• 대한산업공학회지
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• 제37권2호
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• pp.144-152
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• 2011

Most of the models for the vehicle routing problems studied in the literature assumed constant travel times. However, those approaches may give infeasible solutions when traffic congestion causes delays in travel time. To overcome such difficulty, there have been some researches considering the change of the travel time which is called the time dependent vehicle routing problem (TDVRP). TDVRP assumes that the travel time between two locations is not only affected by the distance traveled, but by many other factors including the time of the day. In this paper, we propose a branch-and-price algorithm to solve the TDVRP. The time dependent property of the travel time is dealt with an enumeration scheme with bounding procedures in the column generation procedure identifying a profitable route. The proposed algorithm guarantees the "Non-passing" property to be held in the solutions. The algorithm was tested on problems composed of the Solomon's benchmark instances for 25 and 50 nodes. Computational results are reported.

• Industrial Engineering and Management Systems
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• 제3권2호
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• pp.92-99
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• 2004

We consider the ATM switching node location problem (ANLP). In this problem, there are two kinds of facilities, hub facilities and remote facilities, with different capacities and installation costs. We are given a set of customers with each demand requirements, a set of candidate installation sites of facilities, and connection costs between facilities. We need to determine the locations to place facilities, the number of facilities for each selected location, the set of customers who are connected to each installed hub via installed remote facilities with minimum cost, while satisfying demand requirements of each customer. We formulate this problem as a general integer programming problem and solve it to optimality. In this paper, we present a preprocessing procedure to tighten the formulation and develop a branch-and-price algorithm. In the algorithm, we consider the integer knapsack problem as the column generation problem. Computational experiments show that the algorithm gives optimal solutions in a reasonable time.

• Management Science and Financial Engineering
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• 제12권2호
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• pp.37-62
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• 2006

This paper considers the problem of designing logical tunnels in virtual private networks considering QoS guarantee which restricts the number of tunnel hops for each traffic routing. The previous researches focused on the design of logical tunnel itself and Steiner-tree based solution algorithms were proposed. However, we show that for some objective settings it is not sufficient and is necessary to consider both physical and logical connectivity at the same time. Thereupon, the concept of the layered network is applied to the logical tunnel design problem in virtual private networks. The layered network approach considers the design of logical tunnel as well as its physical routing and we propose a modified branch-and-price algorithm which is known to solve layered network design problems effectively. To show the performance of the proposed algorithm, computational experiments have been done and the results show that the proposed algorithm solves the given problem efficiently and effectively.

• 대한산업공학회지
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• 제33권1호
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• pp.33-43
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• 2007

The pickup and delivery problem with time windows generally involves the construction of optimal routeswhich satisfy a set of transportation requests under pairing, precedence, time window, vehicle capacity, andavailability constraints. In this paper, we added some constraints to the problem and adopted an objectivefunction based on number of used vehicles, total travel distance and total schedule duration to consider morerealistic problems. A branch and price algohthm for the problem is proposed and an enumeration method is usedfor the subproblems. The algorithm was tested on randomly generated instances and computational results werereported.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2003년도 춘계공동학술대회
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• pp.381-385
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• 2003

We consider the bandwidth parking problem arising from telecommunication networks The problem is to determine the set of calls to be routed and an assignment or them to the paths in arc capacitated network. The objective is to maximize profit. We formulate the problem as an integer programming and propose an algorithm to solve it. Column generation technique to solve the linear programming relxation is proposed with two types of columns in addition, to obtain an optimum integer solution, we consider a new branching strategy. Computational experiments show that the algorithm gives option at solutions within reasonably small time limits.

• 디지털콘텐츠학회 논문지
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• 제3권2호
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• pp.221-233
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• 2002

본 논문에서는 용량제약이 있는 설비의 위치선정 및 수요자 할당 문제(Capacitated Facility Location-Allocation Problem)에 대한 정수계획 모형과 해법을 제시하였다. 이 문제는 설비를 설치할 수 있는 후보지의 집합과 각 후보지별로 설치 가능한 설비의 용량 및 설치비용, 수요를 만족시켜야 할 수요자의 집합 및 각 수요자와 설치 후보지 사이의 운반비용이 주어져 있을 때, 설비들의 설치비용과 수요의 운반비용의 합을 최소화하는 설비의 설치 위치 및 대수 그리고 수요자와 설비간의 연결상태를 구성하는 문제이다. 본 논문에서는 이 문제에 대한 두 가지 정수계획모형을 제시하고, 이 모형에 대한 최적해를 구하기 위한 다면체적 절단평면을 이용한 분지-절단해법(Branch-and-cut algorithm)과 열생성기법을 이용한 분지-평가해법(Branch-and-Price algorithm)을 제시하였다. 제시된 모형과 해법은 물류시스템의 설계 및 정보통신시스템의 통신설비 위치선정 등에 활용될 수 있다.

• 산업공학
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• 제21권1호
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• pp.1-7
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• 2008

In this paper we study the Minimum Edge Addition Problem(MEAP) to decrease the diameter of a graph. MEAP can be used for improving the serviceability of telecommunication networks with a minimum investment. MEAP is an NP-hard optimization problem. We present two mathematical programming models : One is a multi-commodity flow formulation and the other is a path partition formulation. We propose a branch-and-price algorithm to solve the path partition formulation to the optimality. We develop a polynomial time column generation sub-routine conserving the mathematical structure of a sub problem for the path partition formulation. Computational experiments show that the path partition formulation is better than the multi-commodity flow formulation. The branch-and-price algorithm can find the optimal solutions for the immediate size graphs within reasonable time.

• 한국경영과학회지
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• 제32권4호
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• pp.51-60
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• 2007

In this study, we consider the minimum ADM problem which is the fundamental problem for the cost-effective design of SONET ADM embedded in WDM ring networks. To minimize the number of SONET ADMs, efficient algorithms for the routing and wavelength assignment are needed. We propose a mathematical model based on the graph theory for the problem and propose a branch-and-price approach to solve the suggested model effectively within reasonable time. By exploiting the mathematical structure of ring networks, we developed polynomial time algorithms for column generation subroutine at branch-and-bound tree. In a computer simulation study, the suggested approach can find the optimal solution for sufficient size networks and shows better performance than the greedy heuristic method.

• 한국인터넷방송통신학회논문지
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• 제21권4호
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• pp.171-176
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• 2021

본 논문은 설비 설치비용과 판매단가로 구성된 다수의 구매처 입찰정보로부터 구성품을 구매함에 있어 최소의 비용으로 구매하기 위해 구매처와 구매 물량을 선정하는 입찰평가 문제를 다룬다. 이 문제에 대해 기존에 알려진 방법은 분기한정 법(BB)과 분기절단 법(BC)이 알려져 있다. 그러나 이들 방법으로 얻은 해가 최적 해가 되지 않는 문제점이 있다. 본 논문에서는 판매단가 순위 또는 설치비용 순위 우선 구매물량 배정원칙을 적용하여 초기 실현 가능 해를 얻고, 판매단가 또는 설치비용을 고려하여 물량을 이동(구매업체 변경)시키는 최적화를 수행하는 방법을 제시하였다. 제안된 방법을 실험 데이터에 적용한 결과 BB와 BC에 비해 구매비용을 크게 절감할 수 있었다.

• 대한산업공학회지
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• 제30권3호
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• pp.213-223
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• 2004

We consider the traffic grooming problem for the design of SONET/WDM(Synchronous Optical NETwork/Wavelength Division Multiplexing) ring networks. Given a physical network with ring topology and a set of traffic demands between pairs of nodes, we are to obtain a stack of rings with the objective of minimizing the number of ADMs installed at the nodes. This problem arises when a single ring capacity is not large enough to accommodate all the demands. As a solution method, an efficient algorithm based on the branch-and-price approach has been reported in the literature for the problem in which only unidirecional path switched ring (UPSR) was considered. In this study, we suggest integer programming models and the algorithms based on the same approach as the above one, considering two-fiber bidirectional line switched ring(BLSR/2), and BLSR/4 additionally. Using the results, we compare the number of required ADMs for all types of the ring architecture.