A new solution approach to two-stage fuzzy location problems with risk control

Yan Yang, Jian Zhou, Ke Wang, Athanasios A. Pantelous

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In the present paper, a two-stage fuzzy facility location problem under the Value-at-Risk (VaR) criterion is considered for controlling the risk in location decisions. Because the fuzzy parameters involved are represented in the form of regular fuzzy numbers (e.g., triangular, Gaussian, and Cauchy fuzzy numbers), it is shown that the VaR of a location decision can be determined exactly by solving the corresponding linear programming problem. This new solution approach has a significantly lower computation complexity compared with the already known approximation treatment of the problem. In this regard, the VaR-based two-stage fuzzy location model is transformed into a one-stage mixed-integer linear programming model, and is then solved using some standard programming techniques. Furthermore, the VaR-based solutions are shown to be linked to the robust optimization counterparts, and new results for the location decisions and the loss distribution under perfect information are deduced. Finally, numerical examples illustrate the effectiveness of our treatment.

Original languageEnglish
Pages (from-to)157-171
Number of pages15
JournalComputers and Industrial Engineering
Volume131
DOIs
Publication statusPublished - May 2019

Keywords

  • Facility location problem
  • Loss distribution
  • Risk control
  • Robust optimization
  • Value-at-Risk

Cite this

@article{896cc0a39fe347ab9be89bcefe0a9db4,
title = "A new solution approach to two-stage fuzzy location problems with risk control",
abstract = "In the present paper, a two-stage fuzzy facility location problem under the Value-at-Risk (VaR) criterion is considered for controlling the risk in location decisions. Because the fuzzy parameters involved are represented in the form of regular fuzzy numbers (e.g., triangular, Gaussian, and Cauchy fuzzy numbers), it is shown that the VaR of a location decision can be determined exactly by solving the corresponding linear programming problem. This new solution approach has a significantly lower computation complexity compared with the already known approximation treatment of the problem. In this regard, the VaR-based two-stage fuzzy location model is transformed into a one-stage mixed-integer linear programming model, and is then solved using some standard programming techniques. Furthermore, the VaR-based solutions are shown to be linked to the robust optimization counterparts, and new results for the location decisions and the loss distribution under perfect information are deduced. Finally, numerical examples illustrate the effectiveness of our treatment.",
keywords = "Facility location problem, Loss distribution, Risk control, Robust optimization, Value-at-Risk",
author = "Yan Yang and Jian Zhou and Ke Wang and Pantelous, {Athanasios A.}",
year = "2019",
month = "5",
doi = "10.1016/j.cie.2019.03.039",
language = "English",
volume = "131",
pages = "157--171",
journal = "Computers and Industrial Engineering",
issn = "0360-8352",
publisher = "Elsevier",

}

A new solution approach to two-stage fuzzy location problems with risk control. / Yang, Yan; Zhou, Jian; Wang, Ke; Pantelous, Athanasios A.

In: Computers and Industrial Engineering, Vol. 131, 05.2019, p. 157-171.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - A new solution approach to two-stage fuzzy location problems with risk control

AU - Yang, Yan

AU - Zhou, Jian

AU - Wang, Ke

AU - Pantelous, Athanasios A.

PY - 2019/5

Y1 - 2019/5

N2 - In the present paper, a two-stage fuzzy facility location problem under the Value-at-Risk (VaR) criterion is considered for controlling the risk in location decisions. Because the fuzzy parameters involved are represented in the form of regular fuzzy numbers (e.g., triangular, Gaussian, and Cauchy fuzzy numbers), it is shown that the VaR of a location decision can be determined exactly by solving the corresponding linear programming problem. This new solution approach has a significantly lower computation complexity compared with the already known approximation treatment of the problem. In this regard, the VaR-based two-stage fuzzy location model is transformed into a one-stage mixed-integer linear programming model, and is then solved using some standard programming techniques. Furthermore, the VaR-based solutions are shown to be linked to the robust optimization counterparts, and new results for the location decisions and the loss distribution under perfect information are deduced. Finally, numerical examples illustrate the effectiveness of our treatment.

AB - In the present paper, a two-stage fuzzy facility location problem under the Value-at-Risk (VaR) criterion is considered for controlling the risk in location decisions. Because the fuzzy parameters involved are represented in the form of regular fuzzy numbers (e.g., triangular, Gaussian, and Cauchy fuzzy numbers), it is shown that the VaR of a location decision can be determined exactly by solving the corresponding linear programming problem. This new solution approach has a significantly lower computation complexity compared with the already known approximation treatment of the problem. In this regard, the VaR-based two-stage fuzzy location model is transformed into a one-stage mixed-integer linear programming model, and is then solved using some standard programming techniques. Furthermore, the VaR-based solutions are shown to be linked to the robust optimization counterparts, and new results for the location decisions and the loss distribution under perfect information are deduced. Finally, numerical examples illustrate the effectiveness of our treatment.

KW - Facility location problem

KW - Loss distribution

KW - Risk control

KW - Robust optimization

KW - Value-at-Risk

UR - http://www.scopus.com/inward/record.url?scp=85063459656&partnerID=8YFLogxK

U2 - 10.1016/j.cie.2019.03.039

DO - 10.1016/j.cie.2019.03.039

M3 - Article

VL - 131

SP - 157

EP - 171

JO - Computers and Industrial Engineering

JF - Computers and Industrial Engineering

SN - 0360-8352

ER -