Introducing a New Approach in Stand Tending Planning and Thinning Block Designation by Using Mixed Integer Goal Programming

Long-term management plans have been developed for nearly all of the forests in Turkey. These plans are applied at a sub-district management unit level and may contain guidance for both intermediate yield and final yield harvests. To implement an intermediate yield plan, which involves the scheduling of forest thinnings (stand tending), consideration in Turkey is given to the advantages of working in the same terrain and the same general area each year. Therefore, compartments are often clumped together to create thinning blocks, taking into consideration the thinning priority of the stands, road conditions, site index, age, and proximity of the compartments. Further, when preparing annual budgets and planning to meet the market’s needs, forest enterprises require an even flow of intermediate wood volume each year. In this paper, we introduce a new approach in stand tending planning designed to schedule an equal amount of intermediate wood volume each year and to create thinning blocks by minimizing the distance to pre-defined ramps (landings). We developed both linear and nonlinear goal programming models to minimize both the deviations from a harvest volume (annual intermediate yield allowable cut) target and the deviations from a target value determined for the distances (total and average) of the centroid of each compartment to the hypothetical forest ramps. By using the extended version of Lingo 16, we solved the problem with different weights for the deviations in volume and distance that ranged from 0.0 to 1.0, in 10% intervals, which created 11 scenarios. We carefully analyzed the results of each scenario by taking into consideration the wood volume and distance of compartments to the ramps. The best scenario using the linear model produced a deviation in volume scheduled for the entire decade of 6 m3, while the deviation in total distance between harvest areas and ramps was 59.7 km. Scenario 5, with weights of 0.6 for volume and 0.4 for distance, produced these results, where compartments were closest to one another. The best scenario using the nonlinear model also produced a deviation in volume of 0 m3 and the total average deviation in distance between harvest areas and ramps was 8.7 km. Scenario 3, with weights of 0.8 for volume and 0.2 for distance, produced these results. The approach and models described through this study may be appropriate for further integration into forest management planning processes developed for the planning of Mediterranean forests.