Application of Positive Mathematical Programming (PMP) in Sustainable Water Resource Management: A Case Study of Hetao Irrigation District, China

Water scarcity and soil salinization pose significant challenges to sustainable agricultural development in arid and semi-arid regions globally. This study applies Positive Mathematical Programming (PMP) to analyze agricultural water resource management in the Hetao Irrigation District (HID), China. The research constructs a comprehensive multi-stress-factor integrated PMP model to evaluate the compound impacts of water resource constraints, pricing policies, and environmental stress on agricultural production systems. The model incorporates crop-specific salinity tolerance thresholds and simulates farmer decision-making behaviors under various scenarios including water supply reduction (0–100%), water pricing increases (0.2–1.0 CNY/m3), and soil salinity stress (0–10 dS/m). The results reveal that the agricultural system exhibits significant vulnerability characteristics with critical thresholds concentrated in the 60–70% water resource utilization interval. Water pricing policies show limited effectiveness in low-price ranges, with wheat demonstrating the highest price sensitivity (−23.8% elasticity). Crop salinity tolerance analysis indicates that wheat–sunflower rotation systems maintain an 85% planting proportion even under extreme salinity conditions (10 dS/m), significantly outperforming individual crops. The study proposes a hierarchical water resource quota allocation system based on vulnerability thresholds and recommends promoting salt-tolerant rotation systems to enhance agricultural resilience. These findings provide scientific evidence for sustainable water resource management and agricultural adaptation strategies in water-stressed regions, contributing to both theoretical advancement of the PMP methodology and practical policy formulation for irrigation districts facing similar challenges.