Project Scheduling With Feeding Precedence Relations: An Application to Production Planning

Production planning in Manufacturing-to-Order environments producing complex items must manage the execution of fabrication and/or assembling activities. In case of activities executed by workers, the committed effort can vary over time. To model this behavior, the Variable Intensity formulation has been proposed in the literature. In addition, the activities to be scheduled often represent whole production phases made of distinct production operations. Hence, the utilization of simple finish-to-start precedence relations does not correctly represent the real production process. In such cases Generalized Precedence Relations are used to allow overlapping among activities. However, since in Variable Intensity formulations the percentage execution of the activities is no more univocally related to their time execution, Generalized Precedence Relations cannot completely describe the constraints among activities. In this paper two mathematical formulations of precedence relations based on processing execution are presented to model overlapping between activities. The formulations are applied to an industrial case of production of machining centers and compared in terms of computational efficiency.