Interactive, multiobjective programming for forest resources management

Forest resources management is approached by a visual "free search" type of interactive procedure for multiple objective linear programming, which accounts for imprecision in the model by use of fuzziness. Specifically, a ponderosa pine forest resources management problem is examined. The problem is concerned with performing on given subwatersheds six different levels of vegetation treatment strategies ranging between 0 and 100% tree basal area cut in the forest. This problem is evaluated to "satisfice" six multiple and usually conflicting objective functions, namely, water yield, herbage production, sediment yield, recreational use, economicbenefit, and cost. The problem is subject to physical constraints, some of which, such as the total area that may be subjected to high percentage tree basal area removal, are not precisely defined and may be taken as fuzzy. Further, one objective, recreational use level, is defined as a fuzzy goal. The problem is formulated as a multiple objective linear programming model, in which fuzzy set membership value is also considered as an objective to be optimized. The effects of the fuzziness on the trade-offs between the conflicting objectives is examined using a visual interactive system called PARETO RACE. The system enables a decision-maker to search freely any part of the efficient frontier by controlling the speed and direction of motion. By using PARETO RACE, the decision-maker is also able to analyze relationships between the objective function values and visualize interactively how fuzziness in resources and objectives is reflected in objective functions. The model appears to lead to compromise policies acceptable to the decision-maker.