Which way to send a truck to make its journey as fast and cheap as possible? The work of logistics company dispatchers will now be facilitated by advanced tracing software. Experts from the Institute of Mathematics of the Faculty of Mechanical Engineering of the Brno University of Technology cooperated on its development with the Brno company Wereldo.com, which intends to use the software commercially.

Currently, logistics companies need to purchase maps for route planning and, if there is a change, they have to update them. The most suitable route is chosen according to the number of kilometers and the experience of the dispatcher, who knows where to send the truck and where not, for example, because of a low underpass or a bridge with a low load capacity.

"Typical navigation is designed for drivers of passenger cars, none of them is going to tell you: Attention, truck transport is prohibited in this place," says Petr Vašík, director of the Institute of Mathematics and head of the research team. The new tracing software contains this information and takes it into account when planning the optimal route, as well as other parameters that are not taken into account by available applications: heights and weight limits of bridges and underpasses, elevations, road gradients or traffic data such as the number of traffic lights or detours.

"In addition, our software offers an interface in which the users can make updates themselves. We give dispatchers the opportunity to use the most valuable thing – their many years of experience. For example, if it snows and the dispatcher knows that this given hill is problematic in winter, he himself marks the "closure" and the software recalculates the route," adds Vašík.

The software plans the optimal route not according to the number of kilometers traveled, as has been customary so far, but according to the total cost of transport. The software takes into account not only distance, but also time, elevation and other parameters. "For example, we had to introduce penalization of some maneuvers: for example, if you turn left at a traffic light, you spend more time on it, the journey becomes longer and thus more expensive," says Ivan Eryganov, who worked on software development as a doctoral student of the Applied Mathematics program and is now an employee of the Institute of Mathematics.

We faced many mathematical challenges during the software development. For example, experts also dealt with so-called forbidden sequences, i.e. sections that are partially passable, but not as a whole. The challenge was also how to set up the system so that the software would not be slowed down by complex calculations. "We use a hierarchical data structure. At the very bottom, there are complete data with other data layers above them. If we were to recalculate the basic level after each partial change, the calculation would take two days and the software would be unusable in practice," explains Vašík. If a change occurs, for example by entering a new "road closure", the system itself can determine the depth of the impact and recalculates only the relevant part accordingly.

The tracing software will be beneficial not only for dispatchers, but also for the start-up Wereldo.com, which commissioned the development with Brno mathematicians. The company will not have to buy new maps with every change and thanks to this innovative software it can offer its customers even better services.

"Wereldo has benefited greatly from this collaboration. It's great to work with experts from the university on a real problem that our customers face in their daily business. We believe that we have managed to contribute to the shift in this industry and we look forward to further cooperation," says Wereldo.com co-founder Tomáš Zahradník.

The development of the software took two years, so far it is ready for use in logistics within the Czech Republic. The company Wereldo.com licensed the tracing software from the university for almost a million CZK. But the work of the team of mathematicians does not end there. "We will continue to work on the basis of real data to make optimization as effective as possible. We also expect to add other parameters to the system if necessary," concludes Vašík.

The project called Advanced tracing software for different types of trucks was financed by the Operational Programme Enterprise and Innovation for Competitiveness.