Earticle

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.

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.

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.

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.

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.

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.

본 연구에서는 부유식 해상풍력발전의 운영 및 유지보수에 필요한 체계적인 정비계획 수립을 위해 최적화기법을 활용한 수리 모형을 제안하고자 한다. 주간 단위로 선박과 기술자를 운용하는 계획정비와 고장정비 작업의 배정에 혼합정수계획법(Mixed Integer Linear Programming, MILP)을 도입하였다. 본 연구의 최적화 모델을 활용한 사례연구에서는 선박과 기술자의 투입 규모가 유지정비 비용에 미치는 영향을 확인하였으며 1년간 정비계획 수립에서 더 나아가 정비작업별 상세 스케줄링까지 연계되는 단계적 최적화 방법론을 함께 제시하였다. 세부적으로는 기상 데이터와 정비 데이터를 활용한 발전량 손실을 비가동 비용으로 반영하여 정비 우선순위를 선정하였으며, 이를 통해 국내 실정에 맞는 해상풍력단지의 유지보수 전략을 제시할 수 있을 것으로 기대한다.

In this paper, we propose operations and maintenance (O&M) planning approach for floating offshore wind farm using the mathematical optimization. To be specific, we present a MILP (Mixed Integer Linear Programming that suggests the composition of vessels, technicians, and maintenance works on a weekly basis. We reflect accessibility to wind turbines based on weather data and loss of power generation using the Jensen wake model to identify downtime cost that vary from time to time. This paper also includes a description of two-stage approach for maintenance planning & detailed scheduling and numeric analysis of the number of vessels and technicians on the O&M cost. Finally, the MILP model could be utilized in order to establish the suitable and effective maintenance planning reflecting domestic situation.

Minimizing the total number of setup changes of a machine increases the throughput and improves the stability of a production process, and as a result enhances the product quality. In this context, we consider a new product-mix problem that minimizes the total number of setup changes while producing the required quantities of a product over a given planning horizon. For this problem, we develop a mixed integer programming model. Also, we develop an efficient heuristic algorithm to find a feasible solution of good quality within reasonable time bounds. Computational results show that the developed heuristic algorithm finds a feasible solution as good as the optimal solution in most test problems. Also, we developed a web based scheduling and monitoring system for a zinc alloy production process using the developed heuristic algorithm. By using this system, we could find a monthly zinc alloy production schedule that significantly reduces the total number of setup changes.

In this paper, we propose a lot-sizing and scheduling problem that seeks to minimize the sum of production cost and inventory cost over a given planning horizon while considering idle state of a machine in a batch production system. For this problem, we develop an integer programming model. And, we develop an efficient 2-phase heuristic algorithm to find a high quality feasible solution within reasonable time bounds. In the first phase, we seek to minimize the production cost by assigning batches to machines. Then, in the second phase, we find a production sequence of batches that reduces the inventory cost, while considering adding or deleting idle states between batches. Computational results show that the developed heuristic algorithm finds excellent feasible solutions within reasonable time bounds. Also, we could significantly reduce the total cost consisting of production cost and inventory cost by using the developed heuristic algorithm at a real manufacturing system that produces zinc alloys.

This paper describes a mathematical programming model for constructing the rolling stock assignment plan. This plan is a schedule which assigns daily routings, maintenance activities, and other tasks to trainsets. A generalized set partitioning model which is a kind of integer programming model is suggested as a model for constructing the assignment plan. And a column generation method are suggested as a solution method.

This paper presents a short-term scheduling algorithm for the operation of steelmaking processes. The scope of the problem covers refining of the hot iron transferred form a blast furnace, ladle treatment, continuous casting, hot-rolling, and coiling for the final products that should satisfy the given demand. The processing time at each unit depends on how much the batch amount is treated, and te dedicated intermediate storage with finite capacity between the units is considered. Resource constraints and initial amount of each state are incorporated into the presented scheduling model for the algorithm of on-line scheduling. We propose amixed integer linear programming (MILP) model with two objectives for the scheduling. The first is to maximize the total profit while atisfying the due date constraint for each product. And the second is to minimize the total processing time, makespan, while satisfying the demand for each product. Especially, we observe the effect of penalizing the intermediate storage and the inventory level of the final product on the scheduling results.

The purpose of this research is to develop a method for part-machine grouping subject to production and management constraints. In the proposed integer programming model, minimization of operating and material-handling costs are considered as an objective function. The model allows one to recognize the existing parts and machines into disaggregated cells. New constraints are introduced in the model to resolve unbalancing capacity and bottleneck problems. It is found that this approach could have a better flexibility on cell size design for mote alternatives than conventional methods. Experimental grouping and comparison studies with ROC algorithm are given for evaluation purposes.

The topic of this study is the field of humanitarian logistics for disaster response. Many existing studies have revealed that compliance with the golden time in response to a disaster determines the success or failure of relief activities, and logistics costs account for 80% of the disaster response cost. Besides, the agility, responsiveness, and effectiveness of the humanitarian logistics system are emphasized in consideration of the disaster situation's characteristics, such as the urgency of life-saving and rapid environmental changes. In other words, they emphasize the importance of logistics activities in disaster response, which includes the effective and efficient distribution of relief supplies. This study proposes a mathematical model for establishing a transport plan to distribute relief supplies in a disaster situation. To determine vehicles' route and the amount of relief for cities suffering a disaster, it mainly considers the urgency, effectiveness (restoration rate), and uncertainty in the logistics system. The model is initially developed as a mixed-integer nonlinear programming (MINLP) model containing some nonlinear functions and transform into a Mixed-integer linear programming (MILP) model using a logarithmic transformation and piecewise linear approximation method. Furthermore, a minimax problem is suggested to search for breakpoints and slopes to define a piecewise linear function that minimizes the linear approximation error. A numerical experiment is performed to verify the MILP model, and linear approximation error is also analyzed in the experiment.

ELECTRE IS requires the decision maker (DM) to specify several parameters such as weights, pseudo-criteria thresholds and the concordance level. Among these parameters, the concordance level has a significant effect on the outranking relation. And the number of alternatives selected may be sensitive to the value of these parameters. Therefore the DM may have to perform many iterations to obtain the desired number of alternatives in the kernel set. In this study, we developed a mixed-integer programming (MIP) model to elicit the concordance level and thereby to choose the desired number of alternatives in the kernel set. The MIP model can be applied in the interactive process so that the pseudo-criteria thresholds are adjusted according to the results of MIP model. Using the MIP model in the interactive process, we can reduce the number of iterations needed to perform ELECTRE IS.

본 연구에서는 조수조건이 고려된 벌크항만의 하역 최적화를 위한 정수계획모형을 제안한다. 특히, 본 연구에서는 실제 벌크항만의 운영 환경과 조건들을 반영하여 체선료(Demurrage Cost)와 조출료(Dispatch Money)를 모두 고려한 하역비용 최소화를 목적함수로 설정하고, 벌크항만의 서비스 수준을 결정하는 최소재고 제약조건 또한 고려한다. 일반적으로 비선형 함수 형태로 표현되는 체선료 계산식을 선형화(Linearize)하여 스케줄 해상도를 향상하고, 조수조건을 고려한 선석할당 문제의 경우 전통 자원할당 모형에서 필수적인 Big-M 제약식이 대체 가능함을 확인한다. 실험결과를 통해 기존 모형 대비 계산복잡도와 전역최적성이 크게 향상 가능함을 검증한다.

We examine berth allocation problems in tidal bulk ports with an objective of minimizing the demurrage and dispatch associated berthing cost. In the proposed optimization model inventory (or stock) level constraints are considered so as to satisfy the service level requirements in bulk terminals. It is shown that the mathematical programming formulation of this research provides improved schedule resolution and solution accuracy. We also show that the conventional big-M method of standard resource allocation models can be exempted in tidal bulk ports, and thus the computational efficiency can be significantly improved.

In this study, a Multiple Objective Mixed Integer Programming (MOMIP) Model is developed for sewer rehabilitation planning by considering cost, inflow/infiltration. A sewer rehabilitation planning model is required to decide the economic life of the sewer by considering trade-off between cost and inflow/infiltration. And it is required to find the optimal rehabilitation timing, according to the cost effectiveness of each sewer rehabilitation within the budget. To develop such a model, a multiple objective mixed integer programming model is formulated based on network flow optimization. The network is composed of state nodes and arcs. The state nodes represent the remaining life and the arcs represent the change of the state. The model consider multiple objectives which are cost minimization and minimization of inflow/infiltration. Using the multiple objective optimization, the trade-off between the cost and inflow/infiltration is presented to the planner so that a proper sewer rehabilitation plan can be selected.

Previous researches have focused on the efficiency of project execution and the satisfaction of internal customers In view of the fact that a project is successful if any defects are not found in the short-term performance test of the project final outcome. To execute a project that both internal customer and external customer are satisfied in terms of longer-term benefit perspective, the project claim costs (PCC) which may occur for the warranty period of the project final outcome should be considered. We propose a model included PCC to the linear programming between time and cost to expedite a project and perform the validity test by applying the model to an example project. This model and related procedure will contribute to overall project activities' cost reduction by taking preventive actions for PCC.

This paper presents a sophisticated mixed-integer linear programming model that may help regional decision-maker to develop long term plan of solid waste management The model revises Ni-Bin Chang(1996)'s integrated waste management models to fit Korean solid waste management system We apply this model to evaluate impact of facility sharing and coordinated operation among three self-governing districts in Seoul city Our study results indicate that facility sharing and coordinated operation among districts eliminate unnecessary landfilling and facility expansion.

Quality function deployment (QFD) is a widely adopted customer-oriented product development methodology by analyzing customer requirements. It is a main activity in QFD planning process to determine the optimal values of the technical attributes (TAs) so as to achieve the customer requirements (CRs) from the House of Quality (HoQ). In most of the previous research, all the TAs in QFD are assumed to have either continuous or discrete values. In the real world applications, the continuous TAs and the discrete TAs are often mixed in QFD. In this paper, a mixed integer linear programming model is formulated to obtain the optimal values for the continuous TAs and the discrete TAs in QFD planning as well as Branch and Bound (B and B) algorithm is proposed as the solution approach. Finally, the proposed model and solution approach are illustrated with an office chair under multi-segment market, and the sensitivity analysis is performed to study how the proposed model and its solutions respond to the variation for the two elements which are budget and CRs' weights.