Indexing in Modeling Languages for Mathematical Programming
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.
Volume (Year): 38 (1992)
Issue (Month): 3 (March)
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