Database structures for mathematical programming models

Abstract

In the design and use of large-scale mathematical programming systems, a substantial portion of the effort has no direct relation to the variables and constraints, but is instead concerned with the description, manipulation and display of data. Established principles of database design do not apply directly to mathematical programming, however, because there are significant differences of organization and content between the data for an optimization model and the data for a conventional database application such as payroll or order entry. The goal of this work is thus to derive and elucidate fundamental principles of database construction for the specific case of large-scale mathematical programming. Alternative formulations of a steel mill planning model, combining aspects of production and network linear programming, are presented as an example; these formulations are shown to correspond to relational and hierarchical database schemes that have contrasting strengths and weaknesses. A particular implementation of a database system for steel optimization is then introduced and discussed, and a variety of promising generalizations are surveyed.