Whole-herd optimization with the Cornell Net Carbohydrate and protein system. I. Predicting feed biological values for diet optimization with linear programming

Abstract We developed a diet optimizer for least-cost diet formulation with the Cornell Net Carbohydrate and Protein System (CNCPS) using linear programming. The CNCPS model is intrinsically nonlinear, and feed biological values vary with animal and feed characteristics. To allow linear diet optimization, we first used the CNCPS model to generate biological values to characterize the energy and protein content of each feed for the specific group for which the diet was being formulated. The biological values used were metabolizable energy (Mcal/kg), metabolizable protein [(% dry matter (DM)], passage rate (%/h), bacteria yield efficiencies (g/g), and degradation rate of the carbohydrate B2 fraction (%/h). In addition, the ruminal balances for nitrogen and peptides were included in the optimizer to optimize ruminal degradation of fiber. The objective function was to minimize diet cost subject to animal requirement and feed availability constraints. The animal constraints were set by requirements for DM intake (kg/d), metabolizable energy (Mcal/kg), metabolizable protein (%DM), and effective neutral detergent fiber (%DM) for a given level of production. Data from a dairy farm were used to evaluate this linear diet optimizer. Across all classes of dairy cattle, the CNCPS 4.0 model typically obtained a solution in less than six iterations that met the requirements with nearly 100% accuracy. We conclude this linear optimizer can be used to accurately formulate least-cost diets with the CNCPS model.