Management of a forest stand : determination of optimal thinning rate, fertilization rate and rotation age in the presence of risk of catastrophic destruction
Date
1988
Authors
Apaloo, Joseph
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Abstract
A continuous time model for determining the optimal thinning, fertilization and rotation age for a forest, and optimal expenditure and rotation age for a cocoa plantation under the assumption of catastrophic destruction are studied. The hazard is assumed to be age dependent in the first instance . The analysis is then carried over to age and volume, and age and thinning rate dependent hazards.
In each case the resulting problem is transformed appropriately to enable the use of the Pontryagin Maximum Principle of Optimal Control Theory in its solution. Both single and ongoing rotations of the stand are considered and the optimal policies can be determined using numerical iterations.
It is shown that the singular path in the thinning model for the age dependent hazard satisfies an implicit equation. In the cases of age and volume, age and thinning rate dependent hazards, the singular paths satisfy ordinary differential equations which can be solved for given boundary conditions. Similarly optimal fertilization under age, age and volume dependent hazards are shown to obey ordinary differential equations which again could be solved for given boundary conditions. In the cocoa plantation problem, an implicit equation for the optimal accumulated expenditure is derived; from this one can obtain the optimal expenditure for the treatment of the plantation.
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UN SDG 15: Life on Land