• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2000년도 춘계공동학술대회 논문집
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• pp.613-616
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• 2000

This paper considers the problem of subway crew scheduling. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper, we propose two basic techniques that solve the problem in a reasonable time, though the optimality of the solution is not guaranteed. To reduce the number of variables, we adopt column-generation technique. We could develop an algorithm that solves column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational results show column-generation makes the problem of treatable size, and variable fixing enables us to solve LP relaxation in shorter time without a considerable increase in the optimal value. Finally, we were able to obtain an integer optimal solution of a real instance within a reasonable time.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2002년도 춘계공동학술대회
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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.

• Management Science and Financial Engineering
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• 제11권2호
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• pp.85-103
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• 2005

In this paper, we consider the routing and wavelength assignment problem in survivable WDM transport network without wavelength conversion. We assume the single-link failure and a path protection scheme in optical layer. When a physical network and a set of working paths are given, the problem is to select a link-disjoint protection path for each working path and assign a wavelength for each working and protection path. We give an integer programming formulation of the problem and propose an algorithm to solve it. Though the formulation has exponentially many variables, we solve the linear programming relaxation of it by using column generation technique. We devise a branch-and price algorithm to solve the column generation problem. After solving the linear programming relaxation, we apply a variable fixing procedure combined with the column generation to get an integral solution. We test the proposed algorithm on some randomly generated data and test results show that the algorithm gives very good solutions.

• 한국철도학회논문집
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• 제8권5호
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2004년도 추계학술대회 및 정기총회
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• pp.389-392
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• 2004

The column generation process for the set-partitioning model of the vehicle routing problem requires repeated solutions of column generation subproblems which has a combinatorial structure similar to that of the traveling salesman problem. This limits the size of the problem that can be addressed. We introduce a new modeling approach, termed route-splitting, which splits each vehicle route into segments, and results in more tractable subproblems. A lower bounding scheme that yields an updated bound at each iteration of the column generation process is developed. Implementation issues, including a technique of controlling columns in the master problem, are explored. Lower bounds are computed on standard benchmark problems with up to 199 customers.

• 한국국방경영분석학회지
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• 제13권1호
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• pp.101-115
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• 1987

This paper presents an optimization based heuristic algorithm for a tour bus scheduling problem where buses consist of various kinds of sightseeing and commutation services. First, this algorithm transforms the prolem into a vehicle routing problem on whose nodes denote trips and arcs denote connections between trips. Second, a greedy heuritic routing technique is applied to find a good feasible bus-route set. Then the greedy feasible solution is improved by the simplex method using column generation technique. The algorithm provides a better near-optimal solution which gives much reductions in the total tour distance and the number of tour buses.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2001년도 추계학술대회 논문집
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• pp.124-127
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• 2001

We consider the routing and wavelength assignment problem in survivable WDM transport network without wavelength conversion. We assume the single-link failure and a path protection scheme in optical layer. When a physical network and a set of working paths are given, the problem is to select a link-disjoint protection path for each working path and assign a wavelength for each working and protection path. We give an integer programming formulation of the problem and propose an algorithm to solve it based on column generation technique and variable fixing. We devise a branch-and-price algorithm to solve the column generation problem. We test the proposed algorithm on some randomly generated data and test results show that the algorithm gives very good solutions.

• 한국경영과학회지
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• 제27권4호
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• pp.67-86
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• 2002

This paper considers subway crew scheduling problem. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper. we propose two basic techniques that solve the subway crew scheduling problem in a reasonable time, though the optimality of the solution is not guaranteed. We develop an algorithm that solves the column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational result for a real instance is reported.

• 대한교통학회지
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• 제26권2호
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• pp.89-100
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• 2008

교통신호와 개별 통행자의 경로선택은 서로 상호작용하는 관계이다. 통행자의 경로 선택은 교통신호에 따라 결정될 수 있으며 또한 최적의 교통신호 역시 이동류별 교통량에 따라 달라지게된다. 본 연구는 양방향 링크를 포함하는 4현시 교차로로 구성된 네트워크에서 모든 이동류에 대하여 교통신호의 영향을 반영할 수 있는 통행배정 모형을 구축하고 이를 신호최적화 문제와 결합하여 네트워크의 총 지체를 최소화하는 신호제어변수와 통행배정 결과를 산출하는 모형을 bi-level problem으로 구축하였다. 본 연구에서 사용된 경로기반 통행배정 모형은 M.H. Xu 등이 제한한 Column Generation 방법의 일종인 heuristic Equilibrium Assignment 기법을 기반으로 하여 교차로의 이동류별 통행비용을 고려할 수 있도록 수정하여 구성하였으며 지체최소화를 목적함수로하는 신호최적화 방법론으로는 Genetic Algorithm을 사용하였다. 본 모형을 모의네트워크에 적용하여 실험한 결과 네트워크의 통행비용함수를 최소화하는 신호변수와 통행자의 경로선택 결과를 산출하였다.

• 경영과정보연구
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• 제29권4호
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• pp.109-121
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• 2010

본 연구는 전형적인 차량경로 문제에서 각 노드간의 이동 시간이 일정하지 않은 특수한 경우의 상황에 대한 해법 절차를 제공한다. 본 연구는 상황에 따라 변화하는 이동시간을 갖는 외판원 문제의 특별한 경우인 '한 노드까지 도달한 경로가 다음 노드로 이동하는 데 걸리는 시간에 영향을 주는 외판원 문제'(경로의존 이동비용을 갖는 외판원 문제(RDTSP: Route Dependent Travelling Salesman Problem))의 해법을 제시한다. RDTSP 문제의 해결을 위해 먼저 문제 상황을 묘사하는 정수 계획 모형을 개발하였다. 본 연구에서 제시한 정수계획 모형에서는, 모든 가능한 경로에 대하여 각각의 경로를 하나의 변수로 정의하고 이 변수들 중에서 하나를 선택하는 형태로 개발되었다. 이 모형에서는 변수에 해당하는 가능한 경로의 수가 노드수에 지수적(exponentially)으로 증가하기 때문에, 처음부터 모든 변수를 문제에 포함시켜 풀 수 없게 된다. 그러나, 개발된 정수계획 모형의 변수를 실수로 완하시킨 선형완화(LP relaxation) 문제에 대해서는 열 생성(column generation) 기법을 통해 그 해를 구할 수 있다. 또한 본 연구의 결과가 PCB 조립 공정의 작업시간 최적화 문제에 어떻게 적용될 수 있는가를 제시한다.