In this article a mathematical model is presented to assist management decisions on an integrated crop and livestock farm. Risk is incorporated into the model as the negative deviation of the actual gross income from the expected value of an activity's gross income. The model includes crop production (permitting and optimising a crop rotation system), dairy production and wool sheep production. Relevant data from a farm in the Swartland region of the Western Cape were used to test and validate the model. The results show that the adoption of crop rotation is superior in terms of gross margin to that generated from a mono-crop strategy. Empirical results also indicate that the complex interrelationships involved in a mixed crop-livestock farm operation play a major role in determining optimal farm plans. These complex interrelationships favour the introduction of crop rotation in the crop production activities of the farm under investigation. Solutions of the model with risk indicate that the crop rotation strategy and animal production levels are sensitive to different risk levels, and that the incorporation of risk greatly affects the level of land allocation to crop rotation and animal production level of the farm. Finally, the results suggest that the introduction of crop rotation is of paramount importance in improving the profitability and sustainability of the farm, thus the inclusion of forage crops such as medics into the integrated crop-livestock production is beneficial for sustained profitability.

Numerous studies have analysed farm planning decisions focusing on producer risk preferences. Few studies have focussed on the farm planning decisions in an integrated croplivestock farm context. Income variability and means of managing risk continues to receive much attention in farm planning research. Different risk programming models have attempted to focus on minimising the income variability of farm activities. This study attempts to identify the optimal mix of crops and the number of animals the farm needs to keep in the presence of crop production risk for a range of risk levels. A mixed integer linear programming model was developed to model the decision environment faced by an integrated crop-livestock farmer. The deviation of income from the expected value was used as a measure of risk. A case study is presented with representative data from a farm in the Swartland area. An investigation of the results of the model under different constraints shows that, in general, strategies that depend on crop rotation principles are preferred to strategies that follow mono-crop production practices.