• 한국경영과학회지
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• 제15권1호
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• pp.23-35
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• 1990

A mathematical model for a dynamic capacitate facility location problem is formulated by a mixed integer problem. The objective of the model is to minimize total discounted costs that include fixed charges and distributed costs. The Cross Decomposition method of Van Roy is extended and applied to solve the dynamic capacitated facility location problem. The method unifies Benders Decomposition and Lagrangean relaxation into a single framework. It successively solves a transportation problem and a dynamic uncapacitated facility location problem as two subproblems. Computational results are compared with those of general mixed integer programming.

• 대한산업공학회지
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• 제27권3호
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• pp.250-259
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• 2001

Given a tree structured network in which each node has its own demand and also stands for a candidate location of a potential facility, such as plant or warehouse, a capacitated facility location problem on the network (CFLPOT) is to decide capacitated facility locations so that the total demand occurred on the network can be satisfied from those facilities with the minimum cost. In this paper, we first introduce a mixed integer programming formulation for CFLPOT with two additional assumptions, the indivisible demand assumption and the contiguity assumption and then show that it can be reformulated as a tree partitioning problem with an exponential number of variables. We then show that it can be solved in O($n^2b$) time by utilizing the limited column generation method developed by Shaw (1993), where n is the total number of nodes in the network and b is the maximum facility capacity. We also develop a depth-first dynamic programming algorithm with a running time of O(nb) for finding the locally maximal reduced cost which plays an important role in the limited column generation method. Finally, we implement our algorithms on a set of randomly generated problems and report the computational results.

• Industrial Engineering and Management Systems
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• 제8권1호
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• pp.29-36
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• 2009

We present two local-search based metaheuristics for the multi-source capacitated facility location problem. In such a problem, each customer's demand can be supplied by one or more facilities. The problem is NP-hard and the number of locations in the optimal solution is unknown. To keep the search process effective, the proposed methods adopt the following features: (1) a multi-exchange neighborhood structure, (2) a tabu list that keeps track of recently visited solutions, and (3) a multi-start to enhance the diversified search paths. The transportation simplex method is applied in an efficient manner to obtain the optimal solutions to neighbors of the current solution under the algorithm framework. Two in-and-out selection rules are also proposed in the algorithms with the purpose of finding promising solutions in a short computational time. Our computational results for some of the benchmark instances, as well as some instances generated using a method in the literature, have demonstrated the effectiveness of this approach.

• 대한산업공학회지
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• 제37권2호
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• pp.124-131
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• 2011

In this research report, we propose a heuristic algorithm with some primal recovery strategies for capacitated facility location problems (CFLP), which is a well-known combinatorial optimization problem with applications in distribution, transportation and production planning. Many algorithms employ the branch-and-bound technique in order to solve the CFLP. There are also some different approaches which can recover primal solutions while exploiting the primal and dual structure simultaneously. One of them is a MVCD (Mean Value Cross Decomposition) ensuring convergence without solving a master problem. The MVCD was designed to handle LP-problems, but it was applied in mixed integer problems. However the MVCD has been applied to only uncapacitated facility location problems (UFLP), because it was very difficult to obtain "Integrality" property of Lagrangian dual subproblems sustaining the feasibility to primal problems. We present some heuristic strategies to recover primal feasible integer solutions, handling the accumulated primal solutions of the dual subproblem, which are used as input to the primal subproblem in the mean value cross decomposition technique, without requiring solutions to a master problem. Computational results for a set of various problem instances are reported.

• 대한산업공학회지
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• 제12권2호
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• pp.21-31
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• 1986

Consider a capacitated facility location problem in which the demands of customers are all equal and so are the capacities of facilities. Under the restriction that each customer's uniform demand be met by exactly one facility, the objective is to select a set of facilities to open, and to assign customer's demand to them so as to minimize the total cost which includes fixed costs of opening facilities as well as variable assignment costs. The problem is modelled as a pure zero-one program which may be viewed as a variant of well-known capacitated facility location problems. The purpose of this study is to develop efficient computational procedures for solving the pure zero-one facility location problems. Due to the special structure of our zero-one location problem with uniform demand, it can be converted to a location problem with the unimodular property. A Lagrangean relaxation algorithm is developed to solve the location problem. The algorithm is made efficient by employing a device which exploits the special structure of a surrogate constraint. The efficiency of the algorithm is analyzed through computational experiments with some test problems.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2003년도 춘계공동학술대회
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• pp.137-144
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• 2003

We consider Two-echelon Single source Capacitated Facility Location Problem (TSCFLP). TSCFLP is a variant or Capacitated Facility Location Problem (CFLP). which has been an important issue in boa academic and industrial aspects. Given a set or possible facility locations in two echelons (warehouse / plant), a set or customers, TSCFLP is a decision problem to find a set or facility locations to open and to determine an allocation schedule that satisfies the demands or the customers and the capacity constraints or the facilities, while minimizing the overall cost. It ran be shown that TSCFLP Is strongly NP-hard For TSCFLf, few algorithms are known. which are heuristics. We propose a disaggregated version or the standard mixed integer programming formulation or TSCFLP We also provide a class or valid Inequalities Branch-and-price algorithm with rutting plane method Is used to find an optimal solution Efficient branching strategy compatible with subproblem optimization problems Is also provided. We report computational results or tests on 15 randomly generated instances.

• 한국콘텐츠학회논문지
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• 제10권9호
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• pp.107-116
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• 2010

시설물 입지 선정 문제(FLP)는 전통적인 최적화 문제중에 하나이다. FLP에 공급제약과 하나의 고객은 하나의 시설물에서만 제품을 공급받을 수 있다는 제약을 추가하면 단일 시설물 공급제약을 가지는 시설물 위치 설정 문제(SSFLP)가 된다. SSFLP는 NP-hard 문제로 알려져 있으며 진화 알고리즘과 같은 휴리스틱 알고리즘을 사용하여 해결하는 것이 일반적이다. 본 논문에서는 SSFLP를 위한 효율적인 진화 알고리즘을 제안한다. 제안하는 알고리즘은 적응형 링크 조절 진화 알고리즘과 3가지 휴리스틱 해 개선 방법을 조합하여 고안되었다. 제안하는 알고리즘을 벤치마크 문제에 적용하여 다른 알고리즘과 성능을 비교분석해 본 결과, 제안하는 알고리즘은 중간 크기의 문제에서 대부분 최적해를 찾았으며 큰 문제에서도 안정된 결과를 보여주었다.

• 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.

• 한국경영과학회지
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• 제19권1호
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• pp.69-83
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• 1994

This paper deals with a capacitated ring-star network design problem (CRSNDP) with node capacity constraints. The CRSNDP is formulated as a mixed 0-1 integer problem, and a 2-phase heuristic solution procedure, ADD & VAM and RING, is developed, in which the CRSNDP is decomposed into two subproblems : the capacitated facility location problem (CFLP) and the traveling sales man problem (TSP). To solve the CFLP in phase I the ADD & VAM procedure selects hub nodes and their appropriate capacity from a candidate set and then assigns them user nodes under node capacity constraints. In phase II the RING procedure solves the TSP to interconnect the selected hubs to form a ring. Finally a solution of the CRSNDP can be achieved through combining two solution of phase I & II, thus a final design of the capacitated ring-star network is determined. The analysis of computational results on various random problems has shown that the 2-phase heuristic procedure produces a solution very fast even with large-scale problems.

• Industrial Engineering and Management Systems
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• 제12권3호
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• pp.190-197
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• 2013

People are living longer than ever before. As a result, life expectancy is going up and the demand of long-term care facilities is increasing in most countries. The facilities provide rehabilitative, restorative, and skilled nursing care to patients or residents in need of assistance with activities of daily living. This study deals with the capacitated location and allocation problem of long-term care facilities in a city that consists of a finite number of regions. Assuming that in each region candidate locations for three types of facilities are already given, two integer programming models are developed under the closest assignment rule reflecting the demand characteristics of the facilities. Both the location and type of the facilities to be built become decision variables. To show the validity of the models, numerical problems are solved with commercial software, CPLEX. Also, sensitivity studies were conducted to identify relationships between the system parameters.