• Journal of the Korean Society for Railway
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• v.8 no.5
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• pp.391-397
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• 2005

In this paper we present a model for the maintenance routing construction and the trainset allocation (maintenance routing problem). The model solves the maintenance routing problem using column generation algorithm which was used to combine constraint programming and linear programming. Ilog-cplex was used to solve the linear programming model and Ilog-solver was used to solve the constraint programming model. The computational experience is also provided.

• Journal of the Korean Society for Railway
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• v.15 no.2
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• pp.185-192
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• 2012

Line planning is to determine the frequency of trains on each line to satisfy origin-destination demand while minimizing total operation cost. However, different from the line planning in passenger transportation, it is more important at which intermediate stations each train should be stopped and shunted because the freight car handling works like drop-off or(and) pick-up can incur much time and high cost so that the delay deteriorates the quality of rail freight transportation service. We present an optimization model for constructing line plan in rail freight transportation to simultaneously minimize the train operation cost and total transportation time of freights. And we suggest a column generation approach for our problem, which can solve the real network instances in reasonable computation times.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.410-417
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• 2002

We consider the constraint based explicit routing problem in MPLS based IP Network. In this problem, we are given a set of traffic demands and a network with different link capacities. The problem is to assign the demand commodities to the paths in the network while minimizing the maximum link load ratio. We formulate this problem as an integer programming problem and propose an efficient column generation technique. To strengthen the formulation, we consider some valid inequalities. We also incorporate the column generation technique with variable fixing scheme Computational results show that the algorithm gives high quality solutions in a short execution time.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.7
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• pp.2955-2963
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• 2012

This study presents a column generation approach for multiple product dynamic lot-sizing problem. The basic idea of this approach is to have a master problem which allocates limited capacity among n different products and a sub-problem that performs the optimal lot sizing for each product subject to capacity allocation given by the master problem. In the sub-problem, we develop M/G/1 queuing model based clearing function which captures nonlinear relationship between the lot size, the work in process level and the throughput. A large number of test problems are randomly generated to evaluate the performance. Computational results show that the proposed model can find better solutions within reasonable CPU times.

• Journal of the Korean Society for Railway
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• v.19 no.6
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• pp.833-843
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• 2016

Recently, in the field of rail freight transportation, the number of trains dedicated for shippers has been increasing. These dedicated trains, which run on the basis of a contract with shippers, had been restricted to the transportation of containers, or so called block trains. Nowadays, such commodities have extended to cement, hard coal, etc. Most full freight cars are transported by dedicated trains. But, for empty car distribution, the efficiency still remains questionable because the distribution plan is manually developed by dispatchers. In this study, we investigated distribution models delineated in the KTOCS system which was developed by KORAIL as well as mathematical models considered in the state-of-the-art. The models are based on optimization models, especially the network flow model. Here we suggest a new optimization model with a framework of the column generation approach. The master problem can be formulated into a transportation problem with additional constraints. The master problem is improved by adding a new edge between the supply node and the demand node; this edge can be found using a simple shorted path in the time-space network. Finally, we applied our algorithm to the Korean freight train network and were able to find the total number of empty car kilometers decreased.

• Proceedings of the KSR Conference
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• 2007.11a
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• pp.1731-1737
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• 2007

This paper considers subway routing problem. Given a schedule of train to be routed by a railway stock, the routing problem determines a sequence of trains while satisfying turnaround time and maintenance restrictions. Generally, the solution of routing problem is generated from set partition formulation solved by column generation method, a typical integer programming approach for train-set. However, we find the characteristics of metropolitan subway which has a simple rail network, a few end stations and 13 departure-arrival patterns. We reflect a turn-around constraint due to spatial limitations has no existence in conventional railroad. Our objective is to minimize the number of daily train-sets. In this paper, we develop two basic techniques that solve the subway routing problem in a reasonable time. In first stage, we formulate the routing problem as a Min-cost-flow problem. Then, in the second stage, we attempt to normalize the distance covered to each routes and reduce the travel distance using our heuristic approach. Applied to the current daily timetable, we could find the subway routings, which is an approximately 14% improvement on the number of train-sets reducing 15% of maximum traveling distance and 8% of the standard deviation.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.6
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• pp.3851-3857
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• 2014

Shippers' requests of freight trains vary with time, but generating an additional schedule of freight trains is not easy due to many considerations, such as the line capacity, operation rules, and conflicts with existing trains. On the other hand, an additional freight train schedule has been continuously requested and manually processed by domestic train operation companies using empirical method, which is time consuming. This paper proposes a model to determine the additional freight train schedule that assesses the feasibility of the added freight trains, and generates as many additional schedules as possible, while minimizing the delay of the existing schedules. The problem is presented using time-space network, modeled as multi-commodity flow problem, and solved using the column generation method. Three levels of experiment were conducted to show validity of the proposed model in the computation time.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.10a
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• pp.57-78
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• 2005

The vehicle routing problem (VRP) is to determine a set of feasible vehicle routes, one for each vehicle, such that each customer is visited exactly once and the total distance travelled by the vehicles is minimized. A feasible route is defined as a simple circuit including the depot such that the total demand of the customers in the route does not exceed the vehicle capacity. While there have been significant advances recently in exact solution methodology, the VRP is not a well solved problem. We find most approaches still relying on the branch and bound method. These approaches employ various methodologies to compute a lower bound on the optimal value. We introduce a new modelling approach, termed route-splitting, for the VRP that allows us to address problems whose size is beyond the current computational range of set-partitioning models. The route-splitting model splits each vehicle route into segments, and results in more tractable subproblems. Lifting much of the burden of solving combinatorially hard subproblems, the route-splitting approach puts more weight on the LP master problem, Recent breakthroughs in solving LP problems (Nemhauser, 1994) bode well for our approach. Lower bounds are computed on five symmetric VRPs with up to 199 customers, and eight asymmetric VRPs with up to 70 customers. while it is said that the exact methods developed for asymmetric instances have in general a poor performance when applied to symmetric ones (Toth and Vigo, 2002), the route splitting approach shows a competent performance of 93.5% on average in the symmetric VRPs. For the asymmetric ones, the approach comes up with lower bounds of 97.6% on average. The route-splitting model can deal with asymmetric cost matrices and non-identical vehicles. Given the ability of the route-splitting model to address a wider range of applications and its good performance on asymmetric instances, we find the model promising and valuable for further research.