Delineation of Rectangular Management Zones Under Uncertainty Conditions

Jose L. Saez, Victor M. Albornoz


In this article we cover the problem of generating a partition of an agricultural field into rectangular and homogeneous management zones or quarters according to a given soil property, which has variability in time that is presented as a number of possible scenarios. This problem combines aspects of precision agriculture and optimization with the purpose of achieving a site and time specific management of the field properties that is consistent and effective in time for a medium term horizon. More specifically, we propose a two stage integer stochastic linear programming model with recource that solves the problem of generating a partition facing a finite number of future scenarios, with a solution that gives satisfactory results to any possible value of the chosen soil property. We describe the proposed model, the adopted methodology and the results achieved with this methodology.


  1. Ahumada O., Villalobos J. R., Mason A. N. (2012), Tactical planning of the production and distribution of fresh agricultural products under uncertainty. Agricultural Systems 112, 1726.
  2. Albornoz V. M., Cid-Garcia N. M., Ortega R., Rios-Solis, Y. A. (2013). Rectangular shape management zone delineation using integer linear programming. Computers and Electronics in Agriculture 93, 1-9.
  3. Albornoz, V.M., Cid-Garcia, N.M., Ortega, R. and RiosSolis, Y.A. (2015). A hierarchical planning scheme based on precision agriculture. In Handbook of Operational Research in Agriculture and the Agri-Food Industry, Pla-Aragones, L.M. (Ed.), 129-162, Springer.
  4. Albornoz, V.M. and Nanco, L.J. (2015) An empirical design of a column generation algorithm applied to a management zone delineation problem. Lecture Notes in Economics and Mathematicasl Systems, to appear.
  5. Birge, J. and Loveaux, F. (2011). Introduction to Stochastic Programming. 2nd ed., New York: Springer.
  6. Bravo M., Gonzalez I. (2009). Applying stochastic goal programming: A case study on water use planning. European Journal of Operational Research 196, 11231129.
  7. Gassmann, H.I and Ziemba, W.T. (2012). Stochastic Programming. Applications in Finance, Energy, Planning and Logistics. World Scientific Publishing Company.
  8. Haghverdi A., Leib B.G., Washington-Allen R.A., Ayers P.D., and Buschermohle M.J. (2015) Perspectives on delineating management zones for variable rate irrigation. Computers and Electronics in Agriculture 117, 154-167.
  9. Higle, J.L. (2005). Stochastic Programming: Optimization when uncertainty matters. Tutorials in Operations Research. INFORMS, New Orleans.
  10. Itoh T., Ishii H., Nanseki T. (2003), A model of crop planning under uncertainty in agricultural management. Int. J. Production Economics 8182, 555558.
  11. Jaynes D., Colvin T., Kaspar T., (2005). Identifying potential soybean management zones from multi-year yield data. Computers and electronics in agriculture 46 (1), 309327.
  12. Jiang Q., Fu Q., Wang Z. (2011). Study on delineation of irrigation management zones based on management zone analyst software. Computer and Computing Technologies in Agriculture IV, 419427.
  13. Li M., Guo P., (2015), A coupled random fuzzy two-stage programming model for crop area optimizationA case study of the middle Heihe River basin, China. Agricultural Water Management 155, 5366.
  14. Liu J., Li Y.P., Huang G.H., Zeng X.T., (2014). A dualinterval fixed-mix stochastic programming method for water resources management under uncertainty. Resources, Conservation and Recycling 88, 5066.
  15. Ortega J.A., Foster W. and Ortega R. (2002). Definition of sub-stands for Precision Forestry: an application of the fuzzy k-means method.Ciencia e Investigacin Agraria 29 (1), 3544.
  16. Ortega. R. & Santibanez, O. A. (2007). Determination of management zones in corn (Zea mays L.) based on soil fertility. Computers and Electronics in Agriculture, 58, 49-59.
  17. Ramos, A., Alonso-Ayuso, A. and Perez, G.(2008). Optimizacion bajo incertidumbre. Espaa, Biblioteca Comillas. Publicaciones de la Universidad Pontificia Comillas.
  18. Ruszczynski A. and Shapiro A.(2003). Stochastic Programming. Handbooks in Operations Research and Management Science, Vol. 10. New York, North-Holland.
  19. Wallace S.W. and Ziemba W.T. (2005). Applications of Stochastic Programming. MOS-SIAM Series on Optimization.
  20. P. (2010). Fuzzy multi-objective linear programming applying to crop area planning. Agricultural Water Management 98 , 134142.

Paper Citation

in Harvard Style

Saez J. and Albornoz V. (2016). Delineation of Rectangular Management Zones Under Uncertainty Conditions . In Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-171-7, pages 271-278. DOI: 10.5220/0005708202710278

in Bibtex Style

author={Jose L. Saez and Victor M. Albornoz},
title={Delineation of Rectangular Management Zones Under Uncertainty Conditions},
booktitle={Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

in EndNote Style

JO - Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Delineation of Rectangular Management Zones Under Uncertainty Conditions
SN - 978-989-758-171-7
AU - Saez J.
AU - Albornoz V.
PY - 2016
SP - 271
EP - 278
DO - 10.5220/0005708202710278