• 한국경영과학회지
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• 제15권2호
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• pp.97-104
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• 1990

The problem is a variation of the weighted set-covering problem (SCP) which requires the minimum-cost cover to be self-covering. It is shown that direct extension of the well-known greedy heuristic for SCP can have an arbitrarily large error in the worst case. It remains an open question whther these exists a greedy heuristic with a finite error bound.

• 산업경영시스템학회지
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• 제32권3호
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• pp.188-193
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• 2009

본 논문은 조립과 분리시스템이 혼합된 Fork-and-Join 시스템에서의 일정계획문제를 고려하고 있다. 최초 단계에서는 구성품단위로 분리가 발생하고 두 번째 단계에서는 부품생산단계에서 각 부품 또는 구성품이 서로 다른 설비와 경로를 통해 독립적으로 생산된 후 최종 조립단계로 이동하게 되고, 그곳에서 조립공정을 통해 제품으로 완성된다. 본 논문에서는 이러한 Fork-and-Join 시스템에서 최종완료시간(makespan)을 최소화 할 수 있는 발견적 해법을 제안하고 이 해법의 최악오차한계(worst-case error bound)가 2라는 것을 증명한다. 또한, 제안된 문제의 효과적인 3가지 하한값(lower bound)을 제시하고 다양한 수치실험을 통해 제안된 발견적 해법의 결과와 하한값과의 비교를 통해 제안된 해법이 성능이 우수함을 증명한다.

• Industrial Engineering and Management Systems
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• 제14권1호
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• pp.22-31
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• 2015

In this paper, a two-stage hybrid flow shop problem is considered. Specifically, there exist identical parallel machines at stage 1 and two dedicated machines at stage 2, and the objective of the problem is to minimize makespan. After being processed by any machine at stage 1, a job must be processed by a specific machine at stage 2 depending on the job type, and one type of jobs can have different processing times on each machine. First, we introduce the problem and establish complexity of several variations of the problem. For some special cases, we develop optimal polynomial time solution procedures. Then, we establish some simple lower bounds for the problem. In order to solve this NP-hard problem, three heuristics based on simple rules such as the Johnson's rule and the LPT (Longest Processing Time first) rule are developed. For each of the heuristics, we provide some theoretical analysis and find some worst case bound on relative error. Finally, we empirically evaluate the heuristics.

• Journal of Positioning, Navigation, and Timing
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• 제12권1호
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• pp.51-58
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• 2023

Geofencing supports unmanned aerial vehicle (UAV) operation by defining stay-in and stay-out regions. National Aeronautics and Space Administration (NASA) has developed a prototype of the geofencing function, SAFEGUARD, which prevents stayout region violation by utilizing position estimates. Thus, SAFEGUARD depends on navigation system performance, and the safety risk associated with the navigation system uncertainty should be considered. This study presents a methodology to compute the safety risk assessment-based along-track position error bound under nominal and Global Navigation Satellite Systems (GNSS) failure conditions. A Kalman filter system using pseudorange measurements as well as pseudorange rate measurements is considered for determining the position uncertainty induced by velocity uncertainty. The worst case pseudorange and pseudorange rate fault-based position error bound under the GNSS failure condition are derived by applying a Receiver Autonomous Integrity Monitor (RAIM). Position error bound simulations are also conducted for different GNSS fault hypotheses and constellation conditions with a GNSS/INS integrated navigation system. The results show that the proposed along-track position error bounds depend on satellite geometries caused by UAV attitude change and are reduced to about 40% of those of the single constellation case when using the dual constellation.

• Management Science and Financial Engineering
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• 제13권2호
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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.

• 산업경영시스템학회지
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• 제27권2호
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• pp.24-28
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• 2004

This paper considers a scheduling problem concerned with an assembly system where two components are first treated In their own parallel machines and then pulled to be assembled into a final product at a single assembly machine. The objective measure is the mean completion time of jobs(a finite number of products). Through characterizing solution properties, we obtain the worst case error bounds of an arbitrary permutation and a SPT based heuristic.

• 전자공학회논문지A
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• 제30A권4호
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• pp.11-19
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• 1993

The complex permittivity and the linewidth of microwave ferrites are measured using the well known cavity perturbation method. The cavity perturbation method has been widely used for the measurement of complex permittivity and conductivity of low loss magnetic and dielectric materials at microwave frequencies. TT1-2000, TT73-2200, and G-113 samples ordered from Trans-Tech Inc, are tested. TE$_{103}$ and TE$_{106}$ rectangular waveguide cavities are fabricated and the ferrite sample of cylidrical rod and sphere shapes are prepared. The error between the measurement values and the supplier's data is less than 1 percent in case of $\varepsilon$’ and about 10 percent in case of linewidth ($\Delta$H). Worst case error analysis shows that our measured results are well within the error bound calculated from the accuracy specification of the measuring instruments.

• Journal of Communications and Networks
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• 제6권2호
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• pp.182-191
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• 2004

In this paper, performances of different ultra-wideband (UWB) modulation schemes in the presence of timing jitter are evaluated and compared. Static and Rayleigh fading channels are considered. For fading channels, Oat and dispersive channels are assumed. First, bit error rate (BER) performances for each case are derived for a fixed value of timing jitter. Later, a uniform distribution of jitter is assumed to evaluate the performance of the system, and the theoretical results are verified by computer simulations. Finger estimation error is treated as timing jitter and an appropriate model is generated. Furthermore, a worst case distribution that provides an upper bound on the system performance is presented and compared with other distributions. Effects of timing jitter on systems employing different pulse shapes are analyzed to show the dependency of UWB performance on pulse shape. Although our analysis assumes uniform timing jitter, our framework can be used to evaluate the BER performance for any given probability distribution function of the jitter.

• Industrial Engineering and Management Systems
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• 제15권1호
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• pp.32-40
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• 2016

This paper considers a special case of a three machine flow shop scheduling problem in which operation processing time of each job is ordered such that machine 1 has the longest processing time, whereas machine 3, the shortest processing time. The objective of the problem is the minimization of the total completion time. Although the problem is simple, its complexity is yet to be established to our best knowledge. This paper first introduces the problem and presents some optimal properties of the problem. Then, it establishes several special cases in which a polynomial-time optimal solution procedure can be found. In addition, the paper proves that the recognition version of the problem is at least binary NP-complete. The complexity of the problem has been open despite its simple structure and this paper finally establishes its complexity. Finally, a simple and intuitive heuristic is developed and the tight worst case bound on relative error of 6/5 is established.

• 한국통신학회논문지
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• 제33권6A호
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• pp.577-582
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• 2008

본 논문에서는 Sphere decoder의 최대 복잡도 문제를 극복하기 위한 기법을 소개한다. 최소 근접 격자점을 탐색하는 과정 중 접근하는 노드의 회수에 제한을 두고, 만약 노드 접근 회수가 제한치를 넘으면, 가장 최근에 접근한 노드와 초기 단계의 ZF 검출 값을 이용해서 제 1 후보 심볼을 얻는다. 그리고 ZF 검출 값을 이용해서 제 2 후보 심볼 벡터를 얻은후, 이 두 후보 심볼 벡터 중 수신 신호와 유클리드 거리가 작은 후보 심볼 벡터를 최종적으로 검출한 심볼 벡터로 얻는다. 또한 제한치 설정에 따른 SER 성능의 upper bound를 이론적으로 분석하였다. 전산 실험 결과 제안한 방법은 높은 SNR 영역에서는 SER 성능에서 최대 0.5dB의 열화가 있었으나, 평균 복잡도와 최대 복잡도가 기존의 제안된 sphere decoder에 비해 상당히 줄어든 것을 확인하였다.