard to a healthy development of biofuel sector but also to unintended consequences related to pollutions. This suggests that oversight from various regulatory agencies, such as FERC (Federal Energy Regulatory Commission) and state Energy Commission, through anti-trust and market monitoring practices is needed to safeguard a healthy development of future biofuel sector. Our analysis is subject to a number of limitations. First, our market models taking an infrastructure system as a result of a planning model as default actually understates the possible extent of market power in the supply chain. If a firm can fully incorporate their operational decisions while making their strategic decisions on infrastructure investment, a full-fledged model that is formulated based on sub-game perfect equilibrium should be considered, which can be solved by dynamic programming or backward induction approaches. Such model would likely predict a more concentrated ownership with less refining and blending capacities. Secondly, we assume that biofuel is the single commodity in the market. The linear inverse demand function is then calibrated using the pair of price and quantity from the planning model with a demand elasticity from existing literature. In practice, there exist multiple fuel choices in the market. For example, flexfuel vehicles can run on both biofuel, e.g., E85, as well as conventional gas. Optimized consumers would effectively arbitrage between these two fuel choices. In this paper, our analysis does not account for this substitution and might overstate the market power of biofuel alone, since the demand of biofuel could be more price-responsive than we considered. One possibility is to consider multiple commodities by imposing a constant-elasticity demand function with a cross-elasticity to account for substitutability among different fuels. The resulting complementarity problem would likely be nonlinear and might pose significant computational challenges. Thirdly, the collection prices of biomass resources are treated as constant in this study. It would be more realistic to consider a non-linearly related collection price with quantity of biomass purchased. However, the nonlinear cost, though resulting in different numerical solutions, will not change our model structure. Reference Acharya, A.M., Eksßiog˘lu, S.D., Petrolia, D., 2008. In-bound supply chain design for biomass-to-ethanol industry: a study of Mississippi. In: The 2008 Industrial Engineering Research Conference, pp. 1296–1301. An, H., Wilhelm, W.E., Searcy, S.W., 2011. A mathematical model to design a lignocellulosic biofuel supply chain system with a case study based on a region in Central Texas. Bioresour. Technol. 102 (17), 7860–7870. Awudu, I., Zhang, J., 2012. Uncertainties and sustainability concepts in biofuel supply chain management: a review. Renew. Sustain. Energy Rev. 16 (2), 1359–1368. Bai, Y., Hwang, T., Kang, S., Ouyang, Y., 2011. Biofuel refinery location and supply chain planning under traffic congestion. Transp. Res. Part B: Methodol. 45 (1), 162–175. Bai, Y., Ouyang, Y., Pang, J.-S., 2012. Biofuel supply chain design under competitive agricultural land use and feedstock market equilibrium. Energy Econ. 34 (5), 1623–1633. Beamon, B.M., 1998. Supply chain design and analysis: models and methods. Int. J. Prod. Econ. 55 (3), 281–294. BSI Group, 2011. PAS 2050: 2011: Specification for the Assessment of the Life Cycle Greenhouse Gas Emissions of Goods and Services. BSI British Standards Institution. Bushnell, J.B., Mansur, E.T., Saravia, C., 2007. Vertical Arrangements, Market Structure, and Competition: An Analysis of Restructured U.S. Electricity Markets. National Bureau of Economic Research Working Paper Series No. 13507.

14

Y. Huang, Y. Chen / Transportation Research Part E 72 (2014) 1–14

California Energy Commission, 2013. . Chen, C.-W., Fan, Y., 2012. Bioethanol supply chain system planning under supply and demand uncertainties. Transp. Res. Part E: Logistics Transp. Rev. 48 (1), 150–164. Chen, X., Huang, H., Khanna, M., Önal, H., 2011a. Meeting the Mandate for Biofuels: Implications for Land Use, Food and Fuel Prices. National Bureau of Economic Research Working Paper Series No. 16697. Chen, Y., Liu, A.L., Hobbs, B.F., 2011b. Economic and emissions implications of load-based, source-based, and first-seller emissions trading programs under California AB32. Oper. Res. 59 (3), 696–712. Cottle, R.W., Pang, J.S., Stone, R.E., 1992. The Linear Complementarity Problem. Society for Industrial and Applied Mathematics Philadelphia, PA. Cundiff, J.S., Dias, N., Sherali, H.D., 1997. A linear programming approach for designing a herbaceous biomass delivery system. Bioresour. Technol. 59 (1), 47– 55. Dirkse, S.P., Ferris, M.C., 1994. The PATH solver for complementarity problems. (accessed on June 18, 2013). EISA, 2007. Energy Independence and Security Act of 2007. Eksßiog˘lu, S., Li, S., Zhang, S., Sokhansanj, S., Petrolia, D., 2010. Analyzing impact of intermodal facilities on design and management of biofuel supply chain. Transp. Res. Rec. J. Transp. Res. Board 2191, 144–151. Eksßiog˘lu, S.D., Acharya, A., Leightley, L.E., Arora, S., 2009. Analyzing the design and management of biomass-to-biorefinery supply chain. Comput. Ind. Eng. 57 (4), 1342–1352. Energy Information Administration, 2010. The Ethanol Blend Wall http://www.eia.gov/oog/info/twip/twiparch/100708/twipprint.html, accessed on January 6, 2014. EPA, 2011. EPA and Biofuels: A Primer on EPA’s Authorities, Responsibilities, and Research. EPA inter-office biofuels steering committee. EPA, 2013. New Source Review. . Evans, D.A., Hobbs, B.F., Oren, C., Palmer, K.L., 2007. Modeling the effects of changes in new source review on national SO2 and NOx emissions from electricity-generating units. Environ. Sci. Technol. 42 (2), 347–353. Fourer, R., Gay, D., Kernighan, B., 2003. AMPL: A Modeling Language for Mathematical Programming, second ed. Duxbury Press, Boston. Gan, J., Smith, C.T., 2011. Optimal plant size and feedstock supply radius: a modeling approach to minimize bioenergy production costs. Biomass Bioenergy 35 (8), 3350–3359. Geunes, J., Pardalos, P.M., 2003. Network optimization in supply chain management and financial engineering: an annotated bibliography. Networks 42 (2), 66–84. Gunnarsson, H., Rönnqvist, M., Lundgren, J.T., 2004. Supply chain modelling of forest fuel. Eur. J. Oper. Res. 158 (1), 103–123. Hobbs, B.F., 2001. Linear complementarity models of Nash-Cournot competition in bilateral and POOLCO power markets. IEEE Trans. Power Syst. 16 (2), 194–202. Huang, Y., Chen, C.-W., Fan, Y., 2010. Multistage optimization of the supply chains of biofuels. Transp. Res. Part E: Logistics Transp. Rev. 46 (6), 820–830. Huang, Y., Pang, W., 2014. Optimization of resilient biofuel infrastructure systems under natural hazards. J. Energy Eng. 140 (2), 04013017. Jenkins, B., Dempster, P., Gildart, M., Kaffka, S., 2007. California Biomass and Biofuels Production Potential (Draft). California Energy Commission. Jing-Yuan, W., Smeers, Y., 1999. Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices. Oper. Res. 47 (1), 102– 112. Kreps, D.M., Scheinkman, J.A., 1983. Quantity precommitment and bertrand competition yield Cournot outcomes. Bell J. Econ. 14 (2), 326–337. Limpaitoon, T., Chen, Y., Oren, S., 2011. The impact of carbon cap and trade regulation on congested electricity market equilibrium. J. Regul. Econ. 40 (3), 237–260. Lin, C.Y.C., Prince, L., 2013. Gasoline price volatility and the elasticity of demand for gasoline. Energy Econ. 38, 111–117. Mas-Colell, A., Whinston, M.D., Green, J.R., 1995. Microeconomic Theory. Oxford University Press. Meixell, M.J., Gargeya, V.B., 2005. Global supply chain design: a literature review and critique. Transp. Res. Part E: Logistics Transp. Rev. 41 (6), 531–550. Melo, M.T., Nickel, S., Saldanha-da-Gama, F., 2009. Facility location and supply chain management – a review. Eur. J. Oper. Res. 196 (2), 401–412. Metzler, C., Hobbs, B., Pang, J.-S., 2003. Nash-Cournot equilibria in power markets on a linearized DC network with arbitrage: formulations and properties. Netw. Spatial Econ. 3 (2), 123–150. Min, H., Zhou, G., 2002. Supply chain modeling: past, present and future. Comput. Ind. Eng. 43 (1–2), 231–249. Nagurney, A., 2006. On the relationship between supply chain and transportation network equilibria: a supernetwork equivalence with computations. Transp. Res. Part E: Logistics Transp. Rev. 42 (4), 293–316. Nagurney, A., 2010. Supply chain network design under profit maximization and oligopolistic competition. Transp. Res. Part E: Logistics Transp. Rev. 46 (3), 281–294. Nagurney, A., Dong, J., Zhang, D., 2002. A supply chain network equilibrium model. Transp. Res. Part E: Logistics Transp. Rev. 38 (5), 281–303. Parker, N., 2007. Optimizing the design of biomass hydrogen supply chains using real-world spatial distributions: a case study using California rice straw (Master thesis). University of California, Davis. Parker, N., Tittmann, P., Hart, Q., Lay, M., Cunningham, J., Jenkins, B., 2007. Strategic Development of Bioenergy in the Western States Development of Supply Scenarios Linked to Policy Recommendations, Task 3: Spatial Analysis and Supply Curve Development. Western Governors’ Association. Raphael, S., Ausilio, B., Nilay, S., 2009. The greenhouse gas emissions performance of cellulosic ethanol supply chains in Europe. Biotechnol. Biofuels 2 (1). Solecki, M., Scodel, A., Epstein, B., 2013. Advanced Biofuel Market Report 2013: Capacity through 2016. Enviornmental Enterpreneurs, San Francisco, CA. Stoft, S., 2002. Power System Economics: Designing Markets for Electricity. IEEE Press. Sun, J., Chen, J., Xi, Y., Hou, J., 2011. Mapping the cost risk of agricultural residue supply for energy application in rural China. J. Cleaner Prod. 19 (2–3), 121– 128. Tirole, J., 1988. The Theory of Industrial Organization. MIT Press, Cambridge, Mass. Walther, G., Schatka, A., Spengler, T.S., 2012. Design of regional production networks for second generation synthetic bio-fuel – a case study in Northern Germany. Eur. J. Oper. Res. 218 (1), 280–292. Wang, M., Wu, Y., Elgowainy, A., 2005. Operating Manual for GREET: Version 1.7. Argonne National Laboratory. Wang, X., Ouyang, Y., Yang, H., Bai, Y., 2013. Optimal biofuel supply chain design under consumption mandates with renewable identification numbers. Transp. Res. Part B: Methodol. 57, 158–171. White, E.M., 2010. Woody Biomass for Bioenergy and Biofuels in the United States: A Briefing Paper. DIANE Publishing. Zhang, D., 2006. A network economic model for supply chain versus supply chain competition. Omega 34 (3), 283–295. Zhang, D., Dong, J., Nagurney, A., 2003. A Supply Chain Network Economy: Modeling and Qualitative Analysis. Edward Elgar Publishing Inc.