Forecasting herd structure and milk production for production risk management

Substantial increases in milk price volatility have resulted from changes in federal dairy policies. For a dairy farm, however, monthly gross milk receipts are a function of unit price and quantity produced. Both can vary substantially over time. Therefore, to be effective, risk management strategies must address milk and input price volatility (price risk management) and fluctuations in milk production per cow and cow numbers (production risk management). Herd milk production through time can be modeled as a discrete stochastic process using finite Markov chains. Cows at time t = 0 are assigned to homogeneous production cells in four-dimensional arrays with coordinates determined by parity (1, 2, 3), week in milk (1, ..., 104), pregnancy status (0, 1), and week pregnant (1, ..., 40). The processes of aging, pregnancy, involuntary cull, voluntary cull, abortion, dry-off, and freshening from week i-1 to week i are accounted for, using nonstationary transition probabilities. Bayesian estimates of transition probabilities are derived from historical herd data, assuming that individual outcomes are from Bernoulli distributions. The values of parameters theta(i) for the Bernoulli distributions are unknown but have prior distributions that follow beta distributions with parameters alpha(i) and beta(i) estimated from historical data. Herd observations are then used to generate posterior distributions of theta(i), also from beta distributions. Projecting from one week to the next is accomplished by moving virtual animals from one production cell to the next based on the transition probability assigned to that path. Summing production estimates and variances of all independent cells provides for an expected herd production with an associated variance. As expected, the forecast variance increases with time, reflecting increased uncertainty of distant projections. Model validation presents an interesting problem because future observations used for validation are under human control and are not independent of the forecast.