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UBC Theses and Dissertations

Integrating stand and forest models for decision analysis Williams, Douglas Harold

Abstract

Models of forest stands and management units have gained wide acceptance as tools for planning forest lands management. This thesis integrates their use in a framework amenable to decision analysis. The forest lands planning process of the British Columbia Forest Service involves a multilevel hierarchical structure. At each level, a planning problem was identified and characterized by one or more management objectives and a set of management decisions, some of which are constrained by neighbouring levels of the planning chain. At any level, a model of the decision problem should be capable of linking to the other levels of the planning process. The chain should not be 'separated' and optimized at each level. Multistage analysis was used to examine the underlying mathematical structure of the combined management unit and stand decision problem, identifying the decision and state variables, and objective and constraint functions. The components of the combined problem were identified as scheduling management actions on a stand or treatment unit, and allocating constrained commodities across a management unit. Several approaches to optimization of the two level problem were considered. Scheduling management actions on a treatment unit is best accomplished through algorithms that exploit the serial multistage structure of the problem. However, the commodity allocation component cannot be optimized via the usual dynamic programming recursions, due to a continuous and multidimensional state space. The discrete maximum approach improves computational efficiency with regard to the state space but, as with dynamic programming, it requires decision inversion of the transition functions to handle boundary values of the commodity states. Conversely, approximation of the commodity allocation problem with a linear model and optimization by linear programming is very efficient, but treats the stand level subproblem inadequately. fitter consideration of the role of Lagrange multipliers in the discrete optimum formulation of the problem, the linear and multistage approaches were synthesized through Dantzig-Wolfe decomposition. The general problem of finding an optimal sequence of management actions with a stand simulation model was examined and two techniques considered. First, a conversational supervisor system was used interactively to explore the objective surface of a model. The optimum was sought by a pattern search technique, the sequential simplex algorithm. Second, the stand model was embedded in a network formulation that vas optimized through dynamic programming. Both techniques were tested with single tree/distance independent and whole stand models. The network formulation of the stand model was combined with a linear management unit model (Timber RAM) and optimized by Dantzig-Wclfe decomposition. The decomposition system was demonstrated with a management unit of 85,000 ha. simulated by 8 submodels, under conventional present net worth and mixed goal objectives. The decomposition system combines three powerful components: an existing, operational model of management unit planning is optimized by a commercially available mathematical programming system, with forest stand models providing accurate and detailed estimates of responses to management actions. The decomposition approach was economically attractive, solving problems of far greater complexity than could be attempted under conventional linear programming formulations.

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