A Progressive Hedging Approach to Solve Harvest Scheduling Problem under Climate Change

Due to the long time horizon typically characterizing forest planning, uncertainty plays an important role when developing forest management plans. Especially important is the uncertainty related to recently human-induced global warming since it has a clear impact on forest capacity to contribute to biogenic and anthropogenic ecosystem services. If the forest manager ignores uncertainty, the resulting forest management plan may be sub-optimal, in the best case. This paper presents a methodology to incorporate uncertainty due to climate change into forest management planning. Specifically, this paper addresses the problem of harvest planning, i.e., defining which stands are to be cut in each planning period in order to maximize expected net revenues, considering several climate change scenarios. This study develops a solution approach for a planning problem for a eucalyptus forest with 1000 stands located in central Portugal where expected future conditions are anticipated by considering a set of climate scenarios. The model including all the constraints that link all the scenarios and spatial adjacency constraints leads to a very large problem that can only be solved by decomposing it into scenarios. For this purpose, we solve the problem using Progressive Hedging (PH) algorithm, which decomposes the problem into scenario sub-problems easier to solve. To analyze the performance of PH versus the use of the extensive form (EF), we solve several instances of the original problem using both approaches. Results show that PH outperforms the EF in both solving time and final optimality gap. In addition, the use of PH allows to solve the most difficult problems while the commercial solvers are not able to solve the EF. The approach presented allows the planner to develop more robust management plans that incorporate the uncertainty due to climate change in their plans.