the world can be found in (Zamparini, 2007; de Jong,
2009; Feo-Valero, 2011; Report for the Ministry of
Infrastructure and the Environment, Significance,
The Hague, 2013). The study (RAND Europe, SEO
and Veldkamp/NIPO, 2004) is one of the first to
present the value of freight transportation reliability
in the form of standard deviation of transportation
time. The key result in (Significance, VU University,
John Bates Services, TNO, NEA, TNS NIPO and
PanelClix, 2013) is that most of the empirical results
of freight reliability assessment are related to the
proportion of shipments that arrive too late
(sometimes with a minimum delay threshold).
The works (Hague Consulting Group, Rotterdam
Transport Centre and NIPO, 1992) discuss the use of
the factor cost method for the cost estimation of
transportation time. It is argued that the study of the
cost estimate of time for freight transportation is
necessary to determine the "marginal time
transportation costs": transportation costs that will
change as a result of changes in transportation time.
It is a derivative of the total logistics cost function of
transportation time. Total logistics costs are
comprised of transportation personnel costs, fuel and
energy costs, vehicle costs, overhead costs, which are
all costs incurred by carriers and transportation
companies, as well as costs of damage to goods,
interest costs on the value of goods during
transportation and the cost of having a safety reserve
(the last three factors directly affecting the
transportation component in the price of goods).
A number of authors consider the use of
mathematical models to assess the reliability of the
transport process and the creation, on their basis, of
appropriate modules in information management
systems. The use of methods to assess and ensure the
reliability of transportation based on business process
modeling is particularly important for increasing the
competitiveness of transport companies in unstable
economic conditions (Kurganov, 2018).
Studies have appeared recently in the field of
reliability of intermodal transportation, in particular
transportation with the use of railway-automotive and
railway-water transport. According to the goals stated
by many countries, by 2030 30% of freight transport
over 300 km should be transferred from road
transport to other, more environmentally friendly
modes of transport. Most importantly, this
assumption applies to rail transport and water
transport. Rail transport has the best chance of taking
over some of the freight traffic in the coming years.
Rail transport, like water transport, has much
more inertia (larger vehicles and ships used for
transportation, longer transportation times, etc.).
Goods transported by these modes of transport tend
to have a lower cost per tonne than goods transported
by road and air, therefore, the transport component in
the price of goods will be relatively small.
The development of rail transportation depends
on its ability to adapt to a number of market
requirements related to transportation time, cost,
flexibility, information flow and reliability of the
production process. Currently, the main obstacle to
development is its low competitiveness, especially in
relation to road transportation. This is mainly
influenced by low flexibility, limited cost-
effectiveness over long distances, and lack of
reliability, manifested mainly in problems with timely
transportation (Zhao, 2020). The bottleneck may be
an underdeveloped railway connection (Roso, 2013),
the low flexibility of rail transport (Behrends, 2015),
the low quality of railway infrastructure, the use of
different information systems, the reluctance to share
information (Kramarz, 2021), the higher priority of
passenger trains over freight trains, the lack of
integration between transportation tasks and terminal
tasks (Hu, 2019). Such limitations reduce the
reliability of the entire transport system.
Transportation services performed with such
restrictions will not be able to meet the requirements
of modern supply chains, which require a high degree
of flow reliability (Elbert, 2017).
3 MATERIALS AND METHODS
Carriers, operators and owners of railway rolling
stock estimate delivery time through the costs of
providing transportation services. If transportation
time were reduced, vehicles and personnel would be
freed up to perform other productive activities,
resulting in savings in vehicles and labor. Greater
reliability means that the carrier and operator can
have confidence when planning transportation. The
results of foreign researchers obtained to date show
that the value of time related to transport services is
indeed more or less equal to the cost of the vehicle
and labor per hour (de Jong, 2009).
For shippers, the valuation of transportation time
is directly related to the goods themselves. It includes
the working capital invested in the goods during the
time required for transportation (especially important
for high-value goods), the potential reduction in value
of perishable goods during transportation, and the
possibility of disruption of the production process due
to lack of resources or inability to deliver due to lack
of inventory. The two latter factors play a significant
role in assessing the reliability of freight