A project scheduling approach to production planning with feeding precedence relations

In Manufacturing-to-Order or Engineering-to-Order systems producing complex and highly customised items, each item has its own characteristics that are often tailored for a specific customer. Project scheduling approaches are suitable for production planning in such environments. However, when we consider the production of complex items, the distinct production operations are often aggregated into activities representing whole production phases. In such cases, the planning and scheduling problem works on the aggregate activities, considering that, in most cases, such activities also have to be manually executed. Moreover, simple finish-to-start precedence relations no longer correctly represent the real production process, but overlapping among activities should be allowed. In this paper, a project scheduling approach is proposed for production planning in Manufacturing-to-Order systems. The Variable Intensity formulation is used to allow the effort committed to the execution of activities to vary over time. Feeding precedences are developed to model generalised precedence relations when the execution mode of activities is not known a priori. Two mathematical formulations of these precedence relations are proposed. The formulations are applied both to randomly generated instances and to an industrial system producing machining centres and are compared in terms of computational efficiency.