• 산업경영시스템학회지
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• 제21권45호
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• pp.93-100
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• 1998

The researches of Linear Programming are Khachiyan Method, which uses Ellipsoid Method, and Karmarkar, Affine, Path-Following and Interior Point Method which have Polynomial-Time complexity. In this study, Karmarkar Method is more quickly solved as 50 times then Simplex Method for optimal solution. but some special problem is not solved by Karmarkar Method. As a result, the algorithm by APL Language is proved time efficiency and optimal solution in the Primal-Dual interior point algorithm. Furthermore Karmarkar Method and Primal-Dual interior point Method is compared in some examples.

• 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 1995년도 추계학술대회 논문집 학회본부
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• pp.113-116
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• 1995

In this study, we formulate production costing problem with environmental and operational constraints into an optimization problem of LP form. In the process of formulation, auxiliary constraints on which reflect unit loading order are constructed to reduce the size of optimization problem by economic operation rules. As a solution of the optimization problem in LP form, we use Karmarkar's method which performs much faster than simplex method in solving large scale LP problem. The proposed production costing algorithm is applied to IEEE Reliability Test System, and performs production simulation under environmental and operational constraints. Test and computer results are given to show the accuracy and usefulness of the proposed algorithm in the field of power system planning.

• 대한산업공학회지
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• 제13권1호
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• pp.53-60
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• 1987

Karmakar suggested two methods to transform the general linear programming into his specially structured linear programming problem. We show that there are bad cases that cause difficulties in the use of Karmakar's methods. We also develop a new transformation method which can handle those difficulties.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 하계학술대회 논문집 B
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• pp.793-796
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• 1996

This study proposes a new algorithm which performs a production simulation under various constraints and maintains computational efficiency. In order to consider the environmental and operational constraints, the proposed algorithm is based on optimization techniques formulated in LP form In the algorithm, "system characteristic constraints" reflect the system characteristics such as LDC shape, unit loading order and forced outage rate. By using the concept of Energy Invariance Property and two operational rules i.e. Compliance Rule for Emission Constraint, Compliance Rule for Limited Energy of Individual Unit, the number of system characteristic constraints is appreciably reduced. As a solution method of the optimization problem, the author uses Karmarkar's method which performs effectively in solving large scale LP problem. The efficiency of production simulation is meaningful when it is effectively used in power system planning. With the proposed production simulation algorithm, an optimal expansion planning model which can cope with operational constraints, environmental restriction, and various uncertainties is developed. This expansion planning model is applied to the long range planning schemes by WASP, and determines an optimal expansion scheme which considers the effect of supply interruption, load forecasting errors, multistates of unit operation, plural limited energy plants etc.