Optimal harvest of a forest in the presence of uncertainty

1989 ◽  
Vol 19 (10) ◽  
pp. 1267-1274 ◽  
Author(s):  
Horand I. Gassmann
Keyword(s):  
Lower Bound ◽  
Forest Fires ◽  
Model Uncertainty ◽  
Original Problem ◽  
Environmental Hazards ◽  
Numerical Results ◽  
Finite Horizon ◽  
Type Ii ◽  
Optimal Harvest ◽  
Random Fraction

A method is described for finding logging levels to maximize harvest in a finite horizon type II model. Uncertainty is considered in the form of the risk of forest fires and other environmental hazards, which may destroy a random fraction of the existing forest. Numerical results include upper and lower bound approximations to the original problem.

scholarly journals A Global Optimization Algorithm for Sum of Linear Ratios Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yuelin Gao ◽  
Siqiao Jin
Keyword(s):  
Global Optimization ◽  
Lower Bound ◽  
Programming Problem ◽  
Branch And Bound ◽  
Numerical Experiments ◽  
Original Problem ◽  
Bilinear Programming ◽  
Global Optimization Algorithm ◽  
Product Function ◽  
Optimal Value

We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

scholarly journals A New Global Optimization Algorithm for a Class of Linear Fractional Programming

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 867 ◽  
Author(s):  
X. Liu ◽  
Y.L. Gao ◽  
B. Zhang ◽  
F.P. Tian
Keyword(s):  
Global Optimization ◽  
Lower Bound ◽  
Objective Function ◽  
Programming Problem ◽  
Optimization Algorithm ◽  
Fractional Programming ◽  
Original Problem ◽  
Global Optimization Algorithm ◽  
Linear Fractional Programming ◽  
Advantages And Disadvantages

In this paper, we propose a new global optimization algorithm, which can better solve a class of linear fractional programming problems on a large scale. First, the original problem is equivalent to a nonlinear programming problem: It introduces p auxiliary variables. At the same time, p new nonlinear equality constraints are added to the original problem. By classifying the coefficient symbols of all linear functions in the objective function of the original problem, four sets are obtained, which are I i + , I i − , J i + and J i − . Combined with the multiplication rule of real number operation, the objective function and constraint conditions of the equivalent problem are linearized into a lower bound linear relaxation programming problem. Our lower bound determination method only needs e i T x + f i ≠ 0 , and there is no need to convert molecules to non-negative forms in advance for some special problems. A output-space branch and bound algorithm based on solving the linear programming problem is proposed and the convergence of the algorithm is proved. Finally, in order to illustrate the feasibility and effectiveness of the algorithm, we have done a series of numerical experiments, and show the advantages and disadvantages of our algorithm by the numerical results.

BIFURCATION STRUCTURE OF SCALAR DIFFERENTIAL DELAYED EQUATIONS

1991 ◽  
Vol 01 (03) ◽  
pp. 657-665 ◽  
Author(s):  
C. P. MALTA ◽  
C. GROTTA RAGAZZO
Keyword(s):  
Lower Bound ◽  
Periodic Solutions ◽  
Negative Feedback ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Feedback Condition ◽  
Numerical Results ◽  
The Other ◽  
Bifurcation Structure ◽  
Dominant Frequencies

We study periodic solutions of the equation [Formula: see text], with f(X) given by f1(X) = AX(1 − X) or f2(X) = πµ (1 − sin X), grouped in some sets characterized by different dominant frequencies. Numerical results with f(X) = f1(X) are given. One of these sets is shown to exhibit period-doubling cascade in the direction of both parameters A and τ. The other sets are shown to exhibit many other period-doubling cascades as τ is varied establishing a relation between the bifurcation structure within the sets. Furthermore we obtain a lower bound on A and µ for the existence of more complex dynamics. We conjecture that this fact is related to the violation of the so-called "negative-feedback condition."

scholarly journals Ratio Edits Based on Statistical Tolerance Intervals

2015 ◽  
Vol 31 (1) ◽  
pp. 77-100 ◽  
Author(s):  
Derek S. Young ◽  
Thomas Mathew
Keyword(s):  
Numerical Results ◽  
Type I ◽  
Type Ii ◽  
Weibull Distributions ◽  
Tolerance Intervals ◽  
Annual Survey ◽  
Statistical Tolerance ◽  
Type Ii Errors

Abstract The role of statistical tolerance intervals for developing ratio edit tolerances in a parametric setup is investigated. The performance of the methodology is assessed for the normal and Weibull distributions. The numerical results show that in terms of Type I and Type II errors, statistical tolerance intervals exhibit better performance compared to other ratio edit procedures available in the literature. The methodology is illustrated using 2010 and 2011 data from the Annual Survey of Manufacturers.

New Characteristic Relations in Type-II and III Intermittency

1997 ◽  
Vol 07 (04) ◽  
pp. 831-836 ◽  
Author(s):  
M. O. Kim ◽  
Hoyun Lee ◽  
Chil-Min Kim ◽  
Hyun-Soo Pang ◽  
Eok-Kyun Lee ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Lower Bound ◽  
Probability Distribution ◽  
Critical Exponent ◽  
Simulation Study ◽  
Critical Exponents ◽  
Control Parameter ◽  
The Other ◽  
Square Root ◽  
Type Ii

We obtained new characteristic relations in Type-II and III intermittencies according to the reinjection probability distribution. When the reinjection probability distribution is fixed at the lower bound of reinjection, the critical exponents are -1, as is well known. However when the reinjection probability distribution is uniform, the critical exponent is -1/2, and when it is of form [Formula: see text], -3/4. On the other hand, if the square root of Δ, which represents the lower bound of reinjection, is much smaller than the control parameter ∊, i.e. ∊ ≫ Δ1/2, critical exponent is always -1, independent of the reinjection probability distribution. Those critical exponents are confirmed by numerical simulation study.

An Eigenfunction Expansion Method in the Stress Concentration Analysis

2012 ◽  
Vol 204-208 ◽  
pp. 4406-4409
Author(s):  
Yang Bai ◽  
Li Chen
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Linear Combination ◽  
Eigenfunction Expansion ◽  
Original Problem ◽  
Expansion Method ◽  
Numerical Results ◽  
Eigenfunction Expansion Method ◽  
Completeness Property

This paper deals with the traditional stress concentration problems based on the eigenfunction expansion approach. Due to the completeness property of the eigenfunction space obtained by the previous researches, the solution of an arbitrary problem can be expressed by their linear combination. Thus the original problem is transformed into finding the combination of these eigenfuctions satisfying boundary conditions. By applying adjoint symplectic relationships of the ortho-normalization, the combination can be obtained numerically. Numerical results in tensional problems show that stress concentration appears when one of the ends of the solid is clamped. The concentration is seriously confined near the boundary of the fixed, and decrease rapidly with the distance of the boundarys.

A Functionally Graded Plane With a Circular Inclusion Under Uniform Antiplane Eigenstrain

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
X. Wang ◽  
E. Pan ◽  
A. K. Roy
Keyword(s):  
General Solution ◽  
Shear Modulus ◽  
Helmholtz Equation ◽  
Series Expansion ◽  
Original Problem ◽  
Circular Inclusion ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Fields ◽  
Homogeneous Material

The problem of a functionally graded plane with a circular inclusion under a uniform antiplane eigenstrain is investigated, where the shear modulus varies exponentially along the x direction. By introducing a new function which satisfies the Helmholtz equation, the general solution to the original problem is derived in terms of series expansion. Numerical results are then presented which demonstrate clearly that for a functionally graded plane, the strain and stress fields inside the circular inclusion under uniform antiplane eigenstrains are intrinsically nonuniform. This phenomenon differs from the corresponding homogeneous material case where both the strain and stress fields are uniform inside the circular inclusion.

scholarly journals Performance of Dual-Hop Relaying Over Shadowed Ricean Fading Channels

2011 ◽  
Vol 62 (4) ◽  
pp. 244-248 ◽  
Author(s):  
Aleksandra Cvetković ◽  
Jelena Anastasov ◽  
Stefan Panić ◽  
Mihajlo Stefanović ◽  
Dejan Milić
Keyword(s):  
Lower Bound ◽  
Fading Channels ◽  
Cumulative Distribution Function ◽  
Numerical Results ◽  
Cumulative Distribution ◽  
Performance Gain ◽  
Channel State ◽  
Ricean Fading ◽  
Average Bit Error Probability ◽  
Probability Density Function Pdf

Performance of Dual-Hop Relaying Over Shadowed Ricean Fading Channels In this paper, an analytical approach for evaluating performance of dual-hop cooperative link over shadowed Ricean fading channels is presented. New lower bound expressions for the probability density function (PDF), cumulative distribution function (CDF) and average bit error probability (ABEP) for system with channel state information (CSI) relay are derived. Some numerical results are presented to show behavior of performance gain for the proposed system. Analytical exact and lower bound expression for the outage probability (OP) of CSI assisted relay are obtained and required numerical results are compared.

Antiplane Shear Interface Cracks in Anisotropic Bimaterials

1991 ◽  
Vol 58 (2) ◽  
pp. 399-403 ◽  
Author(s):  
Kuang-Chong Wu ◽  
Yu-Tsung Chiu
Keyword(s):  
Stress Intensity ◽  
Lower Bound ◽  
Cross Sections ◽  
Antiplane Shear ◽  
Numerical Results ◽  
Composite Body ◽  
Interface Cracks ◽  
Integral Equation Formulation ◽  
Anisotropic Bimaterials ◽  
Shear Interface

An analysis of antiplane shear interface cracks in a finite anisotropic composite body is presented. The analysis is done by a new complex-variable integral equation formulation based on the solutions of a dislocation and body force in an infinite composite body. Numerical results of the stress intensity factors are presented for the composite bodies with finite rectangular cross-sections under uniform shear. The composite bodies are formed by bonding an orthotropic material to an isotropic material. The numerical results show that there exists a lower bound for the stress intensity factor for a fixed crack-length-to-height ratio and that the lower bound is attained in the case of isotropic bimaterial.

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