The situation of the COVID-19 pandemic has had enormous social and economic impacts and has significantly affected the modal split. Many cities worldwide have adopted various blocking policies that affect how people travel. Micromobility systems, such as scooters and bicycle sharing, were among the transport systems affected by COVID-19. Electric scooters and shared bicycles provide comfortable and fast first-/last-mile connections for short-distance rides. The shared nature of these modes, together with the spread COVID-19, has contributed to the declining use of these services. The quantification of the impact of COVID-19 on shared services was demonstrated by this research through various mathematical methods. Satisfaction with the use of alternative modes of transport during the pandemic was determined based on the evaluation of a questionnaire survey. Independence tests of qualitative features and statistically significant associations that were demonstrated with a correspondence analysis were used for comparison. The main conclusion of the research was to point out the reasons for the preference for alternative modes of transport and to highlight the impacts on health and fears of contracting COVID-19 when using micromobility services.

Current business trends push transport companies to improve the efficiency of their entrepreneurial activities, what is closely related to costs reduction and revenues increase. Many transport companies achieve it empirically, but some mathematical algorithms, mainly from operational research, can be used to improve the efficiency of railway transport by finding the optimal solution of specific problems. The paper is focused on using of selected methods from applied mathematics in railway transport. These methods are used mainly for improving the operational efficiency of the transport company, what tends to decrease overall operating costs. Major impact is done by efficient use of railway vehicles and train staff. It can be achieved by optimization as a flow network problem or assignment problem, what is further described in the paper. Mathematical approaches can also positively influence the whole logistic process.

The last mile is characterized as the last step of delivery to the customer from the logistics point of view. It is necessary to aim and fulfill all customers’ needs mainly during the process of the last mile, because it is directly connected to them. Customer orientation can cause many complications that must be solved according to their will. This part of the supply chain is currently under pressure. Nowadays, trends have changed the last mile into a more ecological process mostly in the transport field. Railway transport is considered as an ecological transport mode therefore the last mile should be done by the railway transport. Preconditions for doing the last mile by the railway transport is the existence of siding (special purpose tracks) at the place of delivery. Our research focuses on minimizing the negative impacts of the last mile to customers in the context of using sidings. This research is based on the real conditions of the Slovak rail network, and on consultation with some experts from freight transport companies.

Logistics is defined as an interdisciplinary science, which deals with coordination, harmonization, connection and optimization of material, product and service flows including flows of information and finance. The main aim of logistics is to satisfy needs of the customer with importance of quality aspect and optimal costs. The paper is focused on practical logistic problems within the company, its suppliers and customers so overall supply chain is analyzed there. The aim of the paper is to provide practical simulation and calculation of selected logistic examples such as procurement, storage and distribution on case studies. These logistic aspects are analyzed in way, how are they explained to students in university educational process on school subjects that deal with logistics in some case. The simulation of storage process is done with specialized software called Byron, which is also used for educational purposes.

Main challenge of logistics is delivering right assortment of products in exact amount, to exact place, in exact time, ecologically and for exact price. Logistics deals with freight transport but when the word ‘products’ is changed to ‘passengers’, then many principles can be applied to passenger transport. Railway passenger transport is the key part of passenger transport system, so it is necessary to optimize it on logistics philosophy at first.

In the field of railway operation, it is essential to establish uniform conditions for interconnectivity requirements and compatibility of equipment in the Pan-European railway area to ensure effective interoperability. It also includes, for example, the introduction of a control system with modern and advanced interlocking systems (safety devices). The European Train Control System (ETCS) is a single European train protection system that will increase safety in rail transport. Nevertheless, this system may have an impact on the throughput on those railway lines where it is applied. The main research objective is to determine the impacts and effects of the configuration of track signaling equipment on the operational management of traffic and especially on the creation of a traffic plan. The optimization of transport processes on the railway infrastructure means creating the conditions for achieving higher throughput performance, especially including a higher number of train paths into the train traffic diagram. This paper examines and compares the impacts of ETCS and its levels (in particular ETCS L3) on the practical throughput of the selected national infrastructure manager. A heuristic procedure is used with the application of the analytical methodology of the Railways of the Slovak Republic (ŽSR), which uses the principles of mathematical statistics and probability. Significant comparative indicators are occupancy times and the degree of utilization of practical throughput. These are used in investment decisions in the modernization of line sections to achieve interoperability of the railway system.