• Management Science and Financial Engineering
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• v.13 no.2
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• pp.47-77
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• 2007

This paper considers a scheduling problem where a customer orders multiple products(jobs) from a production facility. The objective is to minimize the sum of the order(batch) completion times. While a machine can process only one job at a time, multiple machines can simultaneously process jobs in a batch. Although each job has a unique processing time, we consider the case where batch processing times are identical. This simplification allows us to develop heuristics with improved performance bounds. This problem was motivated by a real world problem encountered by foreign electronics manufacturers. We first establish the complexity of the problem. For the two parallel machine case, we introduce two simple but intuitive heuristics, and find their worst case relative error bounds. One bound is tight and the other bound goes to 1 as the number of orders goes to infinity. However, neither heuristic is superior for all instances. We extend one of the heuristics to an arbitrary number of parallel machines. For a fixed number of parallel machines, we find a worst case bound which goes to 1 as the number of orders goes to infinity. Then, a tighter bound is found for the three parallel machine case. Finally, the heuristics are empirically evaluated.

• Journal of KIISE:Software and Applications
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• v.28 no.9
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• pp.681-687
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• 2001

In order to raise a class discrimination power by combining multiple classifiers under the Bayesian decision theory, the upper bound of a Bayes error rate bounded by the conditional entropy of a class variable and decision variables obtained from training data samples should be minimized. Wang and Wong proposed a tree dependence first-order approximation scheme of a high order probability distribution composed of the class and multiple feature pattern variables for minimizing the upper bound of the Bayes error rate. This paper presents an extended high order product approximation scheme dealing with higher order dependency more than the first-order tree dependence, based on the minimization of the upper bound of the Bayes error rate. Multiple recognizers for unconstrained handwritten numerals from CENPARMI were combined by the proposed approximation scheme using the Bayesian formalism, and the high recognition rates were obtained by them.

• Journal of The Korean Society of Agricultural Engineers
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• v.48 no.1
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• pp.3-10
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• 2006

The chemical fractions of heavy metals were investigated in the soils of reclaimed and natural tidelands of southwest coastal area of Korea. The distribution pattern of each heavy metal in different fractions was in the order: 1) Cu : organic bound > organic complex > residual > exchangeable = water soluble. 2) Cr : residual > organic bound > organic complex > water soluble > exchangeable. 3) Pb : organic bound > residual > organic complex > water soluble > exchangeable. 4) Cd residual > organic bound > organic complex > water soluble = exchangeable. 5) Zn : organic bound > residual > organic complex > water soluble > exchangeable. The content of residual Zn showed positive correlation with organic matter content but organic bound Zn showed negative correlation with CEC. The content of residual and exchangeable Cd showed highly positive correlation with organic matter content but residual, organic bound, and exchangeable Cd showed negative correlations with CEC. Water soluble Pb showed positive correlation with CEC but organic bound Pb showed negative correlation with CEC.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.9
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• pp.664-668
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• 2003

A new sliding mode control method based on the lower bound of control gain is presented. Although the magnitube of the proposed control input is larger than that of the conventional control input using both lower and upper bounds, the positive-negative exchanging chattering is reduced and reaching mode is shorter. Because the proposed scheme needs only the lower bound of control gain, it is applicable to the system whose upper bound of control gain is doubtful to determine such as the control gain depends on the system states. It is proved that the proposed control method guarantees the sliding condition. The analysis of differences between the conventional method and the proposed method is given. The validity of the proposed control strategy is shown through a 2nd-order nonlinear system example.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.1081-1094
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• 2017

For a poset $P=(X,{\leq}_P)$, the linear discrepancy of P is the minimum value of maximal differences of all incomparable elements for all possible labelings. In this paper, we find a lower bound and an upper bound of the linear discrepancy of a product of two posets. In order to give a lower bound, we use the known result, $ld({\mathbf{m}}{\times}{\mathbf{n}})={\lceil}{\frac{mn}{2}}{\rceil}-2$. Next, we use Dilworth's chain decomposition to obtain an upper bound of the linear discrepancy of a product of a poset and a chain. Finally, we give an example touching this upper bound.

• Microbiology and Biotechnology Letters
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• v.23 no.1
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• pp.87-90
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• 1995

A process of organically bound germanium preparation was developed for healthy food using inorganic germanium adapted Saccharomyces cerevisiae. Adaptations of Saccharomyces cerevisiae against inorganic germanium were successively carried out through stepwise increase of GeO$_{2}$ concentration in order to produce high quantities of germanium bound yeast. Productivity of yeast and quantities of germanium in yeast were obtained 70.2 g/l and 9780 ppm, repectively, when adapted yeast and fed batch culture were used. Germanium taken-up yeast is to be organically bound germanium by evidence of no difference of germanium content after dialysis.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.783-797
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• 2019

In this paper, we introduce and investigate a subclass ${\Im}_{\Sigma}({\alpha},{\beta},{\gamma})$ of analytic and bi-univalent functions of complex order in the open unit disk U in complex plane. Here, we obtain an upper bound for the second Hankel determinant of the functions belonging to this class. Moreover, several interesting conclusions of the results obtained here are also discussed.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.631-638
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• 2018

Chellai et al. [3] gave an upper bound on the [1, 2]-domination number of tree and posed an open question "how to classify trees satisfying the sharp bound?". Yang and Wu [5] gave a partial solution for tree of order n with ${\ell}$-leaves such that every non-leaf vertex has degree at least 4. In this paper, we give a new upper bound on the [1, 2]-domination number of tree which extends the result of Yang and Wu. In addition, we design a polynomial time algorithm for solving the open question. By using this algorithm, we give a characterization on the [1, 2]-domination number for trees of order n with ${\ell}$ leaves satisfying $n-{\ell}$. Thereby, the open question posed by Chellai et al. is solved.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.115-124
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• 1993

A structural system reliability analysis is studied for the safety assessment of midship section. Probabilistically dominant collapse modes are generated by Element Replacement Method and Incrimental Load Method. In order to avoid generating the same modes repeatedly, it is branched at final plastic hinge. Using first and second order bound methods, system failure probability of midship section is computed and compared with deterministic load factor method to show the usefulness of the proposed method.

• KIEE International Transactions on Power Engineering
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• v.2A no.3
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• pp.121-128
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• 2002

This study proposes a new method for transmission system expansion planning using fuzzy integer programming. It presents stepwise cost characteristics analysis which is a practical condition of an actual system. A branch and bound method which includes the network flow method and the maximum flow - minimum cut set theorem has been used in order to carry out the stepwise cost characteristics analysis. Uncertainties of the permissibility of the construction cost and the lenient reserve rate and load forecasting of expansion planning have been included and also processed using the fuzzy set theory in this study. In order to carry out the latter analysis, the solving procedure is illustrated in detail by the branch and bound method which includes the network flow method and maximum flow-minimum cut set theorem. Finally, case studies on the 21- bus test system show that the algorithm proposed is efficiently applicable to the practical expansion planning of transmission systems in the future.