Profit Optimization in Corn Weed Control using Atrazine under Interval Uncertainty

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.