• 대한산업공학회지
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• 제17권2호
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• pp.131-142
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• 1991

The concept of criterion function is proposed as a framework for comparing the geometric and computational characteristics of various nonlinear programming approaches to linear programming such as the method of centers, Karmakar's algorithm and the gravitational method. Also, we discuss various computational issues involved in obtaining an efficient parallel implementation of these methods. Clearly, the most time consuming part in solving a linear programming problem is the direction finding procedure, where we obtain an improving direction. In most cases, finding an improving direction is equivalent to solving a simple optimization problem defined at the current feasible solution. Again, this simple optimization problem can be seen as a least squares problem, and the computational effort in solving the least squares problem is, in fact, same as the effort as in solving a system of linear equations. Hence, getting a solution to a system of linear equations fast is very important in solving a linear programming problem efficiently. For solving system of linear equations on parallel computing machines, an iterative method seems more adequate than direct methods. Therefore, we propose one possible strategy for getting an efficient parallel implementation of an iterative method for solving a system of equations and present the summary of computational experiment performed on transputer based parallel computing board installed on IBM PC.

• 대한전기학회논문지:전력기술부문A
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• 제55권11호
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• pp.447-452
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• 2006

This paper presents a scheme to solve the congestion problem with phase-shifting transformer(PST) controls and power generation controls using linear programming method. A good design of PST and power generation control can improve total transfer capability(TTC) in interconnected systems. This paper deals with an application of optimization technique for TTC calculation. Linear programming method is used to maximize power flow of tie line subject to security constraints such as voltage magnitude and real power flow in interconnected systems. The results are compared with that of repeat power flow(RPF) and sequential quadratic programming(SQP). The proposed method is applied to 10 machines 39 buses model systems to show its effectiveness.

• 경영과학
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• 제13권2호
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• pp.205-213
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• 1996

This paper develops a simple interactive procedure which can be efficiently used to solve a bicriteria linear programming problem. The procedure exploits the relatively simple structure of the bicriterion linear programming problem. Its application to a transportation problem is also presented. The results demonstrate that the method developed in this paper could be easily applicable to any bicriteria linear program in general.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.506-511
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• 1998

In this paper we consider multiobjective linear programming problems with coefficients of the objective functions specified by possibility distributions. Possibly and necessarily efficient solution sets are defined as funny solution sets whose membership grades represent possibility and necessity degrees to which a feasible solution is efficient. Considering efficiency condition and its dual condition in ordinary multiobjective linear programming problem, we propose efficiency test methods based on an extreme ray generation method. Since the proposed methods can be put in the part of a bi-section method, we can develop calculation and methods of the degree of possible and necessary efficiency for feasible solutions.

• 한국경영과학회지
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• 제18권3호
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• pp.101-111
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• 1993

The purpose of this paper is to show the graphic representation of a linear programming problem by a projection method. First, we develop a projection method which conserves the optimality in the projected space, and next we introduce an algorithm to visualize the feasible solution set and the solution process by the projection method. Finally, we give an example to represent a 4-dimensional linear programming problem graphically.

• East Asian mathematical journal
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• 제35권5호
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• pp.597-612
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• 2019

In this study, we propose a new logarithmic barrier approach to solve linear programming problem using the projective method of Karmarkar. We are interested in computation of the direction by Newton's method and of the step-size using minorant functions instead of line search methods in order to reduce the computation cost. Our new approach is even more beneficial than classical line search methods. We reinforce our purpose by many interesting numerical simulations proved the effectiveness of the algorithm developed in this work.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년도 제37회 하계학술대회 논문집 A
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• pp.262-263
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• 2006

This paper presents a scheme to solve the congestion problem with phase-shifting transformer(PST) and power generation using linear programming method. A good design of PST and power generation control can improve total transfer capability(TTC) in interconnected systems. This paper deals with an application of optimization technique for TTC calculation. linear programming method is used to maximize power flow of tie line subject to security constraints such as voltage magnitude and real power flow. The proposed method is applied to 10 machines 39 buses model systems to show its effectiveness.

• 한국국방경영분석학회지
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• 제9권2호
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• pp.57-60
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• 1983

We show that the complexity of Simplex Method for Linear Programming problem is equivalent to the complexity of finding just an adjacent basic feasible solution if exists. Therefore a simplex type method which resolves degeneracy in polynomial time with respect to the size of the given linear programming problem can solve the general linear programming problem in polynomial steps.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1995년도 하계학술대회 논문집 B
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• pp.516-518
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• 1995

This paper presents the optimal short-term operation scheduling by using fuzzy linear programming method on cogeneration systems connected with auxiliary equipments. Simulation is performed in case of the bottomming cycle. Modeling of cogeneration systems and auxiliary equipments is done, the effectiveness of modeling is evaluated through the detailed simulation. After the optimal operation scheduling is established by using linear programming method, the last optimal operation scheduling is established by using fuzzy linear programming method. The results of simulation show the auxiliary equipments can be effeciently operated in case of the bottomming cycle by modeling proposed in this paper.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권3호
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• pp.232-239
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• 2006

This paper is for applying interactive fuzzy linear programming for the problem of product mix planning, which is one of the aggregate planning problem. We developed a modified algorithm, which has two-phase approach for interactive fuzzy linear programming to get a better solution. Adding two-phase method, we expect to obtain not only the highest membership degree, but also a better utilization of each constrained resource.