• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.402-408
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• 2002

Multicast technology allows the transmission of data from one source node to a selected group of destination nodes. Multicast routes typically use trees, called multicast routing trees, to minimize resource usage such as cost and bandwidth by sharing links. Moreover, the quality of service (QoS) is satisfied by distributing data along a path haying no more than a given number of arcs between the root node of a session and a terminal node of it in the routing tree. Thus, a multicast routing tree for a session can be represented as a hop constrained Steiner tree. In this paper, we consider the hop-constrained multicast route packing problem with bandwidth reservation. Given a set of multicast sessions, each of which has a hop limit constraint and a required bandwidth, the problem is to determine a set of multicast routing trees in an arc-capacitated network to minimize cost. We propose an integer programming formulation of the problem and an algorithm to solve it. An efficient column generation technique to solve the linear programming relaxation is proposed, and a modified cover inequality is used to strengthen the integer programming formulation.

• Korean Management Science Review
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• v.24 no.2
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• pp.43-56
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• 2007

VRP(Vehicle Routing Problem) is studied in this paper, where two different kinds of missions are to be completed. The objective is to minimize the total vehicle operating distance. A mixed integer programming formulation and a heuristic algorithm for a practical use are suggested. A heuristic algorithm consists of three phases such as clustering, constructing routes, and adjustment. In the first phase, customers are clustered so that the supply nodes are grouped with demand nodes to be served by the same vehicle. Vehicle routes are generated within the cluster in the second phase. Clusters and routes are adjusted in the third phase using the UF (unfitness) rule designed to determine the customers and the routes to be moved properly. It is shown that the suggested heuristic algorithm yields good performances within a relatively short computational time through computational experiment.

• Journal of Communications and Networks
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• v.4 no.3
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• pp.246-255
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• 2002

Constrained minimum Steiner tree (CMST) problem is a key issue in multicast routing with quality of service (QoS) support. Bounded shortest path algorithm (BSMA) has been recognized as one of the best algorithms for the CMST problem due to its excellent cost performance. This algorithm starts with a minimumdelay tree, and then iteratively uses a
-shortest-path (KSP) algorithm to search for a better path to replace a “superedge” in the existing tree, and consequently reduces the cost of the tree. The major drawback of BSMA is its high time complexity because of the use of the KSP algorithm. For this reason, we investigate in this paper the possibility of more efficient implementations of BSMA by using different methods to locate the target path for replacing a superedge. Our experimental results indicate that our methods can significantly reduce the time complexity of BSMA without deteriorating the cost performance.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.29 no.4
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• pp.75-82
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• 2006

The main objective of this study is to find out the shortest path of the vehicle routing problem with time window constraints by using both genetic algorithm and heuristic. Hard time constraints were considered to the vehicle routing problem in this suggested algorithm. Four different heuristic rules, modification process for initial and infeasible solution, 2-opt process, and lag exchange process, were applied to the genetic algorithm in order to both minimize the total distance and improve the loading rate at the same time. This genetic algorithm is compared with the results of existing problems suggested by Solomon. We found better solutions concerning vehicle loading rate and number of vehicles in R-type Solomon's examples R103 and R106.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.14 no.24
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• pp.141-147
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• 1991

This paper presents extended model for the vehicle routing problem, which allows multiple visits to a node by multiple vehicles. Multiple visits enables us split delivery. After formulating this multiple visits model mathematically, a two stage heuristic algorithm is developed by decomposition approach. This model consists of two sub-problem. The one is fixed cost transportation problem and the other is transportation problem.

• Journal of Korean Society of Transportation
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• v.22 no.5
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• pp.89-97
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• 2004

The Korea Air Force(KAF) has operated freight flights based on the prefixed time and route schedule, which is adjusted once in a month. The major purpose of the operation of freight flights in the KAF is to distribute necessary supplies from the home air base to other air bases. The secondary purpose is to train the young pilots to get more experiences in navigation. Each freight flight starts from and returned to the home air base everyday except holidays, while it visits several other air bases to accomplish its missions. The study aims to forecast freight demand at each base by using time series analysis, and then it tried to optimize the cost of operating flights by solving vehicle routing problem. For more specifically, first, several constraints in operating cargos were defined by reviewing the Korea Air Force manuals and regulation. With such constraints, an integer programming problem was formulated for this specific routing problem allowing several visits in a tour with limitation of maximum number of visits. Then, an algorithm to solve the routing problem was developed. Second, the time series analysis method was applied to find out the freight demand at each air base from the mother air base in the next month. With the forecasted demands and the developed solution algorithm, the oprimum routes are calculated for each flight. Finally, the study compared the solved routing system by the developed algorithm with the existing routing system of the Korea Air Force. Through this comparison, the study proved that the proposed method can provide more (economically) efficient routing system than the existing system in terms of computing and monetary cost. In summary, the study suggested objective criteria for air routing plan in the KAF. It also developed the methods which could forecast properly the freight demands at each bases by using time series analysis and which could find the optimum routing which minimizes number of cargo needed. Finally, the study showed the economical savings with the optimized routing system by using real case example.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.795-804
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• 2003

In this article, a tomography for the estimation of the origin-destination(OD) traffic intensities in dynamic routing network is considered. Vardi(1996)'s approach based on fixed route is not directly applicable to dynamic routing protocols, which arises from the fact that we cannot access the route at every observation time. While it uses link-wise traffics as the observations, the proposed method considers the triple of ingress/outgress/relayed traffics data at each node so that we can transform the problem into a routing-independent tomography. An EM algorithm for implementation and some simulated experiments are provided.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.1
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• pp.1-9
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• 2011

This paper presents a new method that can solve the integrated problem of combined location routing and inventory problem (CLRIP) efficiently. The CLRIP is used to establish facilities from several candidate depots, to find the optimal set of vehicle routes, and to determine the inventory policy in order to minimize the total system cost. We propose a mathematical model for the CLRIP with budget constrained. Because this model is a nonpolynomial (NP) problem, we propose a endosymbiotic evolutionary algorithm (EEA) which is a kind of symbiotic evolutionary algorithm (SEA). The heuristic method is used to obtaining the initial solutions for the EEA. The experimental results show that EEA perform very well compared to the existing heuristic methods with considering inventory control decisions.

• Korean Management Science Review
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• v.29 no.1
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• pp.89-99
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• 2012

In this paper, we deal with the dual-depot heterogeneous vehicle routing problem with simultaneous delivery and pick up(DH-VRPSDP) in reverse logistics. The DH-VRPSDP is a problem of designing vehicle routes in a day of given vehicle to minimize the sum of fixed cost and variable cost over the planning horizon. Each customer can be visited only once according to the service combinations of that customer. Due to the complexity of the problem, we suggest a heuristic algorithm in which an initial solution is obtained by changing the customer and the vehicle simultaneously and then it is improved. A performance of the proposed algorithm was compared to both well-known results and new test problems.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.1
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• pp.33-44
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• 2001

In this paper, we address a problem of traffic grooming and wavelength routing in all optical WDM ring networks. Given a traffic demand for each node pair, we should aggregate the traffic onto lightpaths between pairs of nodes to transport the demand, and set up the routing path for each lightpath with minimum number of wavelengths to be assigned to lightpaths. In this paper, we formulate our problem as a mixed Integer Programming model. Owing to the problem complexity, it is hard to find an optimal solution for our problem. hence, we develop a heuristic algorithm to solve our problem efficiently. From the computational experiments, we can find the proposed heuristic is very satisfactory in both the computation time and the solution quality generated.