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Transportation optimization with fuzzy trapezoidal numbers based on possibility theory.

Dayi He1, Ran Li1, Qi Huang1

  • 1School of Humanities & Economic Management, Lab of Resources & Environment Management, China University of Geosciences (Beijing), Beijing, P. R. China.

Plos One
|August 20, 2014
PubMed
Summary

This study presents a parametric method to solve the fuzzy transportation problem by transforming uncertain parameters into a crisp linear model. The approach uses possibility theory and a fractile-modality method for defuzzification, validated with a numerical example.

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Area of Science:

  • Operations Research
  • Fuzzy Mathematics
  • Optimization Theory

Background:

  • Traditional transportation problems assume precise parameters.
  • Real-world supply chains involve inherent uncertainties in supply, demand, and costs.
  • Existing fuzzy transportation models may not fully capture decision-maker subjectivity.

Purpose of the Study:

  • To introduce a parametric method for solving the fuzzy transportation problem.
  • To develop a generalized fuzzy transportation problem incorporating fuzzy supply, demand, and cost.
  • To transform fuzzy transportation problems into crisp linear programming problems for practical solutions.

Main Methods:

  • Modeling supply, demand, and cost as fuzzy trapezoidal numbers.
  • Applying possibility theory for fuzzy constraint and objective handling.
  • Utilizing the fractile and modality approach for defuzzification.
  • Converting the fuzzy transportation problem into a crisp linear transportation problem.

Main Results:

  • A parametric method for solving fuzzy transportation problems is successfully developed.
  • The proposed method effectively transforms fuzzy parameters into a solvable crisp linear model.
  • Defuzzification using fractile and modality approaches is demonstrated.

Conclusions:

  • The parametric method provides a robust framework for addressing uncertainties in transportation logistics.
  • The approach aligns with decision-maker subjectivity and practical requirements.
  • The validity of the proposed fuzzy transportation programming method is confirmed through a numerical example.