Composition Rules for Building Linear Programming Models from Component Models

This paper describes some rules for combining component models into complete linear programs. The objective is to lay the foundations for systems that give users flexibility in designing new models and reusing old ones, while, at the same time, providing better documentation and better diagnostics than is provided by current systems. The results presented here rely on two different sets of properties of LP models: first, the syntactic relationships among indices that define the rows and columns of the LP, and second, the meanings attached to these indices. These two kinds of information allow us to build a complete algebraic statement of a model from a collection of components provided by the model builder.