In this paper, we consider the problem of sustainable harvesting. We explain how the manager maximizes his/her profit according to the quantity of natural resource available in a harvesting area and under the constraint of penalties and fines when the quota is exceeded. We characterize the optimal values and some optimal strategies using a verification result. We then show by numerical examples that this optimal strategy is better than naive ones. Moreover, we define a level of fines which insures the double objective of the sustainable harvesting: a remaining quantity of available natural resource to insure its sustainability and an acceptable income for the manager.

在本文中，我们考虑可持续采伐的问题。我们解释了管理者如何根据采伐地区可用的自然资源数量以及在超过配额时的处罚和罚款的约束下最大化他/她的利润。我们使用验证结果来描述最优值和一些最优策略。然后，我们通过数值示例证明这种最优策略比朴素策略更好。此外，我们定义了一定的罚款水平，以确保可持续采伐的双重目标：确保其可持续性的可用自然资源的剩余数量和管理者可接受的收入。