The search for sustainable agriculture is leading many economies to turn to crop rotation systems and to abandon monoculture systems which generally require increased use of pesticides and synthetic fertilizers. But the optimization of crop rotation remains a challenge, especially when considering organic farming. This work tackles the optimization of crop rotation in traditional organic farms with plot adjacency constraints and nutrient amendments. In the present configuration, each farmer owns a certain quantity of rudimentary equipment and a number of workers, all considered as resources. Farms are subdivided into plots and each plot allows only one crop at a given period. At a given interval of time, each plot receives a certain quantity of nutrient. The generated rotations are of fixed durations for all plots and the objective is to maximize farmers’ income. A linear programming approach is used to determine the solution of the proposed farming model. Three levels of constraints are combined in the linear program to generate realistic rotations: (i) biophysical constraints including crop succession and plot adjacency; (ii) structural constraints including budget and resources; (iii) organizational constraints such as nutrient amendment and market demand. To evaluate the performance of the model, scenarios based on real-world data has been defined and solved using free solvers. The solutions obtained indicate that all the constrains are satisfied. In addition, farmers’ revenue is improved, reaching a stationary position when the quantity of available resources is equal or greater than the quantity of required resources. Finally, Cbc solver is faster than GLPK solver; and it provides solutions on larger instances where GLPK does not.

中文翻译：

---

通过营养修正的有机农场地块邻接约束提高作物轮作系统中农民的收入

对可持续农业的探索导致许多经济体转向轮作系统，并放弃通常需要更多使用杀虫剂和合成肥料的单一栽培系统。但轮作的优化仍然是一个挑战，尤其是在考虑有机农业时。这项工作解决了传统有机农场作物轮作的优化问题，包括地块邻接限制和养分修正。在目前的配置中，每个农民拥有一定数量的基本设备和一定数量的工人，所有这些都被视为资源。农场被细分为地块，每个地块在特定时期只能种植一种作物。在给定的时间间隔内，每个地块都会收到一定数量的养分。所产生的轮作对所有地块都有固定的持续时间，目的是使农民的收入最大化。线性规划方法用于确定所提出的农业模型的解决方案。线性程序中结合了三个级别的约束以产生现实的轮作：(i) 生物物理约束，包括作物演替和地块邻接；(ii) 结构性限制，包括预算和资源；(iii) 组织限制，如营养修正和市场需求。为了评估模型的性能，我们使用免费求解器定义并解决了基于真实世界数据的场景。获得的解表明满足所有约束。此外，农民收入提高，当可用资源的数量等于或大于所需资源的数量时，到达固定位置。最后，Cbc 求解器比 GLPK 求解器更快；并且它在 GLPK 没有的较大实例上提供了解决方案。