A Dynamic Programming Approach to Culling Decisions in Commercial Dairy Herds

A dynamic programming model was developed in which cows were described in terms of lactation number, body weight, 305-day milk yield, and milk fat percent. Milk returns, beef sales, feed costs, replacement costs, and cow depreciation costs were included. A 10-yr planning horizon was used. Three prices were assigned to each economic component and to the interest rate in the discounting procedure. Ninety-five percent of the optimal policies were unaffected by changes in prices or interest rate. All cows producing less than 4500 kg of 4.1% milk were replaced. Those producing more than 6500 kg of 3.9% were kept. Optimal policies for other milk yields were dependent on lactation number, body weight, and prices. Increasing milk price or decreasing feed price resulted in more intensive culling of lighter cows and less intensive culling of heavier cows. Increasing interest rate resulted in less intensive culling for all categories of body weight. The model was insensitive to changes in price of beef. Optimal policies for 94% of the states did not change with different feeding. With a 5-yr planning horizon, culling was more intensive.