Timber harvest scheduling in a fuzzy decision environment

1992 ◽  
Vol 22 (4) ◽  
pp. 423-428 ◽  
Author(s):  
B. Bruce Bare ◽  
Guillermo A. Mendoza
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Deterministic Model ◽  
Programming Model ◽  
Timber Harvest ◽  
Harvest Scheduling ◽  
Fuzzy Decision ◽  
Decision Environment ◽  
Objective Function Values ◽  
Scheduling Models

Linear programming is a widely used tool for timber harvest scheduling in North America. However, some potential problems related to infeasible harvest schedules, overly optimistic objective function values, and the need to strictly satisfy all constraints included in deterministic model formulations have been raised. This paper describes a fuzzy approach for explicitly recognizing the imprecise nature of the harvest flow constraints usually included in harvest scheduling models. The objective function and selected constraints are viewed as soft, and satisfactory solutions are derived and discussed for several scenarios. An illustrative sample problem is presented to demonstrate the methodology, and a comparison with solutions derived from a traditional linear programming model is presented.

Influence of land classification systems on timber harvest scheduling models

1990 ◽  
Vol 20 (2) ◽  
pp. 172-178 ◽  
Author(s):  
M. S. Jamnick ◽  
L. S. Davis ◽  
J. K. Gilless
Keyword(s):  
Objective Function ◽  
Timber Harvest ◽  
Management Unit ◽  
Harvest Scheduling ◽  
Land Classification ◽  
Decision Variables ◽  
Optimal Harvest ◽  
Stand Type ◽  
Objective Function Values ◽  
Scheduling Models

Differences between linear program based timber harvest schedules that use decision variables based on stand types (homogeneous but generally noncontiguous areas) and management units (generally heterogeneous but contiguous areas) were investigated. It was proposed that (i) optimal harvest schedules identified using stand type decision variables should have larger present net value objective function values than those identified using models with management unit decision variables, (ii) optimal present net value objective function values in management unit models should decline as management unit size is increased, and (iii) as the number of management choices increases, differences between stand type and management unit optimal present net values should decrease. The propositions were tested using 48 linear programming timber harvest scheduling models constructed for the University of California's Blodgett Forest Experiment Station. These models, which form 12 model groups, differ in the numbers and type of prescriptions considered for existing or regenerated stands, and harvest flow or ending inventory policies. The results generally supported the propositions and indicate that the number of management choices considered in the timber harvest scheduling model is probably a more important factor influencing the optimal harvest schedules than is land classification.

scholarly journals A replanning approach for maximizing woodland caribou habitat alongside timber production

2017 ◽  
Vol 47 (7) ◽  
pp. 901-909 ◽  
Author(s):  
Andrew B. Martin ◽  
Jonathan L.W. Ruppert ◽  
Eldon A. Gunn ◽  
David L. Martell
Keyword(s):  
Linear Programming ◽  
Rangifer Tarandus ◽  
Programming Model ◽  
Timber Harvest ◽  
Management Plan ◽  
Harvest Scheduling ◽  
Woodland Caribou ◽  
Habitat Amount ◽  
Trout Lake ◽  
Preferred Habitat

We present a forest harvest scheduling model that meets timber harvest targets while maximizing a proxy measure of woodland caribou (Rangifer tarandus caribou (Gmelin, 1788)) habitat based on the configuration of preferred habitat on the landscape. Woodland caribou within the boreal forest region in Canada tend to prefer mature jack pine forest stands, which tend to be rich in their preferred resource, lichen, and also reduce predation pressure. This can create conflict with industrial wood supply needs. We designed a model that can be used to identify good harvest scheduling plans given these competing objectives. Our approach is to use a series of sequential linear programming models that are solved within a replanning framework. Specifically, each individual linear programming model seeks to produce a solution that will meet timber harvest targets while minimizing the harvest of high-quality woodland caribou habitat stands. Stands are assessed with respect to their suitability as woodland caribou habitat based on their contribution to the overall landscape equivalent connected area (ECA), a combined spatial measure of preferred habitat amount and its connectivity. We used our model for a case study of the Trout Lake Forest in northwestern Ontario, Canada, and found that our model creates approximately 10% more caribou habitat than an earlier heuristic procedure and 30% more caribou habitat than the prevailing woodland caribou habitat forest management plan in the Trout Lake Forest while meeting the same timber harvest targets.

An Integer Programming Approach to Optimize the Plantation in Order to Reduce Global Warming

2012 ◽  
Vol 548 ◽  
pp. 767-771 ◽  
Author(s):  
C. Vanlisuta ◽  
Suksan Prombanpong
Keyword(s):  
Mathematical Model ◽  
Linear Programming ◽  
Objective Function ◽  
Programming Model ◽  
Programming Approach ◽  
Profit Function ◽  
Carbon Credit ◽  
Integer Linear Programming Model ◽  
The Mathematical Model

The objective of this paper is to determine the number and species of trees to be planted in order to maximize a profit through an integer linear programming model. The mathematical model is developed in terms of the profit function. This objective function is therefore, a difference between carbon credit revenue and costs of plantation. The economical plants are only considered in the model. Consequently, fourteen different tree species are to be investigated. The objective function is subjected to several constraints i.e. planting area, carbon sequestration and so on. The planting envelope of each tree is assigned 4 by 4 meters. In this paper, the Eastern part of Thailand is considered the case study. It is found that three kinds of plants, Copper pod, Cananga, and Bullet wood are suitable for planting. A number of trees to be planted in 1600 square meter are twenty, thirty, and fifty plants respectively. The profit earned is of 12,112 $ per year in the next fifth year.

A Simulation/Linear Programming Approach to Timber Supply Modeling

1989 ◽  
Vol 4 (3) ◽  
pp. 80-84 ◽  
Author(s):  
William McKillop ◽  
Bruce Krumland
Keyword(s):  
Linear Programming ◽  
Programming Model ◽  
Timber Harvest ◽  
Growth And Yield ◽  
Programming Approach ◽  
Forest Industry ◽  
Timber Supply ◽  
Inventory Constraints ◽  
Stand Type ◽  
Time Subject

Abstract A growth and yield simulator was combined with a forest inventory processor and a linear programming model to analyze and project timber inventory, growth and harvest for industrial and nonindustrial lands in each of five regions in California. Harvest priorities for each stand type were chosen by maximization of conifer output over alternative periods of time subject to volume, species, and inventory constraints. Results indicated that timber harvest from forest industry land would decline in the next several decades, but that this decline would be offset by increased output from nonindustrial holdings. A substantial buildup of hardwood inventories on small private ownerships is anticipated. West. J. Appl. For. 4(3):80-84, July 1989.

A comparison of FORMAN and linear programming approaches to timber harvest scheduling

1990 ◽  
Vol 20 (9) ◽  
pp. 1351-1360 ◽  
Author(s):  
Mark S. Jamnick
Keyword(s):  
Linear Programming ◽  
Timber Harvest ◽  
The Other ◽  
Scheduling Problem ◽  
Harvest Scheduling ◽  
Wood Supply ◽  
Supply Model

Harvest schedules are developed and compared for two hypothetical 129 900-ha forests using the FORMAN wood supply model and linear programming. The purpose is to determine how the harvest schedules and models differ and under what conditions one model would be preferred over the other. The results clearly demonstrate that compared with FORMAN, linear programming is able to find solutions with higher harvest volumes in every case considered. Additionally, fundamental differences between the model capabilities were discovered. The FORMAN model is preferred in situations where the harvest scheduling problem is relatively simple and conforms to the activities included in the model. Linear programming is preferred when the analyst is concerned with the economics of wood supply and controlling a variety of activities and outputs.

scholarly journals Farm household modelling for estimating the effectiveness of price instruments in land use policy

1995 ◽  
Vol 43 (1) ◽  
pp. 111-123 ◽  
Author(s):  
G. Kruseman ◽  
R. Ruben ◽  
H. Hengsdijk ◽  
M.K. Van Ittersum
Keyword(s):  
Land Use ◽  
Linear Programming ◽  
Objective Function ◽  
Programming Model ◽  
Farm Household ◽  
Socioeconomic Environment ◽  
Farm Type ◽  
Structure Adjustment ◽  
Peasant Household ◽  
Micro Level

A farm household modelling approach using linear programming is presented that integrates biophysical and socioeconomic information for simulating micro-level responses to specific changes in the socioeconomic environment. The linear programming model includes separate modules for prices, production activities and expenditures from which the objective function is derived. Moreover, the model comprises a production structure adjustment coefficient to account for incomplete specification of the objectives of the farmer in the objective function. The model was calibrated for one specific farm type in the Atlantic Zone of Costa Rica, a peasant household growing basic grains and other food crops for household consumption and sale, and applied to calculate effects of several price instruments. The results, in terms of response multipliers, give an indication of the pace and direction of land use change at the micro-level as a result of (induced) change in the socioeconomic environment. The overall effect of an increase in biocide prices (taxation) is a change in cultivated crops and decrease in biocide use, but at the expense of a reduction in income. Increasing fertilizer prices affects income and utility positively. Thus, changes in fertilizer prices would seem to be an appropriate instrument to induce land use modifications.

scholarly journals Didáctica de la programación lineal con el método gráfico

2007 ◽  
pp. 17
Author(s):  
Fernando León Parada
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Model ◽  
Geometric Analysis ◽  
Linear Programming Model ◽  
Feasible Region ◽  
Optimal Point ◽  
Decision Variables ◽  
Programación Lineal

Every Linear Programming model has a Objective Function determined by the coefficients of the decision variables. The Objective Function can be represented as a line evaluated on an optimal point which slope depends from the variation of the coefficients. The segments adjacent to the optimal point in the Feasible Region can also determine the variation of this slope. Finally a geometric analysis allows to establishing the constraining of the boundary for the Feasible Region keeping as a domain for the Objective Function.

scholarly journals Transportation Optimization Models for Intermodal Networks with Fuzzy Node Capacity, Detour Factor, and Vehicle Utilization Constraints

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2109
Author(s):  
Chia-Nan Wang ◽  
Thanh-Tuan Dang ◽  
Tran Quynh Le ◽  
Panitan Kewcharoenwong
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Deterministic Model ◽  
Mixed Integer ◽  
Model Parameters ◽  
Total Cost ◽  
The Impact ◽  
Node Capacity

This paper develops a mathematical model for intermodal freight transportation. It focuses on determining the flow of goods, the number of vehicles, and the transferred volume of goods transported from origin points to destination points. The model of this article is to minimize the total cost, which consists of fixed costs, transportation costs, intermodal transfer costs, and CO2 emission costs. It presents a mixed integer linear programming (MILP) model that minimizes total costs, and a fuzzy mixed integer linear programming (FMILP) model that minimizes imprecise total costs under conditions of uncertain data. In the models, node capacity, detour, and vehicle utilization are incorporated to estimate the performance impact. Additionally, a computational experiment is carried out to evaluate the impact of each constraint and to analyze the characteristics of the models under different scenarios. Developed models are tested using real data from a case study in Southern Vietnam in order to demonstrate their effectiveness. The results indicate that, although the objective function (total cost) increased by 20%, the problem became more realistic to address when the model was utilized to solve the constraints of node capacity, detour, and vehicle utilization. In addition, on the basis of the FMILP model, fuzziness is considered in order to investigate the impact of uncertainty in important model parameters. The optimal robust solution shows that the total cost of the FMILP model is enhanced by 4% compared with the total cost of the deterministic model. Another key measurement related to the achievement of global sustainable development goals is considered, reducing the additional intermodal transfer cost and the cost of CO2 emissions in the objective function.

Low Glycemic Index Diets for Subjects With Diabetes by Minimizing Glycemic Load of Individual Foods

2019 ◽  
Vol 7 (1) ◽  
pp. 1-17
Author(s):  
Maximino Navarro Mentado ◽  
Esther Segura Pérez
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Glycemic Index ◽  
Programming Model ◽  
Glycemic Load ◽  
Linear Programming Model ◽  
Macronutrient Content ◽  
Low Glycemic Index

In this article, the authors develop and analyze a linear programming model to obtain an ideal diet for individuals with diabetes by setting the glycemic load as the objective function. Additionally, a standardized system is used in order to facilitate the substitutability of foods present in a diet since those are classified according to their macronutrient content (proteins, lipids, and carbohydrates) and these values are, on average, very similar. Finally, the diet glycemic index is calculated with the model's outcome to corroborate that it is indeed a diet with low glycemic index and that, at the same time, it complies with the nutrient restrictions, which proves that the model can be a useful tool both to generate low glycemic index diets and to restrict certain nutrients from the diet.

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