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A global satisfaction degree method for fuzzy capacitated vehicle routing problems.

Juan Carlos Figueroa-García1, Jhoan Sebastián Tenjo-García2, Carlos Franco3

  • 1Universidad Distrital Francisco José de Caldas, Bogotá - Colombia.

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This study introduces a novel fuzzy logic approach to solve uncertain vehicle routing problems. The method effectively handles data scarcity by using expert-derived fuzzy numbers to find optimal delivery routes.

Keywords:
Capacitated vehicle routingFuzzy optimizationGlobal satisfaction degree

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Area of Science:

  • Operations Research
  • Fuzzy Logic
  • Optimization

Background:

  • Capacitated Vehicle Routing Problems (CVRP) often face uncertainty in delivery costs and demands.
  • Deterministic methods fail when data is scarce or unreliable.
  • Expert knowledge is a valuable alternative for estimating uncertain parameters.

Purpose of the Study:

  • To develop a method for solving uncertain CVRP with limited data.
  • To integrate expert-derived fuzzy numbers into an optimization framework.
  • To achieve a global optimal solution for fuzzy CVRP.

Main Methods:

  • Utilizing fuzzy numbers to represent uncertain costs and demands derived from expert information.
  • Employing an iterative-integer programming method combined with a global satisfaction degree.
  • Introducing auxiliary variables and cumulative membership functions for fuzzy set analysis.
  • Iteratively finding equilibrium between fuzzy costs/demands using alpha and lambda parameters.

Main Results:

  • The proposed algorithm successfully finds a global optimal solution for uncertain CVRP.
  • The method demonstrates convergence regardless of initial parameter selection.
  • Algorithm performance remains consistent across various problem sizes and instances.

Conclusions:

  • Expert-derived fuzzy numbers provide a robust solution for data-scarce CVRP.
  • The iterative fuzzy optimization approach is effective and reliable.
  • This method enhances decision-making in logistics and supply chain management under uncertainty.