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Indexing in Modeling Languages for Mathematical Programming

Author

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  • Arthur M. Geoffrion

    (Anderson Graduate School of Management, University of California, Los Angeles, California 90024)

Abstract

Indexing structures are of fundamental importance to modeling languages for mathematical programming as a device for mathematical abstraction, and because they facilitate achieving conciseness, stability, and error-resistance. The aim of this article is to stimulate discussion of such structures, especially the two most common kinds found in algebraic style languages: sets and relations. We offer a taxonomy of set-based and relation-based indexing structures, a suite of detailed examples illustrating this taxonomy, and a number of specific principles (some arguable and some not) for incorporating indexing structures into modeling languages. We also examine four modeling languages in detail with respect to their indexing capabilities: AMPL, GAMS, LINGO, and SML. By attempting to work all of the illustrative examples in each language, we are able to reach some conclusions concerning relative expressive power, economy of notation, obedience to our principles of "good" language design, ease of data handling, and other criteria.

Suggested Citation

  • Arthur M. Geoffrion, 1992. "Indexing in Modeling Languages for Mathematical Programming," Management Science, INFORMS, vol. 38(3), pages 325-344, March.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:3:p:325-344
    DOI: 10.1287/mnsc.38.3.325
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    Cited by:

    1. Makowski, Marek, 2005. "A structured modeling technology," European Journal of Operational Research, Elsevier, vol. 166(3), pages 615-648, November.
    2. Tsai, Yao-Chuan, 2001. "Comparative analysis of model management and relational database management," Omega, Elsevier, vol. 29(2), pages 157-170, April.
    3. Huh, S. Y. & Chung, Q. B., 1995. "A model management framework for heterogeneous algebraic models: Object-oriented database management systems approach," Omega, Elsevier, vol. 23(3), pages 235-256, June.
    4. Lin, Suh-Yun Elva & Schuff, David & St. Louis, Robert D., 2000. "Subscript-free modeling languages: A tool for facilitating the formulation and use of models," European Journal of Operational Research, Elsevier, vol. 123(3), pages 614-627, June.

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