A goal programming approach for balancing diet costs and feed water use under different environmental conditions

Water is essential in livestock production systems. In typical dairy production systems, 90% of the total water used by a dairy farm is attributed to feed production. Theoretically, ration manipulation is a method to potentially reduce the irrigation water needed for feed crops without dramatically increasing diet costs. However, published quantitative studies on the relationship between feed production and water use that are integrated with linear programming models are scarce. The overall objective of this study was to develop an optimization framework that could achieve a balance between minimization of dietary costs and dietary irrigation water usage, and that could be used as a framework for future research and models for various livestock production systems. Weighted goal programming models were developed to minimize the dietary costs and irrigation water usage for a hypothetical cow under 8 different environmental scenarios. The environmental conditions used a 2 × 2 × 2 factorial design, including 2 atmospheric CO₂ concentrations (400 and 550 ppm), 2 water years (dry and wet), and 2 irrigation methods (furrow and drip). A systematic weighting scheme was used to model the trade-off between minimizing diet cost and minimizing irrigation water use for feedstuffs. Each environmental condition generated a set of distinct diets, which each met the same nutrient requirements of the hypothetical cow but had a different water usage when the weighting scheme was changed from weighting minimum diet costs to minimum irrigation water usage. For water resource planning in areas of dairy production, this set of unique solutions provides the decision maker with different feeding options according to diet cost, water usage, and available feeds. As water was more constrained, dietary dry matter intake increased, concentrations of neutral detergent fiber, ether extract, and energy decreased, and the concentration of lignin increased because less nutritive but more water-saving feedstuffs were included in the diet. Mitigation costs of water usage were calculated from goal programming results and indicated that the potential value of water under water-limited conditions (e.g., in a drought region) was higher than that under water-sufficient conditions. However, a smaller increase in feed costs can initially significantly reduce water usage compared with that of a least-cost diet, which implies that the reduction of water usage through ration manipulation might be possible. This model serves as a framework for the study of irrigation water usage in dairy production and other livestock production systems and for decision-making processes involved in water resources planning in the broader area of animal production.