The major difficulties of the animal replacement problem are identified as uniformity, herd restraints and the ‘curse of dimensionality’. Approaches for circumventing these difficulties using Markov decision programming methods are systematically discussed, and possible optimisation techniques are described and evaluated. Assuming that the objective of the farmer is maximum net returns from the entire herd, relevant criteria of optimality are discussed. It is concluded that a Bayesian technique is a promising approach as concerns the uniformity problem, that parameter iteration may be used under herd restraints, and that hierarchic Markov processes have contributed to the solution of the dimensionality problem