Linear Programming in Selection of Livestock

Linear programming is described as a tool for selecting breeding stock in a production unit facing constraints of resources, marketing, or preference. The predicted performance of an animal for major input and output traits is incorporated into the objective function reflecting, for example, farm profits, and into a matrix of coefficients specifying the constraints. An example demonstrates the method and contrasts the selection decision indicated by a simple profit equation ignoring constraints to that of the linear programming solution. Direct consideration of constraints and alternative production possibilities is the chief advantage of linear programming over a profit equation. I N T R O D U C T I O N The major difficulty with selection index is the difficulty of determining an appropriate function of traits and corresponding economic weights to reflect a producer's selection goals. One approach to this problem is to derive a profit equation for animals as a function of input and output traits and to substitute estimated breeding values of those traits to obtain indexes (4). Unfortunately, tailoring a profit equation to reflect characteristics of a production unit may be necessary and is also a difficult task. The producer must choose from many possible combinations of production processes that combination that uses his limited resources in the most profitable way. Linear programming (LP) is a mathematical technique derived for just such problems. The purpose of this paper is to describe LP as a tool for selecting breeding stock in a production unit facing Received July 13, 1983. resource constraints and to compare it to an index for selection based on a profit equation. LINEAR P R O G R A M M I N G A detailed discussion of LP will not be given here as there are abundant texts on the subject and as LP is not new to animal breeders (3, 5, 6, 9, 10, 11). Selection decisions are to maximize an objective function,