Continuous Approximations in the Study of Hierarchies

Timothy van Zandt
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Timothy van Zandt: CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

No 1995002, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: Large organizations are typically modeled as hierarchies. Hierarchies are discrete structures (trees), but researchers frequently use continuous approximations. The purpose of this note is to study the validity of these approximations. We show that modeling hierarchies with a continuum of tiers is not a good approximation. We also show that ignoring rounding operators and integer constraints in formulae derived from discrete models call be a valid approximation, when hierarchies are suitably large. This is made precise by tight bounds on the relative errors of the approximations.

Date: 1995-01-01
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