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Mathematical models of formation of rational organizational hierarchies

  • Control in Social Economic Systems
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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.

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References

  1. Elektronnyi slovar’ (Electronic Glossary) (http://www.glossary.ru).

  2. Filosofskii entsiklopedicheskii slovar’ (Philosophical Encyclopaedia), L.F. Il’ichev, P.N. Fedoseev, S.M. Kovalev, and V.G. Panov, Eds., Moscow: Sovetskaya Entsiklopediya, 1983.

    Google Scholar 

  3. Gubko, M.V., Matematicheskie modeli optimizatsii ierarkhicheskikh struktur (Mathematical Models of Hierarchical Structures Optimization), Moscow: LENAND, 2006.

    Google Scholar 

  4. Ovsievich, B.L., Modeli formirovaniya organizatsionnykh struktur (Models of Formation of Organizational Structures), Leningrad: Nauka, 1979.

    Google Scholar 

  5. Tsvirkun, A.D., Osnovy sinteza struktury slozhnykh sistem (Synthesis of the Structure of Complex Systems), Moscow: Nauka, 1982.

    Google Scholar 

  6. 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.

    Google Scholar 

  7. Mintzberg, H., The Structuring of Organizations, Englewood Cliffs: Prentice-Hall, 1979. Translated under the title Struktura v kulake: sozdanie effektivnoi organizatsii, Moscow: Piter, 2001.

    Google Scholar 

  8. 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.

  9. Radner, R., Hierarchy: The Economics of Managing, J. Econom. Lit., 1992, vol. 30, no. 3, pp. 1382–1415.

    Google Scholar 

  10. 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.

  11. Simon, H.A., The Compensation of Executives, Sociometry, 1957, vol. 20, no. 1, pp. 32–35.

    Article  Google Scholar 

  12. Knight, F.H., Risk, Uncertainty and Profit, Boston: Houghton Mifflin, 1921.

    Google Scholar 

  13. Kaldor, N., The Equilibrium of the Firm, Econom. J., 1934, vol. 44, no. 173, pp. 60–76.

    Google Scholar 

  14. Robinson, A., The Problem of Management and the Size of Firms, Econom. J., 1934, vol. 44, no. 174, pp. 242–257.

    Google Scholar 

  15. Coase, R.H.,The Nature of the Firm, Economica, New Ser., 1937, vol. 4, no. 16, pp. 386–405.

  16. Beckmann, M.J., Some Aspects of Returns to Scale in Business Administration, Quarterly J. Econom., 1960, vol. 74, no. 3, pp. 464–471.

    Article  Google Scholar 

  17. Williamson, O., Hierarchical Control and Optimal Firm Size, J. Polit. Econom., 1967, vol. 75, no. 2, pp. 123–138.

    Article  MathSciNet  Google Scholar 

  18. Mirrlees, J.A., The Optimal Structure of Incentives and Authority within an Organization, Bell J. Econom., 1976, vol. 7, no. 1, pp. 105–131.

    Article  MathSciNet  Google Scholar 

  19. Calvo, G.A., Supervision, and Utility and Wage Differentials across Firms, Columbia Univ. Econ. Workshop, 1977, discussion paper no. 76-7711.

  20. 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.

    Article  Google Scholar 

  21. Williamson, O., Markets and Hierarchies, New York: Free Press, 1975.

    Google Scholar 

  22. 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.

    Article  Google Scholar 

  23. Qian, Y., Incentives and Loss of Control in an Optimal Hierarchy, Rev. Econom. Stud., 1994, vol. 61, no. 3, pp. 527–544.

    Article  MATH  Google Scholar 

  24. Van Zandt, T., Continuous Approximation in the Study of Hierarchies, RAND J. Econom., 1995, vol. 26, no. 4, pp. 575–590.

    Article  Google Scholar 

  25. Rosen, S., Authority, Control, and the Distribution of Earnings, Bell J. Econom., 1982, vol. 13, no. 2, pp. 311–323.

    Article  Google Scholar 

  26. Mikhailov, A.P., Model of Corrupt Power Hierarchies, Mat. Model., 1999, vol. 11, no. 1, pp. 3–17.

    MathSciNet  Google Scholar 

  27. 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.

    Google Scholar 

  28. Hayek, F.A. von., The Use of Knowledge in Society, Am. Econom. Rev., 1945, vol. 35, pp. 519–530.

    Google Scholar 

  29. Garicano, L., Hierarchies and Organization of Knowledge in Production, J. Polit. Econom., 2000, vol. 108, no. 5, pp. 874–904.

    Article  Google Scholar 

  30. Beggs, A.W., Queues and Hierarchies, Rev. Econom. Stud., 2001, vol. 68, no. 2, pp. 297–322.

    Article  MATH  MathSciNet  Google Scholar 

  31. Kleinrock, L., Queueing Systems, New York: Wiley, 1975. Translated under the title Teoriya massovogo obsluzhivaniya, Moscow: Mashinostroenie, 1979.

    MATH  Google Scholar 

  32. Marschak, T.A. and Reichelstein, S., Network Mechanisms, Information Efficiencies and the Role Of Hierarchies, Unpub. Ms. Grad. Sch. Bus. Administr., Stanford Univ., 1987.

  33. Radner, R., The Organization of Decentralized Information Processing, Econometrica, 1993, vol. 61, no. 5, pp. 1109–1146.

    Article  MATH  Google Scholar 

  34. Van Zandt, T., Efficient Parallel Addition, Unpub. Ms. AT&T Bell Lab., Murray Hill, 1990.

  35. Radner, R. and Van Zandt, T., Information Processing in Firms and Returns to Scale, An. Econom. Stat., 1992, vols. 25/26, pp. 265–268.

    Google Scholar 

  36. Van Zandt, T., Hierarchical Computation of the Resource Allocation Problem, Mimeo, 1994.

  37. Bolton, P. and Dewatripont, M., The Firm as a Communication Network, Quarterly J. Econom., 1994, vol. 109, no. 4, pp. 809–839.

    Article  MATH  Google Scholar 

  38. Marschak, T.A. and Radner, R., Economic Theory of Teams, New Haven: Yale Univ. Press, 1972.

    MATH  Google Scholar 

  39. Myerson, R.B., Game Theory: Analysis of Conflict, London: Harvard Univ. Press, 1991.

    MATH  Google Scholar 

  40. Gubko, M.V. and Novikov, D.A., Teoriya igr v upravlenii organizatsionnymi sistemami (Game Theory in Controlling Organizational Systems), Moscow: Sinteg, 2002.

    Google Scholar 

  41. Cremer, J., A Partial Theory of the Optimal Organization of a Bureaucracy, Bell J. Econom., 1980, vol. 11, no. 2, pp. 683–693.

    Article  Google Scholar 

  42. Aoki, M., Horizontal vs. Vertical Information Structure of the Firm, Am. Econom. Rev., 1986, vol. 76, no. 5, pp. 971–983.

    MathSciNet  Google Scholar 

  43. 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.

    Article  Google Scholar 

  44. Gautier, A. and Paolini, D., Delegation and Organizational Design, Mimeo. IRES and UCL, 2001.

  45. 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.

    Google Scholar 

  46. Sah, R.K. and Stiglitz, J.E., Committees, Hierarchies and Polyarchies, Econom. J., 1988, vol. 98, no. 391, pp. 451–470.

    Google Scholar 

  47. 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.

    Article  MathSciNet  Google Scholar 

  48. Ioannides, Y., Compexity and Organizational Architecture, Working Paper, Dep. of Econom., Taft Univ., 2003.

  49. Hart, O. and Moore, J., On the Design of Hierarchies: Coordination vs Specialization, J. Polit. Econom., 2005, vol. 113, pp. 675–702.

    Article  Google Scholar 

  50. Bolton, P. and Dewatripont, M., Contract Theory, Cambridge: MIT Press, 2005.

    Google Scholar 

  51. Burkov, V.N. and Novikov, D.A., Teoriya aktivnykh sistem: sostoyanie i perspectivy (Theory of Active Systems State and Prospects), Moscow: SINTEG, 1999.

    Google Scholar 

  52. 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.

    Google Scholar 

  53. Melumad, D.N., Mookherjee, D., and Reichelstein, S., Hierarchical Decentralization of Incentive Contracts, RAND J. Econom., 1995, vol. 26, no. 4, pp. 654–672.

    Article  Google Scholar 

  54. Myerson, R.B., Optimal Coordination Mechanisms in Generalized Principal-Agent Problem, J. Math. Econom., 1982, no. 10, pp. 67–81.

  55. 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.

    Article  Google Scholar 

  56. 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.

  57. Maskin, E., Qian, Y., and Xu, C., Incentives, Information and Organizational Form, Rev. Econom. Stud., 2000, no. 67(2), pp. 359–378.

  58. Qian, Y., Roland, G., and Xu, C., Coordinating Changes in M-form and U-form Organizations, Mimeo, 1997.

  59. Mishin, S.P., Optimal’nye ierarkhii upravleniya v ekonomicheskikh sistemakh (Optimal Hierarchies of Control in Economic Systems), Moscow: PMSOFT, 2004.

    Google Scholar 

  60. Harris, M. and Raviv, A., Organization Design, Mimeo, 2000.

  61. Novikov, D.A., Setevye struktury i organizatsionnye sistemy (Network Structures and Organizational Systems), Moscow: Inst. Problem Upravlen., 2003.

    Google Scholar 

  62. Germeier, Yu.B., Igry c neprotivopolozhnymi interesami (Games with Non-antagonistic Interest) Moscow: Nauka, 1976.

    Google Scholar 

  63. Novikov, D.A., Mekhanizmy funktsionirovaniya mnogourovnevykh organizatsionnykh sistem (Mechanisms of Performance of Multilevel Organizational Systems), Moscow: Fond “Problemy Upravleniya,” 1999.

    Google Scholar 

  64. 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.

  65. 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.

  66. Voronin, A.A. and Mishin, S.P., Optimal’nye ierarkhicheski struktury (Optimal Hierarchial Structures), Moscow: Inst. Problem Upravlen., 2003.

    Google Scholar 

  67. Mishin, S.P., Optimal Controllability Norm for the Power Cost Function, Avtom. Telemekh., 2006, no. 8, pp. 154–168.

  68. Gubko, M.V., The Search for Optimal Organizational Hierarchies with Homogeneous Manager Cost Functions, Avtom. Telemekh., 2008, no. 1, pp. 97–113.

  69. 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.

    Article  Google Scholar 

  70. Zhou, X., CEO Pay, Firm Size, and Corporate Performance: Evidence from Canada, Canad. J. Econom., 2000, vol. 33, no. 1, pp. 213–251.

    Article  Google Scholar 

  71. 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.

    Google Scholar 

  72. 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.

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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.

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Gubko, M.V. Mathematical models of formation of rational organizational hierarchies. Autom Remote Control 69, 1552–1575 (2008). https://doi.org/10.1134/S0005117908090105

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