### Abstract

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).

Original language | English |
---|---|

Article number | 5152981 |

Pages (from-to) | 465-482 |

Number of pages | 18 |

Journal | IEEE Transactions on Industrial Informatics |

Volume | 5 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Nov |

### Fingerprint

### Keywords

- Approximate approach
- Binary particle swarm optimization (BPSO)
- Facility location
- Fuzzy variable
- Genetic algorithm (GA)
- Tabu search (TS)

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Control and Systems Engineering
- Computer Science Applications
- Information Systems

### Cite this

*IEEE Transactions on Industrial Informatics*,

*5*(4), 465-482. [5152981]. https://doi.org/10.1109/TII.2009.2022542

**Value-at-risk-based two-stage fuzzy facility location problems.** / Wang, Shuming; Watada, Junzo; Pedrycz, Witold.

Research output: Contribution to journal › Article

*IEEE Transactions on Industrial Informatics*, vol. 5, no. 4, 5152981, pp. 465-482. https://doi.org/10.1109/TII.2009.2022542

}

TY - JOUR

T1 - Value-at-risk-based two-stage fuzzy facility location problems

AU - Wang, Shuming

AU - Watada, Junzo

AU - Pedrycz, Witold

PY - 2009/11

Y1 - 2009/11

N2 - 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).

AB - 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).

KW - Approximate approach

KW - Binary particle swarm optimization (BPSO)

KW - Facility location

KW - Fuzzy variable

KW - Genetic algorithm (GA)

KW - Tabu search (TS)

UR - http://www.scopus.com/inward/record.url?scp=70449532358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449532358&partnerID=8YFLogxK

U2 - 10.1109/TII.2009.2022542

DO - 10.1109/TII.2009.2022542

M3 - Article

AN - SCOPUS:70449532358

VL - 5

SP - 465

EP - 482

JO - IEEE Transactions on Industrial Informatics

JF - IEEE Transactions on Industrial Informatics

SN - 1551-3203

IS - 4

M1 - 5152981

ER -