A Multi-Objective Fuzzy Optimization Model for Crop Planting Patterns and Agricultural Water Management Based on Water Footprint Theory: A Case Study of the Hanjiang River Basin, China

This study develops a multi-objective fuzzy programming model (MOFPM) that integrates water-footprint accounting with fuzzy chance-constrained programming for multi-objective optimization. It sets differentiated constraints for green-blue-grey water-footprint components and adds fuzzy chance-constraints for crop-trade net benefit and virtual-water outflow loss, which simultaneously addresses uncertainties from both credibility parameters and decision-makers’ conflicting objective preferences. The model aims to maximize economic benefits and agricultural water productivity and minimize agricultural grey-water footprint under food-security restrictions. This optimization framework was applied to the Hanjiang River Basin, China. Under credibility levels γ ranging from 0.55 to 0.95, modelling outputs identify rice as the priority crop for expansion, while wheat and maize acreage should be largely reduced across most sub-basins. Relative to the baseline, crop economic benefits increase by 29–39%, water productivity improves by 10–11% (rising from 1.30kg/m3 to 1.43–1.45kg/m3), basin-scale blue water footprint declines by 10.4%, and grey water footprint falls by 11–15%. Spatially, green and blue water footprints rise in central-southern zones whereas grey water footprint decreases in the northwest; water-footprint losses induced by inter-regional crop trade are substantially reduced. Four decision-weight scenarios further verify that optimized schemes can achieve the system-wide economic, water-productivity and pollution-control targets. This study helps to adjust crop planting patterns and advance sustainable agricultural water management.