• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.2
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• pp.89-97
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• 2007

We study the maximum integer multiflow problem and the minimum multicut problem in a ring network. Both problems in a general network are known to be NP-hard. In this paper, we develop polynomial time algorithms to solve the problems. We also prove that even In a ring network, maximum multiflow is not always integral, which implies that the amount of maximum integer flow does not always reach the minimum capacity of multicut.

• Journal of Korean Society of Transportation
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• v.23 no.6 s.84
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• pp.115-125
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• 2005

The line planning problem is to determine the origin and destination stations of the lines with their frequencies so as to meet the OD demands. Since the advent of high speed trains, Korea railway is confronted with the urgent difficulty to reconstruct the line configuration with the frequencies of each line and each fleet type so the demands could be newly created as well as satisfied. Furthermore. the existing trains except the high speed trains suffer from a longer traveling time than before. Now, to reduce the passenger traveling time, the trains with the various halting patterns are run in the same line. Therefore, it is necessary to develop a new line planning model to consider the various halting patterns. Most of studies find the frequencies of each lines which meet the link traffic loads or minimum link frequencies. But these are based on the assumption of all stop patterns. Furthermore, it is not easy to include the actual constraints as like the minimum number of stops at a station, the maximum number of stops or a train, etc. We develop the line planning model considering not only the various halting patterns but also the actual constraints which is based on the multicommodity network flow model with the additional constraints.