Simulation and Optimization for Crop Planning Under Risk

The intensification of agricultural practices, in particular the growing use of fertilizers and pesticides, and the specialization and concentration of crop and livestock production, have an increasing impact on environment. This paper presents a crop planning model based on portfolio theory. The model takes into account several uncertainties as weather risks, market risks and environmental risks. Several environmental levels for the application of fertilizers/pesticides are defined. Monetary penalties for overcoming these levels, are considered. The sum of the penalties is called the environmental risk of the crop plan. The model has several constraints: budget constraints, expected return constraints and crop demand constraints. The objective map is the environmental risk. The decision variables are represented by the crop plan that is: a binary matrix that describes the crop allocations to plots and the quantities of chemical fertilizers and pesticides that are applied to crops. The goal of the model is to find the crop plans that minimize the objective map. A numerical example is considered. Simulations of the return - environmental risk efficient frontier for various lengths of historical data are analyzed.