Modeling Framework for Uncovering System Behaviors in Biofuels Supply Chain Network

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(1)Third International Engineering Systems Symposium CESUN 2012, Delft University of Technology, 18-20 June 2012. Modeling Framework for Uncovering System Behaviors in Biofuels Supply Chain Network Datu B. Agusdinata1, Seokcheon Lee2, Fu Zhao3, Dan DeLaurentis4, and Wil Thissen5 1. System-of-Systems Laboratory and Division of Environmental and Ecological Engineering 2 School of Industrial Engineering 3 School of Mechanical Engineering and Division of Environmental and Ecological Engineering 4 School of Aeronautics & Astronautics, Purdue University 5 Faculty of Technology, Policy, and Management, Delft University of Technology 701 West Stadium Avenue, West Lafayette, IN, 47907, USA Telephone: (765) 494-0418; Fax. : (765) 494-0307. bagusdin@purdue.edu, lee46@purdue.edu, fzhao@purdue.edu, ddelaure@purdue.edu, w.a.h.thissen@tudelft.nl Abstract. A full realization of alternative energy such as biofuels depends on the existence of a viable supply chain (SC) network. This work seeks to understand the dynamics of biofuels SC network by developing an approach to model the dynamics and characterize system behavior. A multi-actor approach is pursued in which the interests of three supply chain actors are represented: users, biorefineries, and farmers with a simple binary decision option: adoption or non-adoption of biofuels. The decision dynamics of these actors is modeled using a computational ecosystem construct. This SC network model is characterized by distributed control, time asynchrony, and resource contention among actors who interact in collaborative and competitive mode and who make decision based on incomplete knowledge and delayed information. A preliminary set of coupled payoff function for each actor type and each decision is developed to represent interdependencies among SC actors. It also serves as a mechanism to incorporate the effects of policy interventions and other exogenous factors. The SC network shows behavior ranging from fixed point equilibrium under no delay and perfect knowledge to periodic and chaotic oscillations. It is very sensitive to the time delay parameters that partly influence the quality of information on which actors’ decision are based. Using non-linear time series analysis, several regions of SC behavior are identified. In particular, chaotic behavior was observed. The work provides a basis for further development including identification of policies to control undesirable behaviors. Keywords. Distributed system, agent based model, computational ecosystems, biofuels supply chain network.

(2) 1. Introduction. In 2010 27.5 quadrillion Btu of energy was consumed by the US transportation sector, with more than 90% of which in the form of petroleum products. According to US Energy Information Administration (EIA, 2010), this leads to emission of 1917 million MT of carbon dioxide, accounting for 27% of total U.S. greenhouse gas (GHG) emission. The mounting concern on global warming has led to continuing efforts on developing technologies to reduce GHG emission from transportation fuel systems. Biomass-derived liquid fuel (i.e. biofuel) represents a promising candidate due to its high energy density and compatibility with the existing infrastructure for distribution and delivery. Currently biofuel accounts for about 3% of total transportation fuel consumed, mainly in the form of ethanol derived from corn grain. Due to favorable market conditions and government incentives, the past decade sees significant increase on fuel ethanol production i.e. from 1.6 billion gallons in 2000 to 13.2 billion gallons in 2010. However, the first generation biofuels including corn derived ethanol, which are mainly produced from traditional food crops, are limited in their ability to achieve targets for petroleum substitution and climate change mitigation. In addition, the diversion of food crops to biofuels has already raised concerns about food prices, and has exacerbated food security to poor people in developing countries. In response to these concerns, research attention has shifted to second generation biofuels derived from non-food feedstocks. Second generation biofuels have significantly larger GHG emission reduction potential than first generation biofuels and they only use agricultural wastes and forest residues. Unlike first generation biofuel, the economic viability of the second generation biofuel has not been established. A recent NAE report argues that lignocellulosic derived liquid fuels can only become competitive under high oil price scenario and the biorefineries will likely face large financial uncertainties (National Research Council, 2011). For the near future, due to imperfect market conditions, government interventions are critical to maintain the establishment and development of the industry (Tyner, 2011). In addition to the efforts to improve feedstock yield and conversion efficiency, creating the conditions for biofuel to achieve significant market penetration requires a deep understanding of the dynamics of the supply chain. Fig. 1 shows a depiction of the SC network along fuel life cycle stages. The stages cover processes from farming to fuel distribution to usage. The biofuels are used for ground and air transportation to include a wide variety of actors such as individual car user/owner, airlines, and military. From the perspective of each SC actor, it is desirable to obtain maximum payoff from decisions. A decision that is perfectly rational from an individual actor perspective, however, may have repercussion that results in a non-optimal outcome when measured by the overall system performance. An understanding of such dynamics is critical in order to steer the overall system towards stability in the system performance and avoid persistence oscillations. Unfortunately, biofuel supply chain studies to date take the bio-refinery as the default customer under the assumption that the biorefinery is in control of the entire supply chain. Most of these studies adopted the.

(3) classical production/distribution MIP approach in order to design a network that maximizes bio-refinery profits. This paper aims at filling this gap by developing a SC model that captures interactions of multiple actors and the evolution dynamics. Airlines + Military. Farmers and feedstock producers. Automobile owner +operators. Use Farming. Feedstock Harvester + Transporters. Harvesting Biofuel Life Distribution Fuel & Transport Cycle Distributors Stages Pre-processing & Refining. Biorefineries. Fig. 1. Biofuels Supply Chain Network. 2. Supply Chain Network Model. The SC model is developed based on computational ecosystems construct (Kephart, Hogg, & Huberman, 1989). The original idea is that such an ecosystem consists of multiple agents (i.e. a network of interconnected computers) for performing a large number of tasks. To perform the tasks, the agents are free to choose among multiple resources (e.g. specific hardware, software, or communication line). The decision is based on perceived payoff (e.g. time for performing the task or accuracy of solution)of individual computer, which is rational but may not be necessarily yield the most desirable performance from the overall system point of view. Clearly, a computational ecosystem lacks a central controller since it is up to the individual actor to decide on action. In addition, decisions are made in an uncoordinated fashion and time asynchronous. The shape of payoff function may differ depending on whether actors compete or collaborate. Another important characteristic that drives the dynamics of a computational system is the quality of information. Due to uncertainties and delayed availability of information, actors often use imperfect and obsolete knowledge to base their decisions. The computational ecosystem construct is considered appropriate and is therefore adopted for modeling SC network because a SC network shares most of the characteristics. Since the SC network consist of a large number of firms from multiple interrelated industries, a complex adaptive system (CAS) perspective allows a supply network manager to make local decisions while considering the complexity of the.

(4) overall system (Pathak, Day, Nair, Sawaya, & Kristal, 2007). Furthermore, it is argued that due to the prevalence of the use of information technology, supply chains have greatly increased in complexity almost to the level of biological system (Surana, Kumara, Greaves, & Raghavan, 2005). In this environment there is a need for coordination strategies among supply chain actors to achieve adaptive collective behavior. 2.1. Basic model structure. For two types of decision: decision 1 and 2, the dynamics is governed by: .

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(7) .. (1). where, α is rate in which actors reevaluate their decisions, ρ is preference probability function and f is the proportion of actors taking decision 1 at any given time. ρ can be estimated by: 1 erf .

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(9) . .. (2). where Gi (f) is a payoff function of taking decision i, erf is an error function operator (Weisstein, MathWorld). Clearly, an actor will prefer a decision with relatively higher payoff. Evaluation rate,α, is a form of exponential timeout. An actor reconsiders its current state and if the condition is right will transition to another state. The execution of the transition follows an exponentially distributed timeout with parameter α. If the rate is 2, the reevaluation of the decision takes place on average 2 times per time unit. Uncertainty and time delay Uncertainty in the payoff is represented by parameter σ. The actual payoff may deviate from the expected value due to imperfect information. The time delay τ, reflects how actors factor in (un)timely information available to their decision. The f value that enters ρ at time t is the one that occurs at time (t- τ). In this case: .

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(11) . (3). The erf function is a main mechanism that drives the dynamics of the supply chain model through the uncertainty and delay factor. Fig. 2 illustrates how these factors affect actors’ preference function by depicting two values of (1/2σ) over relative payoff difference (G1-G2)..

(12) error function erf [1/(2σ σ ) * (G1-G2)] 1 1/(2σ) =3.0 0.5 1/(2σ) =0.3 0 -3. -2. -1. 0. 1. 2. 3. -0.5 -1. (G1 - G2). Fig. 2. Error function. When the uncertainty is small (i.e. 1/σ is large), the erf function will resemble a step function. That is, the preference probability, ρ value will be close to 1 when G1 > G2 and close to 0 when G1 < G2. In contrast, when payoff uncertainty is large (i.e. 1/σ is small), for large difference in payoff (G1 >> G2), ρ will be close to 0.5 and will vary almost linearly with (G1-G2). Form of payoff function The shape of the payoff function can vary depending whether actors cooperate or compete with one another. In a cooperation mode: the more actors are taking the decisions, the greater the payoffs until the sector “crowds out”. In a competition mode: payoff monotonically decreases with an increased number of resource users. In this context, for instance, profit margin will decrease due to competition. 2.2. A Simple case involving one actor type and two decisions. A simple model of two decisions was implemented in an agent-based modeling software AnyLogic (www.xjtek.com) using the original Kephart et al. (1989) model. The payoff function for Decision1(i.e. use of resource 1) and Decision2 (i.e. use of resource 2) is given by: G1= 4+ 7f - 5.333f 2 and G2 = 4 + 3f, respectively. With no delay and uncertainty, the system will come to a fixed point equilibrium when G1= G2 (Fig. 3). 8 7 6. Payoff. 5 4. G1. 3. G2. 2 1 0 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 1. f. Fig. 3. Equilibrium point under no uncertainty and delay.

(13) For comparison, three types of system behavior (i.e. fixed point equilibrium, periodic, and chaotic oscillation) are presented under different parameter setup for delayed and imperfect knowledge and a mixture of cooperative and competitive behavior with 1000 actors (Fig.4).. 1. 1. 0.9. 0.9. 0.8. 0.8. 0.7. 0.7. 0.6. 0.6. 0.5. 0.5. f1. f1. (a) Fixed point equilibrium (α=0.1, σ=0, τ=0). 0.4. 0.4. 0.3. 0.3. 0.2. 0.2. 0.1. 0.1 0. 0 0. 10. 20. 30. 40. time. (b) Periodic oscillation (α=0.1, σ=0.5, τ=2). 50. 0. 10. 20. 30. 40. 50. time. (c) Chaotic oscillation (α=1, σ=1, τ=5). Fig. 4. The three mode of system behavior for the basic model. Fig. 4 a (bottom right) also shows how the preference probability function for taking Decision 1 changes over time. A chaotic oscillation occurs through period doubling bifurcations as the oscillation frequency abruptly changes at the stochastic nature of value of α (with τ constant). Adaptation to biofuels SC network The issue is how to expand the simple model to include interactions among SC actors at different level. Main challenge includes specification of payoff function that should be derived from data. The model exhibits a three level supply chain network structure, in which, demand signals flow from airlines to biorefineries to farmers. In this setting, biorefineries respond to demand after it has reached a certain threshold value. Farmers are assumed to conduct business with biorefineries under some contractual terms..

(14) The SC model is assumed to be hierarchical in which demand and policy signal comes from the upper actor level to the lower one (Fig. 5). The scope of the decision by each actor is also given in Fig. 5. Sustainabilityimpacts= f(life cycle inventory). Decision1: support biofuels Decision2: not support biofuels policies Decision1: adopt biofuels Decision2: not adopt biofuels. life cycle inventory. Utility= f(policies, fuel price, refineries supply, competition) demand. Decision1: adopt biofuels Decision2: not adopt biofuels. Users. supply. Profitability= f(users’ demand, farmers supply, competition, policies) demand. Decision1: biofuel crops Decision2: food crops. Policymakers. Biorefineries. supply. Profitability= f(refineries demand, competition, policies). Farmers. Fig. 5. Some interdependencies in biofuels supply chain network. The overall system payoff comes in two measures: economic and environmental impact. First is the total monetized payoff experienced by each actor. Second is the GHG emissions measured by the total sum of the life cycle inventory. System inertia In addition to delays associate of information, there are inherent system delays. As actors respond to demand signal, it will take time for biorefineries to build the plant and for farmers cultivate the land and harvest the energy crops. This system delay provides some inertia to the system when it is experiencing structural changes such as change in relative competitiveness among energy crops and external policies/ regulations imposed to it. Coupled Payoff functions Coupled payoff functions imply that the decision taken by an actor depends on that of other actors of the same type and across the SC network. The decision of an actor in any level will be either adopting biofuel or not. The following is defined: f1: fraction of farmers (or acres) dedicated for biofuel f2: fraction of biorefineries (or barrels) dedicated for biofuel f3: fraction of users (or barrels) dedicated for biofuel Gi1: payoff (profit) of level i actor from biofuel adoption Gi2: payoff of level i actor from non-biofuel adoption..

(15) An actor’s payoff on an option depends on the supply of the option (from suppliers) and demand of the option (from consumers) as well as the competition within the same level. The payoff will increase with a) the increase of supply b) the increase of demand c) the decrease of internal competition. Table 1 provides a general form of the payoff function using linear equations and specifies some hypothetical coefficients for the purpose of this paper. Table 1. Actors’ payoff function Actor type. General form of the Payoff Function Decision 1 G11 = -cf1 + cf2 + d Users Decision 2 G12 = cf1 – cf2 + d Decision 1 G21 = cf1 – cf2 + cf3 + d Biorefineries Decision 2 G22 = -cf1 + cf2 – cf3 + d Decision 1 G31 = cf2 – cf3 + d Farmers Decision 2 G32 = -cf2 + cf3 + d Note: c’s and d’s are all parameters and c’s are non-negative.. Coefficients used -10 f11 + 5 f21 + 5 3 f11 – 1 f21 + 5 4 f11 – 9 f21 + 3 f31 + 3 -2 f11 + 3 f21 – 4 f31 + 3 8 f21 – 10 f31 + 2 -5 f21 + 2 f31 + 1. This construct of coupled payoff allows us to associate some real-world interpretations. Parameter c’s imply how the sensitivity of payoff to changes in the adoption level. Parameter d’s imply the initial (dis) advantage that a certain decision has. For example, for farmers, the initial conditions favor energy crop production, which may true is a high oil price scenario. Biorefineries have both upper and lower level couplings. In addition, the construct provides a mechanism to model the influence of certain policies and exogenous factors (e.g. subsidies). The initial conditions are all actors are taking Decision 2 (i.e. not adopting biofuels). The three main SC model parameters (i.e. α, σ, and τ) will be varied one at a time to reveal effect on system behavior. To uncover regions of system behaviors, different kind of analysis will be employed for different system behaviors.. 3. Results and Analysis. Under a condition of no delay and no uncertainty, the SC network reaches equilibrium in terms of the proportion of actors adopting biofuels after about 10 time units (Fig. 6). The system inertia due to delayed responses of biorefineries and farmers to demand is visible. When the reevaluation rate, α, is changed to a faster rate, the SC network will achieve the state of equilibrium in less time. The more uncertain the payoff function is (i.e. higher σ), the lower the value of equilibrium f1 will be. The rate of achieving equilibrium, however, is not affected by the change in σ..

(16) Fig. 6. (a) Fixed point equilibrium (α=0.1, σ=0, τ=0). When the extent of time delay, τ, is changed from 0 to 1 with other two parameters remain the same, the SC network shows a different behavior (Fig. 7). A periodic oscillation occurs around the equilibrium value. 1. 0.75. users. f1. 0.5. biorefineries farmers. 0.25. 0 0. 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. time. Fig. 7. Periodic oscillation (α=0.1, σ=0, τ=1). Next, the reevaluation rate,α is increased ten times from 0.1 to 1; that is actors compare more often the relative difference between payoffs. As a result, the amplitude of the periodic increases ranging from 0 to 1 (Fig.8). It is noticeable in this case that at the beginning, farmers start crop production before users demand materializes. 1. f1. 0.75. users. 0.5. biorefineries farmers. 0.25. 0 0. 10. 20. 30. 40. 50. 60. time. Fig. 8. System behavior with (α=1, σ=0, τ=1). 70. 80. 90. 100.

(17) So far, the three parameters are set to be the same for all three actors. Suppose now that each actor has a distinct reevaluation rate, α. This set up is actually more realistic since actors operate in different time scale. Fig. 9a shows that with no uncertainty and no delay the SC network will converge to a new equilibrium. In contrast, with a slight delay and variable delay, a chaotic oscillation occurs. 0.1 0.08 0.06. f1. users 0.04. biorefineries farmers. 0.02 0 0. 20. 40. 60. 80. 100. time. (a) (α=0.25, σ=0, τ=0)users, (α=0.15, σ=0, τ=0)biorefineries, (α=0.1, σ=0, τ=0)farmers. (b) (α=0.25, σ=0.25, τ=2)users, (α=0.15, σ=0.25, τ=1)biorefineries, (α=0.1, σ=0.25, τ=3)farmers Fig. 9. System behavior with distinct time parameter for each actor type. Using 1000 time-series data points, an attractor is constructed in Fig.10. It is observed that the evolution of the system is highly irregular without any periodic dynamic behavior. Therefore, we suspect the attractor might be chaotic though more careful analyses that include fractal dimension (Grassberger and Procaccia, 1983) and Lyapunov exponent (Wolf et al., 1985) are needed to confirm.. 4. Concluding Remarks. This paper develops a modeling framework to understand different behavior modes of supply chain network. The SC network shares many characteristics of large distributed system lending it appropriate for computational ecosystem construct..

(18) 0.4 0.35. f1 users. 0.3 0.25 0.2 0.15 0.1 0.05 0 0.8 0.6 0.4. f1 biorefineries. 0.2 0. 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. f1 farmers. Equilibrium point (no delay, no uncertainty) Fig. 10. Chaotic behavior of the biofuels SC network. One big challenge for supply chain actors is to achieve an optimal group strategy on the basis of individual actor strategies. This work is intended to support this kind of analysis. Having knowledge of regimes of SC network behavior, how can (some) actors outsmart the system? Are there any ways for all actors to coordinate for everyone’s benefits? What can policymakers do to encourage and provide disincentives to strategies that destabilize the system? These are some of the relevant questions that the model is supposed to answer. Major challenge for future work is a calibration of the coupled payoff function using empirical data, since most of the biofuel pathways do not yet exist. A validation from the production of corn ethanol will be sought. Another validation issue is comparing the assumptions and model outcomes with SC models such as the Beer game (Chen, 1999), and other works on modeling actor decisions to choose among alternatives. The decision choices for SC actors will be expanded to include multiple and nested decision options. In the biofuel SC, once farmers decide to cultivate bioenergy crops they have multiple alternatives to choose from: lignocellulosic biomass such as poplar and switchgrass, or oil seed plants such as camelina and jatropha. Similar options are faced by biorefineries in terms of conversion technologies: thermo-chemical (e.g. Fischer-Tropsch and pyrolysis) or bio-chemical process. Each of these options has its underlying costs and technological readiness level that influence their viability. Furthermore, each chosen pathway will yield different life cycle inventory and therefore environmental impacts.. References Chen F.G. (1999), Decentralized supply chains subject to information delays, Management Science , 45(8) pp. 1076-1090.

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