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A Two-Fold Linear Programming Model with Fuzzy Data

Author

Listed:
  • Saber Saati

    (Islamic Azad University, North Tehran Branch, Iran)

  • Adel Hatami-Marbini

    (Université catholique de Louvain, Belgium)

  • Madjid Tavana

    (La Salle University, USA)

  • Elham Hajiahkondi

    (Payame Noor University, Iran)

Abstract

Linear programming (LP) is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency. Although LP models require well-suited information and precise data, managers and decision makers dealing with optimization problems often have a lack of information on the exact values of some parameters used in their models. Fuzzy sets provide a powerful tool for dealing with this kind of imprecise, vague, uncertain or incomplete data. In this paper, the authors propose a two-fold model which consists of two new methods for solving fuzzy LP (FLP) problems in which the variables and the coefficients of the constraints are characterized by fuzzy numbers. In the first method, the authors transform their FLP model into a conventional LP model by using a new fuzzy ranking method and introducing a new supplementary variable to obtain the fuzzy and crisp optimal solutions simultaneously with a single LP model. In the second method, the authors propose a LP model with crisp variables for identifying the crisp optimal solutions. The authors demonstrate the details of the proposed method with two numerical examples.

Suggested Citation

  • Saber Saati & Adel Hatami-Marbini & Madjid Tavana & Elham Hajiahkondi, 2012. "A Two-Fold Linear Programming Model with Fuzzy Data," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 2(3), pages 1-12, July.
    • Handle: RePEc:igg:jfsa00:v:2:y:2012:i:3:p:1-12
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    Citations

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    Cited by:

    1. Ali Ebrahimnejad, 2015. "A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 2048-2060, August.
    2. P. Senthil Kumar, 2016. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 5(4), pages 121-146, October.
    3. P. Senthil Kumar, 2018. "A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 29(1), pages 102-129.

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