Animal (Sep 2022)
Application of a mathematical framework for the optimization of precision-fed dairy cattle diets
Abstract
Applied tools that allow more precise feeding of animals provide an opportunity to maximize revenue under milk and feed price oscillations. A compact-vectorized version of the 8th revised edition of Nutrient Requirements of Dairy Cattle model was developed to optimize rations for maximum profit by utilizing non-linear programming with linear and non-linear constraints. This study aimed to (1) evaluate feed cost and milk income minus feed cost (IOFC) if individual diets (IND) could be fed, (2) evaluate feed cost and IOFC when deriving three optimal partial mixed diets for group feeding in three pens (fresh, high, and low production) and two optimal grain mixes to be fed individually via auto-feeders (CLU), and (3) briefly compare optimized solutions across pen-averages. The test followed a general diet formulation structure within a mathematical optimization framework. The objective function was set as milk income minus feed cost. Individual animal and pen feeding information from the Virginia Tech dairy herd, and current milk and feed prices were used to conduct the test. The optimizer solved individual diets for all animals in the herd requiring 3.1 s on a single-core processor with a mean number of iterations for each solution of 12.1; thus, the total number of iterations for the herd was ∼2 900. IND solution diet costs averaged US$6.21/cow/d. Utilizing a fixed milk price of US$0.358 /L, from USDA 2015–2021 average price for all milk classes, IOFC averaged US$6.22/cow/d. Mean predicted milk production was 34.7 kg/cow/d. In contrast, CLU optimized diet costs averaged US$6.38 yielding US$5.90 IOFC/cow/d, with a mean predicted milk production of 34.3 kg/d. The pre-existing farm diets had an average cost of US$7.41 and US$5.42 IOFC/cow/d with a mean predicted production of 35.8 kg/d of milk. For IND solutions, the model predicted lower-cost diets (US$0.17 cow/d), greater milk (0.4 L/cow/d), slightly greater milk income (US$0.16 cow/d) and increased IOFC (US$0.32 cow/d) than CLU solutions. Compared to pre-existing pen diets, predicted feed savings approximately equates to US$240 herd/d if the CLU diets were adopted for the 235 animals. This work established computer code and methods to efficiently derive diet solutions for individual animals in the herd and to use clustering techniques to derive mixes that can be used at the pen level to match animal needs more precisely than those achieved with current practices. In future work, we aim to manufacture and apply optimized solutions on farms, calculate returns, and compare them with optimized predictions.
