Fixed and Equilibrium Endpoint Problems in Uneven-Aged Stand Management

Publisher： Society of American Foresters

ISSN： 0015-749X

Source： Forest Science, Vol.33, Iss.4, 1987-12, pp. : 908-931

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Abstract

Studies in uneven-aged management have concentrated on the determination of optimal steady-state diameter distribution harvest policies for single and mixed species stands. To find optimal transition harvests for irregular stands, either fixed endpoint or equilibrium endpoint constraints can be imposed after finite transition periods. Penalty function and gradient methods are presented to solve these problems. The methods are demonstrated with a stage-structured model for projecting stands that contain mixtures of California white fir (Abies concolor [Gord. & Glend.] Lindl. (Iowiana [Gord.])) and red fir (Abies magnifica A. Murr.). With present value as the efficiency criterion, optimal transition strategies are computed for three kinds of target steady states: the extremal steady state associated with an infinite time horizon dynamic optimization problem, an investment-efficient steady state, and a maximum sustainable rent steady state. Harvest regimes that convert to investment-efficient or maximum sustainable rent steady states are dominated by red fir and are suboptimal compared to transition regimes that convert to the extremal steady state, which includes only white fir. The fixed endpoint regimes are compared with transition strategies that are obtained with equilibrium endpoint constraints that do not require a particular steady-state stand structure. Transition regimes that convert to the extremal steady state are suboptimal compared to regimes that solve the more general equilibrium endpoint problem, and the present values of these two kinds of regimes converge as the transition period lengthens. The species composition and structure of the steady states found by solving the equilibrium endpoint problem depend on the transition period length. For. Sci. 33(4):908-931.