A family of hierarchical models for the design of deterministic assembly systems

The purpose of this paper is to propose a family of hierarchical models which incorporate a broad range of features that represent many aspects that are fundamental to deterministic assembly system design problems. The family consists of a set of models that incorporate successively more advanced features so that components representing the more simple cases appear as imbedded structures in the models for more complex cases. The ultimate goal is to develop models that can be exploited, for example by strong cutting plane methods, to resolve assembly system design problems. Cutting plane methods have achieved noteworthy successes in resolving other integer programs and offer the promise of providing a capability to resolve a broad variety of assembly system design problems. Polytopes associated with imbedded structures can be studied and resulting valid inequalities can also be used in solving the more complex, practical cases. This paper is a means of initiating research in this important direction.