• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.307-312
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• 1994

The authors have been devoted to researches on fuzzy theories and their applications, especially control theory and application problems, for recent years. In this paper, the authors present results on a comparison of optimal solutions between ones of an ordinary-typed mathematical linear programming problem(O.M.I.P. problem) and ones of a Zimmerman-typed fuzzy mathematical linear programming problem (F.M.L.P. problem), and comment about the sensitivity (differences and fuzziness on between O.M.L.P. problem and F.M.L.P. problem) on optimal solutions of these mathematical linear programming problems.

• Management Science and Financial Engineering
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• v.14 no.2
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• pp.25-44
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• 2008

This paper concentrates on reduction of a Quadratic Fractional Integer Programming Problem (QFIP) to a 0-1 Mixed Linear Programming Problem (0-1 MLP). The solution technique is based on converting the integer variables to binary variables and then the resulting Quadratic Fractional 0-1 Programming Problem is linearized to a 0-1 Mixed Linear Programming problem. It is illustrated with the help of a numerical example and is solved using the LINDO software.

• Journal of the Korean Operations Research and Management Science Society
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• v.3 no.1
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• pp.75-79
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• 1978

The use of three mathematical programming techniques (quadratic programming, integer quadratic programming and linear programming) is discussed to solve some problems in linear regression analysis. When the criterion is the minimization of the sum of squared deviations and the parameters are linearly constrained, the problem may be formulated as quadratic programming problem. For the selection of variables to find "best" regression equation in statistics, the technique of integer quadratic programming is proposed and found to be a very useful tool. When the criterion of fitting a linear regression is the minimization of the sum of absolute deviations from the regression function, the problem may be reduced to a linear programming problem and can be solved reasonably well.ably well.

• Korean Management Science Review
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• v.13 no.2
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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.

• Korean Management Science Review
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• v.10 no.2
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• pp.1-9
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• 1993

This paper shows the application of fuzzy set and nonlinear membership function to linear programming problems in a fuzzy environment. In contrast to typical linear programming problems, the objectives and constraints of the problem in a fuzzy environment are defined imprecisely. This paper describes that fuzzy linear programming models can be formulated using the basic concepts of membership functions and fuzzy sets, and that they can be solved by quadratic programming methods. In a numerical example, a linear programming problem with two constraints and two decision variables is provided to illustrate the solution procedure.

• Journal of Korean Institute of Industrial Engineers
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• v.17 no.2
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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.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.337-349
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• 2011

This paper is concerned with deriving necessary and sufficient optimality conditions for a fuzzy linear programming problem. Toward this end, an equivalence between fuzzy and crisp linear programming problems is established by means of a specific ranking function. Under this setting, a main theorem gives optimality conditions which do not seem to be in conflict with the so-called Karush-Kuhn-Tucker conditions for a crisp linear programming problem.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.3
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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.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.717-730
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• 2002

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.3
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• pp.95-104
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• 2001

In this paper, we consider a maximin version of the linear programming knapsack problem with extended generalized upper bound (GUB) constraints. We solve the problem efficiently by exploiting its special structure without transforming it into a standard linear programming problem. We present an O(n$^3$) algorithm for deriving the optimal solution where n is the total number of problem variables. We illustrate a numerical example.