A linear programming formulation of the Markovian decision process approach to modelling the dairy replacement problem

In modelling the replacement decision in dairy herd management, the most common approach taken is to use dynamic programming to determine the optimal policy by comparing the future expected profitability of an animal to that of it's potential replacement. It does not, however, take into account the performance of the entire herd or that of all potential replacements, which is particularly important if replacements originate from the same herd. This paper demonstrates how to overcome this inadequacy by formulating the problem as a multi-component Markovian decision process and then solving it as an associated linear programming model. The proposed methodology is illustrated by using a simple, but realistic, example for determining the optimal replacement strategy for a dairy herd over a 10-year planning horizon. The results show that replacements should be bred from heifer cows in order to increase the genetic turnover; however, no more animals than is necessary should be culled to increase this turnover. It is also shown how to include considerations such as problems of milk quota management, and other similar resource allocation decisions into the model. Additional improvements to the model could involve considering culling of animals suffering from disease.