• Management Science and Financial Engineering
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• 제10권1호
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• pp.97-106
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• 2004

In this paper, we propose an effective cut generation method based on the Chvatal-Gomory procedure for a variable-capacity (0,l)-Knapsack problem with two general integer variables. We first derive a class of valid inequalities for the problem using Chvatal-Gomory procedure, then analyze the associated separation problem. Based on the results, we show that there exists a pseudo-polynomial time algorithm to solve the separation problem. By analyzing the theoretical strength of the inequalities which can be generated by the proposed cut generation method, we show that generated inequalties define facets under mild conditions. We also extend the result to the case in which a nontrivial upper bound is imposed on a general integer variable.

• 대한수학회보
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• 제46권3호
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• pp.521-534
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• 2009

In this paper we present new large-update primal-dual interior point algorithms for $P_*$ linear complementarity problems(LAPS) based on a class of kernel functions, ${\psi}(t)={\frac{t^{p+1}-1}{p+1}}+{\frac{1}{\sigma}}(e^{{\sigma}(1-t)}-1)$, p $\in$ [0, 1], ${\sigma}{\geq}1$. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $P_*$ LAPS. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $P_*$ LAPS have $O((1+2+\kappa)n^{{\frac{1}{p+1}}}lognlog{\frac{n}{\varepsilon}})$ complexity bound. When p = 1, we have $O((1+2\kappa)\sqrt{n}lognlog\frac{n}{\varepsilon})$ complexity which is so far the best known complexity for large-update methods.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1998년도 추계학술대회 논문집
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• pp.397-400
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• 1998

This paper has a dual purpose. First, we consider a relaxation algorithm which seems to be particularly suitable for multicasting routing problems. We show that the algorithm has polynomial complexity. Second, to measure the quality of solutions in comparison to the optimal solutions over a wide range of network sizes for which the computation of the optimal costs is too excessive, we also propose a random graph generation scheme in which an asymptotic lower bound on the expected optimal cost can be computed as a function of network node size.

• 대한수학회지
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• 제34권2호
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• pp.293-307
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• 1997

In this paper we present the $L^2$-estimation for the kernel $K_n$ of the remaider term for the Gaussian quadrature with respect to one of four Chebyshev weight functions and the error bound of the type on the contour $$ $\mid$R_n(f)$\mid$ \leq \frac{2\pi}{\sqrt{l(\Gamma)}} max_{z\in\Gamma}$\mid$f(z)$\mid$ (\smallint_\Gamma $\mid$K_n(z)$\mid$^2$\mid$dz$\mid$)^\frac{2}{1}, $$ where $l(\Gamma)$ denotes the length of the contour $\Gamma$.

• 충청수학회지
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• 제22권4호
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• pp.777-787
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• 2009

In this paper we investigate the upper bound on the Castelnuovo-Mumford regularity of a graded module with linear free presentation. Let M be a finitely generated graded module over a polynomial ring R with zero dimensional support. We prove that if M is generated by elements of degree $d{\geq}0$ with a linear free presentation $$\bigoplus^p{R}(-d-1)\longrightarrow^{\phi}\bigoplus^q{R}(-d){\longrightarrow}M{\longrightarrow}0$$, then the Castelnuovo-Mumford regularity of M is at most d+q-1. As an important application, we can prove vector bundle technique, which was used in [11], [13], [17] as a tool for obtaining several remarkable results.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.231-243
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• 2007

The existence of solutions of a class of two-point boundary value problems for higher order differential equations is studied. Sufficient conditions for the existence of at least one solution are established. It is of interest that the nonlinearity f in the equation depends on all lower derivatives, and the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bound of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.

• Management Science and Financial Engineering
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• 제17권1호
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• pp.95-116
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• 2011

This paper considers a flowshop scheduling problem where a customer orders multiple products (jobs) from a production facility. The objectives are to minimize makespan and to minimize the sum of order (batch) completion times. The order cannot be shipped unless all the products in the order are manufactured. This problem was motivated by numerous real world problems encountered by a variety of manufacturers. For the makespan objective, we develop an optimal solution procedure which runs in polynomial time. For the sum of order completion time objective, we establish the complexity of the problem including several special cases. Then, we introduce a simple heuristic and find an asymptotically tight worst case bound on relative error. Finally, we conclude the paper with some implications.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권3호
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• pp.189-202
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• 2009

In this paper we propose new primal-dual interior point algorithms for $P_*(\kappa)$ linear complementarity problems based on a new class of kernel functions which contains the kernel function in [8] as a special case. We show that the iteration bounds are $O((1+2\kappa)n^{\frac{9}{14}}\;log\;\frac{n{\mu}^0}{\epsilon}$) for large-update and $O((1+2\kappa)\sqrt{n}log\frac{n{\mu}^0}{\epsilon}$) for small-update methods, respectively. This iteration complexity for large-update methods improves the iteration complexity with a factor $n^{\frac{5}{14}}$ when compared with the method based on the classical logarithmic kernel function. For small-update, the iteration complexity is the best known bound for such methods.

• 한국컴퓨터정보학회논문지
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• 제21권2호
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• pp.97-103
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• 2016

This paper deals with the cycle time minimization problem that determines the productivity in printed circuit board (PCB) with n components using the m placement machines. This is known as production cycle time determination problem (PCTDP). The polynomial time algorithm to be obtain the optimal solution has been unknown yet, therefore this hard problem classified by NP-complete. This paper gets the initial assignment result with the machine has minimum unit placement time per each component firstly. Then, the balancing process with reallocation from overhead machine to underhead machine. Finally, we perform the swap optimization and get the optimal solution of cycle time $T^*$ within O(mn) computational complexity. For experimental data, the proposed algorithm can be obtain the same result as integer programming+branch-and-bound (IP+B&B) and B&B.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 추계학술대회 논문집 학회본부 B
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• pp.413-416
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• 1998

We investigate the Hurwitz stability condition using the coefficient diagram. The coefficient diagram consists of a plot of logarithmic values of the coefficients of the characteristic polynomial versus the degree of the coresponding coefficients. The logarithmic value of the coefficient of the characteristic polynomials are plotted in the descending order. Using the Bhattacharyya, Chapellat and Keel's algorithm, the sufficient and necessary condition for Hurwitz stability are reconstructed using the coefficient diagram. With the coefficient diagram we also present some necessary or sufficient conditions for Hurwitz stability of polynomials. In addition we obtain a lower bound for the Manabe parameter $\tau$.