Forest planners have traditionally used expected growth and yield coefficients to predict future merchantable timber volumes. However, because climate change affects forest growth, the typical forest planning methods using expected value of forest growth can lead to sub-optimal harvest decisions. In this paper, we propose to formulate the harvest planning with growth uncertainty due to climate change problem as a multistage stochastic optimization problem and use sample average approximation (SAA) as a tool for finding the best set of forest units that should be harvested in the first period even though we have a limited knowledge of what future climate will be. The objective of the harvest planning model is to maximize the expected value of the net present value (NPV) considering the uncertainty in forest growth and thus in revenues from timber harvest. The proposed model was tested on a small forest with 89 stands and the numerical results showed that the approach allows to have superior solutions in terms of net present value and robustness in face of different growth scenarios compared to the approach using the expected growth and yield. The SAA method requires to generate samples from the distribution of the random parameter. Our results suggested that a sampling scheme that focuses on generating high number of samples in distant future stages is favorable compared to having large sample sizes for the near future stages. Finally, we demonstrated that, depending on the level of forest growth change, ignoring this uncertainty can negatively affect forest resources sustainability.

中文翻译：

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气候不确定性下收获调度的多阶段样本平均逼近

传统上，森林规划师使用预期的增长和产量系数来预测未来的可交易木材量。但是，由于气候变化会影响森林生长，因此使用森林生长预期值的典型森林规划方法可能会导致次优的采伐决策。在本文中，我们建议将由于气候变化问题而具有增长不确定性的采伐计划制定为多阶段随机优化问题，并使用样本平均逼近（SAA）作为工具来寻找最佳采伐单位。即使我们对未来的气候知之甚少，第一阶段也是如此。采伐计划模型的目标是考虑到森林生长的不确定性以及木材采伐收入的不确定性，以使净现值（NPV）的期望值最大化。所提出的模型在具有89个林分的小森林上进行了测试，数值结果表明，与使用预期的增长和产量的方法相比，该方法在面对不同的生长场景时，具有净现值和稳健性方面的出色解决方案。SAA方法需要根据随机参数的分布生成样本。我们的结果表明，与在不久的将来阶段拥有大量样本相比，着重于在遥远的将来阶段产生大量样本的抽样方案是有利的。最后，我们证明，根据森林生长变化的程度，