• 한국수학교육학회지시리즈A:수학교육
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• 제51권2호
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• pp.95-114
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• 2012

This study examines the use of ill-structured problem to help the 4th graders' problem solving and reasoning. It appears that children with good understanding of problem situation tend to accept the situation as itself rather than just as texts and produce various results with extraction of meaningful variables from situation. In addition, children with better understanding of problem situation show AR (algorithmic reasoning) and CR (creative reasoning) while children with poor understanding of problem situation show just AR (algorithmic reasoning) on their reasoning type.

• Management Science and Financial Engineering
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• 제12권1호
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• pp.113-125
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• 2006

Bilevel programming problem is a two-stage optimization problem where the constraint region of the first level problem is implicitly determined by another optimization problem. In this paper we consider the bilevel quadratic/linear fractional programming problem in which the objective function of the first level is quasiconcave, the objective function of the second level is linear fractional and the feasible region is a convex polyhedron. Considering the relationship between feasible solutions to the problem and bases of the coefficient submatrix associated to variables of the second level, an enumerative algorithm is proposed which finds a global optimum to the problem.

• Journal of applied mathematics & informatics
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• 제9권2호
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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 applied mathematics & informatics
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• 제9권2호
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• pp.695-703
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• 2002

The fractional order evolutionary integral equations have been considered by first author in [6], the existence, uniqueness and some other properties of the solution have been proved. Here we study the continuation of the solution and its fractional order derivative. Also we study the generality of this problem and prove that the fractional order diffusion problem, the fractional order wave problem and the initial value problem of the equation of evolution are special cases of it. The abstract diffusion-wave problem will be given also as an application.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.1-11
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• 2010

The conditional covering problem is an important variation of well studied set covering problem. In the set covering problem, the problem is to find a minimum cardinality vertex set which will cover all the given demand points. The conditional covering problem asks to find a minimum cardinality vertex set that will cover not only the given demand points but also one another. This problem is NP-complete for general graphs. In this paper, we present an efficient algorithm to solve the conditional covering problem on interval graphs with n vertices which runs in O(n)time.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2000년도 춘계공동학술대회 논문집
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• pp.613-616
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• 2000

This paper considers the problem of subway crew scheduling. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper, we propose two basic techniques that solve the problem in a reasonable time, though the optimality of the solution is not guaranteed. To reduce the number of variables, we adopt column-generation technique. We could develop an algorithm that solves column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational results show column-generation makes the problem of treatable size, and variable fixing enables us to solve LP relaxation in shorter time without a considerable increase in the optimal value. Finally, we were able to obtain an integer optimal solution of a real instance within a reasonable time.

• 한국경영과학회지
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• 제34권3호
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• pp.125-136
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• 2009

The container packing problem Is one of the traditional optimization problems, which is very related to the knapsack problem and the bin packing problem. In this paper, we deal with the quadratic multiple container picking problem (QMCPP) and it Is known as a NP-hard problem. Thus, It seems to be natural to use a heuristic approach such as evolutionary algorithms for solving the QMCPP. Until now, only a few researchers have studied on this problem and some evolutionary algorithms have been proposed. This paper introduces a new efficient evolutionary algorithm for the QMCPP. The proposed algorithm is devised by improving the original network random key method, which is employed as an encoding method in evolutionary algorithms. And we also propose local search algorithms and incorporate them with the proposed evolutionary algorithm. Finally we compare the proposed algorithm with the previous algorithms and show the proposed algorithm finds the new best results in most of the benchmark instances.

• Management Science and Financial Engineering
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• 제16권3호
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• pp.95-102
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• 2010

This paper considers the robust inventory control problem introduced by Bertsimas and Thiele [4]. In their paper, they have shown that the robust version of the inventory control problem can be solved by solving a nominal inventory problem which is formulated as a mixed integer program. As a proper generalization of the model, we consider the problem with non-stationary cost. In this paper, we show that the generalized version can also be solved by solving a nominal inventory problem. Furthermore, we show that the problem can be solved efficiently.

• 경영과학
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• 제14권2호
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• pp.47-61
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• 1997

This paper considers the parallel machines scheduling problem characterized as a multi-objective combinatorial problem. As this problem belongs to the NP-complete problem, genetic algorithms are applied instead of the traditional analytical approach. The purpose of this study is to show how the problem can be effectively solved by using genetic algorithms with a permutation approach. First, a permutation representation which can effectively represent the chromosome is introduced for this problem . Next, a schedule builder which employs the combination of scheduling theories and a simple heuristic approach is suggested. Finally, through the computer experiments of genetic algorithm to test problems, we show that the niche formation method does not contribute to getting better solutions and that the PMX crossover operator is the best among the selected four recombination operators at least for our problem in terms of both the performance of the solution and the operational convenience.

• 한국경영과학회지
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• 제28권4호
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• pp.191-198
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• 2003

The generalized knapsack problem or gknap is the combinatorial optimization problem of optimizing a nonnegative linear function over the integral hull of the intersection of a polynomially separable 0-1 polytope and a knapsack constraint. The knapsack, the restricted shortest path, and the constrained spanning tree problem are a partial list of gknap. More interesting1y, all the problem that are known to have a fully polynomial approximation scheme, or FPTAS are gknap. We establish some necessary and sufficient conditions for a gknap to admit an FPTAS. To do so, we recapture the standard scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a weaker sufficient condition than the strong NP-hardness that a gknap does not have an FPTAS. Finally, we apply the conditions to explore the fully polynomial approximability of the constrained spanning problem whose fully polynomial approximability is still open.