Database structures for mathematical programming models

In both 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. This paper derives fundamental principles of database construction for largescale mathematical programming, by use of a steel mill planning model as an example. Alternative formulations for the model—which incorporate aspects of production and network linear programming—are presented at the outset, and are shown to correspond to relational and hierarchical database schemes that have contrasting strengths and weaknesses. A particular implementation of the steel optimization package is then presented as an illustration. A concluding section puts this work into perspective, by surveying and categorizing a variety of approaches for providing data management features in mathematical programming applications. The views of data offered by this paper’s approach are seen to differ substantially from the views offered by traditional mathematical programming systems, and certain “intermediate” strategies for integration of database and mathematical programming software are identified as having particular promise for future work. Published version: Decision Support Systems 20 (1997) 317–344. This work has been supported in part by grants from the American Iron and Steel Institute, and by grant DDM-8908818 from the National Science Foundation.