Optimization of sire selection based on maximization of guaranteed income and risk associated with sire merit

A method based on discounted income and risk assessment was developed to aid in the selection of dairy sires. The discounted profit generated from milk production of daughters was proposed as the suitable composite selection criterion to combine estimates of predicted transmitting ability (PTA) for yields of milk, fat, and protein and estimates of sire evaluations for dystocia or expected progeny difference. Steps are described to derive discounted profit (defined as expected income) for a sire with known PTA and evaluation for dystocia. The derivation of profit considered costs for semen, dystocia, heifer raising, production and maintenance of the daughter, and income from milk. Variance of income from a sire depended on the reliability of his PTA and evaluation for dystocia. Total variance from a selected set of sires was defined as the risk. A quadratic programming procedure was developed to identify the best set of sires from a given pool of sires that met a desired expected income goal with minimum risk. Combinations of sires with minimum risk for all possible levels of expected income were defined by the expected income variance frontier. The set of sires at the maximum lower boundary for 95% confidence of the expected income variance frontier was defined as the optimum set of sires to be selected; the optimum set maximized the 95% guaranteed expected income. The quadratic programming procedure provided the optimum percentage of cows to be mated to each sire in the selected set.