• Journal of the Korean Operations Research and Management Science Society
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• v.13 no.2
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• pp.47-58
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• 1988

The dynamic uncapacitated facility location model is formulated by a mixed integer programming. It has the objective of minimizing total discounted costs for meeting demands specified in different time periods at various demand centers. Costs include those for operation of facilities to demand centers and a fixed cost associated with the capital investment. The problem is decomposed into two simple Lagrangian relaxed subproblems which are coordinated by Lagrangian multipliers. We explored the effect of using the subgradient optimization procedure and a viable solution approach is proposed. Computational results are presented and further research directions are discussed.

• 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.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.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.13-35
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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.

• 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.

• Proceedings of the KIEE Conference
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• 1986.07a
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• pp.373-375
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• 1986

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.435-442
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• 2010

This paper is concerned with algorithm for calculating one-sided best simultaneous approximation, in the case of continuous functions. we will apply any subgradient algorithm. In other words, we consider the algotithms from a mathematical, rather then computational, point of view.

• 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 Communications and Networks
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• v.15 no.5
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• pp.527-537
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• 2013

Improving resource utilization has been a hot issue in heterogeneous wireless networks (HWNs). This paper proposes a radio resource management (RRM) method based on access proportion optimization. By considering two or more wireless networks in overlapping regions, users in these regions must select one of the networks to access when they engage in calls. Hence, the proportion of service arrival rate that accesses each network in the overlapping region can be treated as an optimized factor for the performance analysis of HWNs. Moreover, this study considers user mobility as an important factor that affects the performance of HWNs, and it is reflected by the handoff rate. The objective of this study is to maximize the total throughput of HWNs by choosing the most appropriate factors. The total throughput of HWNs can be derived on the basis of a Markov model, which is determined by the handoff rate analysis and distribution of service arrival rate in each network. The objective problem can actually be expressed as an optimization problem. Considering the convexity of the objective function, the optimization problem can be solved using the subgradient approach. Finally, an RRM optimization scheme for HWNs is proposed. The simulation results show that the proposed scheme can effectively enhance the throughput of HWNs, i.e., improve the radio resource utilization.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1994.04a
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• pp.303-312
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• 1994

The problem of optimally allocating available communication channels in a cellular mobile system with nonuniform traffic distribution is considered. This problem is to minimize the weighted average blocking probability subject to cochannel interference constraints. We use the concept of pattern to deal with the problem more conveniently. Using Lagrangian relaxation and subgradient optimization techniques, we obtain high-quality solutions with information about their deviations from true optimal solutions. Computational experiments show that our method works very well.