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A Method For Generating All The Efficient Solutions Of A 0-1 Multi-Objective Linear Programming Problem

Author

Listed:
  • 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)

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.

Suggested Citation

  • G. R. Jahanshahloo & F. Hosseinzadeh Lotfi & N. Shoja & G. Tohidi, 2004. "A Method For Generating All The Efficient Solutions Of A 0-1 Multi-Objective Linear Programming Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 127-139.
    • Handle: RePEc:wsi:apjorx:v:21:y:2004:i:01:n:s0217595904000096
    DOI: 10.1142/S0217595904000096
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    Cited by:

    1. S. Razavyan, 2016. "A Method for Generating a Well-Distributed Pareto Set in Multiple Objective Mixed Integer Linear Programs Based on the Decision Maker’s Initial Aspiration Level," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-23, August.

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