Application of the modified feed formulation to optimize economic and environmental criteria in beef cattle fattening systems with food by-products

A simplified ration optimization method was applied to a beef cattle fattening system to evaluate the utilization of food by-products under various situations. The method was extended to reduce feed costs (i.e., economic factors) and nitrogen and phosphorus excretions (i.e., environmental factors) by introducing penalty coefficients of nitrogen and phosphorus contents in each ingredient of the diet in the objective function in traditional linear programming. Six regional food by-products, five commercial concentrates and two roughages were used as ingredients of the fermented total mixed ration. Constraints for the feed formulation were based mainly on nutrient requirements in the Japanese Feeding Standard for Beef Cattle. The replacement price (or acquisition cost) of food by-products was defined as the maximum price of food by-products when the feed cost with the use of food by-products was below the cost with the use of conventional concentrates. The results showed that although the replacement prices were not greatly affected by the penalty levels, they were associated with the changes in the substitution rate of food by-products for concentrates and the price of concentrates. The replacement prices were about 16 (yen/kg, as-fed basis) against the present price level of concentrates, when food by-products were substituted for a half of concentrates. Feed compositions were altered and nitrogen and phosphorus excretions were decreased by the changes of penalties, in spite of the small change in the replacement price of food by-products. Both nitrogen and phosphorus penalties greatly reduced the nitrogen and phosphorus excretions, indicating that nitrogen and phosphorus penalty coefficients should be introduced together in the objective function in order to reduce both excretions efficiently.