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Delineating robust rectangular management zones based on column generation algorithm

Albornoz, Víctor M., Ñanco, Linco J., Sáez, José L.
Computers and electronics in agriculture 2019 v.161 pp. 194-201
algorithms, computer software, models, precision agriculture, soil, temporal variation, vegetation
This paper considers a management zone delineation problem in a precision agriculture framework that defines a partition of a field into rectangular and homogeneous management zones according to certain vegetation or soil indexes. Modeling the problem as a robust optimization model accounts for spatial and temporal variability of the index considered, representing this variability according to a finite set of sampled realizations (scenarios). The model assumes that the complete enumeration of all the possible rectangular management zones is known. To deal with this assumption, we propose a strategy based on a column generation algorithm to exploit the structure of the model. To solve the model and implement the strategy, an algebraic modeling language and state of the art MIP software was used. Results from the modeling approach and the computational strategy were obtained by solving different instances of a real case-study. We show that the robust optimization model can be useful in real situations under temporal variability of the index used for delineating management zones. Results also show that the algorithmic strategy is appropriated for solving the instances considered.