### Abstract

In this paper, two approaches were introduced to obtain Stackelberg solutions for two-level linear fractional programming problems with interval coefficients in the objective functions. The approaches were based on the Kth best method and the method for solving linear fractional programming problems with interval coefficients in the objective function. In the first approach, linear fractional programming with interval coefficients in the objective function and linear programming were utilized to obtain Stackelberg solution, but in the second approach only linear programming is used. Since a linear fractional programming with interval coefficients can be equivalently transformed into a linear programming, therefore both of approaches have same results. Numerical examples demonstrate the feasibility and effectiveness of the methods.

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

Pages (from-to) | 1651-1656 |

Number of pages | 6 |

Journal | Sains Malaysiana |

Volume | 41 |

Issue number | 12 |

Publication status | Published - Dec 2012 |

### Fingerprint

### Keywords

- Interval coefficients
- Linear fractional programming
- Stackelberg solution
- Two-level programming

### ASJC Scopus subject areas

- General

### Cite this

*Sains Malaysiana*,

*41*(12), 1651-1656.

**A stackelberg solution to a two-level linear fractional programming problem with interval coefficients in the objective functions.** / Borza, M.; Rambely, Azmin Sham; Saraj, M.

Research output: Contribution to journal › Article

*Sains Malaysiana*, vol. 41, no. 12, pp. 1651-1656.

}

TY - JOUR

T1 - A stackelberg solution to a two-level linear fractional programming problem with interval coefficients in the objective functions

AU - Borza, M.

AU - Rambely, Azmin Sham

AU - Saraj, M.

PY - 2012/12

Y1 - 2012/12

N2 - In this paper, two approaches were introduced to obtain Stackelberg solutions for two-level linear fractional programming problems with interval coefficients in the objective functions. The approaches were based on the Kth best method and the method for solving linear fractional programming problems with interval coefficients in the objective function. In the first approach, linear fractional programming with interval coefficients in the objective function and linear programming were utilized to obtain Stackelberg solution, but in the second approach only linear programming is used. Since a linear fractional programming with interval coefficients can be equivalently transformed into a linear programming, therefore both of approaches have same results. Numerical examples demonstrate the feasibility and effectiveness of the methods.

AB - In this paper, two approaches were introduced to obtain Stackelberg solutions for two-level linear fractional programming problems with interval coefficients in the objective functions. The approaches were based on the Kth best method and the method for solving linear fractional programming problems with interval coefficients in the objective function. In the first approach, linear fractional programming with interval coefficients in the objective function and linear programming were utilized to obtain Stackelberg solution, but in the second approach only linear programming is used. Since a linear fractional programming with interval coefficients can be equivalently transformed into a linear programming, therefore both of approaches have same results. Numerical examples demonstrate the feasibility and effectiveness of the methods.

KW - Interval coefficients

KW - Linear fractional programming

KW - Stackelberg solution

KW - Two-level programming

UR - http://www.scopus.com/inward/record.url?scp=84870352780&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870352780&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84870352780

VL - 41

SP - 1651

EP - 1656

JO - Sains Malaysiana

JF - Sains Malaysiana

SN - 0126-6039

IS - 12

ER -