The processes of exploitation of military objects are usually characterised by the specificity of the operation and the complexity of both the process itself and the object. This specificity may relate both to the type of tasks that these objects carry out and to the environment in which these processes take place. Complexity is usually reflected in the very structure of an object (for example, a ship, an aircraft or a helicopter) and, consequently, in its operation/maintenance system. The above mentioned features, as well as the limited access to data, naturally limits the set of publications available on this subject. In this article, the authors have presented a method of assessing the readiness of military helicopters operated by the Armed Forces of the Republic of Poland. The readiness of technical objects used in military exploitation systems is a basic indicator of equipment preparation for executing tasks. In exploitation process research, the mathematical models are usually discrete in states and continuous in time stochastic processes, in the set of which Markov models are included. The paper presents an example of using Markov processes with discrete time and with continuous time to assess the readiness of a technical object performing tasks appearing in random moments of time. At the same time, the aim of the examined system to achieve a state of balance is presented.

The evolution of changes in shopping in the modern society necessitates suppliers to seek new solutions consisting of increasing the efficiency of transport processes. When it comes to controlling the flow of goods in modern distribution networks, planning and timely deliveries are of particular importance. The first factor creating a competitive advantage involves the tendency to shorten order delivery times, especially for products with a short shelf life. Shorter delivery times, in turn, extend the period of effective residence of the product “available on the shelf”, increasing the likelihood of its sale. The second component in line with the Sustainable Development Strategy consists of aspects related to the protection of the natural environment, in particular those related to car transport. In this case, the fuel consumption and the level of emitted toxic substances (including carbon dioxide) are analyzed and assessed. Bearing in mind the above, this article presents the problem of optimizing the delivery time within the assumed distribution network and its solution, enabling the company to develop and optimal plan for the transport of products with a short shelf life. The paper proposes a model that takes into account minimization of the delivery time, while estimating the values of fuel consumption and CO2 emissions for the variants considered. The means of transport were medium-duty trucks. Three variants of the assumptions were considered, and algorithms implemented in MS Excel and MATLAB software were used to perform the optimization. Using the MATLAB environment, a more favorable value of the objective function was obtained for the variant without additional constraints. On the other hand, the algorithm implemented in MS Excel more effectively searched the set of acceptable solutions with a larger number of constraining conditions.

The article addressed road transport based on the proprietary numerical example. It is a typical optimization issue consisting in reducing the transportation costs between different drop-off locations. To determine the optimum transport plan, the following methods were used: North West Corner Method, Matrix Minima Method and Vogel’s Approximation Method (VAM).

The article discusses the issue of modelling traffic flows and the transport network. Faced with an increase in the number of vehicles in road networks, the problem of congestion and the need to optimise traffic and adapt the transport infrastructure to changing demand are growing, especially in large cities. With this in mind, the authors of this publication developed a model of the road network in the north-eastern part of the Warsaw agglomeration based on the proposed algorithm. Two methods were used to optimise the distribution of traffic flows: the Nash equilibrium and the Stackelberg approach. The Nash equilibrium assumes the aim of achieving equal average times on all roads for each origin–destination (O-D) pair. This describes the state pursued by a decentralised system guided by the individual benefits of the traffic users. On the contrary, the Stackelberg approach aims to achieve optimal travel times for the entire system. The study was carried out for three scenarios that differed in the assumed traffic demand on the road network. The basic scenario assumed the average hourly traffic demand during the morning peak hour based on traffic measurements. On the other hand, the two alternative scenarios were developed as a 10% variation in traffic volumes from the baseline scenario. On the basis of the results, it was concluded that an increase in traffic volumes for all O-D pairs could result in a decrease in traffic volumes on some links of the road network. This means that the transport network is a complex system and any change in parameters can cause significant and difficult to predict changes. Therefore, the proposed approach is useful in terms of traffic forecasting for road networks under conditions of changing traffic flow volumes. Additionally, the total travel time for the entire system differed for each scenario by a percentage difference of 0.67–1.07% between the optimal solution according to the Nash equilibrium and the Stackelberg approach.

The issue of minimisation of empty runs in transport, assumptions and calculation method were presented. The example of ineffective usage of transport means was described as well as a procedure algorithm for the optimisation of the above-mentioned issues using the Solver module.