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Game Theoretic Optimization of Investment Portfolio Considering the Performance of Information Security Countermeasure (정보보호 대책의 성능을 고려한 투자 포트폴리오의 게임 이론적 최적화)

  • Lee, Sang-Hoon;Kim, Tae-Sung
    • Journal of Intelligence and Information Systems
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    • v.26 no.3
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    • pp.37-50
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    • 2020
  • Information security has become an important issue in the world. Various information and communication technologies, such as the Internet of Things, big data, cloud, and artificial intelligence, are developing, and the need for information security is increasing. Although the necessity of information security is expanding according to the development of information and communication technology, interest in information security investment is insufficient. In general, measuring the effect of information security investment is difficult, so appropriate investment is not being practice, and organizations are decreasing their information security investment. In addition, since the types and specification of information security measures are diverse, it is difficult to compare and evaluate the information security countermeasures objectively, and there is a lack of decision-making methods about information security investment. To develop the organization, policies and decisions related to information security are essential, and measuring the effect of information security investment is necessary. Therefore, this study proposes a method of constructing an investment portfolio for information security measures using game theory and derives an optimal defence probability. Using the two-person game model, the information security manager and the attacker are assumed to be the game players, and the information security countermeasures and information security threats are assumed as the strategy of the players, respectively. A zero-sum game that the sum of the players' payoffs is zero is assumed, and we derive a solution of a mixed strategy game in which a strategy is selected according to probability distribution among strategies. In the real world, there are various types of information security threats exist, so multiple information security measures should be considered to maintain the appropriate information security level of information systems. We assume that the defence ratio of the information security countermeasures is known, and we derive the optimal solution of the mixed strategy game using linear programming. The contributions of this study are as follows. First, we conduct analysis using real performance data of information security measures. Information security managers of organizations can use the methodology suggested in this study to make practical decisions when establishing investment portfolio for information security countermeasures. Second, the investment weight of information security countermeasures is derived. Since we derive the weight of each information security measure, not just whether or not information security measures have been invested, it is easy to construct an information security investment portfolio in a situation where investment decisions need to be made in consideration of a number of information security countermeasures. Finally, it is possible to find the optimal defence probability after constructing an investment portfolio of information security countermeasures. The information security managers of organizations can measure the specific investment effect by drawing out information security countermeasures that fit the organization's information security investment budget. Also, numerical examples are presented and computational results are analyzed. Based on the performance of various information security countermeasures: Firewall, IPS, and Antivirus, data related to information security measures are collected to construct a portfolio of information security countermeasures. The defence ratio of the information security countermeasures is created using a uniform distribution, and a coverage of performance is derived based on the report of each information security countermeasure. According to numerical examples that considered Firewall, IPS, and Antivirus as information security countermeasures, the investment weights of Firewall, IPS, and Antivirus are optimized to 60.74%, 39.26%, and 0%, respectively. The result shows that the defence probability of the organization is maximized to 83.87%. When the methodology and examples of this study are used in practice, information security managers can consider various types of information security measures, and the appropriate investment level of each measure can be reflected in the organization's budget.

A study on the feasibility evaluation technique of urban utility tunnel by using quantitative indexes evaluation and benefit·cost analysis (정량적 지표평가와 비용·편익 분석을 활용한 도심지 공동구의 타당성 평가기법 연구)

  • Lee, Seong-Won;Chung, Jee-Seung;Na, Gwi-Tae;Bang, Myung-Seok;Lee, Joung-Bae
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.21 no.1
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    • pp.61-77
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    • 2019
  • If a new utility tunnel is planned for high density existing urban areas in Korea, a rational decision-making process such as the determination of optimum design capacity by using the feasibility evaluation system based on quantitative evaluation indexes and the economic evaluation is needed. Thus, the previous study presented the important weight of individual higher-level indexes (3 items) and sub-indexes (16 items) through a hierarchy analysis (AHP) for quantitative evaluation index items, considering the characteristics of each urban type. In addition, an economic evaluation method was proposed considering 10 benefit items and 8 cost items by adding 3 new items, including the effects of traffic accidents, noise reduction and socio-economic losses, to the existing items for the benefit cost analysis suitable for urban utility tunnels. This study presented a quantitative feasibility evaluation method using the important weight of 16 sub-index items such as the road management sector, public facilities sector and urban environment sector. Afterwards, the results of quantitative feasibility and economic evaluation were compared and analyzed in 123 main road sections of the Seoul. In addition, a comprehensive evaluation method was proposed by the combination of the two evaluation results. The design capacity optimization program, which will be developed by programming the logic of the quantitative feasibility and economic evaluation system presented in this study, will be utilized in the planning and design phases of urban community zones and will ultimately contribute to the vitalization of urban utility tunnels.

Dose Planning of Forward Intensity Modulated Radiation Therapy for Nasopharyngeal Cancer using Compensating Filters (보상여과판을 이용한 비인강암의 전방위 강도변조 방사선치료계획)

  • Chu Sung Sil;Lee Sang-wook;Suh Chang Ok;Kim Gwi Eon
    • Radiation Oncology Journal
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    • v.19 no.1
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    • pp.53-65
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    • 2001
  • Purpose : To improve the local control of patients with nasopharyngeal cancer, we have implemented 3-D conformal radiotherapy and forward intensity modulated radiation therapy (IMRT) to used of compensating filters. Three dimension conformal radiotherapy with intensity modulation is a new modality for cancer treatments. We designed 3-D treatment planning with 3-D RTP (radiation treatment planning system) and evaluation dose distribution with tumor control probability (TCP) and normal tissue complication probability (NTCP). Material and Methods : We have developed a treatment plan consisting four intensity modulated photon fields that are delivered through the compensating tilters and block transmission for critical organs. We get a full size CT imaging including head and neck as 3 mm slices, and delineating PTV (planning target volume) and surrounding critical organs, and reconstructed 3D imaging on the computer windows. In the planning stage, the planner specifies the number of beams and their directions including non-coplanar, and the prescribed doses for the target volume and the permissible dose of normal organs and the overlap regions. We designed compensating filter according to tissue deficit and PTV volume shape also dose weighting for each field to obtain adequate dose distribution, and shielding blocks weighting for transmission. Therapeutic gains were evaluated by numerical equation of tumor control probability and normal tissue complication probability. The TCP and NTCP by DVH (dose volume histogram) were compared with the 3-D conformal radiotherapy and forward intensity modulated conformal radiotherapy by compensator and blocks weighting. Optimization for the weight distribution was peformed iteration with initial guess weight or the even weight distribution. The TCP and NTCP by DVH were compared with the 3-D conformal radiotherapy and intensitiy modulated conformal radiotherapy by compensator and blocks weighting. Results : Using a four field IMRT plan, we have customized dose distribution to conform and deliver sufficient dose to the PTV. In addition, in the overlap regions between the PTV and the normal organs (spinal cord, salivary grand, pituitary, optic nerves), the dose is kept within the tolerance of the respective organs. We evaluated to obtain sufficient TCP value and acceptable NTCP using compensating filters. Quality assurance checks show acceptable agreement between the planned and the implemented MLC(multi-leaf collimator). Conclusion : IMRT provides a powerful and efficient solution for complex planning problems where the surrounding normal tissues place severe constraints on the prescription dose. The intensity modulated fields can be efficaciously and accurately delivered using compensating filters.

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Memory Organization for a Fuzzy Controller.

  • Jee, K.D.S.;Poluzzi, R.;Russo, B.
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1993.06a
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    • pp.1041-1043
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    • 1993
  • Fuzzy logic based Control Theory has gained much interest in the industrial world, thanks to its ability to formalize and solve in a very natural way many problems that are very difficult to quantify at an analytical level. This paper shows a solution for treating membership function inside hardware circuits. The proposed hardware structure optimizes the memoried size by using particular form of the vectorial representation. The process of memorizing fuzzy sets, i.e. their membership function, has always been one of the more problematic issues for the hardware implementation, due to the quite large memory space that is needed. To simplify such an implementation, it is commonly [1,2,8,9,10,11] used to limit the membership functions either to those having triangular or trapezoidal shape, or pre-definite shape. These kinds of functions are able to cover a large spectrum of applications with a limited usage of memory, since they can be memorized by specifying very few parameters ( ight, base, critical points, etc.). This however results in a loss of computational power due to computation on the medium points. A solution to this problem is obtained by discretizing the universe of discourse U, i.e. by fixing a finite number of points and memorizing the value of the membership functions on such points [3,10,14,15]. Such a solution provides a satisfying computational speed, a very high precision of definitions and gives the users the opportunity to choose membership functions of any shape. However, a significant memory waste can as well be registered. It is indeed possible that for each of the given fuzzy sets many elements of the universe of discourse have a membership value equal to zero. It has also been noticed that almost in all cases common points among fuzzy sets, i.e. points with non null membership values are very few. More specifically, in many applications, for each element u of U, there exists at most three fuzzy sets for which the membership value is ot null [3,5,6,7,12,13]. Our proposal is based on such hypotheses. Moreover, we use a technique that even though it does not restrict the shapes of membership functions, it reduces strongly the computational time for the membership values and optimizes the function memorization. In figure 1 it is represented a term set whose characteristics are common for fuzzy controllers and to which we will refer in the following. The above term set has a universe of discourse with 128 elements (so to have a good resolution), 8 fuzzy sets that describe the term set, 32 levels of discretization for the membership values. Clearly, the number of bits necessary for the given specifications are 5 for 32 truth levels, 3 for 8 membership functions and 7 for 128 levels of resolution. The memory depth is given by the dimension of the universe of the discourse (128 in our case) and it will be represented by the memory rows. The length of a world of memory is defined by: Length = nem (dm(m)+dm(fm) Where: fm is the maximum number of non null values in every element of the universe of the discourse, dm(m) is the dimension of the values of the membership function m, dm(fm) is the dimension of the word to represent the index of the highest membership function. In our case then Length=24. The memory dimension is therefore 128*24 bits. If we had chosen to memorize all values of the membership functions we would have needed to memorize on each memory row the membership value of each element. Fuzzy sets word dimension is 8*5 bits. Therefore, the dimension of the memory would have been 128*40 bits. Coherently with our hypothesis, in fig. 1 each element of universe of the discourse has a non null membership value on at most three fuzzy sets. Focusing on the elements 32,64,96 of the universe of discourse, they will be memorized as follows: The computation of the rule weights is done by comparing those bits that represent the index of the membership function, with the word of the program memor . The output bus of the Program Memory (μCOD), is given as input a comparator (Combinatory Net). If the index is equal to the bus value then one of the non null weight derives from the rule and it is produced as output, otherwise the output is zero (fig. 2). It is clear, that the memory dimension of the antecedent is in this way reduced since only non null values are memorized. Moreover, the time performance of the system is equivalent to the performance of a system using vectorial memorization of all weights. The dimensioning of the word is influenced by some parameters of the input variable. The most important parameter is the maximum number membership functions (nfm) having a non null value in each element of the universe of discourse. From our study in the field of fuzzy system, we see that typically nfm 3 and there are at most 16 membership function. At any rate, such a value can be increased up to the physical dimensional limit of the antecedent memory. A less important role n the optimization process of the word dimension is played by the number of membership functions defined for each linguistic term. The table below shows the request word dimension as a function of such parameters and compares our proposed method with the method of vectorial memorization[10]. Summing up, the characteristics of our method are: Users are not restricted to membership functions with specific shapes. The number of the fuzzy sets and the resolution of the vertical axis have a very small influence in increasing memory space. Weight computations are done by combinatorial network and therefore the time performance of the system is equivalent to the one of the vectorial method. The number of non null membership values on any element of the universe of discourse is limited. Such a constraint is usually non very restrictive since many controllers obtain a good precision with only three non null weights. The method here briefly described has been adopted by our group in the design of an optimized version of the coprocessor described in [10].

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Recent Progress in Air-Conditioning and Refrigeration Research : A Review of Papers Published in the Korean Journal of Air-Conditioning and Refrigeration Engineering in 2016 (설비공학 분야의 최근 연구 동향 : 2016년 학회지 논문에 대한 종합적 고찰)

  • Lee, Dae-Young;Kim, Sa Ryang;Kim, Hyun-Jung;Kim, Dong-Seon;Park, Jun-Seok;Ihm, Pyeong Chan
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.29 no.6
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    • pp.327-340
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    • 2017
  • This article reviews the papers published in the Korean Journal of Air-Conditioning and Refrigeration Engineering during 2016. It is intended to understand the status of current research in the areas of heating, cooling, ventilation, sanitation, and indoor environments of buildings and plant facilities. Conclusions are as follows. (1) The research works on the thermal and fluid engineering have been reviewed as groups of flow, heat and mass transfer, the reduction of pollutant exhaust gas, cooling and heating, the renewable energy system and the flow around buildings. CFD schemes were used more for all research areas. (2) Research works on heat transfer area have been reviewed in the categories of heat transfer characteristics, pool boiling and condensing heat transfer and industrial heat exchangers. Researches on heat transfer characteristics included the results of the long-term performance variation of the plate-type enthalpy exchange element made of paper, design optimization of an extruded-type cooling structure for reducing the weight of LED street lights, and hot plate welding of thermoplastic elastomer packing. In the area of pool boiling and condensing, the heat transfer characteristics of a finned-tube heat exchanger in a PCM (phase change material) thermal energy storage system, influence of flow boiling heat transfer on fouling phenomenon in nanofluids, and PCM at the simultaneous charging and discharging condition were studied. In the area of industrial heat exchangers, one-dimensional flow network model and porous-media model, and R245fa in a plate-shell heat exchanger were studied. (3) Various studies were published in the categories of refrigeration cycle, alternative refrigeration/energy system, system control. In the refrigeration cycle category, subjects include mobile cold storage heat exchanger, compressor reliability, indirect refrigeration system with $CO_2$ as secondary fluid, heat pump for fuel-cell vehicle, heat recovery from hybrid drier and heat exchangers with two-port and flat tubes. In the alternative refrigeration/energy system category, subjects include membrane module for dehumidification refrigeration, desiccant-assisted low-temperature drying, regenerative evaporative cooler and ejector-assisted multi-stage evaporation. In the system control category, subjects include multi-refrigeration system control, emergency cooling of data center and variable-speed compressor control. (4) In building mechanical system research fields, fifteenth studies were reported for achieving effective design of the mechanical systems, and also for maximizing the energy efficiency of buildings. The topics of the studies included energy performance, HVAC system, ventilation, renewable energies, etc. Proposed designs, performance tests using numerical methods and experiments provide useful information and key data which could be help for improving the energy efficiency of the buildings. (5) The field of architectural environment was mostly focused on indoor environment and building energy. The main researches of indoor environment were related to the analyses of indoor thermal environments controlled by portable cooler, the effects of outdoor wind pressure in airflow at high-rise buildings, window air tightness related to the filling piece shapes, stack effect in core type's office building and the development of a movable drawer-type light shelf with adjustable depth of the reflector. The subjects of building energy were worked on the energy consumption analysis in office building, the prediction of exit air temperature of horizontal geothermal heat exchanger, LS-SVM based modeling of hot water supply load for district heating system, the energy saving effect of ERV system using night purge control method and the effect of strengthened insulation level to the building heating and cooling load.

Effect of different light sources and ventilation on in vitro shoot growth and rooting of a rare and endangered species, Tsuru-rindo(Tripterospermum japonicum) (희귀 및 멸종위기 식물 덩굴용담의 기내생장에 미치는 광질 및 환기효과)

  • Moon, Heung-Kyu;Park, So-Young
    • Journal of Plant Biotechnology
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    • v.35 no.3
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    • pp.215-221
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    • 2008
  • Effects of light generated by LEDs on shoot growth and rooting of Tsuru-rindo(Tripterospermum japonicum) were evaluated. Apical shoots(one or two node with 3-4 leaves) were cultured on MS basal medium with 3% sucrose and maintained for four weeks under five different light qualities: fluorescent lamp(F), 100% red LED(R), 70% red LED+30% blue LED(R7B3), 50% red LED+50% blue(R5B5), or 100% blue LED(B). Rooting was promoted by both red light and fluorescent lamp, and the effect was further promoted under the ventilation. Red light enhanced shoot node elongation, whereas blue light appeared to suppress it. Growth of shoots and leaves were enhanced under the ventilation irrespective of the different light qualities. Under the ventilated condition, total fresh weight of plants was highest in R7B3 LED as 257.7 mg per plant. Dry matters, which are used for index of plant growth, were lowest under red light, whereas it was highest under blue light. The dry matter was inclined to getting higher by ascending the ratio of blue light and red light. Total chlorophyll content was highest in both R7B3 LED and R5B5 LED under ventilation as 29.5 and 31.2, respectively. Above results suggest that light quality optimization could be an important factor to foster in vitro growth of the species. Ventilation treatment appeared to be another important factor to induce normal shoot growth and rooting.

Optimization of Growth Medium and Poly-$\beta$-hydroxybutyric Acid Production from Methanol in Methylobacterium organophilum (메탄올로부터 Methylobacterium organophilum에 의한 Poly-$\beta$-hydroxybutyric Acid의 생산과 배지성분의 최적화)

  • Choi, Joon-H;Kim, Jung H.;M. Daniel;J.M. Lebeault
    • Microbiology and Biotechnology Letters
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    • v.17 no.4
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    • pp.392-396
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    • 1989
  • Methylobacterium organophilum, a facultative methylotroph was cultivated on a methanol as a sole carbon and energy source. The cell growth was affected by the various components of minimal synthetic medium and the medium composition was optimized with 0.5% (v/v) methanol at pH 6.8 and at 3$0^{\circ}C$. The maximum specific growth rate of M. organophilum was achieved to 0.26 hr$^{-1}$ in the optimized medium which has following composition: Methanol, 0.5% (v/v):(NH$_4$)$_2$SO$_4$, 1.0g/l:KH$_2$PO$_4$, 2.13g/l:KH$_2$PO$_4$, 1.305g/ι:MgSO$_4$.7$H_2O$. 45g/l and trace elements (CaCl$_2$.2$H_2O$, 3.3mg:FeSO$_4$.7$H_2O$, 1.3mg:MnSO$_4$.4$H_2O$, 130$\mu\textrm{g}$:ZnSO$_4$.5$H_2O$, 40$\mu\textrm{g}$:Na$_2$MoO$_4$.2$H_2O$, 40$\mu\textrm{g}$:CoCl$_2$.6$H_2O$, 40$\mu\textrm{g}$:H$_3$BO$_3$, 30$\mu\textrm{g}$ per liter). By the limitation of nitrogen and deficiency of Mn$^{+2}$ or Fe$^{+2}$, the cell growth was significantly repressed. Methanol greatly repressed the cell growth and the complete inhibition was observed at concentration above 4% (v/v). In order to overcome the methanol inhibition and to prevent the methanol limitation, intermittent feeding of methanol was conducted by a D.O.-stat technique. PHB production by M. organophilum was stimulated by deficiency of nutrients such as NH$_{4}^{+}$, SO$_{4}^{-2}$, $Mg^{+2}$, $K^{+}$, or PO$_{4}^{-3}$ in the medium. The maximum PHB content was obtained as 58% of dry cell weight under deficiency of potassium ion in the optimized synthetic medium.

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Selection of Filamentous Cyanobacteria and Optimization of Culture Condition for Recycling Waste Nutrient Solution (폐양액 활용을 위한 Filamentous Cyanobacteria의 선발 및 최적배양)

  • Yang, Jin-Chul;Chung, Hee-Kyung;Lee, Hyoung-Seok;Choi, Seung-Ju;Yun, Sang-Soon;Ahn, Ki-Sup;Sa, Tong-Min
    • Korean Journal of Soil Science and Fertilizer
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    • v.37 no.3
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    • pp.177-183
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    • 2004
  • The discharge of waste nutrient solution from greenhouse to natural ecosystem leads to the accumulation of excess nutrients that results in contamination or eutrophication. There is a need to recycle the waste nutrient solution in order to prevent the environmental hazards. The amount and kind of nutrients in waste nutrient solution might be enough to grow photosynthetic microorganisms. Hence in the present study, we examined the growth and mass cultivation of cyanobacteria in the waste nutrient solution with an objective of removing N and P and concomitantly, its mass cultivation. Four photosynthetic filamentous cyanobacteria (Anabaena HA101, HA701 and Nostoc HN601, HN701) isolated from composts and soils of the Chungnam province were used as culture strains. Among the isolates, Nostoc HN601 performed faster growth rate and higher N and P uptake in the BG-II ($NO_3{^-}$) medium when compared to those of other cyanobacterial strains. Finally, the selected isolate was tested under optimum conditions (airflow at the rate of $1L\;min^{-1}$. in 15 L reactor, initial pH 8) in waste nutrient solution from tomato hydroponic in green house condition. Results showed to remove 100% phosphate from the waste nutrient solution in the tomato hydroponics recorded over a period of 7 days. The growth rate of Nostoc HN601 was $16mg\;Chl-a\;L^{-1}$ in the waste nutrient solution from tomato hydroponics with optimum condition, whereas growth rate of Nostoc HN601 was only $9.8mg\;Chl-a\;L^{-1}$ in BG-11 media. Nitrogen fixing capacity of Nostoc HN601 was $20.9nmol\;C_2H_4\;mg^{-1}\;Chl-a\;h^{-1}$ in N-free BG-11. The total nitrogen and total phosphate concentration of Nostoc HN601 were 63.3 mg N gram dry weight $(GDW)^{-1}$ and $19.1mg\;P\;GDW^{-1}$ respectively. Collectively, cyanobacterial mass production using waste nutrient solution under green house condition might be suitable for recycling and cleaning of waste nutrient solution from hydroponic culture system. Biomass of cyanobacteria, cultivated in waste nutrient solution, could be used as biofertilizer.

Opportunity Tree Framework Design For Optimization of Software Development Project Performance (소프트웨어 개발 프로젝트 성능의 최적화를 위한 Opportunity Tree 모델 설계)

  • Song Ki-Won;Lee Kyung-Whan
    • The KIPS Transactions:PartD
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    • v.12D no.3 s.99
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    • pp.417-428
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    • 2005
  • Today, IT organizations perform projects with vision related to marketing and financial profit. The objective of realizing the vision is to improve the project performing ability in terms of QCD. Organizations have made a lot of efforts to achieve this objective through process improvement. Large companies such as IBM, Ford, and GE have made over $80\%$ of success through business process re-engineering using information technology instead of business improvement effect by computers. It is important to collect, analyze and manage the data on performed projects to achieve the objective, but quantitative measurement is difficult as software is invisible and the effect and efficiency caused by process change are not visibly identified. Therefore, it is not easy to extract the strategy of improvement. This paper measures and analyzes the project performance, focusing on organizations' external effectiveness and internal efficiency (Qualify, Delivery, Cycle time, and Waste). Based on the measured project performance scores, an OT (Opportunity Tree) model was designed for optimizing the project performance. The process of design is as follows. First, meta data are derived from projects and analyzed by quantitative GQM(Goal-Question-Metric) questionnaire. Then, the project performance model is designed with the data obtained from the quantitative GQM questionnaire and organization's performance score for each area is calculated. The value is revised by integrating the measured scores by area vision weights from all stakeholders (CEO, middle-class managers, developer, investor, and custom). Through this, routes for improvement are presented and an optimized improvement method is suggested. Existing methods to improve software process have been highly effective in division of processes' but somewhat unsatisfactory in structural function to develop and systemically manage strategies by applying the processes to Projects. The proposed OT model provides a solution to this problem. The OT model is useful to provide an optimal improvement method in line with organization's goals and can reduce risks which may occur in the course of improving process if it is applied with proposed methods. In addition, satisfaction about the improvement strategy can be improved by obtaining input about vision weight from all stakeholders through the qualitative questionnaire and by reflecting it to the calculation. The OT is also useful to optimize the expansion of market and financial performance by controlling the ability of Quality, Delivery, Cycle time, and Waste.

A Study on the Production Structure and Biomass Productivity of Quercus variabilis Natural Forest (굴참나무천연림(天然林)의 생산구조(生産構造) 및 물질생산력(物質生産力)에 관(關)한 연구(硏究))

  • Kim, Si Kyung;Jeong, Jwa Yong
    • Journal of Korean Society of Forest Science
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    • v.70 no.1
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    • pp.91-102
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    • 1985
  • Growth and biomass production of natural stands of Quercus variabilis in relation to tree density were studied to obtain basic guide lines for future tending operation. Two natural stands of Quercus variabilis located at 900m (A stand: 6,600trees/ha, $15.84m^2/ha$, $\frac{19}{17-20}$) and 800m (B stand: 4,300trees/ha, $16.65m^2/ha$, $\frac{20}{17-21}$) elevation in Sancheong, Kyongnam Province were selected for the comparative study and following results were obtained through a sample plot method. After diameter of individual trees in the sample plots was measured, twelve average trees from each diameter class were cut felled to measure dry weight of $W_S$, $W_B$, $W_L$, $W_{Ba}$, and standing biomass and biomass production rates by a allometrior regressions related to $D^2H$. Vertical distribution of leaves along the stems indicated that photosynthesis was carried out 2.2m above the ground in Stand A and 1.2m in Stand B. Maximum photosynthesis was located 4.2m and 6.2m above the ground in Stand A and B, respectively. Leaf area index was 4.25ha/ha for Stand A, and 3.89ha/ha for Stand B. Above-ground standing biomass was 49.51 ton/ha for Stand A and 59.20 ton/ha and net annual production was 6.75 ton/ha/yr. for Stand A and 8.99 ton/ha/yr. for Stand B. The ratio of net annual production to standing biomass was 17.5% for Stand A and 16.7% for Stand B. Net assimilation rate was 2.75kg/kg/yr. for Stand A and 3.58kg/kg/yr. for Stand B. Stem wood production rate was 1.46kg/kg/yr. for Stand A and 2.09kg/kg/yr. for Stand B. Bark production rate was 0.60 kg/kg/yr. for Stand A and 0.34kg/kg/yr. for Stand B. Above data indicated that Stand B utilized growing spaces and sites more efficiently than Stand A. It is concluded chat productivity of natural stands of Quercus variabilis can be enhanced through optimization of basal areas and number of tree per hectare and that sound management of natural oak stands should be based on systematic sampling of the area for periodic productivity estimation.

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