An optimal replacement policy for beef cows : a state model under conditions of uncertainty
Graham, Patrick M.
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Cattle ranchers are periodically faced with the decision of whether or not to cull/replace a brood cow. Assets such as beef cows are subject to stochastic elements that affect the cull/replacement decision. Stochastic elements include events such as death, infertility, and the inability to meet specific performance standards. Observations suggest that many Montana ranchers use a period-by-period cull/replacement decision-making strategy. However, varying management practices, stochastic elements, and the lengthy biological process associated with cattle production limit the validity of a single long-run replacement policy applied across all cattle ranches. This thesis examines a long-run optimal replacement policy based on economic criterion that individual cattle ranchers can adapt to their specific operation. Burt's discrete time model for optimal replacement under stochastic conditions is used as the analytical model. Published data measuring the likelihood of stochastic events, Billings, Montana cattle prices, and the long-run average variable costs from a case study of an individual ranch in Eastern Montana are used in the empirical model. Prices and costs are varied to reflect varying cattle prices over time and the heterogeneous nature of management practices with respect to costs. The results indicate that, although a single optimal planned replacement age is not derived, voluntary replacement should occur between cow ages of six and eleven years. These results are insensitive to varying price/cost combinations used in the study. Given the insensitivity of the results to the varying price/cost levels it is likely that the probabilities measuring the stochastic events are the main determinants in deriving an optimal replacement age. The results also show that cattle ranching is profitable except in high cost with average to below average model price conditions.