Sains Malaysiana 41(12)(2012): 1651–1656
A
Stackelberg Solution to a Two-Level Linear Fractional Programming Problem with
Interval Coefficients in the Objective Functions
(Penyelesaian Stackelberg bagi Masalah Pengaturcaraan Pecahan
Linear Dua-Aras
dengan Pekali Selang dalam Fungsi Objektif)
M. Borza & A. S. Rambely*
School of Mathematical Sciences, Faculty of Science &
Technology
Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
M. Saraj
Department of Mathematics, Faculty of Mathematical Sciences
& Computer
Shahid Chamran University, Ahvaz-Iran
Diserahkan: 18 Mei 2012 / Diterima: 31 Julai 2012
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.
Keywords: Interval coefficients; linear fractional programming;
Stackelberg solution; two-level programming
ABSTRAK
Dalam kajian ini, dua kaedah diperkenalkan untuk
mendapatkan penyelesaian Stackelberg bagi masalah pengaturcaraan pecahan linear
dua-aras dengan pekali selang dalam fungsi objektif. Kaedah yang digunakan adalah
berdasarkan kaedah terbaik peringkat-K dan kaedah penyelesaian masalah
pengaturcaraan pecahan linear dengan pekali selang dalam fungsi objektif. Dalam kaedah pertama, pengaturcaraan pecahan linear dengan
pekali selang dalam fungsi objektif dan pengaturcaraan linear digunakan untuk
mendapatkan penyelesaian Stackelberg, tetapi dalam kaedah kedua hanya
pengaturcaraan linear digunakan. Oleh sebab suatu
pengaturcaraan pecahan linear dengan pekali selang boleh dijelmakan secara
setara kepada pengaturcaraan linear. kedua-dua
kaedah menghasilkan keputusan yang sama. Beberapa contoh
berangka menunjukkan kesauran dan keberkesanan kaedah-kaedah ini.
Kata kunci: Pekali selang; pengaturcaraan
dua-aras; pengaturcaraan pecahan linear; penyelesaian Stackelberg
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*Pengarang
untuk surat-menyurat; e-mail: asr@ukm.my