An integrated approach for the rectangular delineation of management zones and the crop planning problems

Abstract

This article proposes an integration of the Delineation of Rectangular Management Zones (DRMZ) with the Crop Planning Problem (CPP) in precision agriculture. The first problem consists in partitioning the agricultural fields into chemical and physical management zones satisfying a specific homogeneity level considering the soil properties. These partitions are commonly used to improve agricultural practices such as fertilization, irrigation and pests control, to name a few. The second problem considers the management zones, to determine the best crop for each plot maximizing the profit. We propose an integrated optimization problem determining the decisions of both problems simultaneously. The latter problem is formulated through a non-linear program, and we implement linearization techniques to obtain high-quality solutions with a commercial solver for instances generated at random based on real-data of agricultural activities in Mexico. We compare our integrated method to a sequential approach based on solving the DRMZ that minimizes the number of management zones, and then, finding a solution for the CPP. Numerical results for the integrated method restricted to the number of management zones found by the sequential one show an average increment of 1.77% in the profit compared to the sequential approach, but the average increment can be up to 5.38% when there are no limitations for the number of management zones. Finally, a sensitivity analysis considering variability for the amount of water shows that it may be recommended to define a non-deterministic approach in further research due to the significant changes in the obtained profits.