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. © 2006 Elsevier Inc. All rights reserved.
Hritonenko, N., & Yatsenko, Y. (2007). The structure of optimal time- and age-dependent harvesting in the Lotka-McKendrik population model. Retrieved from https://digitalcommons.pvamu.edu/mathematics-facpubs/74