Paper 1 outlines a generalization to Hill's equations for predicting response to selection. Equations are developed that account for multiple stage selection in either or both sexes and the flow of genes for animals selected at later stages. The asymptotic response to a single cycle of selection is shown to agree with classical selection theory. The equations applied to a dairy progeny testing scheme representative of an artificial insemination organization in the USA. The predicted asymptotic rates to a single cycle of selection were overestimated by 6% and the cumulative response to continuous selection over 20 years was overestimated by 8% when single stage male selection model was compared to two stage selection model;A linear programming model that accounts for the economic consequences of response to selection to the producer enterprise over a given planning horizon is described in Paper 2. A procedure is given in detail for defining upper lower bound constraints on variables that are correlated in the linear programming model. The optimal response to selection per year for the production traits was closest to their maximums achievable from a gene-flow model. Of all the non-production traits, days open had the greatest proportion of its maximum achievable from a gene-flow model. The linear programming model was used to compute relative economic weights (REV). The REVs for milk, fat, and protein production were considerably larger than the REVs for the non-production traits for all planning horizons. Somatic cell score had the largest REVs of the non-production traits in all planning horizons;In the third paper multiple-trait REML was used to estimate the heritabilities and the genetic and phenotypic correlations for 48- and 72-mo herd life from sire models incorporating sire relationships. Two traits were defined for 48- and 72-mo herd life, true herd life (THL) and functional herd life (FHL), which were adjusted for milk production prior to culling. The genetic correlations were used to compute weights for indirect prediction of true and functional herd-life PTA from linear-type traits PTA. (Abstract shortened by UMI.)