Optimal Cyclic Exploitation of Renewable Resources

The paper contributes to the topic of optimal utilization of spatially distributed renewable resources. Namely, a problem of “sustainable” optimal cyclic exploitation of a renewable resource with logistic law of recovery is investigated. The resource is distributed on a circle and is collected by a single harvester moving along the circle. The recovering and harvesting rates are position dependent, and the latter depends also on the velocity of the harvester, which is considered as a control. The existence of an optimal solution is proved, as well as necessary optimality conditions for the velocity of the harvester. On this base, a numerical approach is proposed, and some qualitative properties of the optimal solutions are established. The results are illustrated by numerical examples, which reveal some economically meaningful features of the optimal harvesting.