Strategic decision-support modeling for robust management of the food–energy–water nexus under uncertainty

Highlights

• A water-energy-food nexus model under uncertainty in water supply is presented.

• •A two-stage stochastic programming approach is used to derive robust solutions.

• •The model is applied to the case study of Shanxi province, China.

• •Dependence of water-saving technologies’ use on the water price is evaluated.

• •Economic benefits from incorporating uncertainty are quantified.

Abstract

Food, energy, and water (FEW) are interconnected pillars that underpin the security of people’s livelihoods. In this paper, we propose a decision-support model to better understand and aid management of regional FEW nexus systems under uncertainty. We apply the model to a case study focusing on fluctuations in water supply, which significantly affect production in the agriculture and energy sectors in Shanxi Province, China. We use a two-stage, stochastic, chance-constrained programming approach to the proposed spatially detailed cost-minimizing FEW nexus model under demand and natural resource (land and water) constraints. This approach translates the target reliability level (i.e., the probability that the devised solution can satisfy all constraints) into a penalty that has to be paid in the case of their non-fulfillment. On this basis, robust decisions (i.e., production options suitable for a broad variation in certainty of water supply) are derived. Using this approach, we estimate the penalties required to achieve given levels of reliability by incentivizing the deployment of water-saving technologies. For example, our model predicts that water storage would become cost-effective if the penalty for exceeding the available water supply were 2.5 times higher than the current price for industrial water; this would enable at least 40% reliability compared to 18% if the penalty were at the current water price level. Taking advantage of the differences in water intensity of crops in different sites, our model optimizes the reservoir location, which allows water withdrawal by agriculture to be reduced by 1.23%. We also evaluate the benefits of incorporating uncertainty and missed opportunity due to a lack of perfect information. In the case study, we show that the benefits of including uncertainty in the form of the two-stage stochastic programming approach appear to be quite significant, reaching 4% of the total solution costs. Water-importing costs, taxes, and subsidies are instruments that translate into the penalty in this model; the modeling approach presented here can thus be used to inform cost-effective and robust management of the FEW nexus in Shanxi Province, China, and other water-scarce regions around the world.

Introduction

Food, energy, and water (FEW) are major pillars that secure people’s livelihoods worldwide. However, increasing demand resulting from population growth, urbanization, and growing living standards are intensifying the scarcity of natural resources, on which food, water, and energy systems are based (Rasul, 2016; Namany et al., 2019a). To emphasize the interconnectedness and interdependency among these three systems and their supply security (Pahl-Wostl, 2017; Cai et al., 2018), “together with the synergies, conflicts and trade-offs that arise from how they are managed, i.e., water for food, energy for water and water for energy, and food for energy and energy for food” (Simpson and Jewitt, 2019, p. 2), researchers and policy makers use the term “FEW nexus.".¹

The concept of the FEW nexus has received considerable attention worldwide since being introduced at the Bonn 2011 Nexus Conference. Through this concept, researchers and policy makers are being encouraged to overcome siloed sectorial perspectives and to focus on the holistic view with regard to FEW systems. Indeed, the holistic approach is required not only for a better understanding of the dynamics of interdependent FEW systems and the constraints they entail, but also to support feasible policy solutions (Bazilian et al., 2011). For a comprehensive review of the evolution of the FEW nexus framework, we refer the reader to Simpson and Jewitt (2019). In line with the definitions in Simpson and Jewitt (2019), we use the term “FEW nexus” in this paper to consider both the supply security of FEW systems and the interconnectedness of FEW components, given that food and energy production each share water resources.

The research around the FEW nexus covers very diverse sets of issues. These include: descriptive studies that focus on revealing, investigating, and analyzing relevant interlinkages within and across water, energy, and food systems (e.g., Kibaroglu and Gürsoy, 2015; Cai et al., 2018; White et al., 2018; Mahjabin et al., 2020); evaluative studies that provide assessments of processes, policies, or institutions according to some desired (or undesired) outcomes or requirements in the context of the FEW nexus (e.g., Karabulut et al., 2019; Lee et al., 2019; Fabiani et al., 2020); and prescriptive studies that provide management options (e.g., Li et al., 2019; Nie et al., 2019, and other modeling-based management studies reviewed in greater detail below). For a review of the different methods used to study the FEW nexus and exemplary case studies, see Endo et al. (2015). This review discusses qualitative methods including questionnaire surveys, ontology engineering, and integrated maps, as well as quantitative methods including physical models, benefit–cost analysis, integrated indices, and optimization management models. Our paper contributes to the literature on prescriptive analysis of the optimal management of regional FEW systems, using mathematical modeling.

The rapid evolution of socioeconomic, technological, and environmental factors continues to make FEW systems ever more complex (Zhang and Vesselinov, 2017). The future of many of the parameters of FEW systems—from precipitation to temperatures to market conditions—is highly uncertain, and this constitutes a challenge in terms of managing these systems. The sustainable development of FEW systems at the regional or national scale requires the use of integrated and robust planning methodologies able to provide cost-effective strategies for a range of plausible futures. This paper suggests a modeling approach to inform the sustainable development of FEW systems that explicitly takes uncertainty into consideration.

A standard approach to modeling optimal management of regional FEW systems involves the development and use of a model that optimizes a certain management goal (e.g., minimization of the total costs) subject to food, energy, and water demand and supply constraints. Multiple objectives and additional constraints can also be included. Clearly, there is no one-size-fits-all model to address nexus-related issues. Rather, the specific management challenges of a particular application dictate the emphasis that the modelers give to the components of the FEW nexus under consideration and how they interact. Here we briefly review different types of optimal management models of regional FEW systems.

Agriculture is a major consumer of water worldwide and a primary economic activity in many regions of the developing world. Several FEW management models with a focus on food security have been developed and applied to case studies. These models typically derive an optimal choice of crops and other agricultural activities, along with suitable and feasible irrigation options and energy sources to underpin agri-food production. Such models can be referred to as “water and energy for food” models. For example, Karnib (2017) suggested a modeling framework that uses linear programming to optimize water and energy allocation for food production based on minimizing the total cost. EL-Gafy et al., 2017a, EL-Gafy et al., 2017b also used linear programming to optimize crop production over 19 Egyptian summer crops, taking into account the reduction of water and energy consumption. Li et al. (2019) used a multi-objective nonlinear programming model to identify a crop production solution for the Heihe River Basin in China that maximizes profits and minimizes CO₂ emissions, taking into account water, land, and electricity availability. Similarly, Namany et al. (2019b) employed multi-objective optimization to optimize agri-food production in Qatar. Zhang et al. (2018) conducted a case study for the southeastern part of Nebraska, United States, where drought is prevalent in agriculture; they found an optimal solution to water and energy supply for irrigation by minimizing the volume of pumped water and maximizing the crop yield and income. Some researchers have also considered livestock as a competitor to crops for land to maximize profit and to minimize water and energy use and also the environmental penalty (Nie et al., 2019). In all these models, energy and water are limited and limiting resources, as their availability directly affects the amount of agriculture that can be done.

Competition for water between agri-food production and the energy sector is a serious FEW management challenge in many industrialized regions. Several recent studies proposed “water for energy and food” models that aim to address this challenge in cases where agri-food production competes with hydropower generation. For example, Allam and Eltahir (2019) optimized the water allocation to agriculture and hydropower generation in the upper Blue Nile Basin by maximizing the total net profit of both sectors. Similarly, using the total economic value as an objective function, Jalilov et al. (2018) used linear and nonlinear programming to identify patterns of water use from expanded reservoir storage for irrigation and hydropower generation in the Amu Darya Basin using dynamic optimization. Si et al. (2019) employed multi-objective nonlinear programming to optimize the operation of reservoirs in the upper Yellow River Basin by minimizing the water shortage in the intake areas and maximizing the profit from the hydropower generation. Zeng et al. (2019), using two-stage stochastic and fuzzy programming, optimized water allocation among households, agriculture, industry, and hydropower in the Jing River Basin. Dhaubanjar et al. (2017) introduced flood risk reduction as a component in a multi-objective optimization setting, while taking into account the needs of various water users.

While hydropower generation is the most obvious competitor for water to agri-food production, other types of energy production also require significant amounts of water and can thus be an integral part of a regional FEW system. In China, water availability is a serious challenge for the coal industry (Pan et al., 2012). In our previous work, we have analyzed the tradeoffs between the agriculture and coal sectors in Shanxi Province, China, under different scenarios for the water availability in a “water for energy and food” model based on linear programming (Gao et al., 2018).

Some FEW nexus studies address the competition between bioenergy and agri-food production. These models combine “water for energy and food” and “food for energy” linkages. For example, López-Díaz et al. (2018) used mixed-integer nonlinear programming to optimize the operation of a biorefining system for feedstocks, grains, and biofuel, by maximizing total profit and minimizing water consumption. Using linear programming, Yuan et al. (2018) optimized the land allocation to rice, sugarcane, and corn under water constraints to minimize the environmental impact of bioenergy.

In addition to “water for energy and food” and “food for energy”, Wicaksono et al. (2019) incorporated “energy for water and food” in a simulation model that optimized the supply of water, energy, and food at the national level in South Korea using multi-objective programming. Zhang and Vesselinov (2017) developed a model that covered “water for energy and food” and “energy for food” linkages and aimed to derive management options to satisfy the FEW demands taking into account environmental impacts; the model was applied to a hypothetical but plausible management problem and was based on the total system cost minimization and linear programming. An interesting interpretation of the FEW nexus on a small scale was developed by Karan et al. (2018). They created a stochastic model for the optimal design of a system that would be able to provide enough food, energy, and water for one family relying only on rainfall, solar radiation, and available land at minimal cost. This model takes into account “water and energy for food” and “energy for water” linkages.

All these studies highlight that a nexus framework is necessary for the sustainable management of FEW systems. The proposed models provide operational decision support and analytical tools to devise integrated solutions. However, the overwhelming majority of published FEW-optimization models are deterministic; indeed, deterministic optimization remains the mainstream approach in FEW modeling. Nevertheless, as shown in our previous work (Gao et al., 2018), solutions in a deterministically optimized FEW model can be highly sensitive to variations in model inputs. As many inputs have inherently uncertain futures, the feasible management of FEW systems requires solutions that are robust with respect to input uncertainty.

Sensitivity and scenario analyses are sometimes used to address uncertainty without departing from a deterministic modeling framework. Among the studies discussed above, Gao et al. (2018) and Nie et al. (2019) analyzed optimal solutions in several scenarios, and López-Díaz et al. (2018) and Namany et al. (2019b) employed Monte Carlo simulation to conduct a comprehensive sensitivity analysis of optimal solutions. While these analyses yield useful insights, sensitivity and scenario analyses cannot be used to formulate robust decisions in a straightforward way.

To derive robust decisions, uncertainty should be incorporated directly into the decision-support model, which can be done in several ways. Ning and You (2019) distinguish three approaches: i) stochastic programming, in which random variables characterized by probability distributions are included (only) in the objective function; in this case, the expected value of the objective function is being optimized; ii) chance-constrained programming, in which random variables characterized by probability distributions are included in the equality and inequality constraints; the constraints use probability thresholds computed based on these probability distributions; and iii) robust optimization, which uses a set membership to characterize uncertainty and optimizes the worst possible case of the problem without involving distributions. Each of these three paradigms generates solutions that are—each in its own way—insensitive, that is to say, robust, with respect to uncertainty according to their definition. Hence, the term “robust solution” is widely used to denote solutions generated both through robust optimization and from stochastic and chance-constrained programming (Kanudia and Loulou, 1998; Ackooij, 2011). Some other methods deal with uncertainty without explicitly including it in the optimization problem. These methods may involve either probabilistic or non-probabilistic treatment of uncertainty, including interval analysis, fuzzy set theory, and possibility theory (Mavromatidis et al., 2018).

Essentially, nearly all parameters in FEW models are uncertain. Some parameters do not allow for probabilistic representation, for example, fertilizer and energy requirements in agriculture. Some other parameters, such as rainfall or temperature, can be represented through probability distributions, using historical data or forecasting models. Only very few models available in the literature search for robust solutions. Among the studies discussed above, Li et al. (2019) considered the utilization of fertilizer, pesticides, energy, and water in agriculture as uncertain and derived solutions corresponding to optimistic as well as pessimistic views of decision makers on these uncertainty in the spirit of robust optimization. Robust optimization is a computationally efficient approach to handling the uncertainties associated with a large set of parameters, while requiring no information regarding the distribution of uncertain parameters. However, such solutions may be too conservative or too optimistic. Using as much information as possible on the probability distribution of the uncertainty can make the solutions more realistic and more efficient. Karan et al. (2018) used a stochastic approach to design a sustainable self-sufficient FEW system for a household, given uncertain rainfall and temperature. Ermolieva et al. (2016) considered the GLOBIOM model, which optimizes the production of food, feed, forestry, and bioenergy in conditions of uncertainty in yields, and derived robust optimal storage facilities.

In this paper, based on our previous work (Gao et al., 2018), we propose a two-stage, stochastic, chance-constrained programming model (Ermoliev and Norkin, 1997) to produce feasible FEW solutions for the coal industry and agriculture that would be robust with respect to uncertainty in the water supply. Water constitutes a limiting factor for energy and agriculture in various water-scarce areas worldwide; moreover, uncertainty in the availability of water resources is increasing due to climate change (Gosling and Arnell, 2016; Knox et al., 2018). Water availability is thus a critical uncertainty variable to be considered in FEW systems. In addition to other results, we highlight the costs and benefits of incorporating uncertainty. This information can be helpful in terms of informing investment decisions for data collection and knowledge acquisition.

A two-stage, stochastic, chance-constrained programming approach has been widely used in other contexts. For example, Paul and Zhang (2019) suggested a model that optimizes the supply of medical supplies under the risk of hurricanes. Under the uncertainty of demands, Weskamp et al. (2019) optimized operations of the apparel industry in a case study in Italy; Nikzad et al. (2019) addressed the medical drug inventory routing problem; Placido Dos Santos and Oliveira (2019) developed a model that optimizes inventory use with partial backorders; Marino et al. (2018) optimized the utilization of renewable energy in microgrids; Peker et al. (2018) focused on power-system expansion planning. To the best of our knowledge, in the literature around the FEW nexus, the two-stage, stochastic, chance-constrained programming approach has been used only in the previous work of some of this paper’s co-authors (Ermolieva et al., 2016). In Ermolieva et al. (2016) robust optimal land use allocation among agriculture, bioenergy, and forestry was derived based on the stochastic version of the GLObal BIOsphere Management model (GLOBIOM); however, water was not considered in this model. Focusing on hydropower generation in the energy pillar, Zeng et al. (2019) used a two-stage, stochastic programming approach. As they did not employ chance constraints, they were unable to assess the reliability levels of different solutions. In this paper, we derive robust FEW solutions for a case study in Shanxi Province, China. Using a two-stage, stochastic, chance-constrained programming approach, we translate the target reliability level (i.e., the probability that the devised solution can satisfy all constraints) into a penalty that has to be paid if their non-fulfillment occurs. We quantify the dependence between reliability and penalties, demonstrate how the use of different penalty levels affects the total cost and the choice of water-saving technologies to be deployed, discuss the potential of the introduction of storage to reduce the pressure on water resources, and evaluate the benefits of incorporating uncertainty and missed opportunity due to a lack of perfect information.