Mathematical Modeling of Multimodal Transportation Risks

  • Vitalii NitsenkoEmail author
  • Sergiy Kotenko
  • Iryna Hanzhurenko
  • Abbas Mardani
  • Ihor Stashkevych
  • Maksym Karakai
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 978)


Research has shown that the risks of multimodal transportation depend as both on stochastic and fuzzy parameters.

Mathematical vehicles for the stochastic and fuzzy quantities are different. Therefore, a mathematical model is suggested to evaluate for the integral risk of cargo transportation. This makes it possible to use this model in support systems while making decisions on logistics of multimodal transportation. The use of a mathematical model requires careful analysis of all risks attributed to the multimodal transportation chain, possible overload options, and taking into account the entire spectrum of control activities.

After determining the most appropriate, from the point of view of risk minimization, the mode of transportation and its first links, the next stage of dynamic risk management is recursive review of the status vector of the chosen variant of the specified transportation route. For this information system it is necessary to process large data sets, while the suggested model economically uses computer resources and reduces the calculation time. The given mathematical model allows real-time changes in the transportation risk at specific stage to offer options for reducing integral risk, leverage it, in particular, choosing other routes and types of transport.


Mathematical model Multimodal transportation Risks Big data Fuzzy variables Stochastic parameters Time-discretization Dynamic system 


  1. 1.
    John A, Paraskevadakis D, Bury A (2014) An integrated fuzzy risk assessment for seaport operation. Safety Sci 68:180–194CrossRefGoogle Scholar
  2. 2.
    Liu Y, Fan ZP, Yuan Y (2014) A FTA-based method for risk decision making in emergency response. Comput Oper Res 42:49–57MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ferdous R, Khan F, Veitch B (2009) Methodology for computer aided fuzzy fault tree analysis. Process Saf 87:217–226CrossRefGoogle Scholar
  4. 4.
    Bansal A (2011) Trapezoidal Fuzzy Numbers (a, b, c, d): arithmetic behavior. Int J Phys Math Sci 2(1):39–44MathSciNetGoogle Scholar
  5. 5.
    Vilko JPP, Hallikas JM (2012) Risk assessment in multimodal supply chains. Int J Product Econ 140(2):586–595, Scholar
  6. 6.
    Frazila RB, Zukhruf F (2017) A stochastic discrete optimization model for multimodal freight transportation. network design. Int J Oper Res 14(3):107–120Google Scholar
  7. 7.
    Steadie Seifi M, Dellaert NP, Nuijten W, Van Woensel T, Raoufi R (2014) Multimodal freight transportation planning. Eur J Oper Res 233:1–15CrossRefGoogle Scholar
  8. 8.
    Yamada T, Febri Z (2015) Freight transport network design using particle swarm optimization in supply chain–transport super network equilibrium. Transp Res Part E 75:164–187CrossRefGoogle Scholar
  9. 9.
    Andrease MM (2008) Non-linear DSGE Models, The Central Di⁄erence Kalman Filter, and The Mean Shifted Particle Filter 46, ( Scholar
  10. 10.
    Wang Y, Yeo G-T, A study on international multimodal transport networks from Korea to Central AsiaGoogle Scholar
  11. 11.
    Litman T (2017) Introduction to multi-modal transportation planning principles and practices victoria transport policy Institute 19Google Scholar
  12. 12.
    Sossoe K (2018) Modeling of multimodal transportation systems of large networks. Automatic Control Engineering. University Paris-Est, 187Google Scholar
  13. 13.
    Jian Z (2017) Multimodal freight transportation problem: model, algorithm and environmental impacts. A dissertation submitted to the graduate school Newark Rutgers, The State University of New Jersey. 117Google Scholar
  14. 14.
    Liu Y, Chen J, Wu W, Ye J (2019) Typical combined travel mode choice utility model in multimodal transportation network,

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Vitalii Nitsenko
    • 1
    Email author
  • Sergiy Kotenko
    • 2
  • Iryna Hanzhurenko
    • 2
  • Abbas Mardani
    • 3
  • Ihor Stashkevych
    • 4
  • Maksym Karakai
    • 4
  1. 1.Private Joint-Stock Company “Higher Education Institution “Interregional Academy of Personnel Management”KievUkraine
  2. 2.Institute of Market Problems and Economic-Ecological Research, National Academy of Sciences of UkraineOdessaUkraine
  3. 3.Azman Hashim International Business SchoolUniversiti Teknologi MalaysiaJohor BahruMalaysia
  4. 4.Donbas State Engineering AcademyKramatorskUkraine

Personalised recommendations