Model management via dependencies between variables: an indexical reasoning in mathematical modeling

Abstract

The design and implementation of computer-based modeling systems and environments are gaining interest and importance in decision sciences and information systems. In spite of the increasing popularity of GUI-based operating systems, most of the algebraic modeling languages, today, are still file-oriented, text-based, and therefore require structured declarations and formal model definitions. The utilization of the standard graphical screen objects of a graphics-based operating system provides enhanced visualization of models and more cohesive human-computer interaction. The approach taken in this thesis is to explore the design and implementation of a graph-based modeling system focusing on computational dependencies between model components. Another important aspect of this research is the development of a user-friendly model formulation interface for algebraic modeling languages and systems; these facilitate the description and implementation of mathematical models by allowing the modeler to employ commonly known and powerful algebraic notation instead of language specific codes. The major conclusion of this thesis is that dependencies between variables are a foundation for building and using models and modeling languages. It also shows that this supports model documentation, validation, formulation, implementation, comprehension, maintenance and reuse. That is, it impacts nearly every step of the modeling life cycle