Comparison of Linear and Nonlinear Programming Techniques for Animal Diet

Linear programming techniques have been extensively used for animal diet formulation for more than last fifty years. To overcome the drawback of linear approximation of objective function for diet formulation, a mathematical model based on nonlinear programming technique is proposed to measure animal performance in terms of milk yield and weight gain. At the second step, it compares the result of proposed program with that of linear programming model. Result of proposed model gives better results using nonlinear programming. Thus the study is an attempt to develop a nonlinear programming model for optimal planning and best use of nutrient ingredients. Research on nutrition is under process for more than hundred years. Diet formulation is a process by which different ingredients are combined to provide necessary nutrition to animals at different stages of production. A diet should supply all essential nutrients and energy to maintain vital physiological functions of growth, reproduction and health of animals. Diet should be highly digestible and should have very less adverse environmental effect. A number of methods have been defined for the formulation of animal diet; square method, two by two matrix methods, simultaneous equation method, trial and error method and linear programming method to formulate least cost diet. Linear programming is widely used for this purpose. Diet formulated by linear programming is based on assumption of linearity between animal yield and nutrient ingredients included in the diet. To overcome the assumption of linearity and to include complexity of different nutrient ingredients, a nonlinear model is proposed in this paper to maximize milk yield. This concept of non-linear programming may be used to maximize the weight gain of the animal or animal yields approximately. A combination spreadsheet is represented for ration formulation using linear programming (VandeHaar M. J., Black J. R., 1991). Chance-constrained programming is used to formulate commercial feeds for animals (William B. Roush, Robert H. Stock, Terri L. Cravener and Thomas H. D'Alfonso, 1994). Genetic algorithms are applied for the cost