Abstract
A survey of Russian and foreign papers devoted to one of the burning trends of the theory of control of social and economic systems, i.e., mathematical models of formational of rational organization hierarchies is made. The following lines of investigations are emphasized: multilevel symmetrical hierarchies, hierarchies of knowledge, multilevel hierarchies of data processing, hierarchies and command theory, hierarchies of decision-making, hierarchies and contracts theory, and general model of optimal hierarchies search.
Similar content being viewed by others
References
Elektronnyi slovar’ (Electronic Glossary) (http://www.glossary.ru).
Filosofskii entsiklopedicheskii slovar’ (Philosophical Encyclopaedia), L.F. Il’ichev, P.N. Fedoseev, S.M. Kovalev, and V.G. Panov, Eds., Moscow: Sovetskaya Entsiklopediya, 1983.
Gubko, M.V., Matematicheskie modeli optimizatsii ierarkhicheskikh struktur (Mathematical Models of Hierarchical Structures Optimization), Moscow: LENAND, 2006.
Ovsievich, B.L., Modeli formirovaniya organizatsionnykh struktur (Models of Formation of Organizational Structures), Leningrad: Nauka, 1979.
Tsvirkun, A.D., Osnovy sinteza struktury slozhnykh sistem (Synthesis of the Structure of Complex Systems), Moscow: Nauka, 1982.
Dement’ev, V.T., Erzin, A.I., Larin, R.M., et al., Zadachi optimizatsii ierarkhicheskikh struktur (Problems of Hierarchical Structures Optimization), Novosibirsk: Novosib. Univ., 1996.
Mintzberg, H., The Structuring of Organizations, Englewood Cliffs: Prentice-Hall, 1979. Translated under the title Struktura v kulake: sozdanie effektivnoi organizatsii, Moscow: Piter, 2001.
Gubko, M.V., Korgin, N.A., and Novikov, D.A., Classification of Models of Analysis and Synthesis of Organizational Structures, Upravlen. Bol’sh. Sist., 2004, no. 6, pp. 5–21.
Radner, R., Hierarchy: The Economics of Managing, J. Econom. Lit., 1992, vol. 30, no. 3, pp. 1382–1415.
Garicano, L. and Hubbard, T.N., Hierarchies, Specialization, and the Utilization of Knowledge: Theory and Evidence from the Legal Services Industry, NBER Working Paper, 2004, no. 10432.
Simon, H.A., The Compensation of Executives, Sociometry, 1957, vol. 20, no. 1, pp. 32–35.
Knight, F.H., Risk, Uncertainty and Profit, Boston: Houghton Mifflin, 1921.
Kaldor, N., The Equilibrium of the Firm, Econom. J., 1934, vol. 44, no. 173, pp. 60–76.
Robinson, A., The Problem of Management and the Size of Firms, Econom. J., 1934, vol. 44, no. 174, pp. 242–257.
Coase, R.H.,The Nature of the Firm, Economica, New Ser., 1937, vol. 4, no. 16, pp. 386–405.
Beckmann, M.J., Some Aspects of Returns to Scale in Business Administration, Quarterly J. Econom., 1960, vol. 74, no. 3, pp. 464–471.
Williamson, O., Hierarchical Control and Optimal Firm Size, J. Polit. Econom., 1967, vol. 75, no. 2, pp. 123–138.
Mirrlees, J.A., The Optimal Structure of Incentives and Authority within an Organization, Bell J. Econom., 1976, vol. 7, no. 1, pp. 105–131.
Calvo, G.A., Supervision, and Utility and Wage Differentials across Firms, Columbia Univ. Econ. Workshop, 1977, discussion paper no. 76-7711.
Calvo, G.A. and Wellisz, S., Supervision, Loss of Control and the Optimal Size of the Firm, J. Politic. Econom., 1978, vol. 86, no. 5, pp. 943–952.
Williamson, O., Markets and Hierarchies, New York: Free Press, 1975.
Keren, M. and Levhari, D., The Internal Organization of the Firm and the Shape of Average Costs, Bell J. Econom., 1983, vol. 14, no. 2, pp. 474–486.
Qian, Y., Incentives and Loss of Control in an Optimal Hierarchy, Rev. Econom. Stud., 1994, vol. 61, no. 3, pp. 527–544.
Van Zandt, T., Continuous Approximation in the Study of Hierarchies, RAND J. Econom., 1995, vol. 26, no. 4, pp. 575–590.
Rosen, S., Authority, Control, and the Distribution of Earnings, Bell J. Econom., 1982, vol. 13, no. 2, pp. 311–323.
Mikhailov, A.P., Model of Corrupt Power Hierarchies, Mat. Model., 1999, vol. 11, no. 1, pp. 3–17.
Mikhailov, A.P. and Savel’ev, A.V., Justification of Macromodels of Power Hierarchies through Their Microdescription, Mat. Model., 2001, vol. 13, no. 4, pp. 19–34.
Hayek, F.A. von., The Use of Knowledge in Society, Am. Econom. Rev., 1945, vol. 35, pp. 519–530.
Garicano, L., Hierarchies and Organization of Knowledge in Production, J. Polit. Econom., 2000, vol. 108, no. 5, pp. 874–904.
Beggs, A.W., Queues and Hierarchies, Rev. Econom. Stud., 2001, vol. 68, no. 2, pp. 297–322.
Kleinrock, L., Queueing Systems, New York: Wiley, 1975. Translated under the title Teoriya massovogo obsluzhivaniya, Moscow: Mashinostroenie, 1979.
Marschak, T.A. and Reichelstein, S., Network Mechanisms, Information Efficiencies and the Role Of Hierarchies, Unpub. Ms. Grad. Sch. Bus. Administr., Stanford Univ., 1987.
Radner, R., The Organization of Decentralized Information Processing, Econometrica, 1993, vol. 61, no. 5, pp. 1109–1146.
Van Zandt, T., Efficient Parallel Addition, Unpub. Ms. AT&T Bell Lab., Murray Hill, 1990.
Radner, R. and Van Zandt, T., Information Processing in Firms and Returns to Scale, An. Econom. Stat., 1992, vols. 25/26, pp. 265–268.
Van Zandt, T., Hierarchical Computation of the Resource Allocation Problem, Mimeo, 1994.
Bolton, P. and Dewatripont, M., The Firm as a Communication Network, Quarterly J. Econom., 1994, vol. 109, no. 4, pp. 809–839.
Marschak, T.A. and Radner, R., Economic Theory of Teams, New Haven: Yale Univ. Press, 1972.
Myerson, R.B., Game Theory: Analysis of Conflict, London: Harvard Univ. Press, 1991.
Gubko, M.V. and Novikov, D.A., Teoriya igr v upravlenii organizatsionnymi sistemami (Game Theory in Controlling Organizational Systems), Moscow: Sinteg, 2002.
Cremer, J., A Partial Theory of the Optimal Organization of a Bureaucracy, Bell J. Econom., 1980, vol. 11, no. 2, pp. 683–693.
Aoki, M., Horizontal vs. Vertical Information Structure of the Firm, Am. Econom. Rev., 1986, vol. 76, no. 5, pp. 971–983.
Geanakoplos, J. and Milgrom, P., A Theory of Hierarchies Based on Limited Managerial Attention, J. Japan. Int. Econom., 1991, vol. 5(3), pp. 205–225.
Gautier, A. and Paolini, D., Delegation and Organizational Design, Mimeo. IRES and UCL, 2001.
Sah, R.K. and Stiglitz, J.E., The Architecture of Economic Systems: Hierarchies and Polyarchies, Am. Econom. Rev., 1986, vol. 76, no. 4, pp. 716–727.
Sah, R.K. and Stiglitz, J.E., Committees, Hierarchies and Polyarchies, Econom. J., 1988, vol. 98, no. 391, pp. 451–470.
Sah, R.K. and Stiglitz, J.E., The Quality of Managers in Centralized Versus Decentralized Organizations, Quart. J. Econom., 1991, vol. 106, no. 1, pp. 289–295.
Ioannides, Y., Compexity and Organizational Architecture, Working Paper, Dep. of Econom., Taft Univ., 2003.
Hart, O. and Moore, J., On the Design of Hierarchies: Coordination vs Specialization, J. Polit. Econom., 2005, vol. 113, pp. 675–702.
Bolton, P. and Dewatripont, M., Contract Theory, Cambridge: MIT Press, 2005.
Burkov, V.N. and Novikov, D.A., Teoriya aktivnykh sistem: sostoyanie i perspectivy (Theory of Active Systems State and Prospects), Moscow: SINTEG, 1999.
Kononeko, A.F., Khalezov, A.D., and Chumakov, V.V., Prinyatie reshenii v usloviyakh neopredelennosti (Decision-making under Uncertainty), Moscow: VTs Akad. Nauk SSSR, 1991.
Melumad, D.N., Mookherjee, D., and Reichelstein, S., Hierarchical Decentralization of Incentive Contracts, RAND J. Econom., 1995, vol. 26, no. 4, pp. 654–672.
Myerson, R.B., Optimal Coordination Mechanisms in Generalized Principal-Agent Problem, J. Math. Econom., 1982, no. 10, pp. 67–81.
Macho-Stadler, I. and Perez-Castrillo, J.D., Centralized and Decentralized Contracts in a Moral Hazard Environment, J. Indust. Econom., 1998, vol. 46, no. 4, pp. 489–510.
Holmstrom, B. and Milgrom, P., Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design, J. Law. Econom., Organizat., 1991, no. 7 (special issue), pp. 24–52.
Maskin, E., Qian, Y., and Xu, C., Incentives, Information and Organizational Form, Rev. Econom. Stud., 2000, no. 67(2), pp. 359–378.
Qian, Y., Roland, G., and Xu, C., Coordinating Changes in M-form and U-form Organizations, Mimeo, 1997.
Mishin, S.P., Optimal’nye ierarkhii upravleniya v ekonomicheskikh sistemakh (Optimal Hierarchies of Control in Economic Systems), Moscow: PMSOFT, 2004.
Harris, M. and Raviv, A., Organization Design, Mimeo, 2000.
Novikov, D.A., Setevye struktury i organizatsionnye sistemy (Network Structures and Organizational Systems), Moscow: Inst. Problem Upravlen., 2003.
Germeier, Yu.B., Igry c neprotivopolozhnymi interesami (Games with Non-antagonistic Interest) Moscow: Nauka, 1976.
Novikov, D.A., Mekhanizmy funktsionirovaniya mnogourovnevykh organizatsionnykh sistem (Mechanisms of Performance of Multilevel Organizational Systems), Moscow: Fond “Problemy Upravleniya,” 1999.
Voronin, A.A. and Mishin, S.P., Modelling the Structure of an Organizational System. On the Algorithms to Seek the Optimal Tree, Vestn. VolGU, Ser. 1: Mat. Fiz., 2001, pp. 78–98.
Voronin, A.A. and Mishin, S.P., Algorithms to Seek the Optimal Structure of the Organizational System, Avtom. Telemekh., 2002, no. 5, pp. 120–132.
Voronin, A.A. and Mishin, S.P., Optimal’nye ierarkhicheski struktury (Optimal Hierarchial Structures), Moscow: Inst. Problem Upravlen., 2003.
Mishin, S.P., Optimal Controllability Norm for the Power Cost Function, Avtom. Telemekh., 2006, no. 8, pp. 154–168.
Gubko, M.V., The Search for Optimal Organizational Hierarchies with Homogeneous Manager Cost Functions, Avtom. Telemekh., 2008, no. 1, pp. 97–113.
Roberts, D.R., A General Theory of Executives Compensation Based on Statistically Tested Propositions, Quarterly J. Econom., 1956, vol. 70, no. 2, pp. 270–294.
Zhou, X., CEO Pay, Firm Size, and Corporate Performance: Evidence from Canada, Canad. J. Econom., 2000, vol. 33, no. 1, pp. 213–251.
Gubko, M.V. and Mishin, S.P., Optimal Structure of the System of Control of Technological Communications, Materialy mezhdunarodnoi konferentsii “Sovremennye slozhnye sistemy upravleniya” (Proc. Int. Conf. “Modern Complex Control Systems”), Stary Oskol: STI, 2002, pp. 50–54.
Voronin, A.A. and Mishin, S.P., A Model of Optimal Control of Structural Changes in an Organizational Systems, Avtom. Telemekh., 2002, no. 8, pp. 136–150.
Author information
Authors and Affiliations
Additional information
Original Russian Text © M.V. Gubko, 2008, published in Avtomatika i Telemekhanika, 2008, No. 9, pp. 114–139.
This work was supported by the Russian Foundation for Basic Research, project no. 07-07-00078-a.
Rights and permissions
About this article
Cite this article
Gubko, M.V. Mathematical models of formation of rational organizational hierarchies. Autom Remote Control 69, 1552–1575 (2008). https://doi.org/10.1134/S0005117908090105
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117908090105