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Two-Level Linear Programming Problems with Two Decision-Makers at the Upper Level: An Interactive Fuzzy Approach

Author

Listed:
  • Mojtaba Borza
  • Azmin Sham Rambely
  • Mansour Saraj

Abstract

The interactive fuzzy programming approach can be used to address two-level programming problems if a mutually cooperative relationship exists between the decision-makers. In this approach, a satisfactory solution is obtained by taking into account the minimum satisfaction level of the decision-maker at the upper level. In addition, the overall satisfaction balance between the decision-maker at the lower level and the decision-maker at the upper level must be appropriate. In this paper, interactive fuzzy programming is used to achieve a satisfactory solution for a two-level linear programming problem with two decision-makers at the upper level. The method is designed in such a way that both decision-makers at the upper level achieve their minimum satisfaction levels together with the appropriate satisfaction balance between the decision-maker at the lower level and each decision-maker at the upper level. A numerical example is given to illustrate the method. Moreover, it is indicated that a three-level program can be considered as a two-level program with two decision-makers at the upper level.

Suggested Citation

  • Mojtaba Borza & Azmin Sham Rambely & Mansour Saraj, 2014. "Two-Level Linear Programming Problems with Two Decision-Makers at the Upper Level: An Interactive Fuzzy Approach," Modern Applied Science, Canadian Center of Science and Education, vol. 8(4), pages 211-211, August.
    • Handle: RePEc:ibn:masjnl:v:8:y:2014:i:4:p:211
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    References listed on IDEAS

    as
    1. Wayne F. Bialas & Mark H. Karwan, 1984. "Two-Level Linear Programming," Management Science, INFORMS, vol. 30(8), pages 1004-1020, August.
    2. Sakawa, Masatoshi & Nishizaki, Ichiro & Uemura, Yoshio, 2002. "A decentralized two-level transportation problem in a housing material manufacturer: Interactive fuzzy programming approach," European Journal of Operational Research, Elsevier, vol. 141(1), pages 167-185, August.
    3. Sakawa, Masatoshi & Nishizaki, Ichiro & Uemura, Yoshio, 2001. "Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: A case study," European Journal of Operational Research, Elsevier, vol. 135(1), pages 142-157, November.
    4. Abd El-Wahed, Waiel F. & Lee, Sang M., 2006. "Interactive fuzzy goal programming for multi-objective transportation problems," Omega, Elsevier, vol. 34(2), pages 158-166, April.
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    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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