Hierarchical sets in mathematical programming modeling languages

The mathematical notation commonly applied for the formulation of mathematical programming models is extended to include hierarchical structures. The proposed notation is related to hierarchical set concepts in the languages UIMP, AMPL, and LPL. With the proposed notation it is possible to aggregate and disaggregate over hierarchical structures. In addition, views are introduced to permit the use of hierarchical substructures and to create new hierarchies out of existing ones. The proposed notation for hierarchical sets and views is illustrated by applying it to the representation and estimation of social accounting matrices (SAMs).