The paper regards a specific class of optimization criteria that possess features of probability. Therefore, constructing objective function of optimization problem, the importance is attached to probability indices that show the probability of some criterial event or events to occur. Factor analysis has been taken for the main method of constructing objective function. Algorithm for constructing objective function of optimization is done for criterion of minimization risk level in multimodal transportations that demanded demonstration data. The application of factor analysis in classical problem solution was shown to give the problem a more distinct analytical interpretation in solving it.


factor analysis; risk function; optimization criterion; multimodal transportation

Ayed H., Galvez-Fernandez C., Habbas Z., Khadraoui D.: Solving time-dependent multimodal transport problems using a transfer graph model. Computers and Industrial Engineering 61, 2011, 391–401 [http://doi.org/10.1016/j.cie.2010.05.018]. DOI: https://doi.org/10.1016/j.cie.2010.05.018

Ayed H., Habbas Z., Khadraoui D., Galvez-Fernandez C.: A parallel algorithm for solving time dependent multimodal transport problem. IEEE Conference on Intelligent Transportation Systems, Proceedings, ITSC, 2011, 722–727 [http://doi.org/10.1109/ITSC.2011.6082973]. DOI: https://doi.org/10.1109/ITSC.2011.6082973

Boyd K. C.: Factor analysis. The Routledge Handbook of Research Methods in the Study of Religion 2013, 204–216 [http://doi.org/10.4324/9780203154281-22].

Chandrakantha L.: Using excel solver in optimization problems. John Jay College of Criminal Justice of CUNY, 2014, 42–49.

Elias D., Nadler B., Nadler F., Hauger G.: OPTIHUBS – Multimodal Hub Process Optimization by Means of Micro Simulation. Transportation Research Procedia 14, 2016, 457–466 [http://doi.org/10.1016/j.trpro.2016.05.098]. DOI: https://doi.org/10.1016/j.trpro.2016.05.098

Ezeokwelume O.: Solving linear programming problems and transportation problems using excel solver. International Journal of Scientific & Engineering Research 7(9), 2016, 134–142.

Flórez J. E., Torralba A., García J., Linares López C., García-Olaya A., Borrajo D.: TIMIPLAN: An Application to Solve Multimodal Transportation Problems. Scheduling and Planning Applications Workshop 2010.

García J., Florez J. E., Torralba A., Borrajo D., López C. L., García-Olaya A., Sáenz J.: Combining linear programming and automated planning to solve intermodal transportation problems. European Journal of Operational Research 227, 2013, 216–226. DOI: https://doi.org/10.1016/j.ejor.2012.12.018

Honcharov A., Mogilei S.: Solving multimodal transportation problems by different program means. Bulletin of Cherkasy State Technological University 3, 2020, 67–74.

Jennrich R. I., Bentler P. M.: Exploratory Bi-Factor Analysis. Psychometrika 76(4), 2011, 537–549 [http://doi.org/10.1007/s11336-011-9218-4]. DOI: https://doi.org/10.1007/s11336-011-9218-4

Journal I., Factor I.: Computational and Mathematical Methods in Medicine. Bio Med Research International 1, 2015, 2–4. DOI: https://doi.org/10.1155/2015/685036

Klami A., Virtanen S., Leppaaho E., Kaski S.: Group Factor Analysis. IEEE Transactions on Neural Networks and Learning Systems 26(9), 2015, 2136–2147 [http://doi.org/10.1109/TNNLS.2014.2376974]. DOI: https://doi.org/10.1109/TNNLS.2014.2376974

Lin C. C., Lin S. W.: Two-stage approach to the intermodal terminal location problem. Computers and Operations Research 67, 2016, 113–119 [http://doi.org/10.1016/j.cor.2015.09.009]. DOI: https://doi.org/10.1016/j.cor.2015.09.009

Ovcharuk V., Vovkodav N., Kryvets T., Ovcharuk I.: Linear programming in Mathcad on the example of solving the transportation problem. Scientific Works of NUFT 21(4), 2015, 110–117.

Sengamalaselvi J.: Solving transportation problem by using Matlab. International Journal of Engineering Sciences & Research Technology 6(1), 2017, 374–381 [http://doi.org/10.5281/zenodo.259588].

Slavova-Nocheva M.: Competitiveness of the transport market in Bulgaria. Economic Studies 21(3), 2012, 15–24.

Vats B., Kumar Singh A.: Solving transportation problem using excel solver for an optimal solution. MIT International Journal of Mechanical Engineering 6(1), 2016, 18–20.

Verga J., Silva R. C., Yamakami A.: Multimodal transport network problem: Classical and innovative approaches. Studies in Fuzziness and Soft Computing, Springer Verlag 358, 2018, 299–332 [http://doi.org/doi:10.1007/978-3-319-62359-7_14]. DOI: https://doi.org/10.1007/978-3-319-62359-7_14

Virtanen S., Klami A., Khan S.A., Kaski S.: Bayesian group factor analysis. The Journal of Machine Learning Research 22, 2012, 1269–1277.

Zabolotnii S., Mogilei S., The methods for determining the parameters of the objective function of multimodal transportation risk. Proceedings of V International Scientific-Practical Conference “ITEST-2020”, 2020, 114–115.

Zabolotnii S., Mogilei S.: Optimization of the method of constructing reference plans of multimodal transport problem. Technological audit and production reserves 2(45), 2019, 15–20 [http://doi.org/10.15587/2312-8372.2019.154561]. DOI: https://doi.org/10.15587/2312-8372.2019.154561

Zelenika R., Sever D., Zebec S., Pirš B.: Logistic operator: Fundamental factor in rational production of services in multimodal transport. Promet - Traffic&Transportation 17(1), 2005, 43–53.

Zhao S., Gao C., Mukherjee S., Engelhardt B. E.: Bayesian group factor analysis with structured sparsity. Journal of Machine Learning Research 17, 2016, 1–47.


Published : 2021-12-20

Zabolotnii, S., Honcharov, A., & Mogilei, S. (2021). FACTOR ANALYSIS METHOD APPLICATION FOR CONSTRUCTING OBJECTIVE FUNCTIONS OF OPTIMIZATION IN MULTIMODAL TRANSPORT PROBLEMS. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 11(4), 28-31. https://doi.org/10.35784/iapgos.2788

Serhii Zabolotnii  zabolotniua@gmail.com
Cherkasy State Business-College  Ukraine
Artem Honcharov 
Cherkasy State Technological University  Ukraine
Sergii Mogilei 
Rauf Ablyazov East European University  Ukraine