Earticle

This research developed an optimization model to locate power supply facilities for on-line electric buses so that the construction cost of the facilities is minimized considering the duplication of electric bus routes. This research regards each bus route as an ordered set of bus stops along that route, and builds a Mixed Integer Programming model which minimizes the total construction cost of power supply facilities of several different types based on the distances between bus stops along each bus route and the average stoppage times at bus stops. This research also developed a simulator to calculate average stoppage times at bus stops which would be used as the coefficients for power supply amounts at those bus stops.

교통약자들을 위한 차량서비스는 dial-a-ride, demand responsive 또는 paratransit으로 불리며 미국과 유럽에서 널리 제공 되고 있는 대중교통의 하나이다. 본 연구는 이러한 교통약자 차량서비스의 배차와 차량경로문제에 관한 것으로 다수차 고지와 예약시간 위반을 고려한다. 본 연구에서는 기존의 연구에서 제안된 clustering first-routing second에 기초한 휴리스 틱 알고리즘을 실제 큰 규모의 교통약자 차량서비스에 적용하였다. 사례연구로서 Maryland Transit Administration (MTA) 의 교통약자 차량서비스를 소개하고 실제 MTA의 운영결과와 제안된 휴리스틱 알고리즘의 결과를 비교하였다. 제안된 모형의 목적함수는 서비스제공자의 비용과 고객들의 불편비용으로 이루어진 전체비용을 최소화하는 것이다. 실제 MTA 의 운영자료에 차량대기시간, 서비스지연시간과 초과승차시간에 대한 정보가 없는 관계로 비교를 위해서 clustering first-routing second에 기초한 휴리스틱 알고리즘의 목적함수 값은 차량의 대기비용, 고객들의 서비스지연비용과 초과 승 차시간 비용를 포함하지 않는다. MTA의 실제운영에 의한 목적함수 값보다 HCR의 목적함수 값이 보다 나은 것으로 나 타났으며 이 결과는 본 연구에서 제안된 휴리스틱 방법이 실제운영을 보다 효율적으로 바꿀 수 있음을 보여준다.

Dial-a-ride is the most widely available transit service for disabled persons or seniors in the United States and Europe. This paper studies a static dial-a-ride problem considering multiple depots, heterogeneous vehicles, and soft time windows. In this paper, we apply a heuristic based on clustering first-routing second(HCR) to a real-world large dial-a-ride problem from Maryland Transit Administration(MTA). MTA’s real operation is compared with the results of developed heuristic for 24 cases. The objective function of the proposed model is to minimize the total cost composed of the service provider’s cost and the customers’ inconvenience cost. For the comparison, the objective function values of HCR do not include waiting cost, delay cost, and excess ride cost. The objective function values from HCR are better than those from MTA’s operation for all cases. This result shows that our heuristic method can make the real operation better and more efficient.

본 연구는 폐기되는 자동차의 리버스물류 네트워크 구축을 위해 폐차수집센터(CC), 분해 및 해체센터(DC) 등의 최적위치와 경로를 결정하는데 활용할 수 있는 모델링을 제시하고자 한다. 폐기되는 자동차의 리싸이클링 네트워크를 구축하는데 따른 비용을 고려하여 리싸이클링 네트워크 구축을 위한 위치-경로문제에 대한 최적모델을 제안하였으며, 이러한 목적을 달성하기 위해 유전적 해법(algorithm)과 Tabu탐색해법을 결합한 혼합해법을 사용하였다. 제안된 모델은 청두의 X 기업에서 실행된 실제사례를 기반으로 수집센터, 분해 및 해체센터의 위치 결정뿐만 아니라 수집센터 혹은 분해 및 해체센터와 리싸리클링 사이트 간 비용 최소화 조건의 최적 경로설정을 제시하였다. 이러한 연구결과는 연구의 대상이 된 X기업에 적용하게 된다면 자동차의 라싸이클링 물류네트워크 구축을 위한 투자비용과 시간을 절감할 수 있을 뿐만 아니라 기업의 경쟁력을 제고효과도 있을 것이다. 아울러 다른 종류의 리버스 물류네트워크를 구축하는데 적용될 수 있을 것이다.

This paper presents modelling approach that could be used to establish one important part of end-of-life vehicles (ELVs) reverse logistics network by identifying optimum location for collection centers, dismantling centers and routing arrangement for vehicles. Considering the cost optimization in ELVs recycling logistics network, this paper suggests optimization model of ELVs recycling logistics network location-routing problem and use the algorithm which combine genetic algorithm and tabu search algorithm for solving the proposed model. The proposed model is validated by a real case performed in X company and determines the location of collection centers (CCs) and dismantling centers (DCs), as well as the route arrangement between CCs or DCs and recycling sites (RSs) in ELVs recycling logistics network of X company in Chengdu city of China. In the result, the investment cost and time in the X company could be diminished and the competitiveness of X company would be enhanced as well. Also, this proposed Model may be used to determines the location and routing of different kinds of facilities organized in a reverse recycling network.

PURPOSES : Pavement Management System contains the data that describe the condition of the road. Under limited budget, the data can be utilized for efficient plans. The objective of this research is to develop a mixed integer program model that maximizes remaining durable years (or Lane-Kilometer-Years) in road maintenance planning. METHODS : An optimization model based on a mixed integer program is developed. The model selects a cluster of sectors that are adjacent to each other according to the road condition. The model also considers constraints required by the Seoul Metropolitan Facilities Management Corporation. They select two lanes at most not to block the traffic and limit the number of sectors for one-time construction to finish the work in given time. We incorporate variable cost constraints. As the model selects more sectors, the unit cost of the construction becomes smaller. The optimal choice of the number of sectors is implemented using piecewise linear constraints. RESULTS : Data (SPI) collected from Pavement Management System managed by Seoul Metropolitan City are fed into the model. Based on the data and the model, the optimal maintenance plans are established. Some of the optimal plans cannot be generated directly in existing heuristic approach or by human intuition. CONCLUSIONS:The mathematical model using actual data generates the optimal maintenance plans.

혼합정수 계획의 최적화 기법으로 유도한 '용수 감량 공급 기준'은 용수를 미리 감량 공급함으로써 가뭄 기간에 상대적으로 많은 물을 확보하여 저수지를 운영하는 기준이다. 우리나라의 다목적 저수지 운영에 적용하고 있는 현행 기준은 모의 운영 기법으로 유도된 '용수공급 조정기준'이다. 2003-2018년 기간의 저수지 유입량을 입력 자료로 하여, 합천 다목적댐 저수지의 모의 운영에 두 방법을 적용한 결과, 두 방법 모두 2015년부터 2018년까지 지속된 가뭄에 장기간 물 공급 부족이 발생하였다. 특히 2017년 하반기에 물을 전혀 공급하지 못하거나 간헐적으로 공급하는 기간이 지속해서 나타났다. 용수공급 조정기준은 '정상 용수공급 환원 기준 저수량'을 둠으로써, 2017년 7월에 용수공급 불가 상태에 이른 다음, 저수량이 정상 용수공급 환원 기준 저수량 보다 커지는 2018년 1월까지 용수공급을 중단하는 결과를 낳았다. 저수지에 물이 유입되어 저수량이 증가하는 상태에도 불구하고 물 공급을 중단하는 결과는 실행 상 개선이 필요하다. 현행 용수공급 조정기준과 용수 감량 공급 기준 모두 가뭄 단계별 용수의 감축 공급 개념을 과학적 수치로 나타낸 저수지 운영 기준으로서 유용하고 현실적이다. 그렇지만 위와 같이 몇 개월간 물을 전혀 공급하지 못하거나 간헐적으로 공급하는 저수지 모의 운영 결과를 개선하기 위하여, 현재 적용 중인 가뭄 단계별 물의 공급 축소량을 증가시킬 필요가 있다.

The authors obtained the discrete hedging rule for a reservoir's water supply operation by applying mixed-integer programming to save more water by earlier rationing of water supply for a drought period. The 'water supply adjustment guide' is the current operational method applied to the multipurpose reservoirs, and it was derived by a simulation method. Applying the two rules to the Hapcheon multipurpose dam's reservoir simulations with the inflow record from 2003 to 2018, the water supply deficit occurred for the long drought from 2015 to 2018. Especially, the no water supply or intermittent water supply persisted for the second half of 2017. The water supply adjustment guide had the 'normal water supply recovery threshold on storage,' which resulted in the water supply being unavailable in July 2017; then, the water supply suspension occurred until January 2018, when the reservoir storage was greater than the normal water supply recovery threshold. Despite the storage increasing due to the inflow of water into the reservoir, the suspension occurrence needs to be improved in practice. The current water supply adjustment guide and the discrete hedging rule for a reservoir's water supply operation are useful and realistic as the reservoir operation guide, which shows the concept of reducing water supply during the drought phase as scientific figures. However, to improve the reservoir simulation results, which do not provide any or intermittent water for several months, it is necessary to increase the current water supply reduction for drought phases.

본 연구는 전형적인 차량경로 문제에서 각 노드간의 이동 시간이 일정하지 않은 특수한 경우의 상황에 대한 해법 절차를 제공한다. 본 연구는 상황에 따라 변화하 는 이동시간을 갖는 외판원 문제의 특별한 경우인 ‘한 노드까지 도달한 경로가 다 음 노드로 이동하는 데 걸리는 시간에 영향을 주는 외판원 문제’(경로의존 이동비 용을 갖는 외판원 문제(RDTSP: Route Dependent Travelling Salesman Problem)) 의 해법을 제시한다. RDTSP 문제의 해결을 위해 먼저 문제 상황을 묘사하는 정수 계획 모형을 개발 하였다. 본 연구에서 제시한 정수계획 모형에서는, 모든 가능한 경로에 대하여 각 각의 경로를 하나의 변수로 정의하고 이 변수들 중에서 하나를 선택하는 형태로 개발되었다. 이 모형에서는 변수에 해당하는 가능한 경로의 수가 노드수에 지수적 (exponentially)으로 증가하기 때문에, 처음부터 모든 변수를 문제에 포함시켜 풀 수 없게 된다. 그러나, 개발된 정수계획 모형의 변수를 실수로 완하시킨 선형완화 (LP relaxation) 문제에 대해서는 열 생성(column generation) 기법을 통해 그 해를구할 수 있다. 또한 본 연구의 결과가 PCB 조립 공정의 작업시간 최적화 문제에 어떻게 적용될 수 있는가를 제시한다.

In this study, we propose a solution procedure to solve travelling salesman problem(TSP) with special cost function, route dependent travelling salesman problem(RDTSP). First, we develop an integer programming model to describe the problem. In the model, a variable means a possible route. And, the number of variables in this model are extremely large. So, we develop a LP relaxation problem of the IP model and solve the relaxation problem by a column generation technique. The relaxation problem does not guarantee the optimal solution. If we get an integer solution in the ralaxation problem, then the solution is an optimal one. But, if not, we cannot get an optimal solution. So, we approach a branch and price technique. The overall solution procedure can be applied a printed circuit board(PCB) assembly process.

MICE산업은 중앙정부와 지방자치단체를 중심으로 대규모 전시컨벤션시설을 지속적으 로 구축 및 확장을 통해 인프라를 갖추고 있으며, 2025년까지 증축 및 개축을 통해 7 개 이상의 컨벤션센터 신규 건립이 예정되어있다. 컨벤션센터의 특성상 높은 초기 건 립비용과 비교하여 수익성도 낮은 실정이다. 하지만, 이를 효과적이고 효율적으로 운영 하여 수익성을 높이는 방안에 대한 논의가 부족하다. 이에 본 연구에서는 컨벤션센터 의 효율적인 운영을 위해 컨벤션센터의 주요 수입원인 전시장 배정에 관한 모델을 제 시한다. 본 연구에서 제시된 모델은 기존 컨벤션센터들의 임대기준을 바탕으로 0-1 정 수계획법을 이용한 수학적 모델을 제시하였다. 본 연구에서 제안한 전시장 대관 최적화 모델을 적용하면 전시장 배정 담당자의 경 험에 의해 판단되던 전시장 대관에 관하여 수리적 근거에 기초한 배정을 통해 효율적 인 전시장 임대 배정에 도움을 줄 수 있을 것으로 보인다. 이는 전시장 재고관리에 도 움을 주며 향후 가격정책 및 임대정책 개선에도 기여 할 수 있을 것으로 보인다. 또한 향후 전시장의 조기 배정과 배정 정책의 개선을 통해 컨벤션센터 이용자의 편의성을 제고하고 전시장의 수익성 개선에도 상단한 기여가 있을 것이다. 더불어 컨벤션센터의 운영에 계량적 모델을 적용하여 이전의 컨벤션센터 연구와 차별화를 갖고 있으며, 컨 벤션센터 성과관리에서 최적화라는 새로운 연구분야를 제시하는 것에 의의가 있다.

The convention center is being built and expanded competitively led by the central government and local governments. However, due to the nature of the convention center, it is also difficult to manage due to its low profitability. In addition the exhibition organizer who is a major customer of the convention center, continues to argue over the lease. Therefore, this study presented an optimization model using the 0-1 integer planning method for allocation of exhibition halls, which are the main sources of income for convention centers. Through this research, the profitability of the convention center and the mathematical model is proposed in the decision-making method, that was allocated for rental based on the internal standards of the convention center. Also, this model can serve as a basis for determining the allocation of exhibition halls. Furthermore, the convenience of using the exhibition convention center will be promoted to customers by establishing the exhibition hall allocation policy and early allocation.

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.

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.

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 considers the design problem of assembly lines which are flow oriented production system suitable for mass production. Sine the installation of an assembly line is a midlong-term decision and usually requires large capital investments, it is important that such a system is optimally designed. The simple assembly line balancing problem(SALBP) is allocating tasks to workstations under the cycle time(sum of task times) constraint of each workstation and precedence constraints between tasks. In addition to the basic constraints of SALBP, the generalized assembly line balancing problem(GALBP) considers assignment restrictions such as incompatibilities between tasks, resource(operator) related workstation restriction, etc. The purpose of this paper is to introduce a new integer programming model for GABLP. We propose mild constraints and task-task/task-workstation relationship matrices. these are useful for presenting and solving GALBP as more realistic form.

A mathematical model using integer programming is introduced in this paper. The model is desinged to provide solutions for menu planning in a feeding unit. A cafeteria in a university is selected for the analysis. In the model formulation, 9 essential nutrients and 221 different food items are considered. The model successfully provides a set of menus satisfying the recommended dietary allowances with minimum costs. The menus provided by the model are compared with those by conventional method. The model is found to contribute in increasing the productivity of a service unit, a cafeteria in this research, in the following three ways. First, the costs for the menus by the model are approximately 10% lower than those by the conventional method. Second, nutritional contents of the menus by the model are closer to the recommended dietary allowances with smaller deviations. Third, the model provides us with better menu plans in a more handy and faster way.

The purpose of this paper is to show the brief empirical measurement using the cross-efficiency model and integer programming method for 13 Asia container seaports in 2009, 2010, and 2013 data for 3 inputs( depth, total area, and number of crane) and 1 output(TEU). After clustering using cross-efficiency model, efficiencies are increased in the Busan and Incheon ports. Results using integer programming method focused on the output(TEU) show that Busan port(Hongkong, Dubai, Ningbo, and Chingtao ports), Incheon port(Ningbo, Gwangyang, and Nagoya ports), and Gwangyang port(Nagoya, and Incheon ports) are clustered with the ports in the parentheses. After clustering, efficiencies are not definite in two ports and three ports clustering. The containerport policy planners should introduce and consider the cross-efficiency model and integer programming method when they measure the efficiency increasing plan for the main Korean containerports.

In this paper, we deal with a Steiner Ring Star (SRS) problem arising from the design of survivable telecommunication networks. We develop two mixed integer programming formulations for the SRS problem by implementing Miller-Tucker-Zemlin (MTZ) and Sarin-Sherali-Bhootra (SSB) subtour elimination constraints, and then apply the reformulation-linearization technique (RLT) to enhance the lower bound obtained by the LP relaxation. By exploiting the ring-star structure of underlying network, we devise some valid inequalities that tighten the LP relaxation. Computational results demonstrate the effectiveness of the proposed solution procedure.

In this paper, we consider the adjustment of convergence on Color Display Tube (CDT). Convergence is a measure of how well the red, green and blue beams are physically aligned with each other to strike the same area on the screen. When misconvergence (convergence error) occurs, one way of compensating it is to attach several ferrite sheets on the inner part of Deflection Yoke (DY). We suggest an optimization model of misconvergence compensation process and report test results for 81 DY samples. As a result, more than 90% of the samples could be made to satisfy the required convergence criteria.

The multiple-choice multidimensional knapsack problem (MMKP) is a variant of the well known 0-1 knapsack problem, which is known as an NP-hard problem. This paper proposes a method for solving the MMKP using the integer programming-based local search (IPbLS). IPbLS is a kind of a local search and uses integer programming to generate a neighbor solution. The most important thing in IPbLS is the way to select items participating in the next integer programming step. In this paper, three ways to select items are introduced and compared on 37 well-known benchmark data instances. Experimental results shows that the method using linear programming is the best for the MMKP. It also shows that the proposed method can find the equal or better solutions than the best known solutions in 23 data instances, and the new better solutions in 13 instances.

A binary integer programming model is proposed for a complex timetabling problem in a university faculty which conducts various degree programs. The decision variables are defined with fewer dimensions to economize the model size of large scale problems and to improve modeling efficiency. Binary matrices are used to incorporate the relationships between the courses and students, and the courses and teachers. The model includes generally applicable constraints such as completeness, uniqueness, and consecutiveness; and case specific constraints. The model was coded and solved using Open Solver which is an open-source optimizer available as an Excel add-in. The results indicate that complicated timetabling problems with large numbers of courses and student groups can be formulated more efficiently with fewer numbers of variables and constraints using the proposed modeling framework. The model could effectively generate timetables with a significantly lower number of work hours per week compared to currently used timetables. The model results indicate that the particular timetabling problem is bounded by the student overlaps, and both human and physical resource constraints are insignificant.

The set partitioning problem is a well-known NP-hard combinatorial optimization problem, and it is formulated as an integer programming model. This paper proposes an Integer Programming-based Local Search for solving the set partitioning problem. The key point is to solve the set partitioning problem as the set covering problem. First, an initial solution is generated by a simple heuristic for the set covering problem, and then the solution is set as the current solution. Next, the following process is repeated. The original set covering problem is reduced based on the current solution, and the reduced problem is solved by Integer Programming which includes a specific element in the objective function to derive the solution for the set partitioning problem. Experimental results on a set of OR-Library instances show that the proposed algorithm outperforms pure integer programming as well as the existing heuristic algorithms both in solution quality and time.