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

2021 ◽  
Vol 43 (1) ◽  
Author(s):  
Mehmet Demirci ◽  
Ahmet Yesil ◽  
Pete Bettinger
Keyword(s):  
Goal Programming ◽  
Site Index ◽  
Mixed Integer ◽  
Mediterranean Forests ◽  
Average Deviation ◽  
New Approach ◽  
Wood Volume ◽  
Forest Management Planning ◽  
District Management ◽  
Forest Enterprises

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.

scholarly journals Using Mixed Integer Goal Programming in Final Yield Harvest Planning: A Case Study from the Mediterranean Region of Turkey

Forests ◽  
2020 ◽  
Vol 11 (7) ◽  
pp. 744
Author(s):  
Mehmet Demirci ◽  
Ahmet Yeşil ◽  
Pete Bettinger
Keyword(s):  
Goal Programming ◽  
Mediterranean Region ◽  
Programming Model ◽  
Mixed Integer ◽  
Forest Management Planning ◽  
Age Class ◽  
Goal Programming Model ◽  
Final Yield ◽  
Harvest Volume ◽  
The Mediterranean

A mixed integer goal programming model is developed to address the regeneration planning problems of even-aged forests in the Mediterranean region of Turkey. The unique aspect of the goal programming formulation is to minimize deviations in scheduled wood product volumes and the size of harvest areas within each time period, as these are important goals for the management area. About 98% of the forests in Turkey are considered even-aged, and 2% are uneven-aged. Therefore, an age class method is used for the planning of even-aged forests. For the areas where this method is applied, reaching the optimal age class structure is the first priority. This involves implementing final harvests (clearcuts) to regenerate an amount of forest area into each age class. To meet the local market’s needs, forest enterprises also require the final yield to be fairly equal each year. Further, it is desired that the harvest area (regeneration area) is relatively equal each year, to address operational considerations. A linear goal programming model is developed to address the problem. The minimization of deviations from both the harvest area and harvest volume targets are incorporated as goals in the objective function of the model. Several scenarios are solved using the extended version of Lingo 16. A scenario with weights of 0.8 for area and 0.2 for volume produces the best results. Here, the total deviation for 20 years is 3.8 ha in area and 2889 m3 in volume. In the actual regeneration plan, the area deviation for 10 years is 54.72 ha (6.2% of total regeneration area), and the volume deviation is 20,472 m3 (9.8% of harvest volume). The model described through this study can be developed further and integrated into forest management planning software and processes used for the planning of even-aged forests in the Mediterranean region.

A Multipoint Felled-Tree Validation of Height–Age Modeled Growth Rates

2020 ◽  
Vol 66 (3) ◽  
pp. 275-283 ◽  
Author(s):  
Halli Hemingway ◽  
Mark Kimsey
Keyword(s):  
Growth Rates ◽  
Rocky Mountain ◽  
Site Index ◽  
Douglas Fir ◽  
Alternative Methods ◽  
Forest Site ◽  
Site Productivity ◽  
Site Factors ◽  
Forest Management Planning ◽  
Breast Height

Abstract Accurate measures of forest site productivity are essential for forest-management planning. The most common measure of site productivity is breast height–age site index (BHASI)—the expected height at a reference age. Error from including early growth in productivity estimates and limited applicability of any one BHASI model warrant development of alternative methods. Exploring alternatives may only be necessary if regional BHASI models are not accurately predicting growth rates. We compared modeled height growth rates for Rocky Mountain Douglas-fir (Pseudotsuga menziesii var. glauca) to felled-tree measurements to evaluate relative performance of a regional BHASI model. An orthogonal sampling design ensured samples were collected across a range of site factors known to influence Douglas-fir growth rates. Growth rates for each 10 m section were calculated and compared to BHASI modeled growth rates. The regional BHASI model underpredicted growth rates from breast height to 30 m. Observed growth rates from 10 to 30 m accounted for the majority of underprediction relative to BHASI modeled growth rates. An alternative multipoint method of defining site productivity is described. More research comparing BHASI and alternative methods is needed, given the growth rate error associated with one-point site productivity assessment.

The Optimal Controlled Partitioning Strategy for Power System Based on Master-Slave Problem

2013 ◽  
Vol 385-386 ◽  
pp. 999-1006
Author(s):  
Wei Wang ◽  
Ting Yu ◽  
Tian Jiao Pu ◽  
Ai Zhong Tian ◽  
Ji Keng Lin
Keyword(s):  
Large Scale ◽  
Optimization Method ◽  
Mixed Integer ◽  
Master Problem ◽  
Decomposition Algorithms ◽  
Integer Programming Problem ◽  
Complete Model ◽  
New Approach ◽  
Mixed Integer Programming Problem ◽  
Partitioning Strategy

Controlled partitioning strategy is one of the effective measures taken for the situation when system out-of-step occurs. The complete splitting model, mostly solved by approximate decomposition algorithms, is a large-scale nonlinear mixed integer programming problem. A new alternate optimization method based on master-slave problem to search for optimal splitting strategy is proposed hereby. The complete model was converted into master-slave problems based on CGKP (Connected Graph Constrained Knapsack Problem). The coupling between master problem and slave problem is achieved through load adjustment. A better splitting strategy can be obtained through the alternating iteration between the master problem and the salve problem. The results of the examples show that the method can obtain better splitting strategy with less shed load than other approximate algorithms, which verifies the feasibility and effectiveness of the new approach presented.

Robust Optimization of Mixed-Integer Problems Using NURBs-Based Metamodels

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
John C. Steuben ◽  
Cameron J. Turner
Keyword(s):  
Robust Optimization ◽  
Numerical Optimization ◽  
Mixed Integer ◽  
Test Problems ◽  
Problem Structure ◽  
New Approach ◽  
Integer Variables ◽  
Classic Problem ◽  
Dependent Variables ◽  
Definition Of

The optimization of mixed-integer problems is a classic problem with many industrial and design applications. A number of algorithms exist for the numerical optimization of these problems, but the robust optimization of mixed-integer problems has been explored to a far lesser extent. We present here a general methodology for the robust optimization of mixed-integer problems using nonuniform rational B-spline (NURBs) based metamodels and graph theory concepts. The use of these techniques allows for a new and powerful definition of robustness along integer variables. In this work, we define robustness as an invariance in problem structure, as opposed to insensitivity in the dependent variables. The application of this approach is demonstrated on two test problems. We conclude with a performance analysis of our new approach, comparisons to existing approaches, and our views on the future development of this technique.

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