• 경영과학
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• 제21권1호
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• pp.77-86
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• 2004

In this paper, we present a methodology for solving the multicommodity network flow problems using interior point methods. In our method, the minimum cost network flow problem extracted from the given multicommodity network flow problem is solved by primal-dual barrier method in which normal equations are solved partially using preconditioned conjugate gradient method. Based on the solution of the minimum cost network flow problem, a warm-start point is obtained from which Castro's specialized interior point method for multicommodity network flow problem starts. In the computational experiments, the effectiveness of our methodology is shown.

• Management Science and Financial Engineering
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• 제15권1호
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• pp.71-79
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• 2009

This paper considers the two kinds of integer multicommodity flow problems, a feasibility problem and a maximization problem, on two types of directed cycles, a unidirectional and a bidirectional cycle. Both multicommodity flow problems on an undirected cycle have been dealt with by many researchers and it is known that each problems can be solved by a polynomial time algorithm. However, we don't find any result on the directed cycles. Here we show that we can also solve both problems for a unidirectional and a bidirectional cycle in polynomial time.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2006년도 춘계공동학술대회 논문집
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• pp.1025-1029
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• 2006

This paper considers the multicommodity flow problem and the integer multicommodity flow problem on cycle graphs. We present two linear time algorithms for solving each of the two problems.

• 대한산업공학회지
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• 제27권3호
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• pp.274-280
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• 2001

In this research, we develop a specialized primal-dual interior point solver for the multicommodity flow problems (MCFP). The Castro's approach that exploits the problem structure is investigated and several aspects that must be considered in the implementation are addressed. First, we show how preprocessing techniques for linear programming(LP) are adjusted for MCFP. Secondly, we develop a procedure that extracts a network structure from the general LP formulated MCFP. Finally, we consider how the special structure of the mutual capacity constraints is exploited. Results of comupational comparison between our solver and a general interior point solver are also included.

• 한국철도학회논문집
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• 제10권5호
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• pp.569-575
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• 2007

본 논문은 철도사고 및 재난 발생시 사상자 및 승객들을 최단시간내에 병원과 대피지점들로 이동시키는 경로를 탐색하는 해법을 제시하고자 한다. 도로용량의 제약이 없이 주요 병원 및 대피지점별로 사상자와 승객을 미리 배정하여 최단경로를 탐색하는 디직스트라 해법활용과 도로의 수송용량과 병원과 대피지점들의 수용용량을 제약조건으로 하여 탐색하는 다수상품유통모형의 활용방안을 제시하고자 한다.

• 한국경영과학회지
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• 제31권3호
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• pp.11-25
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• 2006

Space may be a scarce resource in manufacturing shops, warehouses, freight terminals, and container terminals. This Paper discusses how to locate temporary storage Inventories In limited storage areas. A typical inventory is delivered from the location of the preceding process to the storage area and stored In the storage area during the certain period of time. And it may be relocated from the storage position to another. Finally. it is delivered from the final storage area to the location of the next process. Because this logistic process for an inventory requires handling activities, transportation activities, and storage spaces, the limitation in capacities of handling equipment, transportation equipment, and storage space must be considered when allocating spaces to the inventory. This problem Is modeled as a multicommodity minimal cost flow problem. And a heuristic algorithm for the Problem is proposed. Numerical experiments are presented to validate the mathematical model and the heuristic algorithm.

• Management Science and Financial Engineering
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• 제6권2호
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• pp.29-45
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• 2000

We consider the design of a two-level telecommunication network having logical full-mesh/star topology, with the implementation of conduit systems taken together. The design problem is then viewed as consisting of three subproblems: locating hub facilities, placing a conduit network, and installing cables therein to configure the logical full-mesh/star network. Without partitioning into subproblems as done in the conventional approach, the whole problem is directly dealt with in a single integrated framework, inspired by some recent successes with the approach. We successfully formulate the problem as a variant of the classical multicommodity flow model for the fixed charge network design problem, aided by network augmentation, judicious commodity definition, and some flow restrictions. With our optimal model, we solve some randomly generated sample problems by using CPLEX MIP program. From the computational experiments, it seems that our model can be applied to the practical problem effectively.

• 정보학연구
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• 제3권2호
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• pp.73-85
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• 2000

본 논문에서는 여러가지 상이한 메세지를 전송하는 정보통신 네트워크의 효율적인 해법을 개발하였다. 이 문제는 네트워크 이론에서의 전형적인 다품종 네트워크로의 전환이 가능하다. 이러한 문제는 문제의 크기에 따라 계산의 복잡도가 지수적으로 증가하는 대표적인 NP-완전문제이다. 본 논문에서 개발된 해법은 전통적인 라그랑지 이완법을 보완한 것으로 다음과 같이 구성된다. 우선 우수한 초기 실현가능해(good initial feasible solution)를 얻을 수 있는 휴리스틱 방법을 개발하고 초기 실현가능해가 얻어지면 이를 이용하여 초기 쌍대변수(이완된 제약식에 붙게되는 라그랑지 승수)를 추정한다. 대개의 경우 쌍대 변수를 임의로 0으로 설정하고 해법을 수행하는데, 이 경우 쌍대 최적해와의 차이가 많이 나게되므로 비효율이 발생할 수 있다. 쌍대 최적해를 얻은 후 원문제의 실현가능조건을 위배하는 경우에는 재할당 방법(re-allocation method)를 통해 원문제의 실현가능조건을 충족하도록 한다. 해법의 성능(효율성) 테스트 결과 저자들이 개발한 해법이 수행속도 면에서 상업용 팩키지와 기존의 효율적인 해법들에 비하여 매우 우수하다는 결과를 얻을 수 있었다. 또한 본 해법은 최적해를 보장하지 않지만 최적해와의 차이가 평균 2% 미만의 근사 최적해를 얻을 수 있었다.

• 한국경영과학회지
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• 제32권3호
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• pp.63-80
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• 2007

This study is a generalization of 'stable dynamics' recently suggested by Nesterov and de Palma[29]. Stable dynamics is a new model which describes and provides a stable state of congestion in urban transportation networks. In comparison with user equilibrium model that is common in analyzing transportation networks, stable dynamics requires few parameters and is coincident with intuitions and observations on the congestion. Therefore it is expected to be an useful analysis tool for transportation planners. An equilibrium in stable dynamics needs only maximum flow in each arc and Wardrop[33] Principle. In this study, we generalize the stable dynamics into the model with multiple traffic classes. We classify the traffic into the types of vehicle such as cars, buses and trucks. Driving behaviors classified by age, sex and income-level can also be classes. We develop an equilibrium with multiple traffic classes. We can find the equilibrium by solving the well-known network problem, multicommodity minimum cost network flow problem.

• 한국경영과학회지
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• 제25권1호
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• pp.67-84
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• 2000

In this paper, we address a network design problem including the decision of hub facility locatiions which is typically found in a communicatio and a transportation network design studies. Due to the administrative and the geographical restrictions, it is common to assume that each user should be assigned to only one hub facility. To construct such a network, three types of network costs should be considered: the fixed costs of establishing the hubs and the arcs in the network, and the variable costs associated with transversing the network. The complex problem is formulated as a mixed IP embedding a multicommodity flow problem. Exploiting its special structure, a dual-based heuristic is then developed, which yields near-optimal design plans. The test results indicate that the heuristic is an effective way to solve this computationally complex problem.