Transformation of metric space tools for transport logistics

The numerous logistics problems occurring in power train and transport industry lead to wear of vehicles and trains as well as the road or tracks length. The choice of the proper transport requires selecting the kind of the optimum length of the way. For facilities for transport of bulk commodity, very important meaning has the distance between the place of outgoing (x) and delivery point (y). Such problem will be referring for the one, two and three spaces in the case of land transport for road and rail vehicles as well as sea and air transport for ships and airplane. It is desired that the transport from outgoing point (x) to delivery place (y) ought to be travelled on the shortest way in the presenting geometry sense. In transport, logistics denotes it the least distance between the place of the drive beginning (outgoing) and the place of drive end (delivering place). It is evident that the shortest distance between two points is always if we define this distance in Euclidean geometry sense because Euclidean metric determines the shortest distance between two points. In various transport problems the shortest distance in Euclidean sense, between two various places is not realistic and not possible. Therefore for transport vehicles exists many possibilities of various kinds of access road in Euclidean and non- Euclidean geometry. After Authors, suggestion very interesting is to find the optimum way or optimum track between the trip origin and delivery place. Such problem demands the more and more information referring the describing the tracks geometry using metric space theory. In this article, especially the non-Euclidean modulus Taxi–Car metrics is considered. Presented metric spaces and their properties are needed and applied in practical transport problems occurring among other in assembly rooms where the way of intelligent shortest truck must be considered. Moreover, in this article the various communication ways will be presented and will be suggested an algorithm construction of the optimum distance problem solutions in non-Euclidean geometry presenting the equivalent and simultaneously most simple communication tracks.