Abstract The operational planning for agricultural production systems become an important tool for decision making for farmers. This paper shows a mathematical model as a decision support tool for crop maintenance planning problems. The model seeks the minimization of waste generated by the use of resources necessary for the task of crop maintenance. The model is inspired on the types of wastes from Lean Manufacturing (LM), which includes labor, use of machinery and operations in time windows that preserve the quality of harvest. The problem is modeled as a Mixed Integer Nonlinear Program (MINLP) in a case study on banana farms in Colombia. The model was tested with different scenarios, operations for crop maintaining, and number of workers. Then, we used the Response Surface Methodology (RSM) for sensitivity analysis, and obtain a significant reduction in cost, resources optimization, wastes, and schedule of crop maintenance activities: a reduction of 59% on the total cost was obtained, as well as a new approach for activities and task scheduling. The contributions of this paper to the body of knowledge in agricultural planning are at least twofold. Firstly, in contrast with traditional modeling approaches, this paper integrates the principles of lean manufacturing (LM) into the definition of parameters and constraints in a mathematical model for crop maintenance. Secondly, the paper couples nonlinear mathematical programming with response surface methodology (RSM) to carry out sensitivity analysis on the results obtained by the mathematical model. It is to note also that, although the modeling and solution methodology follow a case study research approach, it can be applied to other agricultural planning problem at operational level, being an economic option to minimize wastes and resources in others crops.

中文翻译：

---

受精益生产启发的作物维护作业规划模型

摘要 农业生产系统运行规划成为农民决策的重要工具。本文展示了一个数学模型作为作物维护计划问题的决策支持工具。该模型寻求最大限度地减少因使用作物维护任务所需的资源而产生的废物。该模型的灵感来自精益制造 (LM) 的废物类型，其中包括劳动力、机械使用和在时间窗口内保持收获质量的操作。在哥伦比亚香蕉农场的案例研究中，该问题被建模为混合整数非线性程序 (MINLP)。该模型在不同的场景、作物维护操作和工人数量下进行了测试。然后，我们使用响应面方法 (RSM) 进行敏感性分析，并获得显着降低成本、资源优化、浪费和作物维护活动时间表：获得总成本降低 59%，以及一种新的活动和任务调度方法。本文对农业规划知识体系的贡献至少是双重的。首先，与传统的建模方法相比，本文将精益制造 (LM) 的原理整合到作物维护数学模型中的参数和约束定义中。其次，本文将非线性数学规划与响应面法（RSM）相结合，对数学模型得到的结果进行敏感性分析。还要注意的是，虽然建模和解决方法遵循案例研究方法，