(373h) Optimization of Water-Energy-Food Nexus Under Uncertainty: A Case Study of Mexico
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 . 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 , 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  and the graph-based modeling abstraction Plasmo  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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