Application of Fuzzy Optimization in Diet Formulation

Feeding cost comprised about 65 to 75 percentage of dairy cattle production systems. Reduction feed cost and consideration seasonal or regional limitation of feed sources especially some forages increased necessity of the optimization of feed formulation in dairy caws. However, without a positive answer and accrue methods based on linear models those used on ration formulation, application of new mathematical models as fuzzy models seems to be very useful to taken account and meeting nutrient requirements and formulation based on ration least cost and composition in different levels. Fuzzy models promise to be a valuable tool as they link measurable information to linguistic interpretation using membership functions. The objective of this paper was using linear fuzzy model in formulation of dairy cow ration in early lactation and compare to linear programming models. Using linear programming models, the final cost of one kilogram of total mixed ration was 1333.5 Rails, and at this level cow nutrients requirements were met. Using fuzzy model and applying all restriction, the least cost for one kilogram of total mixed ration was 1222.5 Rails, and at this level cow nutrients requirements were met. Using fuzzy model in compare to linear programming models, feed cost was reduced about 8 percentages. The result of this experiment guarantees the formulation of ration using fuzzy models can be used to reduce feed cost and obtain different ration that they may met dairy cow nutrients requirements over different situations. In addition, because of the results in an illustrative example, it is concluded that the procedure outlined in this paper suitably deals with ration formulation and, therefore, enables a practical implementation of fuzzy evaluation of agricultural production systems.