Farm management optimization under uncertainty with impacts on water quality and economic risk
构建两阶段随机混合整数规划模型，优化玉米农场在不确定条件下的管理决策，发现农民可能通过增加氮肥施用量来补偿养分减排风险，且作物保险政策会影响水质。
Farm management decisions under uncertainty are important, not only for farmers trying to maximize their net income, but also for policy makers responsible for incentives and regulations to achieve environmental goals. We focus on corn production as a significant contributor to the economy of the US Midwest. Nitrogen is one of the key nutrients needed to increase production efficiency, but its leaching and loss as nitrate through subsurface flow and agricultural drainage systems poses a threat to water quality. We build a novel two-stage stochastic mixed-integer program to find the annual farm management decisions that maximize the expected farm profit. A decomposition-based solution strategy is suggested to reduce the computational complexity resulting from the predominance of binary variables and complicated constraints. Case study results indicate that farmers may compensate for the additional risks associated with nutrient reduction strategies by increasing the planned nitrogen application rate. Significant financial incentives would be required for farmers to achieve substantial reductions in nitrate loss by fertilizer management alone. The complicated interactions between fertilizer management and crop insurance decisions observed in the numerical study suggest that crop insurance programs can affect water quality by influencing the adoption of environmentally beneficial practices.