The selection index is a linear weighted combination of observed measurements constructed so as to maximize genetic gain. The study is focused on the construction of optimum selection methods using analysis of variance, maximum likelihood and restricted maximum likelihood methods in a balanced univariate half-sib sire model. Data sets are simulated employing the Monte Carlo simulation method. Information on candidates themselves and their relatives are incorporated into a selection index. The conventional theory of selection index using analysis of variance method is compared with the likelihood based ones. Both ANOVA and likelihood based methods give similar results of selection responses due to setting the heritability estimates from ANOVA to zero if it is negative. It is found that the predicted response is more sensitive to the heritability and phenotypic variance estimates than the achieved response