(373h) Optimization of Water-Energy-Food Nexus Under Uncertainty: A Case Study of Mexico

The agenda for sustainable development seeks to archive an ambitious set of objectives before 2030 [1]. Most of these objectives are related to inclusive and sustainable economic grown, ensure access to water and energy, food security, and take urgent actions to combat climate change. Therefore, it is necessary to invest in infrastructure and to start up new productive processes that generate economic growth while do not compromise the resources of the future, which represents a major challenge. All productive activities require access to products and services that are always related to water, energy and food. If we analyze the way we obtain the water we drink, the energy we use and the food we consume, it is easy to note that they depend on each other. This interrelation is known as Water-Energy-Food Nexus [2]. The Water-Energy-Food Nexus has become a fundamental issue to achieve the objectives mentioned in the agenda for sustainable development, and it can be an extremely useful tool in the assurance of the basic needs of human beings if it is correctly applied [3]. However, large and complex systems are affected by many variables and their behavior is difficult to predict. This requires strategies able to consider the interdependence between the parts of a productive process and at the same time these strategies must simultaneously maximizes and/or minimizes multiple objectives such as profits, social development, satisfied demand, environmental impact, costs and energy consumption. Despite these difficulties, mathematical modelling and optimization techniques enable considering the link between the different producers and consumers of goods and services [4], [5]. Furthermore, it is possible to consider the uncertainty associated to the system parameters [6], [7]. In addition, optimization techniques let to establish priorities depending on the objectives that want to favor or even give the same weight to all the objectives that want to meet [8], [9]. The optimization approaches that have been developed in recent years are tools with extraordinary potential to propose strategies for combating poverty, ensuring food security, improving the human development index, guaranteeing access to water, energy and promoting sustainable economic growth. Nevertheless, there is still a long way to go in terms of research [2].

This project study the feasibility of investing and developing productive processes in order to meet the demands of water, energy and food of the population and the productive sectors in regions affected by the overexploitation of resources, drought, and / or natural catastrophes. In particular, we develop and implement a mathematical model to propose solutions to the problems that affect the state of Sonora in Mexico.

The state of Sonora is located on the northeast coast of Mexico and is characterized by dry climate, so the climate in the state is a disadvantage for agriculture; however, this state has the first places at the national level of production in the primary sector [10]. The problem that currently affects Sonora is a dispute over available water sources between the agricultural and the domestic sectors of the different hydrological regions. In recent years this region has had a long period of drought and the population has been concentrated in areas where nearby water resources have decreased. For example, the state capital (Hermosillo) concentrates almost a third of the population in the state (884,273 inhabitants). The main water source of this city used to be the Abelardo L. Rodríguez dam; however, currently this resource is practically exhausted. A potential source of water supply that can meet the needs of Hermosillo is the Plutarco Elías Calles dam, located 152 km from the city of Hermosillo, but this dam is in another hydrological region, which means that the water "belongs" to the inhabitants of Obregón. Because of mentioned problems and the scarcity of water in the region, the exploitation of aquifers has increased. Of the 62 aquifers in Sonora, 18 are being overexploited and 5 are being affected by the insertion of seawater. The optimization model seeks to find the optimal distribution network of water and energy that covers the needs of the agricultural, domestic and industrial sectors using all available resources such as wells, dams, bodies of water, storage tanks, and power plants. In addition, it considers the possibility of installing new infrastructure such as storage tanks, pipelines, pumping stations, transmission lines, and power-desalination plants in order to reduce water stress in the region. The mathematical model is based on a previously published model [11], but it is modified to consider uncertainty in different parameters, such as the demands and precipitation, using two-stage stochastic programming. Which provides solutions with greater reliability in face of unfavorable scenarios.

The optimization formulation is implemented using the modeling language for mathematical optimization JuMP [12] and the graph-based modeling abstraction Plasmo [13] and solved with Gurobi in order to answer the following questions:

What is the total annual cost? What should the capacity of the new equipment be? Where should the new infrastructure be installed? What is the optimal water, energy and food distribution network that meets the needs of the agricultural, domestic and industrial sectors and reduces water stress? What should be the cost of services to be sustainable?

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[11] R. González-Bravo, F. Nápoles-Rivera, J. M. Ponce-Ortega, and M. M. El-Halwagi, “Involving integrated seawater desalination-power plants in the optimal design of water distribution networks,” Resources, Conservation and Recycling., vol. 104, pp. 181-193, 2015.

[12] I. Dunning, J. Huchette, and M. Lubin, “JuMP: A Modeling Language for Mathematical Optimization,” SIAM Rev., vol. 59, no. 2, pp. 295–320, 2017.

[13] J. Jalving, Y. Cao, and V. M. Zavala, “Graph-Based Modeling and Simulation of Complex Systems,” Comput. Chem. Eng., vol. 125, pp. 134-154, 2019.