Profit Optimization of Cattle Growth with Variable Prices

We apply a class of stochastic differential equations to model the growth of individual animals in randomly fluctuating environments using real weight data of males of the Mertolengo cattle breed. The use of these more realistic models can help farmers to optimize their profit. To this end we obtain the probability distribution, the first two moments and others quantities of interest of the profit obtained by raising and selling an animal under the more general, and more realistic, situation where the raising costs and the price per kg paid to the farmers depends on the animal’s age and weight category. We also present sensitivity results on how the expected profit and the optimal selling age vary with small changes on the estimates of the model parameters. We conclude that farmers are selling the animals a little earlier than the optimal selling age, which results in a lower profit per animal. The sensitivity analysis of the parameters shows that small changes on the parameters result in very small effects on the optimal profit and negligible effects on the optimal selling age.