Two alternative models for farm management: Discrete versus continuous time horizon

Crop production entails many decision making processes aimed at improving productivity and achieving the best yield from scarce resources. Assuming that there is a set of tasks to be carried out within a given time horizon, and each task can be performed in different ways, the problem consists of determining how and when to carry out each task, in such a way that the tasks are scheduled in sequence at the minimum cost, taking into account any precedence relationships among them, the time window constraints for performing the tasks and the resources availability. This paper presents two alternative mathematical models to attain the proposed objective. The first model splits the time into discrete units spread throughout the planning horizon; it is presented in connection with flexible manufacturing. The second model keeps a continuous time horizon; a scheduling model is used for which a family of incompatibility conditions is introduced to avoid a certain type of simultaneous usage of resources. This type of conditions require to introduce a new structure so-called conditional disjunction. Computational experience is reported for real-life problems.