An inexact multi-objective mixed-integer nonlinear programming approach for water-soil-fertilizer management under uncertainty considering “footprint family-planetary boundary” assessment

Water, energy, and food (WEF) are interlinked and create a dynamic system that impacts both human well-being and ecology. Given the importance of ecology within the WEF system, water resources serve as the core issue. The allocation of water resources in irrigation districts is a challenging problem for the coordinated development of agricultural production, water resources, and the ecological environment. The integration of stochastic multi-objective programming, fuzzy credibility-constrained programming, and mixed integer programming offers a solution to this issue, with the construction of a fuzzy credibility-constrained stochastic multi-objective mixed-integer nonlinear programming model. The applicability and validity of this model were verified by applying it to the Kaikong Irrigation District (KID) of the Tarim River Basin in northwest China, with notable findings indicating that the optimized system reduces agricultural costs by 5.82%, increases irrigation water use efficiency by 1.80%, and reduces global warming potential by 6.45%. This study investigates the effects of diverse allocation strategies of water and land resources on the social, economic, and ecological subsystems and their interactions by downscaling four subprocesses PBs to the KID scale. The optimization model reveals that only the nitrogen footprint of Kuerle City surpasses the nitrogen boundary of the KID. The proposed solutions based on the model can encourage the green and ecologically-friendly development of agricultural production and can be applied to agricultural systems in arid regions with similar conditions.