• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.2
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• pp.19-26
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• 1989

We in this paper have defined the concept of .epsilon.-symmetric relation between the Lagrangean relaxation and the Benders' decomposition. This links the solutions of the Lagrangean subproblems and those of the Benders' subproblems even under positive duality gaps. As an application we have discussed the reduction of the size for a special class of problems.

• Journal of Communications and Networks
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• v.13 no.1
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• pp.26-31
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• 2011

In this paper, we formulate the minimum power multicast problem in wireless networks as a mixed integer linear programming problem and then propose a Lagrangean relaxation based algorithm to solve this problem. By leveraging on the information from the Lagrangean multiplier, we could construct more power efficient routing paths. Numerical results demonstrate that the proposed approach outperforms the existing approaches for broadcast, multicast, and unicast communications.

• Journal of the Korean Operations Research and Management Science Society
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• v.10 no.2
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• pp.24-27
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• 1985

This paper presents sufficient conditions for zero duality gap of Lagrangean relaxation in mixed integer programming problems and discusses about an algorithm which updates multipiers using the dual varibles of the linear programming constructed by fixing integer variables.

• Journal of Korean Institute of Industrial Engineers
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• v.22 no.4
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• pp.741-751
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• 1996

The three dimensional cutting-stock problem is to maximize the total value of pieces which are smaller cubics-cut from a original cubic stock. This paper suggests a method to maximize the total value of different size cut pieces using the orthogonal non-guillotine cut technique. We first formulated a zero-one integer programming, then developed a Lagrangeon relaxation method far the problem. The solutions were given by using a brunch-end-bound technique associates with Lagrangean relaxation, which guarantees an optimal solution.

• 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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.04a
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• pp.161-161
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• 1993

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.2
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• pp.1-13
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• 1998

The purpose of this paper is to formulate the three-dimensional loading problem and to develop an exact algorithm. The three-dimensional loading problem is not only to load as many boxes as possible, but also to ensure load stability. In this Paper, we propose formulation by zero-one integer programming. Further we propose as an algorithm the branch-and-bound enforced by efficient bounding criteria. As an upper bound, we use the solution of the Lagrangean relaxation problem which relaxes constraints of zero-one IP, and as a lower bound, we use a heuristic solution induced by the solution of the Lagrangean relaxation problem. Last, we show computational experiments on convergency of upper and lower bounds.

• Korean Management Science Review
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• v.25 no.2
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• pp.25-42
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• 2008

CDMA/TOD with asymmetric capacity allocation between uplink and downlink is a highly attractive solution to support the next generation mobile systems. This is because flexible asymmetric allocation of capacity to uplink and downlink usually improves the utilization of the limited bandwidth. In this paper, we mathematically formulate an optimal timeslot and code allocation problem, which is to maximize the total utility considering the numbers of codes(channels) allocated to each data class and the forced terminations of previously allocated codes. We also suggest a real-time integrated timeslot and code allocation scheme using Lagrangean relaxation and subgradient optimization techniques. Experimental results show that the proposed scheme provides high-quality solutions in a fast time.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.3
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• pp.1-15
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• 2007

In this paper, the return link of interactive GEO satellite network providing multimedia services is considered. First, we classify data by delay characteristics, and analyze the numbers of expected lost packets and expected delay packets for each data class of each terminal. Next we mathematically formulate optimal rate scheduling model to minimize the weighted sum of the numbers of expected lost packets and expected delay packets considering priority of each data class. We also suggest a dynamic rate scheduling scheme based on Lagrangean relaxation technique and subgradient technique to solve the proposed model in a fast time. Extensive experiments show that the proposed scheme provides encouraging results.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.14-35
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• 1991

The purpose of this study is to develop an efficient exact algorithm for the problem of scheduling n in dependent jobs on m unequal parallel processors to minimize makespan. Efficient solutions are already known for the preemptive case. But for the non-preemptive case, this problem belongs to a set of strong NP-complete problems. Hence, it is unlikely that the polynomial time algorithm can be found. This is the reason why most investigations have bben directed toward the fast approximate algorithms and the worst-case analysis of algorithms. Recently, great advances have been made in mathematical theories regarding Lagrangean relaxation and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining these mathematical tools with branch-and-bound procedures, these have been some successes in constructing pseudo-polynomial time algorithms for solving previously unsolved NP-complete problems. This study applied similar methodologies to the unequal parallel processor problem to find the efficient exact algorithm.