• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.89-92
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• 1992

This paper presents an approach for thermal Unit Commitment by Lagrangian Relaxation with fuzzy technique. A proposed algorithm makes it possible to execute optimal decision making between Generation Cost and Load Demand with membership function. In order to test the validity of the proposed method, we applied to Mid-westerm utility system which has 20 thermal units. So, the usefulness of this method is verified.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.1
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• pp.19-29
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• 2011

Cellular network is comprised of several base stations which serve cellular shaped service area and each base station (BS) is connected to the mobile switching center (MSC). In this paper, the configuration modeling and algorithm of a cellular mobile network with the aim of minimizing the overall cost of operation (handover) and network installation cost (cabling cost and installing cost of mobile switching center) are considered. Handover and cabling cost is one of the key considerations in designing cellular telecommunication networks. For real-world applications, this configuration study covers in an integrated framework for two major decisions: locating MSC and assigning BS to MSC. The problem is expressed in an integer programming model and a heuristic algorithm based on Lagrangian relaxation is proposed to resolve the problem. Searching for the optimum solution through exact algorithm to this problem appears to be unrealistic considering the large scale nature and NP-Completeness of the problem. The suggested algorithm computes both the bound for the objective value of the problem and the feasible solution for the problem. A Lagrangian heuristics is developed to find the feasible solution. Numerical tests are performed for the effectiveness and efficiency of the proposed heuristic algorithm. Computational experiments show that the performance of the proposed heuristics is satisfactory in the quality of the generated solution.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.2
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• pp.47-65
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• 1998

We consider a multiperiod capacity planning problem for determining a mix of flexible and dedicated capacities under budget restriction. These capacities are controlled by purchasing flexible machines and/or new dedicated machines and disposing old dedicated machines. Acquisition and replacement schedules are determined and operations are assigned to the flexible or dedicated machines for the objective of minimizing the sum of discounted costs of acquisition and operation of flexible machines, new dedicated machines, and old dedicated machines. In this research, the Problem is formulated as a mixed integer linear Program and solved by a Lagrangian relaxation approach. A subgradient optimization method is employed to obtain lower bounds and a multiplier adjustment method is devised to improve the bounds. We develop a linear programming based Lagrangian heuristic algorithm to find a good feasible solution of the original problem. Results of tests on randomly generated test problems show that the algorithm gives relatively good solutions in a reasonable amount of computation time.

• IE interfaces
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• v.17 no.spc
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• pp.141-151
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• 2004

As today's business environment has become more and more competitive, forward as well as backward flows of products among members belonging to a supply chain have been increased. The backward flows of products, which are common in most industries, result from increasing amount of products that are returned, recalled, or need to be repaired. Effective management for the backward flows of products has become an important issue for businesses because of opportunities for simultaneously enhancing profitability and customer satisfaction from returned products. Since third party logistics service providers (3PLs) are playing an important role in reverse logistics operations, they should perform two simultaneous logistics operations for a number of different clients who want to improve their logistics operations for both forward and reverse flows. In this case, distribution networks have been independently designed with respect to either forward or backward flows so far. This paper proposes a mixed integer programming model for the design of network integrating both forward and reverse logistics. Since the network design problem belongs to a class of NP-hard problems, we present an efficient heuristic algorithm based on genetic algorithm (GA), of which the performance is compared to the lower bound by Lagrangian relaxation. Finally, the validity of proposed algorithm is tested using numerical examples.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.10
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• pp.3831-3851
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• 2015

This paper is concerned with the problem of joint resource allocation and user-pairing in virtual MIMO SC-FDMA systems to improve service quality of experience (QoE). No-reference logarithmic model is introduced to quantify service experience for each user and the objective is to maximize sum of all user's mean of score (MOS). We firstly formulate the optimal problem into an S-dimensional (S-D) assignment problem. Then, to solve this problem, the modified Lagrangian relaxation algorithm is deduced to obtain the suboptimal result of joint user-paring and subchannel allocation. The merits of this solution are as follows. First, the gap between its results and the global optimal one can be quantified and controlled by balancing the complexity and accuracy, which merit the other suboptimal algorithms do not have. Secondly, it has the polynomial computational complexity and the worst case complexity is O(3LN³), where L is the maximum iteration time and N is the number of subchannels. Simulations also prove that our proposed algorithm can effectively improve quality of experience and the gap between our proposed and the optimal algorithms can be controlled below 8%.

• Industrial Engineering and Management Systems
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• v.3 no.2
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• pp.100-115
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• 2004

The network representation and branch and bound algorithm with efficient lower and upper bounding procedures are developed to determine a global optimal production schedule on a machine that minimizes sequence-dependent setup cost and earliness/tardiness penalties. Lower bounds are obtained based on heuristic and Lagrangian relaxation. Priority dispatching rule with local improvement procedure is used to derive an initial upper bound. Two dominance criteria are incorporated in a branch and bound procedure to reduce the search space and enhance computational efficiency. The computational results indicate that the proposed procedure could optimally solve the problem with up to 40 jobs in a reasonable time using a personal computer.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.611-628
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• 2021

In this paper, we propose a new branch-reduction-and-bound algorithm to solve the nonlinear knapsack problems by using general discrete monotonic optimization techniques. The specific properties of the problem are exploited to increase the efficiency of the algorithm. Computational experiments of the algorithm on problems with up to 30 variables and 5 different constraints are reported.

• Journal of the military operations research society of Korea
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• v.9 no.1
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• pp.51-61
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• 1983

Lagrangian relaxation is used to the problem of scheduling jobs on unrelated parallel processors with the objective of minimizing makespan. The implicit condition for optimality is drawn out explicitly in order to apply the subgradient algorithm. To obtain the optimal solution, branch-and-bound-search method is devised. In the search, the special structure of the problem is exploited effectively, Some computational experiences with the algorithm are presented, and comparisons are made with the Land and Doig method.

• Journal of Korean Institute of Industrial Engineers
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• v.9 no.2
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• pp.3-8
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• 1983

The multiple choice knapsack problem is modified. To solve this modified multiple choice knapsack problem, Lagrangian relaxation is used, and to take advantage of the special structure of subproblems obtained by decomposing this relaxed Lagrangian problem, a modified ranking algorithm is used. The K best rank order solutions obtained from each subproblem as a result of applying modified ranking algorithm are used to formulate restricted problems of the original problem. The optimality for the original problem of solutions obtained from the restricted problems is judged from the upper bound and lower bounds calculated iteratively from the relaxed problem and restricted problems, respectively.

• Journal of information and communication convergence engineering
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• v.1 no.2
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• pp.93-97
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• 2003

This paper proposes a new generation scheduling algorithm which can consider total quantity of contamination and energy limits based on Lagrangian Relaxation. First, we formulate a Lagrangian function which consider quantity of contamination including substitution of fuel, and quantity of fuel. Second, we developed Multi-state S.U.D.P. which can treat multiple fuels. Third, we propose an effective generation scheduling algorithm including Multi-state S.U.D.P.. As a results, unit commitment and generating power can be obtained to meet the environmental and fuel constraints with fuel substitution. By applying it to the test system, effectiveness of the method is verified.