Short communication: Prediction of retention pay-off using a machine learning algorithm

Replacement decisions have a major effect on dairy farm profitability. Dynamic programming (DP) has been widely studied to find the optimal replacement policies in dairy cattle. However, DP models are computationally intensive and might not be practical for daily decision making. Hence, the ability of applying machine learning on a prerun DP model to provide fast and accurate predictions of nonlinear and intercorrelated variables makes it an ideal methodology. Milk class (1 to 5), lactation number (1 to 9), month in milk (1 to 20), and month of pregnancy (0 to 9) were used to describe all cows in a herd in a DP model. Twenty-seven scenarios based on all combinations of 3 levels (base, 20% above, and 20% below) of milk production, milk price, and replacement cost were solved with the DP model, resulting in a data set of 122,716 records, each with a calculated retention pay-off (RPO). Then, a machine learning model tree algorithm was used to mimic the evaluated RPO with DP. The correlation coefficient factor was used to observe the concordance of RPO evaluated by DP and RPO predicted by the model tree. The obtained correlation coefficient was 0.991, with a corresponding value of 0.11 for relative absolute error. At least 100 instances were required per model constraint, resulting in 204 total equations (models). When these models were used for binary classification of positive and negative RPO, error rates were 1% false negatives and 9% false positives. Applying this trained model from simulated data for prediction of RPO for 102 actual replacement records from the University of Wisconsin-Madison dairy herd resulted in a 0.994 correlation with 0.10 relative absolute error rate. Overall results showed that model tree has a potential to be used in conjunction with DP to assist farmers in their replacement decisions.