Binary programming for the simulation of crop rotation and animal transit in an integrated crop-livestock system

ABSTRACT The aim of this study was to develop and implement a linear-programming model (LP) that provides as its result a schedule with the best selection of crops in each plot per period, and with the greatest weight gain for each animal. The linear-programming model was developed from empirical work carried out by Alvarenga and Gontijo Neto (2008) in an area of 24 hectares of Embrapa Milho e Sorgo, in Sete Lagoas, Minas Gerais (MG). For the computational implementation of the model, it was necessary to have data on agricultural suitability and animal weight gain for each period and for each plot. In order to test the developed mathematical model, values were randomly generated for agricultural suitability and for animal weight gain using the MATLAB solver. It was then possible to carry out the computational implementation of the linear-programming model in MATLAB. Two numerical trials were conducted, the first considering four periods, four plots and the transit of two animals, and the second with ten periods, four plots and the transit of three animals. The results show that the linear-programming model is consistent with the empirical work done by Alvarenga and Gontijo Neto (2008). The linear-programming model satisfies all the imposed constraints, maximises the weight gain of each animal, and provides the best selection of crops