• Title/Summary/Keyword: Worst case

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A study on algorithms to minimize makespan of sequence-dependent jobs (작업준비시간을 고려한 총작업완료시간 최소화 해법에 관한 연구)

  • 안상형
    • Korean Management Science Review
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    • v.12 no.2
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    • pp.77-87
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    • 1995
  • In this paper we develop an efficient heuristic algorithm for the problem of scheduling n sequence-dependent jobs on a basic processor to minimize makespan. Efficient solution methods are already known for the sequence- independent case. But for the sequence-dependent case, this problem belongs to a set of strong NP-complete problems. We present a heuristic which is similar to shortest setup time heuristic but opportunity cost of setup time rather than shortest setup time is used for choosing next job. This heuristic algorithm has same computational complexity and worst case ratio as the shortest setup time heuristic. We used Wilcoxon signed rank test to show that our heuristic is superior to nearest setup time heuristic in term of average behavior.

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A Study on Approximate and Exact Algorithms to Minimize Makespan on Parallel Processors (竝列處理機械상에서 總作業完了時間의 最小化解法에 관한 硏究)

  • Ahn, Sang-Hyung;Lee, Song-Kun
    • Journal of the Korean Operations Research and Management Science Society
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    • v.16 no.2
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    • pp.14-35
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    • 1991
  • The purpose of this study is to develop an efficient exact algorithm for the problem of scheduling n in dependent jobs on m unequal parallel processors to minimize makespan. Efficient solutions are already known for the preemptive case. But for the non-preemptive case, this problem belongs to a set of strong NP-complete problems. Hence, it is unlikely that the polynomial time algorithm can be found. This is the reason why most investigations have bben directed toward the fast approximate algorithms and the worst-case analysis of algorithms. Recently, great advances have been made in mathematical theories regarding Lagrangean relaxation and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining these mathematical tools with branch-and-bound procedures, these have been some successes in constructing pseudo-polynomial time algorithms for solving previously unsolved NP-complete problems. This study applied similar methodologies to the unequal parallel processor problem to find the efficient exact algorithm.

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A Study on Approximate and Exact Algorithms to Minimize Makespan on Parallel Processors (병렬처리리례 상에서 동작업완료시간의 최소화해법에 관한 연구)

  • Ahn, Sang-Hyung;Lee, Song-Kun
    • Journal of the Korean Operations Research and Management Science Society
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    • v.16 no.2
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    • pp.13-35
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    • 1991
  • The purpose of this study is to develop an efficient exact algorithm for the problem of scheduling n in dependent jobs on m unequal parallel processors to minimize makespan. Efficient solutions are already known for the preemptive case. But for the non-preemptive case, this problem belongs to a set of strong NP-complete problems. Hence, it is unlikely that the polynomial time algorithm can be found. This is the reason why most investigations have bben directed toward the fast approximate algorithms and the worst-case analysis of algorithms. Recently, great advances have been made in mathematical theories regarding Lagrangean relaxation and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining these mathematical tools with branch-and-bound procedures, these have been some successes in constructing pseudo-polynomial time algorithms for solving previously unsolved NP-complete problems. This study applied similar methodologies to the unequal parallel processor problem to find the efficient exact algorithm.

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The research of application plan for the twist absorption structure type brake holder hanger (비틀림 흡수구조형 제륜자 홀더행거의 적용방안에 관한 연구)

  • Hong Jai-Sung;Ham Young-Sam;Paik Young-Nam
    • Proceedings of the KSR Conference
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    • 2004.06a
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    • pp.903-908
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    • 2004
  • Among welded structure bogies in use for high speed freight car, a part of bogies manufactured in 1999 and 2000 have found problems that crack occurs in its end beam. In case of a freight car the difference of weight between empty and loading conditions are worse than in case of a passenger car. Moreover its brake system is tread brake without second suspension system. Cracks of end beam is supposed to be due to loading by brake system rather than vertical loading by freight. These cracks can make brake system useless and may be a cause of derailment in the worst case. In this study, we have proposed a simple torsion-free brake shoe holder hanger to remove torsion of hanger bracket which was supposed to be one of causes of cracks and performed finite element analyses. Also static load test was applied in torsion free brake shoe holder.

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크기가 다양한 bin-packing 문제에 대한 algorithm

  • 강장하;박성수
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2000.04a
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    • pp.205-206
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    • 2000
  • In this paper, we consider variable sized bin packing problem, where the objective is not to minimize the total space used in the packing but to minimize the total cost of the packing when the cost of unit size of each bin does not increase as the bin size increases. A heuristic algorithm is described, and analyzed in two special cases: 1) b$\sub$m/|…|b$_1$and w$\sub$n/|…|w$_1$, and 2) b$\sub$m/|…|b$_1$, where b$\sub$i/ denotes the size of i-th type of bin and w$\sub$j/ denotes the size of j-th item. In the case 1), the algorithm guarantees optimality, and in the case 2), it guarantees asymptotic worst-case performance bounds of l1/9.

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Complex Permittivity and Linewidth Measurements of Microwave Ferrites Using the Cavity Perturbation Method (공진기 섭동방법을 이용한 마이크로파 페라이트의 복소 유전율과 선폭 측정)

  • 엄동진;오호석;박동철;윤상원
    • Journal of the Korean Institute of Telematics and Electronics A
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    • v.30A no.4
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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.

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Finite Element Analysis for Application of Torsion-free Brake Shoe Holder Hanger for the Bogie of Railway Freight Car (화차대차용 비틀림 흡수구조형 제륜자 홀더행거의 적용을 위한 유한요소해석)

  • Jeon Eung-Sik;Ham Young-Sam
    • Proceedings of the KSR Conference
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    • 2003.10c
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    • pp.36-41
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    • 2003
  • Among welded structure bogies in use for high speed freight car, a part of bogies manufactured in 1999 and 2000 have found problems that failure occurs in its end beam. In case of a freight car a difference of weight between empty and loading conditions are worse than in case of a passenger car. Moreover its brake system is tread brake without second suspension system. A failure of end beam is supposed to be due to loading by brake rather than vertical loading by freight. This failure can make brake system useless and may be a cause of derailment in the worst case. In this study, we have proposed a simple torsion-free brake shoe holder hanger to remove torsion of hanger bracket which is supposed to be one of causes of failure and performed finite element analyses for making trial manufactures and its application.

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Load history measurement of end beam of welded structure bogie for railway freight car (화차용 용접구조대차 엔드빔의 하중이력 측정)

  • Ham Young-Sam;Seo Jung-Won;Lee Dong-Hyong;Jeon Eung-Sik
    • Proceedings of the KSR Conference
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    • 2003.10c
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    • pp.103-108
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    • 2003
  • Among welded structure bogies in use for high speed freight car, a part of bogies manufactured in 1999 and 2000 have found problems that failure occurs in its end beam. In case of a freight car a difference of weight between empty and loading conditions are worse than in case of a passenger car. Moreover its brake system is tread brake without second suspension system. A failure of end beam is supposed to be due to loading by brake rather than vertical loading by freight. This failure can make brake system useless and may be a cause of derailment in the worst case. In this study, in order to be proved the cause of failure and to solve the problem it is described that we have measured load history acted on end beam and set up the procedures.

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A Special Case of Three Machine Flow Shop Scheduling

  • Yang, Jaehwan
    • Industrial Engineering and Management Systems
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    • v.15 no.1
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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.

Faultproof Design in Space for Monopropellant Rocket Engine Assembly (단일추진제 로켓 엔진 어셈블리를 위한 우주 공간에서의 과실 방지 설계)

  • Han, Cho-Young;Kim, Jeong-Soo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.27 no.10
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    • pp.1377-1384
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    • 2003
  • An analysis has been performed for active thermal control of the KOMPSAT monopropellant rocket engine assembly, i.e., dual thruster module(DTM). The main efforts of this work have been directed at determining proper heater sizes for propellant valves and catalyst beds necessary to maintain their temperatures within specified temperature ranges under KOMPSAT environment and operational conditions. The TAS incorporated with TRASYS thermal radiation analyzer was used to establish a complete heat transfer model which allows to predict the DTM temperature as a function of time. The thermal analysis has been performed in transient mode to verify the appropriate power for catalyst bed heaters necessary to increase catalyst bed temperature to the required value within a specified period of time. Similar analysis has been executed to validate the heater power for the thermostatically controlled primary and redundant heater circuits used to prevent hydrazine freezing, i.e., single fault. Moreover the effect of the radiative property of thermal control coating of heat shield was examined. Thruster firing condition was also simulated for the heat soakback condition. As a consequence, all thermal analysis results for DTM satisfactorily met the thermal requirements for the KOMPSAT DTM under the worst case average voltage, i.e. 25 volt.