A Two-Fold Linear Programming Model with Fuzzy Data

  • Authors:

  • Madjid Tavana;Adel Hatami-Marbini;Saber Saati;Elham Hajiahkondi

  • Affiliations:

  • La Salle University, USA;Université catholique de Louvain, Belgium;Islamic Azad University, North Tehran Branch, Iran;Payame Noor University, Iran

  • Venue:
  • International Journal of Fuzzy System Applications
  • Year:
  • 2012

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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.