Dynamically Optimal and Approximately Optimal Beef Cattle Diets Formulated by Nonlinear Programming

Abstract

Cattle purchasing, feeding, and selling decisions are described by a free-time optimal control model. The nutrient constraints of the National Research Council and a recently published dry matter intake constraint augment the model and make it nonlinear in the feed ingredients, the daily gain, and the weight of the cattle. Optimal feeding programs are calculated by nonlinear programming under two scenarios: first, when the feedlot has excess capacity and, second, when animals must be sold to make room in the feedlot before more can be purchased. An approximately optimal feeding program is calculated by nonlinear programming and is all but identical to the dynamically optimal programs. Since the mid-1970s, net returns from beef cattle feeding have been volatile. Planning of marketing strategies and feeding programs has become crucial to the economic survival of cattle feeders. Cattle feeders must determine which cattle to purchase, what diet to feed the cattle for producing daily gain, and when to sell the cattle. Kennedy, and Meyer and Newett were the first to solve dynamic optimization models of cattle feeding and marketing decisions. Using a hybrid solution algorithm of dynamic programming and linear programming, they calculated optimal beef diets and rates of gain over a feeding program of fixed length. Apland developed a linear programming model to minimize the cost for beef cattle to reach a fixed selling weight. Chavas, Kliebenstein, and Crenshaw used nonlinear programming to find the diets and rates of gain for swine when neither the length of the feeding program nor the market weight were fixed. They also considGreg Hertzler is an assistant professor of agricultural economics