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

M. Borza, Azmin Sham Rambely, M. Saraj

Research output: Contribution to journalArticle

4 Citations (Scopus)

### 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 1651-1656 6 Sains Malaysiana 41 12 Published - Dec 2012

### Fingerprint

Fractional Programming
Objective function
Linear programming
Interval
Coefficient
Numerical Examples
Demonstrate

### Keywords

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

• General

### Cite this

In: Sains Malaysiana, Vol. 41, No. 12, 12.2012, p. 1651-1656.

Research output: Contribution to journalArticle

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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.

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