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

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.

[1]  Alexander Mehlmann,et al.  The Recruitment Trajectory Corresponding to Particular Stock Sequences in Markovian Person-Flow Models , 1976, Math. Oper. Res..

[2]  J. Caulkins,et al.  Optimal Control of Nonlinear Processes: With Applications in Drugs, Corruption, and Terror , 2008 .

[3]  Österreichische Akademie der Wissenschaften.  Vienna yearbook of population research , 2003 .

[4]  Nan Li,et al.  Immigration and the dependency ratio of a host population , 2003 .

[5]  Gustav Feichtinger,et al.  Age-structured optimal control in population economics. , 2004, Theoretical population biology.

[6]  W. R. Buckland,et al.  Stochastic Models for Social Processes , 1967 .

[7]  S. Mitra.  Immigration, below-replacement fertility, and long-term national population trends , 2010, Demography.

[8]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[9]  Henri Leridon,et al.  The Demography of a Learned Society: the Académie des Sciences (Institut de France), 1666-2030 , 2004 .

[10]  Joel E. Cohen.  The Demography of the Resident Membership of the American Philosophical Society , 2009 .

[11]  Wenwu Cao,et al.  Applied Numerical Methods Using MATLAB®: Yang/Applied Numerical MATLAB , 2005 .

[12]  James W. Vaupel.  Over-Tenured Universities: The Mathematics of Reduction , 1981 .

[13]  W B Arthur,et al.  Optimal time paths with age-dependence: a theory of population policy. , 1977, The Review of economic studies.

[14]  Sung Joo Park,et al.  OPTIMAL-CONTROL OF PROMOTION AND RECRUITMENT IN A HIERARCHICALLY GRADED MANPOWER SYSTEM , 1985 .

[15]  Maria Winkler-Dworak,et al.  The Low Mortality of a Learned Society , 2008, Institut für Demographie - VID.

[16]  Wŏn-yŏng Yang,et al.  Applied Numerical Methods Using MATLAB , 2005 .

[17]  Gustav Feichtinger,et al.  Immigration into a Population with Fertility below Replacement Level – The Case of Germany , 1992 .

[18]  Vladimir M. Veliov,et al.  Keeping a learned society young , 2009 .

[19]  Vladimir M. Veliov,et al.  On a Distributed Control Problem Arising in Dynamic Optimization of a Fixed-Size Population , 2007, SIAM J. Optim..

[20]  D. J. van de Kaa,et al.  The members of the Royal Netherlands Academy of Arts and Sciences, 1808 to 2000: a demographic view , 2007 .

[21]  Barbara Lee Keyfitz,et al.  The McKendrick partial differential equation and its uses in epidemiology and population study , 1997 .

[22]  D. Bartholomew,et al.  Stochastic Models for Social Processes. , 1970 .

[23]  M. L. Chambers.  The Mathematical Theory of Optimal Processes , 1965 .

[24]  T. Trussell,et al.  Applied Mathematical Demography. , 1978 .

[25]  Carl P. Schmertmann.  Immigrants’ ages and the structure of stationary populations with below-replacement fertility , 2011, Demography.

[26]  Louis Henry.  Perspectives d'évolution du personnel d'un corps , 1975 .

[27]  Vladimir M. Veliov,et al.  Optimality conditions for age-structured control systems☆ , 2003 .

[28]  P. Hartman.  Ordinary Differential Equations , 1965 .

[29]  John Glen,et al.  A model for promotion rate control in hierarchical manpower systems , 1996 .

[30]  Vladimir M. Veliov,et al.  Age-specific dynamic labor demand and human capital investment , 2007 .