### Abstract

The objective of this paper is to study facility location problems under a hybrid uncertain environment involving randomness and fuzziness. A two-stage fuzzy random facility location model with recourse is developed in which the demands and the costs are assumed to be fuzzy random variables. As in general the fuzzy random parameters in the model can be regarded as continuous fuzzy random variables with infinite realizations, the computation of the recourse requires solving infinite second-stage programming problems. Owing to this fact, the recourse function cannot be calculated analytically, which implies that the model cannot benefit from the use of methods of classical mathematical programming. In order to solve the location problems of this nature, we first develop techniques of fuzzy random simulation. In the sequel, by combining the fuzzy random simulation, simplex algorithm and binary particle swarm optimization (BPSO), a hybrid algorithm is proposed to solve the two-stage fuzzy random facility location model. Finally, an illustrative numerical example is provided.

Original language | English |
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Title of host publication | Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics |

Pages | 1846-1851 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2009 |

Event | 2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009 - San Antonio, TX Duration: 2009 Oct 11 → 2009 Oct 14 |

### Other

Other | 2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009 |
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City | San Antonio, TX |

Period | 09/10/11 → 09/10/14 |

### Fingerprint

### Keywords

- Binary particle swarm optimization
- Facility location
- Fuzzy random variable
- Recourse
- Two-stage fuzzy random programming

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Control and Systems Engineering
- Human-Computer Interaction

### Cite this

*Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics*(pp. 1846-1851). [5346731] https://doi.org/10.1109/ICSMC.2009.5346731

**Fuzzy random facility location problems with recourse.** / Wang, Shuming; Watada, Junzo; Pedrycz, Witold.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics.*, 5346731, pp. 1846-1851, 2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009, San Antonio, TX, 09/10/11. https://doi.org/10.1109/ICSMC.2009.5346731

}

TY - GEN

T1 - Fuzzy random facility location problems with recourse

AU - Wang, Shuming

AU - Watada, Junzo

AU - Pedrycz, Witold

PY - 2009

Y1 - 2009

N2 - The objective of this paper is to study facility location problems under a hybrid uncertain environment involving randomness and fuzziness. A two-stage fuzzy random facility location model with recourse is developed in which the demands and the costs are assumed to be fuzzy random variables. As in general the fuzzy random parameters in the model can be regarded as continuous fuzzy random variables with infinite realizations, the computation of the recourse requires solving infinite second-stage programming problems. Owing to this fact, the recourse function cannot be calculated analytically, which implies that the model cannot benefit from the use of methods of classical mathematical programming. In order to solve the location problems of this nature, we first develop techniques of fuzzy random simulation. In the sequel, by combining the fuzzy random simulation, simplex algorithm and binary particle swarm optimization (BPSO), a hybrid algorithm is proposed to solve the two-stage fuzzy random facility location model. Finally, an illustrative numerical example is provided.

AB - The objective of this paper is to study facility location problems under a hybrid uncertain environment involving randomness and fuzziness. A two-stage fuzzy random facility location model with recourse is developed in which the demands and the costs are assumed to be fuzzy random variables. As in general the fuzzy random parameters in the model can be regarded as continuous fuzzy random variables with infinite realizations, the computation of the recourse requires solving infinite second-stage programming problems. Owing to this fact, the recourse function cannot be calculated analytically, which implies that the model cannot benefit from the use of methods of classical mathematical programming. In order to solve the location problems of this nature, we first develop techniques of fuzzy random simulation. In the sequel, by combining the fuzzy random simulation, simplex algorithm and binary particle swarm optimization (BPSO), a hybrid algorithm is proposed to solve the two-stage fuzzy random facility location model. Finally, an illustrative numerical example is provided.

KW - Binary particle swarm optimization

KW - Facility location

KW - Fuzzy random variable

KW - Recourse

KW - Two-stage fuzzy random programming

UR - http://www.scopus.com/inward/record.url?scp=74849094098&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74849094098&partnerID=8YFLogxK

U2 - 10.1109/ICSMC.2009.5346731

DO - 10.1109/ICSMC.2009.5346731

M3 - Conference contribution

AN - SCOPUS:74849094098

SN - 9781424427949

SP - 1846

EP - 1851

BT - Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics

ER -