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A new fuzzy approach of vehicle routing problem for disaster-stricken zones

  • Gia Sirbiladze , Bezhan Ghvaberidze , Bidzina Midodashvili , Bidzina Matsaberidze and Irina Khutsishvili EMAIL logo
Published/Copyright: December 13, 2023
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 31 Issue 4

Abstract

Route planning problems are among the activities that have the highest impact in emergency logistical planning, goods transportation and facility location-distribution because of their effects on efficiency in resource management, service levels and client satisfaction. In the extreme conditions, such as disaster-stricken zones, the difficulty of vehicle movement between nearest different affected areas (demand points) on planning routes cause the imprecision of time of movement and the uncertainty of feasibility of movement. In this paper, the imprecision is presented by triangular fuzzy numbers and the uncertainty is presented by a possibility measure. A new two-stage, fuzzy bi-criterion optimization approach for the vehicle routing problem (VRP) is considered. On the first stage, the sample of so-called “promising” closed routes are selected based on a “constructive” approach. On the second stage, triangular fuzzy valued Choquet aggregation (TFCA) operator is constructed for the selected closed routes. The evaluation of constructed routes, levels of failure and possibility of vehicle movement on the roads are aggregated by the TFCA operator by the new criterion – minimization of infeasibility of movement. The new criterion together with the classic criterion – minimization of the total distance traveled – creates a bi-criteria fuzzy VRP. The constructed VRP is reduced to the bi-criteria fuzzy partitioning problem, and an 𝜀-constraint approach is developed for solving it. For numerical experiments, a parallel algorithm is created on the basis of D. Knuth’s algorithm of Dancing Links (DLX). An example is presented with the results of our approach for the VRP, where all Pareto-optimal solutions are found from the set of promising routes. The optimal solutions tend to avoid roads that are problematic because of extreme situations.

Keywords: Multi-criteria vehicle routing problem; fuzzy measure; possibility measure; fuzzy numbers; Choquet integral; partitioning problem; Pareto solution
MSC 2010: 28E10; 62A86; 68T30; 90C70

Funding source: Shota Rustaveli National Science Foundation

Award Identifier / Grant number: STEM-22-226

Funding statement: This research was funded by the Shota Rustaveli National Science Foundation of Georgia (SRNSFG), grant # STEM-22-226.

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Received: 2023-04-28
Revised: 2023-07-06
Accepted: 2023-07-24
Published Online: 2023-12-13
Published in Print: 2024-08-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Additivity of multiplicative (generalized) skew semi-derivations on rings
  3. On statistical convergence of order α in partial metric spaces
  4. Generalized derivations over amalgamated algebras along an ideal
  5. Numerical radii of operator matrices in terms of certain complex combinations of operators
  6. Centralizing identities involving generalized derivations in prime rings
  7. Two presentations of a weak type inequality for geometric maximal operators
  8. Existence and exponential stability of solutions for a Balakrishnan–Taylor quasilinear wave equation with strong damping and localized nonlinear damping
  9. Identities with generalized derivations on Lie ideals and Banach algebras
  10. Essential norm of Riemann–Stieltjes operator on weighted Bergman spaces with doubling weights
  11. Concerning the Nakayama property of a module
  12. Multiplicity result for a (p(x),q(x))-Laplacian-like system with indefinite weights
  13. Finite groups in which some particular invariant subgroups are TI-subgroups or subnormal subgroups
  14. The Dirichlet problem in an infinite layer for a system of differential equations with shifts
  15. Signless Laplacian spectrum of the cozero-divisor graph of the commutative ring ℤ𝑛
  16. A new fuzzy approach of vehicle routing problem for disaster-stricken zones
https://doi.org/10.1515/gmj-2023-2097
Keywords for this article
Multi-criteria vehicle routing problem; fuzzy measure; possibility measure; fuzzy numbers; Choquet integral; partitioning problem; Pareto solution

Articles in the same Issue

  1. Frontmatter
  2. Additivity of multiplicative (generalized) skew semi-derivations on rings
  3. On statistical convergence of order α in partial metric spaces
  4. Generalized derivations over amalgamated algebras along an ideal
  5. Numerical radii of operator matrices in terms of certain complex combinations of operators
  6. Centralizing identities involving generalized derivations in prime rings
  7. Two presentations of a weak type inequality for geometric maximal operators
  8. Existence and exponential stability of solutions for a Balakrishnan–Taylor quasilinear wave equation with strong damping and localized nonlinear damping
  9. Identities with generalized derivations on Lie ideals and Banach algebras
  10. Essential norm of Riemann–Stieltjes operator on weighted Bergman spaces with doubling weights
  11. Concerning the Nakayama property of a module
  12. Multiplicity result for a (p(x),q(x))-Laplacian-like system with indefinite weights
  13. Finite groups in which some particular invariant subgroups are TI-subgroups or subnormal subgroups
  14. The Dirichlet problem in an infinite layer for a system of differential equations with shifts
  15. Signless Laplacian spectrum of the cozero-divisor graph of the commutative ring ℤ𝑛
  16. A new fuzzy approach of vehicle routing problem for disaster-stricken zones
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