• 전자공학회논문지B
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• 제33B권7호
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• pp.107-115
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• 1996

The average distortio of the vector quantizer is calcualted using a probability function F of the input source for a given codebook. But, since the input source is unknown in geneal, using the sample vectors that is realized from a random vector having probability function F, a time-average opeation is employed so as to obtain an approximation of the average distortion. In this case the size of the smple set should be large so that the sample vectors represent true F reliably. The theoretical inspection about the approximation, however, is not perfomed rigorously. Thus one might use the time-average distortion without any verification of the approximation. In this paper, the convergence characteristics of the time-average distortions are theoretically investigated when the size of sample vectors or the size of codebook gets large. It has been revealed that if codebook size is large enough, then small sample set is enough to obtain the average distortion by approximatio of the calculated tiem-averaged distortion. Experimental results on synthetic data, which are supporting the analysis, are also provided and discussed.

• 한국산업정보학회논문지
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• 제28권1호
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• pp.27-34
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• 2023

최상의 에이전트-작업 할당을 결정하는 문제는 조합 최적화(combinatorial optimization)의 대표적인 문제이자 NP-난해(NP-hard)임이 알려져 있다. 본 연구에서는 에이전트와 작업의 할당 시 결정되는 작업 수행 확률(completion probability)이 불확실한 상황에서의 문제를 다룬다. 에이전트나 작업 내부의 요인 혹은 시스템 외적인 요소로 인한 작업 수행 확률은 고정적이기보다 불확실성을 갖는 것이 일반적이다. 불확실성을 고려하지 않은 할당 결정은 변동성이 있는 현실 상황에서 효과적이지 않은 결정이 될 수 있다. 작업 수행 확률의 불확실성을 수학적으로 반영하기 위해 본 연 구에서는 추계적 계획법(stochastic programming)을 활용한 수리 모형을 제시한다. 본 연구에서는 효율적으로 문제를 풀기 위해 표본 평균 근사법(sample average approximation)을 활용한 알고리즘을 제안한다. 본 문제 해결 방법론을 이용해 효과적인 할당 결정과 상한값과 하한값을 구할 수 있고, 결과의 성능을 확인하기 위해 최적 격차(optimality gap)와 분산을 실험을 통해 제시한다. 이를 통해 알고리즘으로 구한 할당 결정의 우수성 및 강건성을 보인다.

• 한국경영과학회지
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• 제37권3호
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• pp.135-150
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• 2012

This paper presents a portfolio model for a long-term power generation mix problem. The proposed portfolio model evaluates generation mix by considering the tradeoffs between the expected cost for power generation and its variability. Unlike conventional portfolio models measuring variance, we introduce Conditional Value-at-Risk (CVaR) in designing the variability with aims to considering events that are enormously expensive but are rare such as nuclear power plant accidents. Further, we consider uncertainties associated with future electricity demand, fuel prices and their correlations, and capital costs for power plant investments. To obtain an objective generation by each energy source, we employ the sample average approximation method that approximates the stochastic objective function by taking the average of large sample values so that provides asymptotic convergence of optimal solutions. In addition, the method includes Monte Carlo simulation techniques in generating random samples from multivariate distributions. Applications of the proposed model and method are demonstrated through a case study of an electricity industry with nuclear, coal, oil (OCGT), and LNG (CCGT) in South Korea.

• 산업경영시스템학회지
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• 제34권4호
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• pp.189-196
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• 2011

In this paper, we propose a logical control-based actor-critic algorithm as an efficient approach for the approximation of the capacitated fab scheduling problem. We apply the average reward temporal-difference learning method for estimating the relative value functions of system states, while avoiding deadlock situation by Banker's algorithm. We consider the Intel mini-fab re-entrant line for the evaluation of the suggested algorithm and perform a numerical experiment by generating some sample system configurations randomly. We show that the suggested method has a prominent performance compared to other well-known heuristics.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.107-117
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• 2003

We study the integration problem in which one wants to compute the approximation to the definite integral in the average case setting. We choose the composite Newton- Cotes quadratures as our algorithm and the function values at equally spaced sample points on the given interval［0, 1］as information. We compute the average case error of composite Newton-Cotes quadratures and show that it is minimal (modulo a multi-plicative constant).

• 한국경영과학회지
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• 제17권2호
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• pp.91-106
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• 1992

It an inventory control system, the demand over time are often assumed to be independently identically distributed (i. i. d.). However, the demands may well be correlated over time in many situations. The estimation of reorder points is not simple for correlated demands with variable lead time. In this paper, a general class of autoregressive and moving average processes is considered for modeling the demands of an inventory item. The first four moments of the lead-time demand (L) are derived and used to approximate the distribution of L. The reorder points at given service level are then estimated by the three approximation methods : normal approximation, Charlier series and Pearson system. Numerical investigation shows that the Pearson system and the Charlier series performs extremely well for various situations whereas the normal approximation show consistent underestimation and sensitive to the distribution of lead time. The same conclusion can be reached when the parameters are estimated from the sample based on the simulation study.

• Journal of Communications and Networks
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• 제12권3호
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• pp.222-230
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• 2010

In this paper, we present a closed-form approximation of the average sum rate of zero-forcing (ZF) beamforming (BF) with semi-orthogonal user selection (SUS). We first derive the survival probability associated with the SUS that absolute square of the channel correlation between two users is less than the orthogonalization level threshold (OLT).With this result, each distribution for the number of surviving users at each iteration of the SUS and the number of streams for transmission is calculated. Secondly, the received signal power of ZF-BF is represented as a function of the elements of the upper triangular matrix from QR decomposition of the channel matrix. Thirdly, we approximate the received signal power of ZF-BF with the SUS as the maximum of scaled chisquare random variables where the scaling factor is approximated as a function of both OLT and the number of users in the system. Putting all the above derivations and order statistics together, the approximated ergodic sum rate of ZF-BF with the SUS is shown in a closed form. The simulation results verify that the approximation tightly matches with the sample average for any OLT and even for a small number of users.

• 정보처리학회논문지A
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• 제11A권5호
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• pp.401-406
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• 2004

이 논문에서는 정적분의 근사 값을 계산하는 여러 적분 문제 중에서 보간 법을 사용하는 수치적분법의 평균오차에 대해서 연구한다. 특히 가장 널리 쓰이고 있는 방법 중의 하나인 복합 Newton-Cotes 구적법의 평균오차에 대해서 연구한다. 주어진 구간을 등 간격으로 나누었을 때, 각 점에서의 함수 값을 information으로 사용할 경우, 복합 Newton-Cotes 구적법의 평균오차를 계산하였으며, 이 때 이 오차는 가장 최소임을 이 논문에서 증명한다.

• 산업경영시스템학회지
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• 제35권3호
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• pp.52-61
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• 2012

The design method for cumulative sum (CUSUM) control charts, which can be robust to autoregressive moving average (ARMA) modeling errors, has not been frequently proposed so far. This is because the CUSUM statistic involves a maximum function, which is intractable in mathematical derivations, and thus any modification on the statistic can not be favorably made. We propose residual-based robust CUSUM control charts for monitoring autocorrelated processes. In order to incorporate the effects of ARMA modeling errors into the design method, we modify parameters (reference value and decision interval) of CUSUM control charts using the approximate expected variance of residuals generated in model uncertainty, rather than directly modify the form of the CUSUM statistic. The expected variance of residuals is derived using a second-order Taylor approximation and the general form is represented using the order of ARMA models with the sample size for ARMA modeling. Based on the Monte carlo simulation, we demonstrate that the proposed method can be effectively used for statistical process control (SPC) charts, which are robust to ARMA modeling errors.

• 응용통계연구
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• 제18권1호
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• pp.57-66
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• 2005

본 연구에서는 얼랑(Erlang)분포의 규모모수에 대 한 축차확률비검정(SPRT)과 관련된 적분방정식의 정학한 해를 구하는 법을 살펴보기로 한다. 축차확률비검정에서 그 평균 표본 개수, 그리고 1종 오류 확률과 2종 오류 확률은 프레돔 형태의 적분 방정식으로 나타나게 된다. 이러한 적분 방정식은 보통 가우시안 쿼드러쳐(qudrature)를 이용하여 근사적으로 그 해를 구하는 것이 일반적이다. 얼랑분포의 경우 이러한 적분방정식의 해가 정확하게 구할 수 있음이 알려져 있다. 본 연구에서는 얼랑분포에서 그 해를 구하는 구체적 방법을 살펴보기로 한다.