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UBC Theses and Dissertations

Incorporating spatially explicit objectives into forest management planning Crowe, Kevin

Abstract

The increased incorporation of spatially explicit objectives into forest management planning has arisen from a concern over the ecological consequences of landscape-scale disturbance patterns through harvesting. Given the complexity of the ecosystems of forested landscapes, and our incomplete understanding of them, forest managers now commonly design plans to conserve landscape-scale biodiversity through the emulation of natural disturbance patterns. Harvest-scheduling is thereby constrained to imitate not only the aspatial age-class and cover-type distributions of a forest under natural disturbance, but also the patch-sizes and shapes of disturbed and undisturbed forest. Forest management planning typically requires the use of optimization models because the most efficient allocation of scarce resources is a central economic objective. Incorporating spatially explicit objectives into such models requires that decision variables be binary. This is because, in a spatially explicit plan, a forest stand must be either harvested or not. Hence, integer programming models are needed, and such models are notoriously difficult to solve computationally. The objective of this research has been to make significant advances in formulating, solving, and understanding three difficult forest planning problems involving spatial objectives. The first is a tactical planning problem where the objective is to maximize the net present value of a harvest-schedule, subject to the spatial constraint that stands may not aggregate to form harvest-openings greater than a maximum area. In Chapter II, two integer programming models were formulated and solved, using the branch and bound algorithm. It was found that: a) the number of decision variables, and b) the number of opening constraints, ultimately restricts this method from applicability to larger problem instances. Given these limitations, a metaheuristic algorithm, simulated annealing was evaluated in Chapter II. Using the branch and bound algorithm's solutions as upper bounds, the quality of solutions found by the metaheuristic was evaluated. The mean objective function value was within 5% of the optima. Problems instances ranged in size from 1,269 to 36,270 binary decision variables. The second problem, treated in Chapter IV, concerns the efficient allocation of cutting rights among competing mills within the same management unit. A mixed integer goal programming model was formulated and applied to the Kootenay Lake Timber Supply Area of British Columbia. It was concluded that the model is can a useful tool by which to interactively explore British Columbia's appurtenance policy. The third problem, treated in Chapter V, is a strategic planning problem: determining the optimal, sustainable rate of harvest while selecting spatially explicit old growth reserves. A mixed integer programming model was formulated and tested on three forests. It was concluded that the formulation appears to be integer-friendly, having solved problems instances containing up to 91,000 decision variables. The general conclusion of this work is that integer programming is a powerful paradigm by which to incorporate the complexities of spatially explicit objectives within the pragmatic constraints of forest management planning.

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