Stochastic Differential Equations General Models of Individual Growth in Uncertain Environments and Application to Profit Optimization in Livestock Production

Abstract

Individual animal growth in a randomly varying environment is modeled using stochastic differential equation models. These models are generalizations of the classical deterministic growth models used in regression methods, but incorporate a random dynamical term describing the effects of environmental and other random fluctuations on the growth process. We describe parameter estimation and prediction methods, illustrating with data on cow growth of the Mertolengo breed raised in Alentejo (Portugal) under natural conditions; see models, their properties and statistical techniques in the references below.

We first show that these models outperform the traditional regression models in predictive power for they take into account the dynamical nature of the growth process and its interaction with environmental fluctuations.

We then apply the models to profit optimization in livestock production, taking into account production costs and sales revenues.

Assuming the animal is to be sold when it reaches some prescribed age, we determine the optimal age at which an animal should be sold in order to maximize profit. Another possibility is to sell the animal when it reaches a prescribed size. The first passage time distribution through a prescribed size is studied and used to determine the optimal size at which the animal should be sold. We then determine which policy (selling at a fixed age or selling at a fixed size) is preferable in terms of profit and compare results with the deterministic case.