Aggregation of Product Data for Hierarchical Production Planning

When applying an aggregate view to production planning, the production system is given a hierarchical structure. The problem description at the upper level (which is less detailed) concerns product groups and machine groups rather than individual products and machines. This means that product structures and capacity requirements also must be expressed in terms of product groups and machine groups. In this paper it is shown under what conditions a perfect aggregation of product data can be obtained. If a perfect aggregation is not possible, our problem is to find a good approximate solution. A mathematical formulation of this approximation problem and its general solution is also given.