• Journal of Korean Institute of Industrial Engineers
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• v.37 no.2
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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.

• Journal of Korean Institute of Industrial Engineers
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• v.12 no.2
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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.

• Industrial Engineering and Management Systems
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• v.8 no.1
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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.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.3
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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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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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.

• The Journal of the Korea Contents Association
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• v.10 no.9
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• pp.107-116
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• 2010

The facility location problem is one of the traditional optimization problems. In this paper, we deal with the single source capacitated facility location problem (SSCFLP) and it is known as an NP-hard problem. Thus, it seems to be natural to use a heuristic approach such as evolutionary algorithms for solving the SSCFLP. This paper introduces a new efficient evolutionary algorithm for the SSCFLP. The proposed algorithm is devised by incorporating a general adaptive link adjustment evolutionary algorithm and three heuristic local search methods. Finally we compare the proposed algorithm with the previous algorithms and show the proposed algorithm finds optimum solutions at almost all middle size test instances and very stable solutions at larger size test instances.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.1
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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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• v.12 no.3
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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.

• Journal of the Korean Operations Research and Management Science Society
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• v.11 no.2
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• pp.1-6
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• 1986

Capacitated facility location problems have received a great deal of attention in the past decade, resulting in a proliferation of algorithms for solving them. As is the case with mixed 1-1 integer programming problems, the computational success of such algorithms depends greatly on how to obtain lower bounds in good quality within a resonable time. The objective of this paper is to provide a comparative analysis of those algorithms in terms of lower bounds they produce. Analyses of the strategies for generating lower bounds as well as the quality of generated lower bounds are provided.

• Journal of the Korean Operations Research and Management Science Society
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• v.24 no.3
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• pp.93-107
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• 1999

We consider the development of an integer programming model and algorithm for the ATM switching node location problem. There are two kinds of facilities, hub facilities and remote facilities, with different capacities and installation costs. Each customer needs to be connected to one or more hub facilities via remote facilities, where the hub(remote) facilities need to be installed at the same candidate installation site of hub(remote) facility. 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 facilities via installed remote facilities with minimum costs, 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 develop a branch-and-cut algorithm with path variables. In the algorithm, we consider the integer knapsack polytope and derive valid inequalities. Computational experiments show that the algorithm works well in the real world situation. The results of this research can be used to develop optimization algorithms to solve capacitated facility location problems.