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Uncertainty in Composition of Ingredients and Optimal Rate of Success for a Maximum Profit Total Mixed Ration¹

Department of Dairy Science, The Ohio State University, Columbus 43210

ABSTRACT

Chance constrained programming methodology, which accounts for uncertainty in composition of feedstuffs, was applied to a total mixed ration set for a 650-kg cow producing 27.2 kg of milk/d. Available ingredients were legumegrass hay, legume-grass silage, corn silage, high moisture ground ear corn, soybean meal, dry fat, and a mineral mix. Four models were derived and their performances were compared when both net energy for lactation and crude protein were considered as random constraints. A model based on a Bonferroni inequality with unequal weight on rows' probability appeared to be best over the range of probability considered (.5 to .95). The value of a feed analysis program was assessed by reducing variances in composition of farm-grown ingredients to those equivalent to a coefficient of variation of 3%. Also, an approximate method was derived for assessing the optimal rate of success. It appears that the optimal rate of success is close to .6 and is not greatly affected by a feed analysis program or a change in price of milk. However, such a program increases income over feed cost by an estimated 27 e/cow per d.

¹ Salaries and research support provided by state and federal funds appropriated to the Ohio Agricultural Research and Development Center, The Ohio State University, Journal Article Number 222-85.

² On leave from Government of Canada, Department of Agriculture, Research Station, Lennoxville, Quebec, Canada, JIM 1Z3.

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