Abstract
While optimal forest harvesting regulations (regional forest regeneration schedules) have been established using the linear programming technique, its modeling restriction is still a challenge in practice. In this study, we developed an alternative framework for establishing an optimal forest harvesting regulation using the continuous approximation technique. The regulation problem was reformulated as a problem to find optimal smooth control of regeneration area, thereby overcoming the difficulties in finding the global optimum for the optimization models that include nonlinear or more complex models. A seven-dimensional optimization model was developed involving efficient assurance of the convergence to a stable forest state and prohibition of clearcutting in immature stands. Using this model, we established optimal forest harvesting regulations in Nagano Prefecture, Japan. Simulated annealing was utilized to explore optimal solutions. Analyses based on extreme value theory and comparison with solutions produced by grid search indicated that the best solutions may be sufficiently close to global optima. The best solutions suggested controlling timber supply to keep prices high in the early years, due to the supply–demand log price model and the use of net present value as the objective function. Because of the low profitability of the region, the solution suggested delaying the achievement of the target state as far as possible.
Highlights
Forestry has a much longer crop rotation cycle compared to other agricultural systems
The increase of the number of integer variables associated with the linear approximation may cause considerable increase of computation time; this causes a difficulty in finding the global optimum in practice. These difficulties seem to be the fundamental reason that forest harvesting regulation (FHR) have rarely been modeled as nonlinear programming (NLP) problems
A possible way to develop an FHR with nonlinear models is to develop an optimization model so that it can be optimized with existing techniques. This is similar to the way we have modeled the FHR problem so that it can be solved with the linear programming (LP) technique
Summary
Forestry has a much longer crop rotation cycle compared to other agricultural systems. The increase of the number of integer variables associated with the linear approximation may cause considerable increase of computation time; this causes a difficulty in finding the global optimum in practice These difficulties seem to be the fundamental reason that FHRs have rarely been modeled as NLP problems. Even if an optimal FHR suggested 90% regeneration (in forest area) for 40- and 42-year-old stands but 10% regeneration for 41-year-old stands, the solution may not be practical These requirements indicate that the FHR problem can be modeled as an optimization problem with the few parameters of the smooth control. The constraints for the control of age-class distributions that involves the prevention of clearcutting immature stands and achievement of a stable state in the age-class distribution at the end of a planning horizon were developed We applied this approach for the establishment of FHRs for Nagano Prefecture, Japan. The applicability of the continuous approximation technique for the FHR in other situations is discussed
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