Value-at-Risk-Based Two-Stage Fuzzy Facility Location Problems

Reducing risks in location decisions when coping with imprecise information is critical in supply chain management so as to increase competitiveness and profitability. In this paper, a two-stage fuzzy facility location problem with value-at-risk (VaR), called VaR-FFLP, is proposed, which results in...

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Bibliographic Details
Published in:IEEE transactions on industrial informatics Vol. 5; no. 4; pp. 465 - 482
Main Authors: Shuming Wang, Watada, J., Pedrycz, W.
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.11.2009
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximate approach
Approximation
Approximation algorithms
binary particle swarm optimization (BPSO)
Convergence
Costs
facility location
Fuzzy
Fuzzy logic
Fuzzy set theory
fuzzy variable
genetic algorithm (GA)
Genetic algorithms
Linear programming
Mathematical analysis
Mathematical models
Operations research
Particle swarm optimization
Position (location)
Profitability
Reactive power
Studies
Supply chain management
Supply chains
tabu search (TS)
Value-at-Risk (VaR)
ISSN:1551-3203, 1941-0050
Online Access:Get full text
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Summary:Reducing risks in location decisions when coping with imprecise information is critical in supply chain management so as to increase competitiveness and profitability. In this paper, a two-stage fuzzy facility location problem with value-at-risk (VaR), called VaR-FFLP, is proposed, which results in a two-stage fuzzy zero-one integer programming problem. Some properties of the VaR-FFLP, including the value of perfect information (VPI), the value of fuzzy solution (VFS), and the bounds of the fuzzy solution, are discussed. Since the fuzzy parameters of the location problem are represented in the form of continuous fuzzy variables, the determination of VaR is inherently an infinite-dimensional optimization problem that cannot be solved analytically. Therefore, a method based on the discretization of the fuzzy variables is proposed to approximate the VaR. The approximation approach converts the original problem into a finite-dimensional optimization problem. A pertinent convergence theorem for the approximation approach is proved. Subsequently, by combining the simplex algorithm, the approximation approach, and a mechanism of genotype-phenotype-mutation-based binary particle swarm optimization (GPM-BPSO), a hybrid GPM-BPSO algorithm is being exploited to solve the VaR-FFLP. A numerical example illustrates the effectiveness of the hybrid GPM-BPSO algorithm and shows its enhanced performance in comparison with the results obtained by other approaches using genetic algorithm (GA), tabu search (TS), and Boolean BPSO (B-BPSO).
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ISSN:1551-3203
1941-0050
DOI:10.1109/TII.2009.2022542