Aggregation of resource constraints for groups of similar components in manufacturing systems

Aggregation of resource constraints and detailed allocation decision variables in the presence of groups of similar components is considered in the context of creating aggregate scheduling models within a hierarchical production scheduling framework. Three main types of similar components are distinguished: structurally uniform, productively uniform, and uniform components. For a group of components which are productively uniform, but not necessarily structurally uniform, a strong aggregate problem with the aggregated form of the constraints is formulated so that its solutions can always be disaggregated into feasible solutions of the detailed capacitated problem. Moreover, if the components are uniform, the disaggregate and aggregate solutions have identical values of the objective function. The aggregation of constraints forms a base for further aggregation of variables. The aggregation of variables is analysed for productively uniform and uniform components, and also in a general case of productively nonuniform components. In the latter case, restrictive and relaxed aggregated models are proposed. The aggregated model can be created from the detailed model by an analysis of the structure of the detailed problem, as illustrated by an example. One interesting conclusion of the analysis is that the aggregate scheduling problems become simpler if the production systems have incorporated more flexibility in terms of structural similarity of components.