Dairy waste-to-energy incentive policy design using Stackelberg-game-based modeling and optimization
Introduction
Dairy is a major component of agriculture in New York State, with a gross farm income of over 2.7 billion dollars in 2017 [1] that contributes to 56% of the total farm revenue in the state [2]. There are over 4,000 dairy farms and 600,000 dairy cows in New York State [3], which is a solid foundation for the large amount and variety of dairy products. The large number of dairy farms and cows inevitably lead to the continuous generation of a significant quantity of dairy manure, an unavoidable biomass that requires proper treatment. If the dairy manure is not appropriately processed, it could lead to several environmental and health concerns that include, but are not limited to, (a) groundwater and surface water contamination through runoff from land application of manure [4], or through leaks in the containment units [5]; (b) air pollution [6] and greenhouse gas emissions [7] from the decomposition of dairy manure, with a complex mixture of ammonia, hydrogen sulfide, methane and nitrous oxide [8]; (c) odors that could lead to mental health deterioration and negative mood states to the local community [9]; and (d) pathogen related contamination and disease which may cause severe damage to the physical health of local residents [10].
However, from the perspective of the energy sector, dairy waste can be processed as a valuable source of bioenergy while mitigating its negative impacts on the environment and human health [11]. To promote bioenergy production and tackle the environmental and health issues of dairy manure, the United States Department of Agriculture (USDA) and the Environmental Protection Agency (EPA) launched the AgSTAR program [12], a program promoting the use of anaerobic digestion (AD) method on manure processing. AD is a process through which microbes break down organic matters, such as manure, without oxygen. During the AD process, microbes generate biogas, of which the main composition is methane, and it can be used as a renewable energy source in subsequent processes. Promoting AD not only facilitates bioenergy production, but also benefits the environment by odor control, ground and surface water protection, land-use conservation and methane emission reduction. In terms of environmental impacts, the installation of ADs at dairy and swine operations would reduce methane emissions by 87 percent from these operations, which corresponds to 1.8 million tons in the U.S. per year [12]. The recovered biogas from AD serves as a renewable energy source that could introduce environmental benefits by offsetting the use of fossil fuel. In terms of economic benefits, biogas can be further utilized for heat production, electricity generation, and/or market sale via natural gas pipelines, which could potentially improve the economic performance of dairy farms [12]. Thus, the adoption of on-farm AD could process dairy waste as a source of renewable energy, and could benefit both the government and the dairy farms environmentally and economically.
Proper incentive policy could promote on-farm AD adoption and thus increase bioenergy production. Despite the considerable advantages of AD, there are only 33 dairy farms [13] with anaerobic digesters in New York State, which has over 4,000 dairy farms in total [3]. In comparison, Germany has more than 10,000 large-scale biogas plants, most of which are on-farm AD facilities in dairy farms. One of the reasons behind the booming of biogas plants in Germany is the well-developed financial supporting system by the German government [14]. To reduce the negative effects of unprocessed dairy manure, proper incentive policy by the government would encourage the dairy farms to adopt on-farm AD, which benefits both the government and the dairy farms on the environmental issues and negative externality that comes along with the large amount of unprocessed dairy manure.
Incentive policy is needed to promote AD adoption for manure processing and biomass-based renewable energy production in dairy farms. Although AD is an efficient way to process dairy manure and generate clean energy, there are economic barriers for AD-based bioenergy production at scale [15]. For example, the installation cost of AD typically has a scaling effect that decreases the marginal installation cost with the increase of digester capacity [16]. Because of the economies of scale, larger farms tend to have lower unit cost on bioelectricity generation due to the large amount of dairy waste produced inside these farms. Smaller farms, however, could not benefit from this scaling effect and generally do not prefer a large capital investment to install a new AD facility on-site. Nevertheless, AD adoption in large farms is not common in New York State where no active policies promoting AD-based bioenergy exist. Among the 115 large farms [17] that have over 2,000 cows, only 22 of them currently possess on-farm AD [13]. Therefore, it is crucial to design and determine the optimal bioenergy incentive policies to promote AD adoption in dairy farms.
To the best of our knowledge, there are no existing literature on incentive policies for AD adoption and bioelectricity generation from the perspective of systems optimization. There are several publications focusing on farm-level facilities regarding electricity generation using recovered biogas from AD, which includes the analysis on economic viability of AD and biogas-based combined heat and power (CHP). The techno-economic features of electricity generation from AD of a biogas plant in Çiçekdağı was analyzed [18]. Similarly, the economic feasibility of biogas production for an animal farm in Iran was assessed [19]. Lauer, Hansen, Lamers and Thrän studied the economic viability of using dairy manures to produce biogas and biomethane for dairy farms in Idaho [20]. Feasibility assessment of medium-scale anaerobic digesters and subsequent electricity generation for brewery and dairy farm waste streams has been studied [21]. In addition, a case study for dairy farms in Vermont was conducted focusing on the conversion of cow manure into electricity using AD [22]. Life cycle environmental impacts of AD and the subsequent CHP process were evaluated, and the results showed that AD-based energy is much more economically friendly compared to fossil fuels in terms of global warming potential [23]. Notably, the literature reviewed above are generally at the level of a single farm, instead of the level of a region or a state. Considering the hierarchies in decision making process, the interactions between the government and the dairy farms may lead to a Stackelberg leader-follower game [24]. Several publications proposed bilevel optimization frameworks for the biofuel industry. Bilevel Stackelberg-game-based modeling frameworks were implemented in a non-cooperative biofuel supply chain design problem [25] and a county-level biofuel supply chain study [26]. Biorefinery investment problem was studied in timberlands industry [27]. A bilevel programming formulation of a leader-follower game to determine tax credits for encouraging biofuel production was presented by Bard, Plummer and Sourie [28]. It is worth noting that the role of government is not considered in most of these models, and energy production in the dairy sector is not involved in all aforementioned bilevel modeling frameworks. Thus, there exists a knowledge gap in addressing the optimal design of biomass-based energy incentive policy for the dairy sector, in which policy optimization for the government and technology selections for dairy farms are involved. To fill this knowledge gap, the objective of this work is to develop a Stackelberg-game-based bilevel bioenergy incentive policy optimization model with the government as the leader and the dairy farms as the followers, through which bioenergy incentive policies from the perspectives of both the government and the dairy farms are optimized simultaneously.
Several research challenges should be addressed in this work. The first challenge is to develop a novel and comprehensive model that reflects the hierarchical policy-/decision-making process of policy determination and the reactions of dairy farms, and it requires the application of bilevel programming and game theory. The second challenge is to simultaneously solve the multi-scale optimization problem in both the region level and the farm level until an equilibrium solution is found. During the solution process, the tradeoffs between different intervention methods from the government’s perspective and the facility capacity and technology selection decisions of each farm are considered, under tradeoffs between government objectives. The third challenge is that the resulting bilevel mixed-integer nonlinear programming problem cannot be solved directly by any off-the-shelf optimization solvers due to the multi-level structure of the nonlinear, nonconvex optimization model and the presence of lower-level integer variables [29]. An efficient tailored solution algorithm is necessary to address this computational challenge.
In this article, we address the optimal design of waste-to-energy incentive policy for the dairy sector, aiming to promote dairy farms to adopt on-farm AD and CHP units to generate biomass-based renewable energy. There are two objectives for the government: minimizing total government intervention and minimizing the government’s cost on unit generated bioelectricity. Additionally, the government has a bioelectricity generation target to deliver. The objectives of the dairy farms are to maximize the net present value (NPV) of each farm independently subject to the proposed bioenergy incentive policy. A modeling framework based on the single-leader-multiple-follower Stackelberg-game structure is developed, in which the government is the leader and dairy farms are independent followers. The model accounts for the government’s intervention methods of the bioenergy incentive policy, including subsidy on bioelectricity generation, refund of capital investment and disposal fee, as well as farm-level decisions regarding AD adoption and biogas-to-energy conversion technology selection. Notably, the optimal decisions of the farms are made independently based on the government’s decisions and the conditions of each farm. The problem is formulated as a bi-criterion mixed-integer bilevel fractional program (MIBLFP), which cannot be solved directly using any off-the-shelf optimization solvers. Thus, a tailored global optimization algorithm is developed to solve the problem by integrating the parametric algorithm [30] and a projection-based reformulation and decomposition algorithm [31]. To illustrate the applicability of the proposed modeling framework and solution algorithm, a case study on hundreds of largest dairy farms in New York State is presented.
The major novelties of this work are summarized as follows:
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A novel bioenergy incentive policy optimization modeling framework based on Stackelberg game and applied to the dairy sector, where a multi-objective MIBLFP problem is developed to address the optimal designs;
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Simultaneous optimization of all intervention methods in incentive policies from the perspective of the government, and AD adoption and biogas-to-energy technology selection decisions from the perspective of each farm, where the intervention methods consist of waste disposal fee, subsidy on bioelectricity generation, and refund of capital investment;
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Application of the proposed modeling framework and the tailored solution algorithm to hundreds of largest dairy farms in New York State under different target levels of bioelectricity generation.
The remainder of this article is organized as follows. Background on Stackelberg games, bioenergy production process and government intervention methods are elaborated in Section 2. Problem statement is presented in Section 3. The multi-objective MIBLFP model for the optimal design of bioenergy incentive policies for the dairy sector, as well as the developed solution algorithm, are proposed in Section 4. In Section 5, a case study on the dairy sector of New York State is presented. Conclusions are drawn in Section 6.
Section snippets
Stackelberg game
Game theory is capable of capturing the hierarchical feature of the decision-making process in an optimization problem [32]. Specifically, the Stackelberg game can capture different roles of players in a noncooperative system [24]. The first Stackelberg game model was introduced in 1934 [24], and since then this type of models has found various applications in which a leader-follower relationship exists [33]. In a standard Stackelberg game, there are two players, a leader and a follower. The
Problem statement
The problem of bioenergy incentive policy optimization for the dairy sector following Stackelberg game is formally defined in this section. It is worth to mention that the problem focuses on the long-term planning and design of the bioenergy incentive policy as well as the long-term planning and operations of corresponding farms, thus the dynamic behaviors of the energy systems are not considered in this study.
We are given a set of dairy farms, which act independently. They interact with the
MIBLFP model and algorithm
Following the problem statement, a multi-objective MIBLFP model is proposed in this section, which addresses the optimal design of waste-to-energy incentive policy for the dairy sector while capturing the hierarchical feature of the policy-/decision-making process. Through optimization of the problem based on the proposed model, optimal solutions are found and validated. The upper-level program refers to the leader, i.e. the government; the lower-level programs refer to the followers, i.e. the
Case study
To illustrate the applicability of the proposed modeling framework and solution algorithm, we present a case study on the optimal designs of waste-to-energy incentive policy on hundreds of largest dairy farms in New York State.
Concentrated Animal Feeding Operations (CAFO) data of New York State is used to develop the case study [52]. The time period in this case study is set as one year. The annual manure production in each dairy farm is considered, based on which each dairy farm makes optimal
Conclusion
An optimization framework based on single-leader-multiple-follower Stackelberg game was proposed to address the optimal design of waste-to-energy incentive policy for the dairy sector that aimed to promote dairy farms to adopt on-farm anaerobic digesters and combined heat and power units for bioenergy generation. A bi-criterion mixed-integer bilevel fractional programming problem was formulated to optimize the bioenergy incentive policy. A tailored global optimization algorithm was developed to
Acknowledgments
This work was supported by Cornell University's David R. Atkinson Center for a Sustainable Future.
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