Long time horizons, typical of forest management, make planning more difficult due to added exposure to climate uncertainty. Current methods for stochastic programming limit the incorporation of climate uncertainty in forest management planning. To account for climate uncertainty in forest harvest scheduling, we discretize the potential distribution of forest growth under different climate scenarios and solve the resulting stochastic mixed integer program. Increasing the number of scenarios allows for a better approximation of the entire probability space of future forest growth but at a computational expense. To address this shortcoming, we propose a new heuristic algorithm designed to work well with multistage stochastic harvest-scheduling problems. Starting from the root-node of the scenario tree that represents the discretized probability space, our progressive hedging algorithm sequentially fixes the values of decision variables associated with scenarios that share the same path up to a given node. Once all variables from a node are fixed, the problem can be decomposed into subproblems that can be solved independently. We tested the algorithm performance on six forests considering different numbers of scenarios. The results showed that our algorithm performed well when the number of scenarios was large.

中文翻译：

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具有渐进式套期保值的多阶段随机程序的并行变量固定过程

长期以来（通常是森林管理），由于增加了对气候不确定性的暴露，使得规划变得更加困难。当前的随机规划方法限制了将气候不确定性纳入森林经营规划中。为了解决森林采伐计划中的气候不确定性问题，我们离散化了不同气候情景下森林生长的潜在分布，并解决了由此产生的随机混合整数程序。场景数量的增加允许更好地近似未来森林生长的整个概率空间，但要付出一定的计算费用。为了解决此缺点，我们提出了一种新的启发式算法，该算法设计用于与多阶段随机收获调度问题配合使用。从代表离散化概率空间的方案树的根节点开始，我们的渐进式对冲算法顺序固定与共享相同路径直至给定节点的方案相关的决策变量的值。一旦固定了一个节点的所有变量，就可以将问题分解为可以独立解决的子问题。考虑到场景数量不同，我们在六个森林上测试了算法性能。结果表明，当场景数量很大时，我们的算法表现良好。考虑到场景数量不同，我们在六个森林上测试了算法性能。结果表明，当场景数量很大时，我们的算法表现良好。考虑到场景数量不同，我们在六个森林上测试了算法性能。结果表明，当场景数量很大时，我们的算法表现良好。