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

Abstract

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.

Multistage Sample Average Approximation for Harvest Scheduling under Climate Uncertainty

“…Indeed, the stochastic solution is robust to different climate scenario whereas, the deterministic one is infeasible to many of the tested climate scenarios. These results are in line with the ones obtained by [12,13]. The infeasibility of the deterministic solution stems mainly from the fact that the wood flow constraints are violated due to an intensive harvest in early periods.…”

“…In forestry, this method is well suited for harvest scheduling problem with wood price and demand uncertainties because we can extract samples from historical demand and price without the need to model the price like done in [10,28]. Compared to stochastic programming which require the so-called non-anticipativity constraints [13,29], SAA model is relatively smaller in terms of number of constraints (and possibly in terms of number of variables, depending on the formulation) since it does not require such constraints.…”

“…Regarding climate change data, we used the information of climate change forecast with statistical models developed in [30]. Unlike the data from [11][12][13], which originated from a process-based modeling, statistical models of forest growth under climate change are much more common (for e.g [31]). Hence, the method developed in this study can easily be extended to other forest systems.…”

“…The authors assessed how climate change affected the management decisions of a Eucalyptus forest in Portugal with a planning horizon of 15 years. A similar study was conducted by [12,13] using the same dataset.…”

Multistage Sample Average Approximation for Harvest Scheduling under Climate Uncertainty

“…The authors assessed how climate change affected the management decisions of a Eucalyptus forest in Portugal with a planning horizon of 15 years. A similar study was conducted by Álvarez-Miranda et al [12], Garcia-Gonzalo et al [13] using the same dataset. In addition to optimization methods for incorporating climate change in forest harvest scheduling, some authors invested in developing decision support systems (DSSs).…”