Abstract
This paper proposes a mathematical model to compare a network organization with a hierarchical organization. In order to formulate the model, we define a three-dimensional framework of the coordination structure of a network and of other typical coordination structures. In the framework, we can define a network structure by contrasting it with a hierarchy, in terms of the distribution of decision making, which is one of the main features of information processing. Based on this definition, we have developed a mathematical model for evaluating coordination structures. Using this model, we can derive two boundary conditions among the coordination structures with respect to the optimal coordination structure. The boundary conditions help us to understand why an organization changes its coordination structure from a hierarchy to a network and what factors cause this change. They enable us, for example, to find points of structural change where the optimal coordination structure shifts from a hierarchy to a hierarchy with delegation or from a hierarchy with delegation to a network, when the nature of the task changes from routine to non-routine. In conclusion, our framework and model may provide a basis for discussing the processes that occur when coordination structures change between a hierarchy and a network.
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References
Allen, T.J. and O. Hauptman (1987), “The Influence of Communication Technologies on Organizational Structure—A Conceptual Model for Future Research—, ” Communication Research, 14(5), 575–587.
Alstyne, M. (1997), “The State of Network Organization: A Survey in Three Frameworks, ” Journal of Organizational Computing and Electronic Commerce, 7(2/3), 83–151.
Blau, P.M. (1970), “A Formal Theory of Differentiation in Organizations, ” American Sociological Review, 35, 201–218.
Carley, K.M. (1999), “Organizational Change and the Digital Economy: A Computational Organization Science Perspective, ” in Brynjolfsson, Erik and B. Kahin (Eds.) Understanding the Digital Economy: Data, Tools, Research. MIT Press, Cambridge, MA.
Carley, K.M. and M.J. Preietula (Eds.) (1994), Computational Organization Theory. Lawrence Erlbaum Associates, Hillsdale, NJ.
Carley, K.M. and D.M. Svoboda (1996), “Modeling Organizational Adaptation as a Simulated Annealing Process, ” Sociological Methods and Research, 25(1), 138–168.
Coase, R.H. (1037), “The Nature of the Firm, ” Economica, 4, 386–405.
Emarson, R.M. (1962), “Power Dependence Relations, ” American Sociological Review, 27, 31–41.
Galbraith, J.R. (1977), Organization Design. Addison-Wesley, Reading, MA.
Hennart, J.-F. (1993), “Explaining the Swollen Middle: Why Most Transactions are a Mix of Market and Hierarchy, ” Organization Science, 4(4), 529–547.
Ishida, K. (1998), “A Study of Cooperative Aspect of Collective Phenomena Based on an Operational Organization Model, ” Doctoral thesis, Graduate Department of Information Network Science, Graduate School of Information Systems, University of Electro-Communications, Tokyo.
Ishida, K., T. Yamamoto and T. Ohta (1996), “A Mathematical Study of Organizational Structure and Information Technology, ” Journal of the Japan Society for Management Information, 5(1), 19–49.
Jackson, J.H. and C.P. Morgan (1978), Organization Theory.
Koontz, H., C. O'Donnell and H. Weihrich (1984), Management, 8th ed. McGraw-Hill, New York.
Lawrence, P. and J. Lorsch (1967), Organization and Environment. Harvard Business School, Boston.
Malone, T.W. (1987), “Modeling Coordination in Organizations and Markets, ” Management Science, 33(10), 1317–1332.
Malone, T.W. and S.A. Smith (1988), “Modeling the Performance of Organizational Structures, ” Operations Research, 36(3), 421–436.
Malone, T.W., J. Yetes and R.I. Benjamin (1987), “Electronic Markets and Electronic Hierarchies, ” Communications of ACM, 30(6), 484–497.
March, J.G and H.A. Simon (1958), Organizations. John Wiley and Sons, New York.
March, J.G and J.P. Olsen (1976), Ambiguity and Choice in Organizations. Universitetsforlaget.
Marchak, J and R. Radner (1972), Economic Theory of Teams. Yale University Press, New Haven.
Ohta, T., T. Yamamoto and K. Ishida (1994), “On a Coordination Model among Heterogeneous Agents in Cooperative Environment, ” APORS'94 Abstracts. p. 120.
Powell, W.W. (1990), “Neither Market nor Hierarchy: Network Forms of Organization, ” in B. Staw and T. Cummings (Eds.) Research in Organizational Behavior, Vol. 12, 295–336.
Raymond, E.S. (1998), The Cathedral and the Bazaar, http://www.tuxedo.org/~esr/writings/cathedralbazaar/ cathedral-bazaar.html.
Scott, W.R. (1975), “Organizational Structure, ” Annual Review of Sociology, 1, 1–20.
Thompson, J.D. (1967), Organizations in Action. McGraw-Hill, New York.
Tiffin, J. and E.J. McCormick (1965), Industrial Psychology. Prentice-Hall, Englewood Cliffs, NJ
Williamson, O.E. (1975), Markets and Hierarchies: Analysis and Antitrust Implications. Free Press, New York.
Williamson, O.E. (1986), Economic Organization. Wheatsheaf.
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Ishida, K., Ohta, T. On a Mathematical Comparison between Hierarchy and Network with a Classification of Coordination Structures. Computational & Mathematical Organization Theory 7, 311–330 (2001). https://doi.org/10.1023/A:1013454200524
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DOI: https://doi.org/10.1023/A:1013454200524