Central European Journal of Operations Research

, Volume 20, Issue 4, pp 649–677 | Cite as

Optimal age-specific election policies in two-level organizations with fixed size

  • Gustav Feichtinger
  • Andrey A. KrasovskiiEmail author
  • Alexia Prskawetz
  • Vladimir M. Veliov
Original Paper


Many organizations—faculties, firms, political bodies, societies, national academies—have recently been faced with the problem of aging. These trends are caused by increasing longevity of the members of these organizations as well as a lower intake at younger ages. The aging problem is particularly pronounced in organizations of fixed size, where no dismissal due to age (up to a statutory “retirement” age) is acceptable. Attenuating the aging process in a fixed-size organization by recruiting more young people leads to another adverse effect: the number of recruitments will decline, so the chances to be recruited decrease. For multi-level organizations transition flows between the levels and recruitment at different levels complicate the aforementioned problems. In this paper we present a methodology that can help design election policies based on different objective functions related to the age structure and size of two-level organizations, without compromising too much the already established election criteria. Technically, this methodology is based on multi-objective optimization making use of optimal control theory. The current election policies for both full and corresponding members of the Austrian Academy of Sciences constitute the benchmark with which we compare our results based on alternative objective functions.


OR in manpower planning Control Human resources Age dynamics of learned societies Pontryagin’s maximum principle 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arnold VI (1992) Ordinary differential equations, 3rd edn. Springer, BerlinGoogle Scholar
  2. Arthur WB, McNicoll G (1977) Optimal time paths with age-dependence: a theory of population policy. Rev Econ Stud 44: 111–123CrossRefGoogle Scholar
  3. Bartholomew DJ (1982) Stochastic models for social processes, 3rd edn. Wiley, LondonGoogle Scholar
  4. Chung SK, Park SJ (1996) Optimal control of promotion and recruitment in a hierarchically graded manpower system. IMA J Manag Math 7(3): 197–206CrossRefGoogle Scholar
  5. Cohen JE (2003) How many members could the National Academy of Sciences have? Mimeo. Rockefeller University and Columbia University, New YorkGoogle Scholar
  6. Cohen JE (2009) The demography of the resident membership of the American philosophical society. In: Proceeding of the American Philosophical Society, vol 153, no. 2. Philadelphia, USAGoogle Scholar
  7. Dawid H, Feichtinger G, Goldstein JR, Veliov VM (2009) Keeping a learned society young. Demogr Res 20: 541–558CrossRefGoogle Scholar
  8. Feichtinger G, Mehlmann A (1976) The recruitment trajectory corresponding to particular stock sequences in Markovian person-flow models. Math Oper Res 1: 175–184CrossRefGoogle Scholar
  9. Feichtinger G, Steinmann G (1992) Immigration into a population with fertility below replacement level—the case of Germany. Popul Stud 46: 275–284CrossRefGoogle Scholar
  10. Feichtinger G, Tragler G, Veliov VM (2003) Optimality conditions for age-structured control systems. J Math Anal Appl 288: 47–68CrossRefGoogle Scholar
  11. Feichtinger G, Prskawetz A, Veliov VM (2004) Age-structured optimal control in population economics. Theor Popul Biol 65: 373–387CrossRefGoogle Scholar
  12. Feichtinger G, Winkler-Dworak M, Freund I, Prskawetz A (2007) Age dynamics and optimal recruitment policies of constant sized organizations. An application to the Austrian Academy of Sciences. In: Lutz W (eds) Vienna yearbook of population research. Austrian Academy of Sciences, Vienna, pp 107–131Google Scholar
  13. Feichtinger G, Veliov VM (2007) On a distributed control problem arising in dynamic optimization of a fixed-size population. SIAM J Optim 18(3): 980–1003CrossRefGoogle Scholar
  14. Grass D, Caulkins JP, Feichtinger G, Tragler G, Behrens DA (2008) Optimal control of nonlinear processes with applications in drugs, corruption, and terror. Springer, BerlinGoogle Scholar
  15. Henry L (1975) Perspectives d’evolution d’un corps. Popul 30: 241–270CrossRefGoogle Scholar
  16. Keyfitz N (1977) Applied mathematical demography. Wiley, New YorkGoogle Scholar
  17. Keyfitz BL, Keyfitz N (1997) The McKendrick partial differential equation and its uses in epidemiology and population study. Math Comput Model 26(6): 1–9CrossRefGoogle Scholar
  18. Leridon H (2004) The demography of a learned society. The Académie des Sciences (Institut de France). Popul 59(1): 81–114Google Scholar
  19. Mitra S (1990) Immigration, below-replacement fertility, and long-term national population trends. Demography 27: 121–129CrossRefGoogle Scholar
  20. Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mischenko EF (1962) The mathematical theory of optimal processes. Interscience, New YorkGoogle Scholar
  21. Prskawetz A, Veliov V (2007) Age specific dynamic labor demand and human capital investment. J Econ Dyn Control 31: 3741–3777CrossRefGoogle Scholar
  22. Schmertmann CP (1992) Immigrants’ ages and the structure of stationary populations with below replacement fertility. Demography 29(3): 595–612CrossRefGoogle Scholar
  23. Van de Kaa DJ, de Roo Y (2007) The members of the Royal Netherlands Academy of Arts and Sciences: 1808 to 2000. A demographic view. NIDI Working Paper, The Hague, NIDIGoogle Scholar
  24. Vaupel JW (1981) Over-tenured universities: the mathematics of reduction. Manag Sci 27(8): 904–913CrossRefGoogle Scholar
  25. Winkler-Dworak M (2008) The low mortality of a learned society. Eur J Popul 24(4): 405–424CrossRefGoogle Scholar
  26. Wu Z, Li N (2003) Immigration and the dependency ratio of a host population. Math Popul Stud 10: 21–39CrossRefGoogle Scholar
  27. Yang WY, Cao W, Chung T-S, Morris J (2005) Applied numerical methods using MATLAB. Wiley, New YorkCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Gustav Feichtinger
    • 1
    • 2
  • Andrey A. Krasovskii
    • 2
    • 3
    Email author
  • Alexia Prskawetz
    • 2
    • 4
  • Vladimir M. Veliov
    • 1
  1. 1.Institute of Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria
  2. 2.Vienna Institute of DemographyAustrian Academy of SciencesViennaAustria
  3. 3.Institute of Mathematics and MechanicsUral Branch of Russian Academy of SciencesEkaterinburgRussia
  4. 4.Institute of Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria

Personalised recommendations