HERD SIRE PORTFOLIO SELECTION - A COMPARISON OF ROUNDED LINEAR AND INTEGER PROGRAMMING

Use of linear programming to select portfolios of herd sires can resul t in solutions containing noninteger units per bull. Because semen can not be purchased in partial units, two alternatives were investigated: integer programming and rounded linear programming. Expected net reve nue based on PTA dollars for milk, fat, and protein; udder depth; teat placement; foot angle; and semen price were calculated for 383 Holste in bulls. Maximization of expected net revenue was subject to constrai nts: required lots of 5 units, maximum average price per lot, minimum and maximum lots per bull, minimum average reliability, minimum number of lots from bulls that transmit calving ease, and minimum number of bulls. Multiple formulations were used for expected net revenue and co nstraint combinations. Eighteen of 36 linear programming portfolios co ntained noninteger lots per bull. Five rounded linear programming port folios were identical to their respective integer programming portfoli os. Differences in lots per bull between the remaining 13 pairs of por tfolios were small. Linear programming portfolios that were unconstrai ned by semen price tended to be integer. Six of 18 rounded linear prog ramming portfolios did not stay within bounds set by constraints. For the model used, integer programming did not offer a significant advant age over rounded linear programming.