Alternative Fuzzy Approaches for Efficiently Solving the Capacitated Vehicle Routing Problem in Conditions of Uncertain Demands

  • Brigitte Werners
  • Yuriy Kondratenko
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 125)


This paper deals with the analysis of fuzzy models and fuzzy approaches for efficiently solving transportation and vehicle routing problems (VRP) with constrains on vehicle’s capacity. Authors focused their research on VRP for marine bunkering tankers and planning and optimisation of tanker’s routes in conditions of uncertain fuel demands at nodes. Triangular fuzzy numbers are proposed for modelling uncertain demands and the optimization problem is considered as multi-criteria problem with (a) minimizing total length of planned routes, (b) satisfying all orders at nodes (ships, ports), (c) maximizing total sales volume of unloaded fuel, (d) minimizing fleet size. Two alternative fuzzy approaches for efficiently solving such marine VRP are discussed. The first alternative deals with the development of a multi-stage iterative heuristic procedure and the second alternative concerns the development of a fuzzy decision-making system for the current evaluation of satisfaction values for uncertain order realizations.


Vehicle routing problem (VRP) Capacitated vehicle routing problem (CVRP) Fuzzy demands Iterative heuristic Decision-making Satisfaction value 



The authors gratefully acknowledge the support of this research work by the Ruhr University Bochum and Deutscher Akademischer Austauschdienst (DAAD), Germany, by awarding one of the author with the research 2000 fellowship and research 2010-2011 fellowship.


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute of ManagementRuhr University BochumBochumGermany
  2. 2.Intelligent Information Systems DepartmentPetro Mohyla Black Sea National UniversityMykolaivUkraine

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