Maintenance of Age-structured Populations: Optimal Control, State Constraints, and Bang-bang Regime

Hritonenko, Natali;Yatsenko, Yuri
(2009) Journal of Biological Systems — Vol. 17, n° 4, p. 793-816 (2009)

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  • Hritonenko, NataliDepartment of Mathematics, Prairie View A&M University, P.O. Box 519-MS 2225, Prairie View, Texas 77446-0519, USA
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  • Yatsenko, YuriUCLouvain
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Abstract
The paper analyzes the optimal maintenance of a "fully manageable" biological population with no natural reproduction. Examples of such populations include dairy farms, horse breeding, gardening, and forestry. Mathematically, the problem leads to the non-linear optimal control of a first-order partial differential equation with pointwise state constraints. A necessary extremum condition is proven using the abstract optimization theory in Banach spaces. It is shown that the optimal dynamics has a bang-bang structure with three jumps and involves buying new young individuals and selling the old ones when their anticipated future expenses exceed the profit.
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Hritonenko, N., & Yatsenko, Y. (2009). Maintenance of Age-structured Populations: Optimal Control, State Constraints, and Bang-bang Regime. Journal of Biological Systems, 17(4), 793-816. https://doi.org/10.1142/S0218339009003034 (Original work published 2009)