Establishing optimal forest harvesting regulation with continuous approximation

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.