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A mathematical model for exploring the evolution of organizational structure

Linda K. Gibson (School of Business, Pacific Lutheran University, Tacoma, WA, USA)
Bruce Finnie (Fat Tail Systems Consultancy, Graham, WA, USA)
Jeffrey L Stuart (Department of Mathematics, Pacific Lutheran University, Tacoma, WA, USA)

International Journal of Organizational Analysis

ISSN: 1934-8835

Article publication date: 9 March 2015




This paper aims to explore organizational structure, efficiency and evolution, and its relationship to bureaucracy. A new mathematical model is utilized to generate theoretically consistent relationships between economic performance and organizational scale and structure, and to develop a taxonomy of organizational structure.


A systems approach is used to model structural evolution and generate consistent, testable hypotheses concerning organizational sustainability and financial performance. This theoretical treatment seeks to reconcile contradictory views of bureaucracy, modeling both positive and negative impacts on performance and behavior. A variant of agency theory is used as an organizing paradigm, based on three competing organizational needs: control, autonomy and ownership of consequences.


Simulations reveal that organizations evolve through five stages of development: from an entry (flat/parallel) stage, through a hybrid or mixed stage, to the massively serial (hierarchical) stage. As firms evolve, the risk/return ratio first falls as employment expands, but later rises as higher levels of hierarchy appear. Eventually, organizational complexity rises sufficiently to produce lower levels of managerial ownership of consequences and professional autonomy, as well as higher levels of control, leading to a collapse of organizational efficiency. A subtle variation of agency theory is revealed: upper-management may maximize organizational depth, increasing salary differences between levels.


This paper uses an internally consistent, deductive framework to elucidate relationships between task complexity, skill level, industry life-cycle and firm age – providing the first known attribute-based metric for organizational complexity. This approach is reminiscent of Perrow’s (1999) non-mathematical treatment of organizational systems complexity.



Gibson, L.K., Finnie, B. and Stuart, J.L. (2015), "A mathematical model for exploring the evolution of organizational structure", International Journal of Organizational Analysis, Vol. 23 No. 1, pp. 21-40.



Emerald Group Publishing Limited

Copyright © 2015, Emerald Group Publishing Limited

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