• Journal of Advanced Navigation Technology
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• v.15 no.5
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• pp.781-788
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• 2011

A sphere-packing problem is to find an arrangement of the spheres to fill as large area of the given space as possible, and covering problems are optimization problems which are dual problems to the packing problems. We generalize the concepts of the weight and the Hamming distance for a binary code to those of Boolean algebra. In this paper, we define a weight and a distance on a Boolean algebra and research some properties of the weight and the distance. Also, we prove the notions of the sphere-packing bound and the Gilbert-Varshamov bound on Boolean algebra.

• Journal of Korean Institute of Industrial Engineers
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• v.30 no.2
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• pp.93-106
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• 2004

This paper studied a maximal covering location problem with cost restrictions, to maximize level of service within predetermined cost. It is assumed that all demand have to be met. If the demand node is located within a given range, then its demand is assumed to be covered, but if it is not, then its demand is assumed to be uncovered. An uncovered demand is received a service but at an unsatisfactory level. The objective function is to maximize the sum of covered demand, Two heuristics based on the Lagrangean relaxation of allocation and decoupling are presented and tested. Upper bounds are found through a subgradient optimization and lower bounds are by a cutting algorithm suggested in this paper. The cutting algorithm enables the Lagrangean relaxation to be proceeded continually by allowing infeasible solution temporarily when the feasible solution is not easy to find through iterations. The performances are evaluated through computational experiments. It is shown that both heuristics are able to find the optimal solution in a relatively short computational time for the most instances, and that decoupling relaxation outperformed allocation relaxation.

• Journal of Korean Society of Transportation
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• v.27 no.4
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• pp.103-113
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• 2009

Quick accident spot reaching of 119ERU is the most important role in decrease of accident depth. If 4 minutes of wounded person pass after cardiac arrest, brain damage is begun. and If 10 minutes of wounded person pass after cardiac arrest, possibility to die rises. Accordingly, when establish 119ERU, need to consider travel time to traffic accidents spot. This treatise groped a facility location problem using SCLM and minisum location problem mutually. And existent minisum location problem has a problem that maximum travel time exceed $\lambda$. ERU to need in present situation and also can reduce average travel time. so this treatise propose modified minisum location problem. In case applying modified minisum location theory, 119ERU can arrive all demand and that is optimized about demand and travel time. Can minimise figure of 119 first aids to need in present situation applying this way, and also can reduce average passing time. Finally, this way can minimise figure of 119ERU to need in present situation and also can reduce average travel time.

• Journal of the Korea Society of Computer and Information
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• v.14 no.2
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• pp.27-35
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• 2009

Integer programming is a very effective technique for searching optimal solution of combinatorial optimization problems. However, its applicability is limited to linear models. In this paper, I propose an effective method for solving a nonlinear optimization problem by integrating the powerful search performance of integer programming and the flexibility of neighborhood search algorithms. In the first phase, integer programming is executed with subproblem which can be represented as a linear form from the given problem. In the second phase, a neighborhood search algorithm is executed with the whole problem by taking the result of the first phase as the initial solution. Through the experimental results using a nonlinear maximal covering problem, I confirmed that such a simple integration method can produce far better solutions than a neighborhood search algorithm alone. It is estimated that the success is primarily due to the powerful performance of integer programming.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.613-616
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• 2000

This paper considers the problem of subway crew scheduling. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper, we propose two basic techniques that solve the problem in a reasonable time, though the optimality of the solution is not guaranteed. To reduce the number of variables, we adopt column-generation technique. We could develop an algorithm that solves column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational results show column-generation makes the problem of treatable size, and variable fixing enables us to solve LP relaxation in shorter time without a considerable increase in the optimal value. Finally, we were able to obtain an integer optimal solution of a real instance within a reasonable time.

• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.4
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• pp.67-86
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• 2002

This paper considers subway crew scheduling problem. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper. we propose two basic techniques that solve the subway crew scheduling problem in a reasonable time, though the optimality of the solution is not guaranteed. We develop an algorithm that solves the column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational result for a real instance is reported.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2008.10a
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• pp.525-528
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• 2008

We propose a IDS node selection scheme for intrusion detection in wireless mesh networks. The proposed scheme considers network survivability and energy consumption. To utilize wireless resources efficiently, we apply a set covering problem (SCP) to IDS nodes selection problem. Our proposed scheme also considers congested networks.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.9 no.13
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• pp.79-86
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• 1986

This paper presents a heuristic algorithm for a crew scheduling problem with dead head flights. This paper modifies and improves saving method for finding the Multiple Salesman tours in the graph. The results show that the computing time from this algorithm is implemented very much than those from general crew scheduling algorithms by set covering models.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.207-226
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• 2007

The purpose of this study was to design and develop the processes of tasks and assessment rubrics of open-ended tasks, and those for the 5th graders of elementary school mathematics. 7 tasks were finally developed, and 'problem understanding', 'problem solving process', 'communication' were selected as the criteria for assessment rubrics. The result was that the ability of mathematical power covering problem understanding ability, problem solving ability and mathematical communication ability was low. Specifically, problem understanding ability was the highest, problem solving ability was middle, and mathematical communication ability was the lowest.

• Journal of the Korea Society for Simulation
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• v.15 no.4
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• pp.69-77
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• 2006

In most positioning and allocation practices, many mathematical models are proposed in various fields. The set covering (SC) problem has many practical applications of modeling not only real world problem but also in military. As our air defense weapon systems are getting older and declining the performance, new plans far acquisition of high-tech air defense weapon system are being conducted. In this paper we established simulation model for optimal allocation of KDX which carries new missile defense weapon system by using partial set covering considering both attacker and defender side. By implementating simulation model, we assess the available scenarios and show the optimal pre-positioning of KDX and interceptor's allocation. Furthermore, we provide a variety of experiments and extensive scale sized situations for Korea Indigenous Missile Defense (KIMD) and support decision-making for efficient positioning of unit.