A fuzzy milp-model for the optimization of vehicle routing problem

Kaj-Mikael Björk*, József Mezei

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)


In this article, a novel model for the solution of a fuzzy vehicle routing problem is presented. The model originates from a crisp MILP (Mixed Integer Linear Programming) model previously presented on a conference. This work is motivated by a business context of timber transportation. Within this context, uncertainties arise from the fact that the distances and times between pickup points are inherently fuzzy. The decisions to be made are routing decisions, truck assignment and the determination of the pickup order for a set of loads and available trucks. The paper also presents briefly how the model is implemented in the Microsoft Excel environment, utilizing the LP-solve freeware as the optimization engine. The model is also illustrated with a numerical example. To the authors knowledge, there are no previously reported vehicle routing MILP models, where the times and distances are allowed to be fuzzy numbers.

Original languageEnglish
Peer-reviewed scientific journalJournal of Intelligent and Fuzzy Systems
Issue number3
Pages (from-to)1349-1361
Number of pages13
Publication statusPublished - 20.02.2014
MoE publication typeA1 Journal article - refereed


  • 512 Business and Management
  • Vehicle routing
  • fuzzy numbers
  • MILP
  • Timber pickup


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