A mixed integer nonlinear programming model for site-specific management zone problem

Abstract

Precision agriculture employs sophisticated tools to optimize decision-making in farming, aiming to simultaneously improve crop yields and manage resources more effectively in a context of increasing scarcity and rising costs. A key aspect of precision agriculture is the delineation of site-specific management zones (SSMZs), which involves segmenting a field into areas that are homogeneous in terms of soil physicochemical properties. The problem of delineating SSMZ have been approached using a wide variety of methodologies, all of which, heuristic, focus on finding feasible solutions. Until this work, there was no exact algorithm or mathematical model that would allow for a point of comparison. This paper introduces a novel approach to tackle the delineation of SSMZ with orthogonal shapes through the development of a mixed integer nonlinear programming (MINLP) model. Small instances with different scenarios show the scope of the proposed approach and the significance of the results. It provides a structure for the SSMZ problem with orthogonal shapes and establishes a benchmark for evaluating the performance of heuristic solutions, metaheuristics, or hybrid approaches.