The paper presents a mathematical model of the system of repairs and preventive replacements by age of city buses. The mathematical model was developed using the theory of semi-Markov processes. In the model developed, four types of city bus renewal processes are considered and three types of corrective repairs and preventive replacement. Corrective repairs are considered in two types: minimal repairs (repairs carried out by the Technical Service units) and perfect repairs (repairs carried out at the stations of the Service Station). The models of restoration systems that use semi-Markov processes in which minimal repairs, perfect repairs, and preventive replacements by age, have been examined in the literature to a limited extent. The system under consideration is analysed from the point of view of two criteria: profit per time unit and availability of city buses to carry out the assigned transport tasks. Conditions of criterion functions’ extremum (maximum) existence were formulated for the adopted assumptions. The considerations presented in the paper are illustrated by exemplary results of calculations.

The aim of the conducted research was to compare the functional properties and the cutting accuracy of items produced using Fiber lasers in comparison with CO2 lasers. The object of 6 mm thick sheet plates made of S235JR steel cut with the two different laser types were analyzed. The tests covered dimensional accuracy (in accordance with the PN EN 22768-fH standard) and the surface after cutting (in accordance with the PN-EN ISO 9013: 2017-04). The results of the analysis have demonstrated that for the same welding linear energy, more accurate cutting surface is obtained using Fiber laser cutting.

The article describes the developed model of controlling the process of means of transport operation, in which the choice of control strategy is carried out using non-deterministic methods. The model presented in the paper allows one to evaluate the quality of the transport system operation from the point of view of selected evaluation criteria: the risk of occurrence of undesired events and the availability of means of transport. The article presents a description of the method for determining the optimal (quasi-optimal) strategy for controlling the process of the use of means of transport taking into account the semi-Markov decision- making processes. The selection of the optimal (quasi-optimal) solution is carried out using the genetic algorithm and the simulated annealing algorithm. As a result of numerical calculations, for the criterion functions used, a set of quasi-optimal solutions is obtained in the form of the so- called Pareto front. This applies to the selection of possible decision variants, such a strategy for controlling the operation process, for which the functions constituting the evaluation criteria achieve values belonging to the Pareto-optimal solutions set.