Maintenance of age-structured populations: Optimal control, state constraints, and bang bang regime

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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 nonlinear 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 bangbang structure with three jumps and involves buying new young individuals and selling the old ones when their anticipated future expenses exceed the profit. © 2009 World Scientific Publishing Company.

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