• 산업경영시스템학회지
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• 제3권3호
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• pp.55-58
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• 1980

Today, L.P. model has often been used in solving economic and managemental phenomena. But in case of adopting L.P. model in dealing with practical economic and managemental problems there is a possibility that we have difficulties in solving these problems because of greatness of model size, cost for collecting data, cost for adjusting matrix, and etc. In this respect "Decomposition Algorithm for L.P." has been used in overcoming the difficulties above stated. In this paper therefore, I will try to introduce and them criticize Dantzig -Wolfe's "Decomposition Method" and Kornai - Liptak's "Two - Level Planning".ot;Two - Level Planning".uot;.

• 한국철도학회논문집
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• 제15권2호
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• pp.185-192
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• 2012

노선 계획이란 수요를 만족시키면서 열차 운행 비용(operation cost)을 최소화하는 시종착별 열차 운행횟수를 결정하는 과정을 말한다. 그러나 화물 수송의 경우 화물 취급역에서 발생하는 화물의 연결 혹은 해방 작업은 상당한 시간을 필요로 하여, 잦은 중간 화물역에서의 연결 해방 작업은 수송 서비스의 품질을 저하시킬 수 있으므로, 여객 열차의 노선 계획과 달리, 화물 열차 노선 계획에서는 각 열차의 도중 입환역을 어떻게 설정할 것인가가 매우 중요한 문제이다. 본 연구는 열차의 운행 경로, 운행 횟수뿐만 아니라 열차별 도중 입환역를 포함하는 노선계획을 작성하기 위한 최적화 모형을 제시하고, 이 모형에 대한 열생성 기반 해법 및 실험결과를 제시할 것이다.

• 한국경영과학회지
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• 제11권2호
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• pp.37-50
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• 1986

In combining dispersed optimization models, either primal or dual(or both) decomposition method widely used as an organizing device. Interpreting the methods economically, the concepts of price and resource-directive coordination are generally well accepted. Most of deomposition/ integration methods utilize either primal information of dual information, not both, from subsystems, while some authors have developed mixed decomposition approaches employing two master problems dealing primal and dual proposals separately. In this paper a hybrid decomposition method is introduced, where one hybrid master problem utilizes the underlying relationships between primal and dual information from each subsystem. The suggested method is well justified with respect to the flexibility in information flow pattern choice (some prices and other quantities) and to the compatibility of subdivision's optimum to the systemwide optimum, that is often lacking in conventional decomposition methods such as Dantzig-Wolfe's. A numerical example is also presented to illustrate the suggested approach.

• Management Science and Financial Engineering
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• 제18권1호
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• pp.27-37
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• 2012

This paper is motivated by a military cargo-plane routing problem which is a pickup-and-delivery problem in which load splits and node revisits are allowed (PDPLS). Although this recent evolution of a VRP-model enhances the efficiency of routing, a solution method is more of a challenge since the node revisits entail closed walks in modeling vehicle routes. For such a case, even a compact IP-formulation is not available and an effective method had been lacking until Nowak et al. (2008b) proposed a heuristic based on a tabu search. Their method provides very reasonable solu-tions as demonstrated by the experiments not only in their paper (Nowak et al., 2008b) but also in ours. However, the computation time seems intensive especially for the class of problems with dynamic transportation requests, including the military cargo-plane routing problem. This paper proposes a more scalable algorithm hybridizing a tabu search for pricing subproblem paused as a single-vehicle routing problem, with a column generation approach based on Dantzig-Wolfe decomposition. As tested on a wide variety of instances, our algorithm produces, in average, a solution of an equiva-lent quality in 10~20% of the computation time of the previous method.