A METHOD FOR GENERATING ALL THE EFFICIENT SOLUTIONS OF A 0-1 MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM

G. R. Jahanshahloo (), F. Hosseinzadeh Lotfi (), N. Shoja () and G. Tohidi ()
Additional contact information
G. R. Jahanshahloo: Department of Mathematics, Teacher Training University, Tehran, Iran
F. Hosseinzadeh Lotfi: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
N. Shoja: Department of Mathematics, Islamic Azad University, Firozkoh Branch, Firozkoh, Iran
G. Tohidi: Department of Mathematics, Islamic Azad University, Tehran-Center Branch, Tehran, Iran

Asia-Pacific Journal of Operational Research (APJOR), 2004, vol. 21, issue 01, 127-139

Abstract: In this paper, a method using the concept ofl1-norm is proposed to find all the efficient solutions of a 0-1 Multi-Objective Linear Programming (MOLP) problem. These solutions are specified without generating all feasible solutions. Corresponding to a feasible solution of a 0-1 MOLP problem, a vector is constructed, the components of which are the values of objective functions. The method consists of a one-stage algorithm. In each iteration of this algorithm a 0-1 single objective linear programming problem is solved. We have proved that optimal solutions of this 0-1 single objective linear programming problem are efficient solutions of the 0-1 MOLP problem. Corresponding to efficient solutions which are obtained in an iteration, some constraints are added to the 0-1 single objective linear programming problem of the next iteration. Using a theorem we guarantee that the proposed algorithm generates all the efficient solutions of the 0-1 MOLP problem. Numerical results are presented for an example taken from the literature to illustrate the proposed algorithm.

Keywords: 0-1 Multi-Objective Linear Programming; efficient solution (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0217595904000096

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