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Simultaneous minimization of diet costs and phosphorus excretion on dairy farms.

A. F. White



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Simultaneous minimization of diet costs and phosphorus excretion on dairy farms.
A. F. White*, L. E. Moraes. The Ohio State University Columbus, OH.

The study objective was to develop a mathematical programming model capable of simultaneously optimizing diets with different weights for least cost (LC) and least on farm P-balance (LP). The ration ingredients, herd composition, and animal categories were designed to represent the Jersey herd of the Ohio State University Waterman Dairy Center. The model constraints were set to meet the current recommendations of the NRC (2001), and additional constraints based on industry recommended practices were specified to limit the inclusion of specific feeds in the diet. Using OpenSolver (v.2.9.0,, 3 objective functions were individually optimized to (1) minimize the diet cost; (2) minimize the excess of P balance in the system, computed as the difference between P excreted and P uptake by forage production on-farm; and (3) minimize the weighted deviations from the values of the 2 previously optimized objective functions. A grid of 100 potential weights were used that varied the size of the effect of each deviation from the given optimization model on the current optimized objective. The LC and LP scenarios had whole farm feed costs of $2,285 and $2,719 (19% increase with respect to the LC diet), respectively; the farm P balance was 10.1 kg/d and 3.3 kg/d (67% decrease). Thus, at the extreme points of the weight grid, a substantial decrease in P balance was obtained; however, at a substantial increase in diet costs. The trade-offs between the 2 goals set by the weighting scheme, however, allowed the identification of a set of diets that all met the NRC (2001) requirements while having different costs and determining different P balances on the farm. For example, the weighted goal programming model identified a diet that allowed a 37% reduction of P balance occurring with a 0.4% increase in cost (with respect to LC). These initial reductions in P were generally accompanied by increased forage fed, increase of on-farm corn silage production, and increased purchase of hay. These optimizations suggest a potential use of weighted goal programming as a technique to identify diets that allow a reduction in on-farm P balance with limited effect on whole-farm feed cost.


Biography: April Frye White grew up in Mount Gilead, Ohio. She attended undergrad in animal science at The Ohio State University and is currently completing her master's degree at OSU in dairy nutrition with a project in mathematical programming models. She writes a bimonthly extension article for OSU Buckeye Dairy News summarizing nutrient costs and the relative value of feed stuffs. She plans to continue her education in ruminant nutrition and microbiology through a PhD in OSU's nutrition program.