Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies

Iddrisu Awudu* Quinnipiac University, Hamden, Connecticut, USA

Anthony Asare Quinnipiac University, Hamden, Connecticut, USA

Eric Asa North Dakota State University, Fargo, North Dakota, USA

Atif Osmani Minnesota State University Moorhead, Moorhead, Minnesota, USA

Vinay Gonela Texas A&M University - Central Texas, Killeen, Texas, USA

Anthony Afful-Dadzie University of Ghana Business School (UGBS), Accra, Ghana

In this paper we develop hedging strategies in maximizing profits for an ethanol producer who buys raw materials (corn and cellulosic) and produces end-products (ethanol, corn oil and distillers dried grains soluble). We first develop an optimization model considering maximization of the supply chain profit with hedging. We model the buying (corn and cellulosic feedstock) and selling (ethanol end-product) prices to follow a mean reversion with sample average approximation in order to capture better price volatilities and less usage of sample data to obtain expected results respectively. We use a Multi-cut Benders Decomposition Algorithm to help with efficient computations for the proposed model. We also incorporate the aspect of copula to capture the dependency structures and price relationships between corn and ethanol futures (a hedging strategy that buys or sells a product looking forward into the future). We found that hedging using future prices give additional profit margins for the time period used. We intuitively show that an ethanol price between $2.06 and $2.41 per gallon will allow ethanol producers to make profit or at least break-even. A case study using an ethanol plant in North Dakota is used for this study.

* Corresponding Author. E-mail address: [email protected]

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I. INTRODUCTION manage , minimize losses and improve shareholder value. Ethanol manufacturers Companies face a wide variety of are facing extreme price risks from the operational and financial risks and as such purchase of feedstock to the sale of end- utilize strategies aimed at systematically products (Zhang et al., 2013). These risks are managing exposures to minimize losses caused by several factors that impact margins, and increase firm value (Boyabatli and including prices for ethanol, corn, corn oil, Toktay 2004). Some of the popular ways to Distillers Dried Grains (DDGs), and manage financial risks is to use the variety of Renewable Energy Identification Numbers trading mechanisms such as options, futures (RINs). In addition, recognizing the period and swaps. The volatility, uncertainties and to is challenging and determining how wide price swings associated with energy much of the physical commodity is needed prices has made the energy sector an adds more complexities to hedging decisions attractive industry for hedging. (Wilson et al., 2006). Firms therefore need to While there has been a lot of attention strategize and make decisions on how to in the hedging of traditional energy products hedge over short term, medium term, and such as crude oil and natural gas, relatively long term scenarios and to decide which less attention has been given to managing markets or mechanisms to use. risks of biofuels and other newer renewable Even though ethanol is a very energy sources even though those fuel important energy source, the risks and sources are also vulnerable to the risks and uncertainties associated with ethanol uncertainties associated with the more production and sales are significant making it traditional energy sources. Biofuels such as a prime target for hedging and other forms of ethanol have been increasingly used as a . The review of literature substitute for fossil fuel energy and its demonstrates that very few papers consider adoption has been accelerated by government hedging strategies for renewable energy fuels, mandates across the world. For example, the particularly ethanol. Recognizing that gap in European Union (EU) requires member states the literature, this paper examines hedging to ensure the substitution of 10% of its strategies available to ethanol manufacturers transportation fuel with biofuels by 2020 such as futures, swaps and options. We while the US Environmental Protection utilize Platts, a market that is used by most Agency (EPA) requires that at least 7.5 commodity traders as a trusted source of billion gallons of renewable fuels be blended trading and information on the market. We with conventional gasoline by the year 2012 also introduce a number of methodological (McPhail et al. (2011). These mandates have approaches that have not been traditionally contributed to the widespread use of biofuels used in the hedging literature. Traditionally, as a source of fuel for transportation purposes, hedgers seek to take equal and opposite hence, making ethanol a very important fuel positions in related markets and more source. complex models seek to exploit use of Similar to the conventional energy correlations without incorporating dependent sources, the price of ethanol and its inputs are relationships. Copula is utilized in this paper uncertain, volatile and face wide price swings. since it allows for the incorporation of non- The process of buying feedstock, processing standard dependencies, thus better reflecting the ingredients and selling the finished conditions faced by ethanol processors. This products involves risks that make it important work also utilizes mean reversion in order to for ethanol producers to utilize strategies to better capture the deterministic and stochastic

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222 Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies side of the price volatility. Doing this, soybean crushing industry (Dahlgran, 2005), enables the capture of upside and downside canola and western barley (Mann, 2010), risks more accurately, thus adding extra distillers dried grains (DDGs) (Brinker et al., flexibility in forecasting returns. The paper 2007) and the flour industry (Wagner 2001 also utilizes multi-cut benders decomposition and Oberholtzer, 2011). Although financial and sample average approximation hedging has been well examined, an approaches that are proven to solve the increasing numbers of papers have begun to problem at hand more efficiently with fewer combine financial with operational hedging data points (Osmani and Zhang 2017.). (e.g. Chod et al., 2010). This is because a There are six main contributions of large number of papers that examine this study: 1) Explore the different hedging financial hedging focus on hedging against strategies available to ethanol producers, a currency exposure and price variability while topic that has been inadequately covered in ignoring important operational risks such as the literature. 2) Integrate financial and those associated with capacity constraints operational hedging risks in the proposed and product demand exposure (Chod et al., model in order to provide a more complete 2010). Operational hedging strategies, are assessment of the problem as compared to viewed as real compound options that are focusing only on financial risks. 3) Utilize exercised in response to the demand, price copula to capture a better dependency and exchange rate contingencies faced by structure which enables us to extend one to firms in a global supply chain and have been one relationship of prices (corn and ethanol) examined by a number of studies including beyond correlation 4) Utilize a Multi-cut (Cohen and Huchzermeier 1996); (Cohen and Benders Decomposition methodology and Mallik, 1997) and (Boyabatli and Toktay, also sample average approximation in order 2004). Some operational strategies include to help with efficient computation of the postponing logistics decisions, switching hedged profit margins while using smaller production and sourcing decisions contingent sample data 5) Provide a stylized model for on demand uncertainties and creating buying (corn and cellulosic feedstock) and production capacity flexibilities (Boyabatli selling (ethanol end-product) while these and Toktay, 2004). These operational hedges prices follow a mean reversion (MR) in order are utilized to mitigate risk exposure in the to more accurately capture price volatilities 6) long run by reducing the downside risk Provide managers in ethanol manufacturing (Cohen and Huchzermeier, 1999). companies with risk managing strategies In recent years, with the increasing through hedging, that can enable them to popularity of biofuels and the uncertainty increase profits and shareholder value. associated with their production and sale, a number of studies have focused more II. LITERATURE REVIEW specifically on risk and hedging in the biofuel industry, particularly ethanol. The closest There is a vast literature that focuses article that draws nearer to this manuscript is on the use of financial hedging instruments to (Wiedemann and Geldermann, 2015). The manage risk (example Black and Scholes, authors modeled a planning problem of a 1973; Merton, 1973; Markowitz, 1952). processor of agricultural raw materials and These studies use a variety of methodological illustrates it with data on the industrial use of approaches to examine risk and uncertainty linseed oil. A two-stage stochastic in multiple industries. They include in the optimization model was used in conjunction bakery industry (Wilson et al., 2006), with a decision support analysis to solve the

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problem. (Quintino and David, 2013) development, logistics, and extension are analyzed proposed ethanol futures for the provided. Brazilian markets to attract sufficient Our paper builds upon the liquidity for market agents. Their paper contributions from (Awudu et al., 2016); analyses different cross-hedging scenarios in (Chen et al., 2016). (Awudu et al., 2015); the ethanol supply chain for sugarcane. The (Langholtz et al., (2014); (Quintino and analyses conducted evaluate price volatilities, David, 2013); (Dal-Mas et al., 2011); and and correlations with cross hedging viability (Chang et al., 2010). While these papers have for ethanol futures. contributed substantially to the risk (Chang et al., 2012) examined the management literature in the ethanol industry, long- and short-run asymmetric adjustments there are still gaps in the literature that still of spot and futures prices, namely corn, needs to be addressed. Some of the gaps soybeans, sugar, and three cross pairs of spot include: a dearth of robust or stylized models price for each of the products and an ethanol that consider multiple feedstock (raw futures price. Their study concludes that the materials); risk hedging that focuses corn spread has the strongest long-run primarily on financial hedging while not widening adjustment while sugar showed the paying adequate attention to operational weakest narrowing adjustment. Their hedging; and a heavy reliance on correlations empirical analysis points to the importance of to identify relationships between the prices of hedging the spot prices of agricultural corn and ethanol, an approach that does not commodities with ethanol futures contracts. truly capture the full complexity of those (Dal-Mas et al., 2011) determined relationships. There are also problems that how an ethanol supply chain is optimized focus on computation since there is an according to a comprehensive mathematical inadequate utilization of state of the art framework with multiple decision criteria algorithms that reduce computational time under uncertain market scenarios. A linear and provide faster and better ways of solving programming framework is used to solve the stochastic hedging problems. resulting model. A case study in Italy is used The gaps identified are bridged in this with the results showing that risk mitigating paper by extending optimization models to preferences are essential for hedging risk and include portfolios of ethanol and other decision making within the ethanol supply products such as DDGs and corn oil. We chain with multiple feedstocks. incorporate a hybrid-generation biofuel (Langholtz et al., 2014) developed a risk supply chain with two types of biomass management framework developed using the feedstock; corn and cellulosic to capture the Intergovernmental Panel on Climate Change dynamics of operations. By doing so, we can to review current understanding regarding introduce that is based on climate-related , exposure, and capacity manipulations. As part of the vulnerability of the bioenergy supply chain. uniqueness of our approach to optimize The authors consider a risk management supply chain decisions, and reduce the impact strategy that projects growth of bioenergy of financial and operational risks, we develop feedstocks in regions preferentially exposed a hedging strategy with a stochastic model, to such hazards. The paper discusses and solve the resulting problem using a implications of climate change on expansion Sample Average Approximation (SAA) and of cellulosic feedstocks. In addition, Mean Reversion with which gives a more strategies in advancements of feedstock realistic representation of future and spot price movements of ethanol commodities and

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224 Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies end-products. This assumption is used in Renewable Energy Supply Chain (RESC). because most commodity prices exhibit high These are usually termed as . In and low prices for a temporary period, and order to optimize the supply chain decisions, then the prices move or shift to the average and reduce the impact of financial and prices over time (Bessembinder et al., operational risk, we develop a hedging 1995). We also introduce cross hedging strategy with a stochastic model and solve the strategies involving futures and spot that resulting problem. For computational enable us to manage the risk better. To tractability, we used a Multi-cut improve computing time and speed up the Decomposition Algorithm. process of solving stochastic hedging As part of capturing the uncertainties problems, we develop a Multi-cut in the feedstock and ethanol prices, a Mean decomposition algorithm for better Reversion is used to model the prices of the computation and tractability using scenario feedstock and end-products. This assumption generations. By introducing new is used because most commodity prices methodological approaches that provide exhibit high and low prices for a temporary more realistic scenarios, we also help period, and then the prices will move or shift managers to develop more effective risk to the average prices over time management strategies. (Bessembinder et al., 1995). But we further capture the volatility of the prices in a III. METHODOLOGY different way by observing the sample price over a limited scenario say 1000 instead of We consider a hybrid-generation 10,000 and we still get to capture volatilities biofuel supply chain with two types of with minimum impact on the results. This is biomass feedstock; first and second implemented from the data set obtained from generation. The first generation consists of the Iowa University Energy Research Group. corn and the second generation is cellulosic The corn biomass purchasing mechanism is feedstock. The supply chain network consists based on a heuristic hedging strategy since of pre-determined raw material supply corn as a commodity has high price volatility. sources, warehouses or pre-treatment In order to reduce the price variability and facilities, biorefinery plants, and demand hedge against future uncertainties, the corn is zones. Supply sources are responsible for procured at a futures price. The cellulosic providing the raw materials which are corn feedstock is purchased at a spot price since no and cellulosic feedstock. Warehouse or pre- variability is assumed for its price. The treatment facilities prepare the raw materials heuristic method uses the mean reversion into a suitable form before being transported model to generate sample data for both the to the biorefinery plants. The biorefinery corn spot and futures prices. A method of plants convert the pre-treated raw materials buying corn feedstock using the spot price is into end-products, which is biofuel and then used if futures price is greater than say y ships (via trail or truck) the biofuel produced times the mean of the sample price generated. to the demand. This characterizes a mean of an additional Considering the hybrid-generation say x% increase in each scenario. For biofuel supply chain described above, the example, when futures price of corn is $30 challenges of operational uncertainties (risks) and the sampled price mean is $20, then the from supply, production and demand are increase (x is $10) and the value of y is 1.5). obvious. Uncertainties such as prices of Similarly, the future price is opted if the spot feedstock and end-products are very common price is greater than the y times the mean of

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the sample price generated. We further Pl Cost of corn (cost at hedging); $ per exercise options and swaps in selling the bushel other end products which are distiller’s dried Ph Cost of cellulosic (cost at hedging); grain soluble (DDGS) and corn oil. For the $ per bushel purpose of space, the options and swaps are 1− e referred to as cross hedging. In the next Quality factor (defined as a factor of section, we develop the modeling framework the conversion rate of corn to ethanol); and discuss the case study. gallons per bushel of corn e Quality factor (defined as a factor of IV. MODEL DEVELOPMENT the conversion rate of cellulosic to ethanol);

gallons per bushel of cellosic In this section, we develop a model c Capacity of the ethanol plant; gallons that considers the decision-making process of per year an ethanol plant which includes the amount Dl Demand for corn; gallons per year of feedstock to purchase, ethanol to produce, h feedstock to store, ethanol to store, ethanol D Demand for cellulosic; gallons per sale, DDGs and corn oil. These decision year Selling price for corn ethanol; dollars variables are expected to achieve the desired Sl revenue by the ethanol producer. We explore per gallon

whether the decision to produce and sell Sh Selling price for cellulosic ethanol; ethanol and its by-products based on the dollars per gallon hedging strategies are profitable. We impose no restrictions on the ethanol producer in Variables terms of profit realizations if there is capacity to produce and meet the desired demand. The Q Quantity bought for corn; bushels model input variables, including the index, l Q Quantity bought for cellulosic; parameters and variables are first listed. The h mathematical model is designed to examine tonnage per year l hedging strategies of an ethanol producer. Po Forced market price for corn (market The objective function of the model conditions); dollars maximizes profit of the ethanol producer. h Forced market price for cellulosic The next sub-sections present the model Po input variables, objective function and (market conditions); dollars constraints. y Yield that can be attributed to corn and cellulosic ethanol; bushels for corn and tonnage for cellulosic 4.1. Mathematical model Input variables yl The total amount produced from corn; gallons Index yh The total amount produced from cellulosic; gallons j Supplier index j = 1...J b Buyer index b = 1… B 4.2. Objective function t Time period t=1...T

Parameters

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The proposed model seeks to maximizes the price of corn and cellulosic optimize the profit of the ethanol supply ethanol being sold as revenue, against the chain considering hedging and non-hedging. cost of purchasing corn and cellulosic raw materials at forced market conditions 4.2.1. Supply chain profit maximization (meaning the best price available for these raw materials during the procurement or The supply chain profit purchasing process). maximization being considered here is the ethanol producer. The supply chain

l h l hl Max[Sl Min(Ql (1− e), D )+ Sh Min(Qh (e), D )− P0 Ql − P0 Qh ]− f (e) , ………………...(1) where e ≈ f (e) which is a random variable is explained in the objective function. Equation (1) is defined as the Q ≤ (1− e)y ...... (2) objective function. This objective function is l the profit margin made after selling corn and cellulosic ethanol, and then subtracting the Qh ≤ (e)y …………….……………….(3) cost of buying the corn and cellulosic raw materials. The first two terms, i.e. Note that 1− e and e represent the conversion − l + h Sl Min(Ql (1 e), D ) S h Min(Qh (e), D ) rate (yield quality) of corn and cellulosic represent the revenue function. ethanol respectively. yl is the total amount l Sl Min(Ql (1− e), D ) means the revenue for produced from corn and yh is the amount from the corn ethanol that is sold considers the cellulosic minimum between the demand and production (since you can always sell what c ≥ (1− e)yl + eyh ….…………….…(4) you have produced) times the price of selling h corn ethanol. S h Min(Qh (e), D )on the other l h l h Min(Ql (1− e), D )+ Min(Qh (eh ), D )≤ D + D side represents the revenue for the cellulosic l hl ...... (5) ethanol. P0 Ql and P0 Qh represent the cost of purchasing corn and cellulosic raw l P ≥ P0 ……………….………………..(6) materials respectively. The random factor l expressed as e ≈ f (e) represents other costs h components (which may include Ph ≥ P0 ………………………..…….. (7) transportation, logistics, tariffs, etc). Also, the objective function considers up-scale and Equations (2) and (3) are defined as down scale potential and losses respectively the constraints that consider the low and high in selling the ethanol and buying corn and quality of the total conversion of corn and cellulosic feedstock or raw materials. cellulosic to ethanol in relation to the yield that is gotten from that conversion. These 4.2.2. Constraints equations can be related to the capacity constraints as they provide flexibility in how

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the total operational time is impacted by the zones, other supply chain fixed costs, conversion rate. Equation (4) explains the variables costs, and other capital costs. total capacity of ethanol production available being greater than or equal to the sum of the 4.3. Sample Average Approximation corn and cellulosic ethanol produced. This is (SAA) what we defined as operational hedging since there is flexibility in the production process. In this section, we develop and Equation (5) sales made out of selling corn discuss the sample average approximation and cellulosic ethanol based on their (SAA), multi-cut benders decomposition conversion rates, total quality and (MBD) algorithm, and the procedure for upside/downside potential inputs to the solving the entire proposed model based on function being less than or equal to the SAA and MBD. In the SAA algorithm, we demand. In summary, the total amount of follow the example developed by (Osmani ethanol sold (including corn and cellulosic and Zhang, 2014) with a sample set with B raw materials plus end products) is less than scenarios that is randomly generated from the or equal to the total demand. In equations (6) total number of N scenarios, and then an and (7), the constraints explain that the optimization problem specified by the regular prices of corn and cellulosic as well generated sample set which is solved in as ethanol commodity prices are always (Kleywegt et al., 2002). In the SAA method, greater than or equal to the forced price of the the expected value of the objective function market conditions. Equations (6) and (7) can Eω[Q(x, ξ(ω))] is usually approximated, only be negated under wild market where Q(x, ξ(ω)) is a realization objective speculations and an economic meltdown (at function on scenario ω, and Eω is the least in the commodities markets). expected value. B In the next sections we present the b sample average approximation (SAA), Multi- ∑Q(x,ξ(ω )) / B (8a) Benders Decomposition Algorithm (MBD) b=1 and the concept of copula. The SAA and The optimization problem (given by MBD are adopted to address the Eq. 1-7) corresponding to the original two- computational complexity of the problem as stage stochastic model is then solved using part of the methodology used in this paper. traditional algorithms. The optimal objective The copula concept is drawn to give meaning value zB and an optimal solution provide to the data sets used for hedging in relation to estimates of their true counterparts in the 𝑥𝑥� providing more information about the data stochastic model. This process can be relationships of ethanol and corn prices simplified by alternatively considering the beyond correlation. objective function of the optimization of Eqn We assume the revenue for DDGS (1-7) as equation 8b, where 8a is the and corn oil are same since there is no stochastic part in 8b. Then for each scenario, liquidity for their markets and we hedge a and are obtained. 𝑖𝑖 𝑖𝑖 B through swaps and options by adopting a 𝐵𝐵= T + ξ ω b zB𝑍𝑍 max c𝑥𝑥�x Q(x, ( )) / B (8b) x∈X ∑ cross hedge. The profit for the hedged b=1 equation is always inclusive of the revenue of The SAA method divides N scenarios corn ethanol, revenue of DDGS, revenue of into A equal size independent sample sets, corn oil, corn feedstock purchased cost, cost with each set containing B scenarios. By incurred in taking a futures position, solving the A stochastic problems using Eq. transportation cost of ethanol to demand

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1-7 as the objective function, objective values results show that unanimity in decisions is 1 2 A z , z , …, z and candidate solutions 1, achieved within reasonable iterations of the B B B SAA method. Therefore, a modified SAA 2, …., A are obtained. Eq. 9 denotes the 𝑥𝑥� method is proposed to obtain solutions where average of the A optimal values of the each sample set gives the same values for the 𝑥𝑥� 𝑥𝑥� stochastic problems. binary variables. A z = (1/ A) z a The use of the “modified” SAA B ∑ B (9) a=1 algorithm is explained below. (Kleywegt et al., 2002) shows that B Step 1: Create A sample sets {A = N, N/B1, ≤ zU, where zU is the global upper bound. N/B2, ..., 1} with each set populated Therefore for a maximization problem, 𝑧𝑧̅B with B scenarios {B = 1, B1, B2, ..., N} can be used to estimate the upper bound of randomly drawn without replacement the optimal value for the original stochastic𝑧𝑧̅ from the total N scenarios, such that A problem. For any feasible solution X, the = N/B. objective value given by cT + E[Q( , ξ(ω))] Step 2: Start with the largest value of A (i.e. is a lower bound of the optimal value𝑥𝑥� ∈ for the N) and create A = N sample sets with original stochastic probl𝑥𝑥em� . This𝑥𝑥� lower each set populated with B = 1 scenario bound can be estimated, where {ω1, ω2, …, randomly drawn without replacement ωN} which are the weights, contain the full from the total N scenarios. set of N scenarios. Step 3: Solve each of the A = N sets, and ∧ ∧ N ∧ compute optimality gaps. The SAA = T + ξ ω b z N (x) c x ∑Q(x, ( )) / N (10) algorithm terminates if each sample b=1 set gives the same values for the The SAA procedure provides A binary variables. Else go to Step 4. different candidate solution (i.e. one for each Step 4: If the desired unanimity in the values sample set). Eq. 11 is used to find * with the of the binary decision variables is not largest estimated objective value (for a achieved, then the next largest value of A sets maximization problem) over the full𝑥𝑥� set of N is used (A = N/B1), with each set populated scenarios. with B1 scenarios randomly drawn without * 1 2 A arg max { N( ) | [ , , …., ]} replacement from the total N scenarios. The (11) new upper and lower bound including the 𝑥𝑥� ∈ The accuracy𝑧𝑧̂ 𝑥𝑥� 𝑥𝑥�of∈ the𝑥𝑥� solution𝑥𝑥� 𝑥𝑥� * is optimality gap are updated. If the desired evaluated by computing the optimality gap unanimity in the values of the binary decision (as given by Eq. 12) for the full set 𝑥𝑥�of N variables is not achieved, then Step 4 is scenarios and comparing it against ε, a pre- repeated using the next largest value of A set criteria. until each sample set gives the same values * [ B – N( )]/ B (12) for the binary decision variables. During the traditional use of the SAA The algorithm is adopted from method,𝑧𝑧̅ 𝑧𝑧̂ 𝑥𝑥the� algorithm𝑧𝑧̅ terminates when the (Osmani and Zhang, 2017). desired optimality gap is achieved. However, for problem with large number of variables 4.4. Multi-cut Benders decomposition and stochastic scenarios, the desired (MBD) optimality gap for reasonable accuracy (e.g. less than 0.5%) might not be achievable using Multi-cut Benders decomposition is the traditional SAA method. But the solution then used to determine the remaining first- stage continuous decision variables by

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incorporating the decision variables obtained The Benders decomposition from the modified SAA method. Eq. 13 is algorithm is described as follows: used to describe the general stochastic Step 1: Set iteration counter l = 1 and θ = 0. problem which needs to be minimized (Birge Step 2: Solve master problem Eq. 13a to and Louveaux, 1997). For a maximization obtain a lower bound LBl on the objective problem the signs are to be reversed. e.g. loss value za. minimization is equivalent to profit Step 3: Fix all the first-stage decisions at their maximization. In Eq. 13, x is a vector that optimum value x* and solve Eq. 13b stands for the first-stage continuous decision for each scenario sub-problem to get variables; yω are the continuous second-stage an upper bound UBl = Eω[zb]. decisions for each scenario ω; A and b are Step 4: Proceed to test if [(UBl – LBl)/LBl] < parameter matrices independent of the Tolerance, return the optimal scenarios; and M, hω and Tω are parameter solution, otherwise, set the iteration matrices for each scenario ω. counter to T T Min z = c x + Eω [qω yω ] l = l + 1. Here tolerance is a pre- s.t. Ax = b determined small value (e.g. < 0.5%) (13) to determine the stopping criterion. My = h − T x ω ω ω Step 5: Use the duals of the scenario sub- ≥ ≥ x 0, yω 0 problem to add a Benders cut to Eq. Eq. 13 is decomposed into master 13a and return to Step 2. problem (Eq. 13a), and sub-problem (Eq. 13b). Advantage is taken of the dual Algorithm adopted from (Awudu and properties of Eq. 13b by introducing a new Zhang, 2012). variable θ to approximate Eω[zb] and iterating between master problem and sub-problem. 4.5. Identifying price relationships during The inequalities in Eq. 13a are the “cuts” that hedging link the master problem and the sub-problem. l l d and e are coefficients for the Benders cut, In this section we discuss a novel way and πω are the optimal dual vectors of of defining corn and ethanol price constraint in the sub-problem for scenario ω. relationships in our hedging process using a concept called copula. This price relationship T Min za = c x + θ between corn and ethanol is crucial as it s.t. θ ≥ d l x + el ,l =1,..., L provides the necessary and dependency for a l T better hedging position and strategy d = Eω [π ωTω ], (13a) l, adaptation. This relationship identification l = π T e Eω [ l,ω hω ], and dependency is referred to as copula. The Ax = b, x ≥ 0 next section provides a brief overview of copula (Fernandez 2008). T Min zb = qω yω 4.5.1. Copula

s.t. Wyω = hω - Tω x * Copula represents a powerful tool for

yω ≥ 0 (13b) decomposing the joint distribution into the marginal distribution and dependence structure that can be dealt with separately. One can choose the marginal distribution that

best fits each data asset, and afterwards

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230 Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies integrate everything using a copula function 53 counties. ND has already established corn with some desirable properties. Copulas have ethanol biorefinery plants because of the vast been applied to the measurement of credit availability of corn feedstock (Martin, 1999; and , in particular to the Muir et al., 2001). Studies such as (Zhang et assessment of the (VaR) of a al., 2013) show that ND is suitable for the portfolio. It allows computation of VaR while commercial cultivation of both corn and avoiding the usual assumption of marginal cellulosic feedstock such as switchgrass. and joint normality and linear correlation Raw materials are purchased from four structure. supply sources. Feedstocks are pre-treated at Implementation of copulas involves the warehouse, and the pre-treated raw three steps including: 1) select and construct materials transported to the production a copula, 2) estimate the parameters facility. Four different biofuel refinery associated with the copula, and 3) sample facilities convert the raw materials into end- from the parameterized copula. Copula products; two producing corn-based ethanol, parameters are estimated through a maximum and the other two plants for cellulosic-based likelihood estimation method of the form of ethanol. All the 53 counties in ND are T δˆ = ˆ ˆ δ considered as the demand zones. 22argmaxδˆ ln c( Gxt( x),, H yt( y ), ) (14) 2 ∑ t=1 5.1. Computational analysis where δˆ is the estimated copula parameter, 2 argmax is the mathematical functions that In this section we discuss the provides the argument associated with the resulting solution by using a Multi-cut maximum, ln is the natural logarithm, and Benders Decomposition and SAA methods. ˆ ˆ Gxxt( ), H yt( y) are the estimated marginal The proposed optimization models are coded distributions for x and y. To avoid in General Arithmetic Modeling Software distributional assumptions, a non-parametric (GAMS). The models are solved by the distribution is used for the marginal commercial GAMS 26.3.5 version using a distributions. Schwarz Information Criteria CPLEX solver. A Dell Latitude E6440 of (SIC) and Akaike Information Criteria (AIC) processor speed 5.2 GHz is used. We arrived were utilized for selecting the most at a solution after 23.45 seconds as compared appropriate multivariate copula. AIC and SIC to an intractable solution without the are superior goodness of fit statistics to other algorithm using the GAMS 26.3.5 version fit ranking criteria (e.g. chi-squared). with a CPLEX solver (generally about 2 hours before NEOS Report via the same V. CASE STUDY computer). This demonstrates the superiority of the algorithm used. The results and In this section, we focus on a case subsequent sensitive analyses are presented study involving an ethanol production plant. in the next section. The input parameters used The case study will examine a hybrid- in the case study are provided in Tables 1 and generation biofuel supply chain in the U.S. 2. Values of other key input parameters can state of North Dakota (ND) which consists of be referenced from Zhang et al. (2013).

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231 Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies

TABLE 1. CORN ETHANOL PLANT DATA Parameters Values Units Cost of corn feedstock MR (6.75,0.095) $ (dollars)/bushel Price of corn ethanol MR (2.75,0.095) $ (dollars)/gal Corn ethanol demand Based on county/month gallons Capacity of corn biorefinery plant 1 120,000,000 Gallons/yr Capacity of corn biorefinery plant 2 120,000,000 Gallons/yr Raw material transportation 0.0718/mile $ (dollars) Unit end-products transportation cost 0.0718/mile $ (dollars) Inventory holding cost for raw material 0.005 $ (dollars) Inventory holding cost for end-product 0.005 $ (dollars) Unit penalty cost for unmet demand 0.000285 $ (dollars) Unit cost per processing 1.24/bushel $ (dollars)

TABLE 2. CELLULOSIC ETHANOL PLANT DATA Parameters Values Units Cost of cellulosic feedstock MR (3.8,0.095) $ (dollars)/ton Price of cellulosic ethanol MR (2.75,0.095) $ (dollars)/gal Cellulosic ethanol demand Based on county/month gallons Capacity of cellulosic biorefinery plant 1 120,000,000 Gallons/yr Capacity of cellulosic biorefinery plant 2 120,000,000 Gallons/yr Unit raw material transportation cost to plants 0.158/mile $ (dollars) Unit end-products transportation cost 0.158/mile $ (dollars) Unit inventory holding cost for feedstock 0.0155 $ (dollars) Unit inventory holding cost for ethanol 0.15 $ (dollars) Unit penalty cost for unmet demand 0.005 $ (dollars) Unit cost per processing 1.24/ton $ (dollars)

VI. RESULTS AND ANALYSIS the ethanol producer to understand price relationships that exist between futures and The analysis will be focused on the spot prices of ethanol by understanding the optimal (best) ethanol price adoptions marginal relationships between ethanol spot (meaning prices of ethanol considered as and futures prices. This price marginal good to sell ethanol and buy corn), logistics relationships help the ethanol producer to analysis (storage space for corn and ethanol) contract for the shipments of ethanol to and cluster relationships (copula customer destinations. A motivation for this relationships) between corn and ethanol analysis stems from ethanol sales price which prices. are contracted using the basis price in normal In this section, we outline the market conditions and deliveries are made on importance of using copula to develop an time. Sometimes, deliveries may be late and optimal level of price to sell ethanol. As are delivered at a futures market that is discussed earlier, copula distributions allow inverted. In this case it is typical that a late

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232 Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies delivery is negotiated. To stimulate the uncertainties. Analyses are conducted for the impact of the profit margin variations with derived contract to determine the best price such delivered contracts, we conduct an contract to sell ethanol and still maximize analysis that determines the relationships profit. For the base case, the ethanol price is between ethanol price and revenue margins. reduced by 2 cents and transportation cost We assume an agreement between $0.25 per mile. Fig. 1 presents the ethanol destination markets and ethanol producers price analysis. The best price of ethanol that reduces transit time uncertainties by a contract ranges between $2.34 and $2.44 per factorϕ , and transportation cost is reduced gallon and corresponding to approximately by ℑ . five rail 5 cars per day. In summary the base Assume demand for the product is case for the transit time has stochasticity and normal, the new profit margin is expressed as: reducing this uncertainty increases the profit margin. We further simulated different E(π ) = f (ϕ,ℑ, D ) . The equation suggests ξ ,n margins and compare to the best contracted the margin function is dependent on demand, price for ethanol sale between the ethanol transportation cost, and transit time producer and buyer.

Margin and ethanol contract price 0.521 Contract price

0.52

0.519

0.518 ) 6 0.517

0.516

0.515 Profit margin (X10

0.514

0.513

0.512

0.511 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Ethanol contract price ($)

FIGURE 1. ETHANOL PRICE ANALYSIS.

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233 Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies

6.1. Logistics analysis margins decrease to $0.513M. Corn storage analysis gives a similar trend as ethanol. It is Ethanol hedging process is influenced concluded that extra capacity addition would by logistics strategies including the number result in increased profit for a period of of storage space, rail car allocation for demand trend and sales. automotive, type of transportation routes, etc. It is therefore prudent to conduct a logistic 6.2. Storage (holding) cost impact on profit analysis in one of these areas. We conduct a logistics analysis based on storage space In this section we conduct further available to the ethanol producer which can sensitivity analysis between storage (holding) be termed as a lot size. This lot size cost and ethanol margins. In the base case, the calculation can be related to the previous overall storage cost of input and output are analysis about uncertainties in demand, since incorporated. Inventory issues affect a demand and transit time impact profit significant portion of the decision-making margins. We consider storage cost on profit process especially in determining safety margins based on the number of days of stock and economic order quantities. Two storage. Number of days and ethanol capacity decisions are made; short- and long-term discounted equation for new facility is used. inventory decisions. The analysis here is Fig. 2 illustrates the ethanol and corn storage motivated by the provision of short-term capacity analyses respectively for variations inventory decision which involves the in demand. stochasticity of inventory costs as a result of We note that for decreasing demand, the uncertainty in demand. This set of ethanol storage shows stable profit of analyses is conducted for the overall cost of $0.517M between storage days of 4 and 8 storage and how it impacts the profit margin. days. A different trend is realized if the We introduce a cost factor for the demand decreases by 7.5% and 12.5%. Profit storage which determines how much cost is margins decrease to $0.5145M for this period increased between $2.2 and 3, where $2.2 is but there is a point of intersection which the least cost increase and $3 is the highest measures the breakeven that can result in cost increase. The results show that a optimal expected margin. This analysis decrease in storage cost from a factor of $2.6 concludes the importance of building new or to $2.4 increases profit from $0.5152M to adding extra storage for a certain profit $0.5153M. Subsequent decrease between margin. $2.3 and $2.25 factor of the overall cost Similar analyses are conducted for increases the profit by 0.019%, which is from corn storage capacity (not shown). In $0.5154M to $0.5155M. Interestingly, an addition, 35-38 days of storage for corn increase in the cost factor $2.6 to $2.8 means profit margins become stable, with an provides a stable profit margin between increasing profit level between 20 and 32 $0.5152M and $0.5151M. Further increase in days. This analysis means corn storage cost between $2.8 and $2.9 does not affect capacities lower than 25 to 30 days should profit margins significantly. This consider building extra capacity. When phenomenon is due to the stable cost of demand is decreased, corn storage shows storage throughout the entire horizon and margins of $0.515M and $0.5145M between therefor the impact of the profit margins storage days of 4 and 8 days. Nonetheless, a might be as a result of the fluctuating demand. similar trend is realized if the demand The cost of storage varies from the base case decreases between 9.5% and 12.5%. Profit to approximately 5%, 10%, 15%, and -5%, -

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234 Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies

10%, -15%, to realize the impact of storage indicate a small change in the storage costs price changes and the corresponding demand corresponds to an insignificant profit margin. uncertainties on profit margins. A realization The opposite holds for this change, since of the profit margin is considered with a small there is a greater risk in profit reduction if variation or fluctuations in the storage cost. If storage cost changes are high. This analysis the storage cost is higher, the impact is is shown in Figure 3 below. significant. Conclusions from this analysis

Storage capacity analyses on margin 0.518 Decreasing demand storage-margin Increasing demand storage-margin 0.5175

0.517

0.5165 ) 6 0.516

0.5155 Margin (X10

0.515

0.5145

0.514

0.5135 4 6 8 10 12 14 16 18 20 Ethanol storage capacity (days)

FIGURE 2. ETHANOL LOGISTICS ANALYSIS.

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235 Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies

Entire storage cost and profit margin 5.1555 Profit margin versus storage cost

5.155

5.1545 ) 5 5.154

5.1535 Profit margin($X10

5.153

5.1525

5.152 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 Storage cost ($)

FIGURE 3. ETHANOL LOGISTICS ANALYSIS.

6.3. Price data (ethanol and corn) cluster to the theoretical assumption. The cluster analysis diagram for the hedge ratios is shown in the Fig. 4. The SAA method will therefore give In this section we consider insights ethanol pricing analysts some leverage in from an analytical perspective by clustering identifying fewer trade patterns from a few both corn and cellulosic prices to help with data sets instead of relying only multiple data hedge ratios during hedging. Hedge ratios are points. variable determinants that help an ethanol In relation to the concept of copula, producer maximize the amount of Figs. 5-6 confirm the analysis we conducted corn/cellulosic feedstock to ethanol in Fig. 3. We see that based on the definition production to enable optimal use of of copula (dependency and marginal production plant, scheduling, and other relationships across variables), there is a internal as well as external operations. relationship that follow the different types of Ethanol price data that were clustered over a dependencies between the corn and ethanol period of 1000 scenarios indicated similar spot and futures prices respectively. In Figs. patterns as cluster of 10,000 data points for 4-5, the terms x4 and x3 represent the corn and our analysis. This confirms that the sample ethanol copula distributions. average approximation (SAA) used conform

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236 Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies

FIGURE 4. CLUSTER ANALYSES OF PRICE DATA POINTS.

In addition, although statistical and regression analysis provide a good indication of relationship between and across variables, we use copula to provides a better understanding of the independencies among prices instead of using correlation which is too simplistic or assumes a linear relationship. For instance, a good ellipse relationship can be demonstrated for the ethanol and corn spot, meaning that the prices of corn and ethanol have some relationship that can be calculated and some level of dependence structure between the two variables. However, a scatter set of relationships from a linear perspective might just give a simple relationship. This makes it clear that copula data analysis provides graphical relationships that are more meaningful for hedging against risk than the copula alone as shown.

FIGURE 5. COPULA GRAPH BETWEEN ETHANOL FUTURES AND ETHANOL SPOT.

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237 Iddrisu Awudu, Anthony Asare, Eric Asa, Atif Osmani, Vinay Gonela, Anthony Afful-Dadzie Maximizing Profits in an Ethanol Supply Chain with Hedging Strategies

FIGURE 6. COPULA GRAPH BETWEEN CORN FUTURES AND ETHANOL SPOT.

VII. CONCLUSION AND SUMMARY values for the non-hedging at lower profits are observed to be riskier as compared to the This paper develops a model that uses profit values of the hedged decisions. By hedging strategies in a supplier (farmer) and contracting using hedging positions such as buyer (ethanol producer) setting. We futures and spot based on heuristic price concentrate on the profit maximization on the levels, we indicate that the strategy provides side of the ethanol producer. The hedging a firm a competitive edge by reducing method considers the futures and spot prices exposure to demand and price uncertainties. of corn and cellulosic feedstock respectively, Similarly, we reduce the impact of while the ethanol end-products are hedged production costs with the aim of reducing the using futures. Non-hedging strategy uses spot adverse effects associated with fluctuations prices for the purchase of feedstock and sale in the firm’s expected profit or cost. We of end-products with cross hedging other end conclude that by capturing volatility using a products using options and swaps for weighted sample average approximation for whichever price is higher. different periods of corn feedstock and We concentrate on the computational ethanol prices, which are assumed to follow tractability of the algorithm to achieve better a Mean Reversion (MR) process, realistic results by capturing the volatilities. A two- results are obtained from the case study stage stochastic linear programming method analysis. Counter intuitively, we determine based on the Multi-cut Benders that an ethanol price margin of $2.06-$2.41 Decomposition Algorithm is used to solve per gallon will allow ethanol producers to the resulting model. We analyze differences make profit or at least break-even. in profit margins in relation to hedging and Finally, this model can be used in non-hedging with the non-hedging being less most if not all energy processing than the hedging. We show that the profit environments, i.e. production or processing

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environment that convert inputs to outputs, P.J. and Smoller, M.M.(1995), “Mean such as converting crude oil to gasoline, reversion in equilibrium asset prices: kerosene and other co-products. For example, Evidence from the futures term in this case, corn is bought from elevators structure”, The Journal of according to a contractual agreement that Finance, 50(1), pp.361-375. spans a period of supply and production is done daily with storage capacity for the Bessembinder, H., Coughenour, J.F., Seguin, ethanol. Also, the production is for a future P.J., and Smoller, M.N. (1995), month being hedged. To some extent, the “Mean reversion in equilibrium asset availability of other commodity materials prices: evidence from the futures term within ethanol production such as corn oil, structure”, The Journal of Finance 50: DDGs, affect the decision-making process of 361-375. buying corn and selling ethanol. Similar Black, F. and Scholes, M., (1973), “The analyses can also be drawn from the pricing of options and corporate conclusions in this manuscript for other liabilities”, Journal of political energy sectors such as hydro, wind, etc. economy, 81(3), pp.637-654. This paper is limited in its scope by Blank, S.C., Carter, C.A. and Schmiesing, not incorporating uncertainties and dynamic B.H. (1991), Futures and options hedging scenarios that include transportation markets: trading in commodities and challenges. Also, newer transportation financials (Vol. 1). Prentice Hall. models and traveling distances such Boyabatli, O. and Toktay, L.B. (2004), Riemannian manifolds will be a good a future “Operational hedging: A review with direction. One other limitation is stochastic discussion”. inventory models based on periodic and or Boyabatli, Onur and Toktay, L Beril (2004), continuous inventory management. Also, “Operational Hedging: A Review ethanol transportation involves the use of rail with Discussion”, Research cars that can be owned, leased, sub-leased or Collection Lee Kong Chian School of purchased by an ethanol producer. These rail Business. car strategies affect ethanol transportation Brinker, A., Parcell, J. and Dhuyvetter, K. costs and therefore do affect ethanol margins. (2007), April. Cross-Hedging Finally, using other clustering methods to Distillers Dried Grains: Exploring gather data for copula distribution and Corn and Soybean Meal Futures analyses will be the way to go as algorithms Contracts, In Proceedings of the such as CoCluster (combining copula and NCCC-134 Conference on Applied cluster analysis) from a big data perspective Commodity Price Analysis, will be a good research direction soon. Forecasting, and Market Risk Management. Chicago, IL.[http://www. farmdoc. uiuc. REFERENCES edu/nccc134]. Chang, C.L., McAleer, M. and Tansuchat, R. Awudu, I., Wilson, W. and Dahl, B. (2016), (2010), “Analyzing and forecasting “Hedging strategy for ethanol volatility spillovers, asymmetries and processing with copula hedging in major oil distributions”, Energy markets”, Energy Economics, 32(6), Economics, 57, pp.59-65. pp.1445-1455. Bessembinder, H., Coughenour, J.F., Seguin, Chod, J., Rudi, N. and Van Mieghem, J.A.,

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