Profit Optimization in Corn Weed Control using Atrazine under Interval Uncertainty

Document Type : Research Paper

Authors

1 Associate Professor, Department of Applied Mathematics, Saravan Higher Education Complex, University of Saravan, Sistan and Baluchestan, Iran

2 Associate Professor, Department of Economics, Saravan Higher Education Complex, University of Saravan, Sistan and Baluchestan, Iran

Abstract

This study focuses on profit optimization in maize weed control under interval uncertainty, aiming to enhance maize yield. The objective is to identify an optimal balance between crops and weed dynamics to maximize producers' economic benefits. To achieve this goal, a dose–response function for herbicides and the population dynamics of weeds (such as the invasive Amaranthus retroflexus) were first modeled. Then, considering factors such as planting method, climatic conditions, and pest pressure, the final crop yield was computed. This problem is formulated as an optimal control problem with an interval-valued profit function, using dynamic programming. Dynamic systems are a technique that applies principles of feedback engineering and control theory to simulation, enabling the understanding of complex patterns in causal relationships within systems. Simulation results with the atrazine herbicide show that optimal application rates lead to a stable reduction in the weed seed bank and a significant increase in long-term profitability. Optimal solutions are presented based on the LU (Lower-Upper) ordering relation, which introduces a novel concept of partial ordering in interval spaces via convex, bounded functions associated with intervals. The results suggest that dynamic programming for intelligent weed management significantly improves productivity and long-term economic returns. Therefore, it can serve as an effective tool for decision-making under economic uncertainty in sustainable agriculture.

Keywords

Main Subjects

References

  1. Ahmadi, A. (1999). Determination of critical period of weed control on tomato. M.Sc. Thesis, Dept. of Agronomy and Plant Breeding, Pardis Abouraihan, Tehran University, Iran, 100p (In Persian).
  2. Asa, C. G. (2018). Pengaruh Kesadaran Iklan, Kesadaran Merek, Citra Merek dan Ekuitas Merek Mamahke Jogja dengan Produk Kue di Media Sosial Terhadap Keputusan Pembelian Konsumen.‏
  3. Cousens, R. (1985). A simple model relating yield loss to weed density. Annals of applied biology, 107(2), 239-252.‏
  4. Bellman, R. I. C. H. A. R. D. (1957). Dynamic programming, princeton univ. Press Princeton, New Jersey, 39.‏
  5. Jones, R. E., & Cacho, O. J. (2000). A dynamic optimisation model of weed control.‏
  6. Kennedy, J. O. (Ed.). (2012). Dynamic programming: applications to agriculture and natural resources. Springer Science & Business Media.‏
  7. Kim, D. S., Marshall, E. J. P., Brain, P., & Caseley, J. C. (2006). Modelling the effects of sub‐lethal doses of herbicide and nitrogen fertilizer on crop–weed competition. Weed Research, 46(6), 492-502.‏
  8. Lacerda, A. L. D. S., & Victoria Filho, R. (2004). Dose-response curves in weed species with the use of herbicide glyphosate. Bragantia, 63, 73-79.‏
  9. Leal, U. A., Maqui, G., Silva, G. N., & Lodwick, W. (2022). Single-Level Differentiability for Interval-valued Functions. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 9(1).‏
  10. Leal, U., Lodwick, W., Silva, G., & Maqui-Huaman, G. G. (2021). Interval optimal control for uncertain problems. Fuzzy Sets and Systems, 402, 142-154.‏
  11. Merotto Jr, A., Jasieniuk, M., Osuna, M. D., Vidotto, F., Ferrero, A., & Fischer, A. J. (2009). Cross-resistance to herbicides of five ALS-inhibiting groups and sequencing of the ALS gene in Cyperus difformis L. Journal of agricultural and food chemistry, 57(4), 1389-1398.‏
  12. Pandey, S., & Medd, R. W. (1990). Integration of seed and plant kill tactics for control of wild oats: an economic evaluation. Agricultural Systems, 34(1), 65-76.‏
  13. Pontryagin, L. S. (2018). Mathematical theory of optimal processes. Routledge.‏
  14. Trefethen, L. N., & Bau, D. (2022). Numerical linear algebra. Society for Industrial and Applied Mathematics.‏
  15. Santín-Montanyá, I. (2011). The bioassay technique in the study of the herbicide effects. Herbicides, Theory and Applications. Rijeka: InTech, p431-454.‏
  16. Seefeldt, S. S., Jensen, J. E., & Fuerst, E. P. (1995). Log-logistic analysis of herbicide dose-response relationships. Weed technology, 9(2), 218-227.‏

Files

Share

How to cite

Statistics