Programming Model

Crop production entails many decision making processes aimed at improving productivity and achieving the best yield from scarce resources, which are normally limited. Assuming that there is a certain technical path of tasks to be carried out within a period, and that each task can be done in different ways, the problem addressed in this paper consists of choosing how and when to carry out each one, in such a way that the tasks are scheduled in sequence at the lowest possible cost, taking account of any relations of precedence among them, and in such a way that each task is done within its time window and with the resources being assigned in a feasible way. Time windows are usually defined in a strict way, and thus, if adjusted, can be a cause of infeasibility for some of the problems, implying the need to acquire new resources. Nevertheless, in most cases small deviations from time windows could be acceptable. In this paper a mixed 0-1 programming model to attain the proposed objective is proposed, applying goal programming to model time windows in a more flexible way.