The travelling salesman problem (TSP) is one of combinatorial optimization problems of huge importance to practical applications. However, the TSP in its “pure” form may lack some essential issues for a decision maker—e.g., time-dependent travelling conditions. Among those shortcomings, there is also a lack of possibility of not visiting some nodes in the network—e.g., thanks to the existence of some more cost-efficient means of transportation. In this article, an extension of the TSP in which some nodes can be skipped at the cost of penalties for skipping those nodes is presented under a new name and in a new mathematical formulation. Such an extension can be applied as a model for transportation cost reduction due to the possibility of outsourcing deliveries to some nodes in a TSP route. An integer linear programming formulation of such a problem based on the Gavish–Graves-flow-based TSP formulation is introduced. This formulation makes it possible to solve the considered problem by using any integer linear programming optimization software. Numerical examples and opportunities for further research are presented.

Nanomaterials are a new group that has quickly found a wide range of applications in medicine, cosmetology, the food, weapons or automotive industry. They are also used as a fuel additive. This paper reviews the literature and assesses the current state of knowledge regarding the use of nanoparticles in automotive engine fuels. The results obtained so far are presented and further research directions in this field are identified.

Road accidents are affected by various factors, but many of them are not monitored and collected, and some of them are not even known. Important factors that are often overlooked in research are legislative issues and legal changes regulating road safety, which are the subject of the study in this article. As it is extremely difficult to prove a significant influence of these factors and, therefore, to demonstrate that the impact of legislative changes on the number of road accidents is significant, this variable was considered while analyzing the impact of other variables, which, in the authors' opinion, were the most important and, above all, known over the period in question. Day of the week, month, and year are selected. It was decided that other factors influencing the decreasing number of accidents would be included in the trend. With this assumption, the analysis of an additional variable that marks the periods of changes in legal regulations and the confirmation of its significant impact on the number of accidents will allow us to conclude that it is an important element shaping road safety.

Celem artykułu jest wskazanie różnic między ogólnodostępnym narzędziem prognozującym wykorzystywanym w planowaniu dostaw a dedykowanym, stworzonym specjalnie dla danej