Decomposition-based heuristic for the zoning and crop planning problem with adjacency constraints

Abstract

This paper tackles management zone delineation and crop planning problems in an integrated precision agriculture framework. The zoning problem defines relatively homogeneous management zones regarding their soil properties, and for which specific rates of agricultural inputs are necessary. From a sustainable point of view, the crop planning problem considers cropping of species from different botanic families in adjacent zones at the same time. With this in mind, we propose a novel linear binary integer program for an integrated zoning and crop planning problem with adjacency constraints. In this model, we maximize the incomes of the crop plan subject to zoning constraints and adjacency constraints on crop families. The proposed model has a column-based formulation, and as such, we develop a decompositionbased heuristic which make use of the column generation method with columndependent rows. The decomposition strategy involves a master problem that deals with ensuring homogeneity of the selected management zones within the field partition and ensuring that the crop plan meets adjacency policies. On the other hand, the pricing problem generates rectangular management zones whose incorporation improves the objective value of the master problem. The algorithm is implemented in JuMP, a modeling language for mathematical optimization embedded in Julia. Results from a set of instances show the relevance of the decomposition-based heuristic.

A Branch-and-Price approach for the Continuous Multifacility Monotone Ordered Median Problem

“…The matheuristic procedure described here has been successfully applied in the literature. See, e.g., Albornoz & Zamora (2021); Benati et al (2021); Deleplanque et al (2020), and the references therein. Recall that our pricing problem is N P-hard.…”

Delineation of site‐specific management zones using estimation of distribution algorithms

“…Other works that integrate the delineation of rectangular management zones and the crop planning problems are presented in Cid‐Garcia and Ibarra‐Rojas (2019), Albornoz et al. (2020), and Albornoz and Zamora (2020).…”

“…In Saez and Albornoz (2016), the authors propose an approach to delineate SSMZ under uncertainty conditions. Other works that integrate the delineation of rectangular management zones and the crop planning problems are presented in Cid-Garcia and Ibarra-Rojas (2019), , and Albornoz and Zamora (2020).…”