A Spatial Stochastic Programming Model for Timber and Core Area Management Under Risk of Fires

Previous stochastic models in harvest scheduling seldom address explicit spatial management concerns under the influence of natural disturbances. We employ multistage stochastic programming models to explore the challenges and advantages of building spatial optimization models that account for the influences of random stand-replacing fires. Our exploratory test models simultaneously consider timber harvest and mature forest core area objectives. Random fire samples are built into the model, creating a sample average approximation (SAA) formulation of our stochastic programming problem. Each model run reports first-period harvesting decisions along with recourse decisions for subsequent time periods reflecting the influence of stochastic fires. In each test, we solve 30 independent, identically distributed (i.i.d.) replicate models and calculate the persistence of period one solutions. Harvest decisions with the highest persistence are selected as the solution for each stand in a given test case. We explore various sample sizes in our SAA models. Monte Carlo simulations of these solutions are then run by fixing first-period solutions and solving new i.i.d. replicates. Multiple comparison tests identify the best first-period solution. Results indicate that integrating the occurrence of stand-replacing fire into forest harvest scheduling models can improve the quality of long-term spatially explicit forest plans.