The structure of optimal time- and age-dependent harvesting in the Lotka-McKendrik population model |
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Authors: | Hritonenko Natali Yatsenko Yuri |
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Institution: | Prairie View A&M University, Box 0519, Prairie View, TX 77446, USA. nahritonenko@pvamu.edu |
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Abstract: | The paper analyzes optimal harvesting of age-structured populations described by the Lotka-McKendrik model. It is shown that the optimal time- and age-dependent harvesting control involves only one age at natural conditions. This result leads to a new optimization problem with the time-dependent harvesting age as an unknown control. The integral Lotka model is employed to explicitly describe the time-varying age of harvesting. It is proven that in the case of the exponential discounting and infinite horizon the optimal strategy is a stationary solution with a constant harvesting age. A numeric example on optimal forest management illustrates the theoretical findings. Discussion and interpretation of the results are provided. |
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Keywords: | 92D25 49K22 45G10 37N25 91B76 |
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