A factorial interval chance-constrained diet model for dairy farms under climate change: A case study for the Province of Saskatchewan, Canada

A large amount of greenhouse gases is emitted from the dairy industry in Canada. Actions must be taken to achieve Canada's environmental goals of decreasing greenhouse gas (GHG) emissions by 30% below 2005 levels by 2030. Dietary management plays an important role in reducing such emission in dairy cattle production for current and future climate change conditions. In this study, a factorial interval chance-constrained diet model has been developed for Saskatchewan's dairy cow farms to control emissions by incorporating factorial analysis, interval linear programming, and chance-constrained programming. Multiple uncertainties (e.g., the price of the milk, the price of the feed, and the disease of animals) have been considered in this model. The chance-constrained programming method, which is effective to tackle uncertainties, has been first integrated in the animal nutrition optimization model. This model can provide the schemes of feed selection for diet formulation under trade-offs between farm profit and environmental impact. In addition, it could facilitate decision-makers to identify interactive relationships among various nutrient levels and manage methane emissions and nitrogen excretion from dairy cattle in dairy farms under various risks. Results show that canola meal, rolled barley grain, soybean meal, and whey would be contained in all optimized diets; the forage proportion would have the most significant effect on methane emissions; factors of forage and crude protein would have negative effects on methane emissions, while the neutral detergent fiber (NDF) would have a positive effect on methane emissions. Results indicate that reducing the number of cows is still an important strategy to mitigate carbon emissions under the condition of meeting the growing milk demand. Overall, this model could manipulate the formula of different types of dairy cattle to maximise the benefits of farm and alleviate its negative environmental impact.