Water-Energy-Food integrated management model under Uncertainty-A case study of Yulin City

Water, energy, and food are indispensable human survival and development resources. With the rapid development of the social economy, the systematic risk of water, energy, and food is becoming increasingly prominent. Water, energy, and food security are threatened to varying degrees. At the same time, water, energy, and food are interrelated, restricted, and interdependent. It is of great scientific significance to reveal and optimize the WEF (Water-Energy-Food) nexus. This study relied on Chance constrained programming and Fuzzy credibility constrained programming to deal with randomness and fuzziness in the WEF nexus. Meanwhile, based on Bi-level programming, aiming at minimizing water allocation and maximizing system benefits, a Water-EnergyFood Integrated Management Model to deal with multiple Uncertainties, called IMMU-WEF model was constructed. The model solved the critical effects of the randomness of water supply and the subjective fuzziness of water demand on water resources allocation, power generation, primary energy extraction, and food planting area. The results showed that the IMMU-WEF model could efficiently deal with the game between different departments in the resource management system, the random uncertainty expressed by probability density, and the fuzzy uncertainty caused by subjective factors. It can develop a stable management scheme for resource management. Applying the mode to Yulin City, China, it is found that water supply and demand fluctuation dramatically impacts on the WEF system benefit, water resources allocation, energy and food production. Specifically, the system benefit will increase over time, with a total benefit of 1974.04 x 108-1998.06 x 108 yuan (2021-2025), 3065.69 x 108-3100.50 x 108 yuan (2026-2030), and 4128.80 x 108-4191.07 x 108 yuan (2031-2035). Additionally, the system water allocation, primary energy extraction, power generation, and food planting are expected to increase over three time periods. With the increase of water supply in the future, the energy and food production in Yulin City show an increasing trend. It indicates that water shortage will continue to be a major problem in Yulin in the three periods, and that the city still needs to increase water supply and diversion projects to ensure energy security and food security. The results can provide an optimal management scheme for ensuring Yulin City's water, energy, and food security.