Multi—stage, multi—product planning: a hierarchical approach using time aggregation

Abstract

ABSTRACT In this paper, a multi—product multi-stage planning problem is addressed by means of a two level hierarchical approach. The decision structure is based on an aggregation of time: the upper (aggregate) level involves macro—periods while elementary periods are considered at the lower (detailed) level. Thus, the detailed level refines (disaggregates) the higer level decisions i.e. distributes the production volume defined for each macro-period, over the relevant elementary periods. In such a framework, the global consistency of the decisions is investigated, leading to the basic concept of aggregate consistency. Analytical aggregate consistency conditions are obtained; they rely on a graph modeling of the disaggregation problem and on the analysis of a flow problem within the relevant network. Introduced as additional constraints in the aggregate model, they ensure that the selected aggregate decisions can be further disaggregated in order to provide feasible detailed production plans. In order to reduce the complexity brought about by these constraints a computational structure based on heuristics is proposed. In this context, numerical experiments are carried out to evaluate the quality of this decisional structure.