Earticle

우리나라는 60% 이상이 산간지형에 해당하며 수십 년 전부터 이러한 특성을 이용하여 수력발전소를 다수 건설하고 친환경 적인 에너지를 생산해왔다. 수력발전은 급변하는 에너지 수급에 대처할 수 있고 낙차를 이용하여 친환경적으로 에너지를 생 산한다는 장점이 있으나 댐 설립시 입지 조건에 의해 불가피하게 환경을 훼손해야 하는 경우가 많다. 따라서, 본 연구에서는 기존 발전용댐들의 장기 운영계획을 수립하고자 월별 발전량을 최대화하는 최적 저수지 운영 모형을 개발하였다. 댐 운영 모 형은 자원 최적화 분야에서 널리 이용되는 선형계획법을 기반으로 월단위로 1년 운영계획을 수립할 수 있는 형태로 구축하 였다. 선형계획법은 목적함수와 제약조건 모두 선형식으로 이루어져야 하지만 발전량 산정식은 비선형식이기 때문에 Taylor Expansion 기법을 활용하여 선형화하였다. 개발된 모형을 검토하기 위해 한강수계에 위치하는 5개 발전용댐을 대상으로 2009~2018년의 실적자료와 댐 운영 모형의 결과를 비교, 분석하였다. 결과적으로 발전용댐들의 총 최적 발전량은 총 실적 발전량보다 약 10~37% 정도 향상된 결과를 나타내었다.

In Korea, more than 60% of the whole lands are mountainous area. Since many decades ago, hydroelectric power plants have been constructed and eco-friendly energy has been produced. Hydropower can cope with the rapidly changing energy supply and demand, and produce eco-friendly energy. However, when the reservoir is built, it is often inevitable to damage the environment due to construction of large structure. In this study, the optimal reservoir operation model was developed to maximize power generation by monthly operation for long-term operation planning. The dam operation model was developed using the linear programming which is widely used in the optimal resources allocation problems. And the reservoir operation model can establish monthly operation plan for 1 year. Linear programming requires both object function and constraints to be linear. However, since the power generation equation is nonlinear, it is linearized using the Taylor Expansion technique. The optimization results were compared with the 2009-2018 historical data of five hydropower reservoirs. As a result, the total optimal generation is about 10~37% higher than the historical generation.

본 연구는 국내 산업용수 이용량과 산업연관표를 연계하여 물 투입-산출 모형을 설정하고, 선형계획 법을 이용해 산업 부문(농업, 공업, 서비스업)별 수자원의 잠재가격을 추정하였다. 물 이용량과 산업 연관표 간의 통합을 위해 연동이 가능한 2014년 최근 자료(수자원통계 및 한국은행 산업연관표)를 적용하였으며, 산업용수 이용 업종 분류 체계에 맞추어 산업연관표의 30개 대분류를 12개 산업 부문 으로 재정의하였다. 각 부문별 물 투입 계수를 포함한 물 투입산출표를 설정한 뒤, 가용 수자원량과 업종 간 생산관계의 제약 속에서 각 용수의 잠재가격과 물 부족 시나리오에 따른 부문별 잠재가격 변화를 추정하였다. 주요 결과는 다음과 같다. 농업용수, 공업용수, 서비스업용수의 잠재가격은 각각 864원/㎥, 27,545원/㎥, 275,449원/㎥로 나타났으며, 물 부족 시나리오에 따른 잠재가격 변화 범위 (10% 제약~90% 제약)는 농업용수가 1,518원/㎥ ~ 2,369원/㎥, 공업용수가 61,721원/㎥ ~ 997,092원/㎥, 서비스업용수가 294,923원/㎥ ~ 381,192원/㎥이었다. 특히, 공업부문의 피해 수준이 50% 제약 수준에 서 급격히 증가된다는 점을 확인하였다.

This study set the water input-output model by linking the amount of water use to inter-industry relations table (IRT), and estimated shadow prices of water resources in agricultural, industrial and service sector using linear programming method. The 2014 water data and IRT data were collected and linked for integration of water usage and input-output table, and 30 major categories of IRT were redefined into 12 sub-sectors. Using the data, the shadow prices and their changes in each sector were estimated according to drought scenarios. The main results derived from the water input-output linear programming are as follows. Shadow prices of agriculture water, industrial water and service industry water were 864 won/㎥, 27,545 won/㎥ and 275,449 won/㎥ respectively. The shadow price changes by water shortage (10% to 90% constraint) ranged from 1,518 to 2,369 won/㎥ for agricultural use, 61,721 to 997,092 won/㎥ for industrial use, and 294,923 to 381,192 won/㎥ for service industry. In particular, it was confirmed that the damage level in the industrial sector increased sharply at the 50% restriction level.

퍼지 선형계획법은 불확실성하에서의 문제들을 해결하는데 유용한 의사결정 모형이다. 본 연구에서는 목 적함수 값이 퍼지수이고 우변 상수도 퍼지수인 융합 등식 제약식을 갖는 퍼지 선형계획법 문제를 다룬다. 연구의 목적은 퍼지 해를 정의하고 그것을 구하는 절차를 모색하는 것이다. 목적함수 값에 대한 소속 함수로 부분 선형함수 를, 제약식의 소속 함수로는 사다리꼴 함수를 도입한다. 사다리꼴 함수는 구간별 선형 함수 들로 나누어 나타낼 수 있다. 따라서 모든 소속 함수들을 선형식 들로 대체함으로써 퍼지 선형계획 모형을 Zimmermann의 대칭 선형 모형 으로 바꿀 수 있다. 여기에 최대-최소 기준을 적용하여 일반 선형계획법 문제를 도출해 내고, 이 문제의 최적해로부 터 원 문제의 퍼지 해를 얻게 된다. 본 논문에서는 사다리꼴 소속 함수에 대해 살펴보았는데 앞으로는 오목 부분 선형함수와 같은 좀 더 일반화된 소속 함수에 대한 연구가 필요하다.

The fuzzy linear programming(FLP) is the useful approach to many real world problems under uncertainty. This paper deals with a FLP whose objective value is fuzzy. And the right hand sides of convergent equality constraints are fuzzy numbers. We assume that the membership function of the objective value is piecewise linear and those of the right hand side are trapezoidal. Each of these trapezoidal functions can be algebraically replaced with three linear functions. Then the FLP problem is transformed into the Zimmermann's symmetric model. The fuzzy solution based on the max-min rule can be obtained by solving the crisp linear programming problem derived from the symmetric model. A numerical example has illustrated our approach. The application of our approach to the inconsistent linear system can enable generate us to get define the useful and flexible inexact solutions within acceptable tolerance. Further research is required to generalize the membership function.

Based on data mining of outliers of time series, current studies have developed many methods, but there exist certain disadvantages for each method. This paper developed the method of mining outliers of time series based on linear programming model, verified high efficiency through an actual case and make up for the shortcoming of other methods.

In recent year, multi-layered semiconductor package is one of the most important technologies to enhance its performance. To bond between each layer of multi-chip package, die-bonding film is known as an effective material. We had developed a novel low-modulus die-bonding adhesive film. Properties of the films are widely changed by the ratio of epoxy resin and acrylic polymer contents. To satisfy the target properties, the influence of various parameters on material properties was examined. However, it is not easy for researchers to find out the formulation which satisfy the targets. To solve the problem, this paper proposes the weak conditioned combinatorial linear programming method (WCCLP). By defining solution area as a function of combination index, the optimum formulations are acquired. This optimization can be done by newly developed user-friendly software. The software is applicable not only to semiconductor related materials but also to any such formulation as paint, medicine and food.

제품 포트폴리오 문제(PPP)는 n개 제품 들 중에서 최대 이익을 창출하도록 특정 제품의 생산량을 결정하는 최적 화 문제이다. 이러한 최적화 문제를 풀 수 있는 유일한 방법으로 선형계획법(LP)이 알려져 있다. 선형계획법은 n개의 선형함수를 최적화시키는 문제로 LINGO나 엑셀 해결사 등을 활용하는 실정이다. 본 논문은 제품 원가 대비 이익 비율 인 CPR 개념을 도입하여 CPR 내림차순으로 정렬한 후, 최대 CPR 제품부터 허용된 최대 생산량을 실제 생산량으로 수기 식으로 결정하는 단순한 알고리즘을 제안하였다. 6개의 실험 데이터에 제안된 알고리즘을 적용한 결과 선형계획법 에 비해 보다 정확한 결과를 얻을 수 있음을 보였다.

The product portfolio problem(PPP) is an optimization problem that determines the production quantity of a particular product to obtain the maximum profit among the n products. Linear programming(LP) is known as the only way to solve this optimization problem. The linear programming method is a problem that optimizes n linear functions and uses LINGO or Excel solver. This paper proposes a simple algorithm that uses CPR, a product cost-profit ratio, to sort in CPR descending order and then determines the maximum allowed production quantity by hand as the actual production quantity. As a result of applying the proposed algorithm to six experimental data, it was shown that more accurate results can be obtained compared to the linear programming method.

다양한 원재료를 혼합하여 원하는 성분 함유량을 가진 제품을 최소의 비용으로 생산하는 혼합 최적화 문제에 대해 일반적으로 O(n4)의 수행 복잡도의 선형계획법을 적용하고 있다. 본 논문에서는 이 문제에 대해 O(nlogn)복잡도 로 해를 얻을 수 있는 휴리스틱 알고리즘을 제안한다. 제안된 알고리즘은 합금 강판에서 요구하는 성분들의 함유량 범위 를 충족시키면서 최소의 원자재비용을 얻기 위해, 원재료 단가 오름차순으로 성분별 함유량을 충족시키도록 원재료 양을 결정하였다. 3가지 사례에 대해 적용한 결과 제안된 알고리즘은 O(nlogn) 복잡도로 단순한 결정기법을 적용하였음에도 불구하고, LP의 최적화 기법과 동일하거나 보다 좋은 해를 얻을 수 있었다.

Generally, the linear programming (LP) with O(n4) time complexity is applied to mixture optimization problem that can be produce the given ingredients grade product with minimum cost from mixture of various raw materials. This paper suggests heuristic algorithm with O(nlogn) time complexity to obtain the solution of this problem. The proposed algorithm meets the content range of the components required by the alloy steel plate while obtaining the minimum raw material cost, decides the quantity of raw material that is satisfied with ingredients grade for ascending order of unit cost. Although the proposed algorithm applies simple decision technique with O(nlogn)time complexity, it can be obtains same solution as or more than optimization technique of linear programing.

본 논문은 대규모 불균형 수송 문제의 최적 해를 구하는 발견적 방법을 제안한다. 대규모 수송문제의 최적 해를 찾는 방법은 일반적인 수송문제의 최적 해를 구하는 TSM을 적용하는데 어려움이 있어, 대부분은 상용화된 선 형계획법 패키지를 활용한다. 그러나 상용화된 선형계획법 패키지가 최적 해를 얻었는지 검증할 방법이 없다. 본 논 문은 공급지와 수요지가 31 ×15인 대규모 불균형 수송문제에 대해 공급지를 기준으로 수요지가 몇 개인지를 파악하 여 수요지 개수의 오름차순으로 수행하며, 각 수요지 개수에 대해서는 수요지가 1개인 경우 무조건 요구량을 배정하 고, 수요지가 2개 이상인 경우, 공급지 기준의 최소 비용을 선택하고, 수요지 기준으로 비용 오름차순으로 요구량을 충족시키도록 배정하여 초기 해를 구하였다. 해 개선은 보다 큰 비용에 배정된 량을 보다 작은 비용으로 이동 가능한 조건을 만족하면 배정량을 조정하는 방법을 적용하였다. 제안된 방법을 31 ×15 비용행렬에 적용한 결과, 상용 선형계 획법 패키지의 최적 해를 8.9% 개선하는 효과를 나타내었다.

As the Transportation Simplex Method of the general transportation problem are inapplicable to the large-scale unbalanced transportation problem, a commercialized linear programming package remains as the only viable means. There is, however, no method made available to verify the optimality of solutions attained by the package. This paper therefore proposes a simple heuristic algorithm to the large-scale unbalanced transportation problem. From a given problem of 31 ×15 supply and demand areas, the proposed algorithm determines the number of demands areas for each supply area and executes on the latter in the ascending order of each of their corresponding demand areas. Next, given a single corresponding demand area, it supplies the full demand volume and else, it supplies first to an area of minimum associated costs and subsequently to the rest so as to meet the demand to the fullest extent. This initial optimal value is then optimized through an adjustment process whereby costs are minimized as much as possible. When tested on the 31 ×15 cost matrix, the proposed algorithm has obtained an optimal result improved from the commercial linear programming package by 8.9%.

본 연구는 대학에서 연구와 교육을 통하여 축적된 수학교육에 대한 노하우를 상대적으로 소외된 도서지역 고등학생들에게 제공함으로써 고급지식 및 이론의 확산에 힘쓰고자 한다. 연구는 삶의 지혜를 얻기 위한 수학, 실용능력을 배양하기 위한 실용수학, 자신의 품격을 높이기 위한 교양 수학으로 나누어 진행하며 수학 공부를 해야 하는 이유, 수학문제 해결력을 증진시키는 방안, 수학 기기를 이용한 수학학습, 암호이론 및 게임이론 소개, GPS를 이용한 도형학습, 수학과 스포츠, 수학과 예술 등을 포함하여 교재를 개발하고 개발된 교재를 통하여 대학원생을 훈련하고 수업계획안에 따라 수업을 하게 하는 도서지역 고등학생을 위한 흥미롭고 효과적인 수학지도 방안을 연구한다.

In this study, the goal is to spread profound knowledge and theory through providing with accumulated methods in mathematics education to the students who are relatively neglected in educational benefits. The process is divided into 3 categories: mathematics for obtaining common sense and intelligence, practical math for application, and math as a liberal art to elevate their characters. Furthermore, it includes the reasons for studying math, improving problem-solving skills, machinery application learning, introduction to code(cipher1 theory and game theory, utilizing GSP to geometry learning, and mathematical relations to sports and art. Based on these materials, the next step(goa1) is to train graduate students to conduct researches in teaching according to the teaching plan, as well as developing interesting and effective teaching plan for the remote high school learners.

How to schedule multiple sensing units of a sensor to cover multiple targets becomes a new challenging problem. This problem is formulated as an integer linear programming problem for maximizing the network lifetime. We propose a novel energy-efficient target coverage algorithm to solve this problem based on clustering architecture. First of all, the network probability model is established and the subordinate relation between sensor nodes and the target nodes is presented. Secondly, a series of probability is computed and the related theorems and reasoning are also proven. Thirdly, effective coverage for the monitoring region is achieved through scheduling mechanism of nodes themselves, thus the purpose of increasing network lifetime can be realized. Finally, experimental results show that the proposed algorithm could achieve complete coverage for networks of different scale, and increase the network lifetime. It possesses the good quality of effectiveness and stability.

Currently, issues related to freight at Vietnamese logistics companies are becoming more and more urgent because of typical problems in Vietnam such as traffic, infrastructure, and application of information technology. This problem has been studied by applying many different approaches such as Integer Programming (LP), Mixed Integer Programming (MIP), hybrid, meta search, … In this paper, we applied the ILP model in order to deal with the VRP problem in a small size logistics company which is very popular in Vietnam. The experiments showed promising results with some optimal solutions with some small extra costs.

Renewable sources integration is gaining importance in electrical utilities all over the world. The liberization of power sector in competitive regime, the share of renewable energy sources is increasing and it is essential to carry out the impact of clean energy on the system performance In this paper, analysis has been carried out with the PV-based distribution generation in the power system network. A Mixed Integer Nonlinear Programming (MINLP) approach has been utilized for determining optimal location and number of distributed generators considering minimization of fuel cost of conventional and solar PV power. The pattern of nodal real and reactive power prices have been obtained with and without PV integration. The results are also obtained for, loss reduction, fuel cost saving and voltage profile. The impact of different load models as PQ load and Zip load model has been studied. The proposed MINLP based optimization approach has been applied for IEEE24 bus reliability test system.

This paper presents a multi objective approach to solve a Capacitated Vehicle Routing Problem ith Time Windows (CVRPTW). The proposed model was implemented and tested in a real life roblem of a distribution company “Just in Time Delivery S.A” in Portugal. In this paper we ave considered an objective function with two main goals: the first is to minimize the total number f vehicles used in the distribution of the commodities to the several clients and the second is to inimize the travelling time of the used vehicles. The proposed model has been solved numerically sing the GLPK software and the optimal solution is presented.

Clostridium acetobutylicum is an attention-grabbing bacterium in that it produces several solvents, especially butan-1-ol. We reconstructed a genome-scale metabolic network of C. acetobutylicum ATCC 824 which comprises 502 reactions and 479 metabolites. Then, we carried out flux balance analysis using both linear and non-linear approach which is a modification of previous studies.1,2) Here, we present metabolic features and feasibilities of C. acetobutylicum, and hypothetical annotations derived during the reconstruction of the network. [This work was supported by the Korea–Australia Collaborative Research Project on the Development of Sucrose-Based Bioprocess Platform (N02071165) from the Korean Ministry of Knowledge Economy. Further support by LG Chem Chair Professorship and Microsoft are appreciated.]

The generalized linear impulsive correction problem is applied to make a linear programming problem for optimizing trajectory of an orbiting spacecraft. Numerical application for the stationkeeping maneuver problem of geostationary satellite shows that this problem can efficiently find the optimal solution of the stationkeeping parameters, such as velocity changes, and the points of impulse by using the revised simplex method.