The structure of optimal time- and age-dependent harvesting in the Lotka-McKendrik population model.
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.
Hritonenko
Natali
N
Prairie View A&M University, Box 0519, Prairie View, TX 77446, USA. nahritonenko@pvamu.edu
Yatsenko
Yuri
Y
D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D005298:Fertility; D016468:Forestry / Q000191:economics / Q000379:methods; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D013997:Time Factors