A Risk-Based Interval Two-Stage Programming Model for Agricultural System Management under Uncertainty

Nonpoint source (NPS) pollution caused by agricultural activities is main reason that water quality in watershed becomes worse, even leading to deterioration. Moreover, pollution control is accompanied with revenue’s fall for agricultural system. How to design and generate a cost-effective and environmentally friendly agricultural production pattern is a critical issue for local managers. In this study, a risk-based interval two-stage programming model (RBITSP) was developed. Compared to general ITSP model, significant contribution made by RBITSP model was that it emphasized importance of financial risk under various probabilistic levels, rather than only being concentrated on expected economic benefit, where risk is expressed as the probability of not meeting target profit under each individual scenario realization. This way effectively avoided solutions’ inaccuracy caused by traditional expected objective function and generated a variety of solutions through adjusting weight coefficients, which reflected trade-off between system economy and reliability. A case study of agricultural production management with the Tai Lake watershed was used to demonstrate superiority of proposed model. Obtained results could be a base for designing land-structure adjustment patterns and farmland retirement schemes and realizing balance of system benefit, system-failure risk, and water-body protection.