Optimal timber harvesting in uneven-aged forest stands : a discrete-time optimal-control approach Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/x920g081c

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  • The purpose of this dissertation is to formulate, analyze and numerically solve the dynamic harvesting problem for uneven-aged stands. The problem is to find the optimal numbers of trees to remove from diameter classes over a finite time horizon and is formulated as a discrete-time optimal-control problem with bounded control variables and free terminal point. A solution algorithm called the method of steepest descent is described and demonstrated with a whole-stand/diameter-class simulator for Wisconsin hardwood stands. Optimal management regimes that maximize present net worth (PNW) from harvests taken on a 5-year cutting cycle during a 150-year time horizon are developed for three stumpage value functions. Harvest regimes derived with the gradient method contradicted optimal steady-state management regimes determined with static analysis. Pontryagin's maximum principle is used to establish optimality conditons for the dynamic and static optimization problems. Comparison of these conditions shows that for a stand with any initial diameter distribution: (1) the optimal transition regime does not converge to the steady state that maximizes land expectation value defined by the Faustmann equation; (2) the PNW of the optimal transition and steady-state regime is greater than the PNW of the statically determined regime; and (3) the optimal steady-state regime is invariant. These results invalidate the use of investment-efficient diameter distributions. The gradient method produces stationary solutions for harvest control variables in the first period and beyond; however, because of large discount factors in distant periods, the algorithm fails to provide stationary solutions for long-term management within reasonable execution times. To avoid this problem, a restart procedure that takes advantage of the stability of the first-period solution and the sequential nature of the problem is developed. An economic model for harvesting forest stands is presented and used to contrast the two major timber harvesting systems: even-aged and uneven-aged management. In contrast to even-aged management, the value of uneven-aged stand harvesting cannot be separated into independent components for stand value and land value. Thus, conclusions about the most profitable harvesting system depend on the joint productivity of the land and existing timber. This result is demonstrated by developing optimal management regimes for Arizona ponderosa pine (Pinus ponderosa Laws.) stands.
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