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The mathematics of ageing:

Author

Listed:
  • Gustav Feichtinger

    (Vienna University of Technology
    Vienna Institute of Demography, Austrian Academy of Sciences)

  • Dieter Grass

    (Vienna University of Technology)

  • Maria Winkler-Dworak

    (Vienna Institute of Demography, Austrian Academy of Sciences)

Abstract

Age is a crucial variable in social sciences and particularly in population dynamics. In this paper, we link methods from formal demography and Operations Research to investigate age-structured models to study the greying of academia. As scientific productivity is usually found to decrease at advanced ages, there was a vivid discussion on the ageing among tenured professors and faculty staff of universities. We investigate population ageing in academia from two perspectives. First, we propose a two-state optimal control model to explain the substantial variations of scientific production over the life cycle of researchers. We identify conditions under which typical hump-shaped age-specific patterns of scientific production turn out to be optimal for individual researchers. The second part of the paper deals with the dynamics of the age structure of scientific institutions. Similar to the university professors, many European learned societies experienced a rapid ageing of their member population, where they face the dilemma that keeping young, i.e. electing young entrants, has the drawback of reducing the replacement rate of members. It turns out that electing a mix of young and old members delivers the optimal solution of the problem, i.e. guaranteeing a young age structure, while ensuring a high recruitment rate.

Suggested Citation

  • Gustav Feichtinger & Dieter Grass & Maria Winkler-Dworak, 2020. "The mathematics of ageing:," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 371-399, June.
    • Handle: RePEc:spr:cejnor:v:28:y:2020:i:2:d:10.1007_s10100-019-00661-w
    DOI: 10.1007/s10100-019-00661-w
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    References listed on IDEAS

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    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, September.
    2. Maria Winkler-Dworak & Heiner Kaden, 2013. "The longevity of academicians: evidence from the Saxonian Academy of Sciences and Humanities in Leipzig," Vienna Yearbook of Population Research, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna, vol. 11(1), pages 185-204.
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    Cited by:

    1. Reinhard Neck, 2020. "CEJOR special issue: dynamic optimization in management and economics," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 367-369, June.
    2. Christian Stummer & Ayşegül Engin, 2021. "A tribute to Rudolf Vetschera," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(1), pages 1-6, March.

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