Реалізація мультимодальних транспортних задач в різних програмних середовищах

Abstract

У статті виконано постановку та реалізацію мультимодальної транспортної задачі за допомогою таких програмних засобів, як MS Excel, Mathcad та Matlab. Проаналізовано відмінності та особливості алгоритмів реалізації мультимодальної та класичної транспортних задач в цих середовищах програмування. На основі модельних даних продемонстровано ідентичність результатів, отриманих з використанням різних програмних пакетів.

Multimodal problem is the classic transport problem that assumes simultaneous (parallel) application of several means of cargo delivery. It means, the criterion for optimizing a multimodal transportation problem is, as compared with the classic one, the minimal ultimate transportation cost, whereas there are more than one accessible means of cargo delivery. Today’s scientific description, both in the Ukrainian and foreign investigations, considers the problems of this type insufficiently, therefore the issue of testing their models and methodologies is quite significant. Apparently, the calculations of these problems appear to be as well complicated, so it is rather correct to employ for it special programming methods. The article regards the multimodal transport problem presented and realized through different programming means, among them MS Excel, Mathcad and Matlab. The transportation means are presented as equal to three, since we regard the automobile, the railroad and the river deliveries. The problem requires, for various programming performances, the standard (built-in) functions and methods like Solver for MS Excel, Minimize for Mathcad (as well as Given block) and Linprog for Matlab (using a multimodal transport problem modified into a linear programming problem). The research has resulted in the analysis of peculiar algorithms for multimodal and classic transport problems, the above mentioned programming methods. Also, the model data has demonstrated identical results obtained through the application of various programming means. The obtained algorithms for solving the multimodal transport problem can be expanded for a larger, than three, number of means for transport delivery. In perspective, the research holds to solve the multicriteria, at least, two-criteria, multimodal transport problem that would assume more than one criterion of optimization. One of these would be minimizing the level of risks in transportation logistics