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Solving methods for interval linear programming problem: a review and an improved method

Author

Listed:
  • H. Mishmast Nehi

    (University of Sistan and Baluchestan)

  • H. A. Ashayerinasab

    (University of Sistan and Baluchestan)

  • M. Allahdadi

    (University of Sistan and Baluchestan)

Abstract

Interval linear programming is used for tackling interval uncertainties in real-world systems. An arbitrary point is a feasible point to the interval linear programming model if it lies in the largest feasible region of the interval linear programming model, and it is optimal if it is an optimal solution to a characteristic model. The optimal solution set to the interval linear programming is the union of all solutions that are optimal for a characteristic model. In this paper, we review some existing methods for solving interval linear programming problems. Using these methods the interval linear programming model is transformed into two sub-models. The optimal solutions of these sub-models form the solution space of these solving methods. A part of the solution space of some of these methods may be infeasible. To eliminate the infeasible part of the solution space of above methods, several methods have been proposed. The solution space of these modified methods may contain non-optimal solutions. Two improvement methods have been proposed to remove the non-optimal solutions of the solution space of above modified methods. Finally, we introduce an improved method and its sub-models. The solution space of our method is absolutely both feasible and optimal.

Suggested Citation

  • H. Mishmast Nehi & H. A. Ashayerinasab & M. Allahdadi, 2020. "Solving methods for interval linear programming problem: a review and an improved method," Operational Research, Springer, vol. 20(3), pages 1205-1229, September.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:3:d:10.1007_s12351-018-0383-4
    DOI: 10.1007/s12351-018-0383-4
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    References listed on IDEAS

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    1. Zhou, Feng & Huang, Gordon H. & Chen, Guo-Xian & Guo, Huai-Cheng, 2009. "Enhanced-interval linear programming," European Journal of Operational Research, Elsevier, vol. 199(2), pages 323-333, December.
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    4. J W Chinneck & K Ramadan, 2000. "Linear programming with interval coefficients," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(2), pages 209-220, February.
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