Composition Rules for Building Linear Programming Models from Component Models

This paper describes some rules for combining component modelsinto complete linear programs. The objective is to lay thefoundations for systems that give users flexibility in designingnew models and reusing old ones, while at the same time,providing better documentation and better diagnostics thancurrently available. The results presented here rely on twodifferent sets of properties of LP models: first, the syntacticrelationships among indices that define the rows and columns ofthe LP, and second, the meanings attached to these indices.These two kinds of information allow us to build a completealgebraic statement of a model from a collection of componentsprovided by the model builder