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Continuous Approximations in the Study of Hierarchies

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  • VAN ZANDT, Timothy

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

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.

Suggested Citation

  • VAN ZANDT, Timothy, 1995. "Continuous Approximations in the Study of Hierarchies," LIDAM Discussion Papers CORE 1995002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1995002
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1995.html
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    Cited by:

    1. Meagher, Kieron J., 2003. "Generalizing incentives and loss of control in an optimal hierarchy: the role of information technology," Economics Letters, Elsevier, vol. 78(2), pages 273-280, February.
    2. Andrea Patacconi, 2009. "Coordination and delay in hierarchies," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 190-208, March.
    3. Van Zandt, Timothy, 2004. "Balancedness of Real-Time Hierarchical Resource Allocation," CEPR Discussion Papers 4276, C.E.P.R. Discussion Papers.
    4. Saikat Datta, 1996. "On Control Losses In Hierarchies," Rationality and Society, , vol. 8(4), pages 387-412, November.
    5. Phillip J. Lederer & Xiaobo Zheng, 2021. "Can information economics explain the organization of productive facilities?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 30(3), pages 525-553, August.
    6. Jacek Cukrowski & Manfred M. Fischer, 2007. "Efficient organization of information processing," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(1), pages 13-26.
    7. Andrea Patacconi, 2005. "Optimal Coordination in Hierarchies," Economics Series Working Papers 238, University of Oxford, Department of Economics.

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