Article
citation information:
Shramenko, N., Merkisz-Guranowska, A., Trojanowska,
J., Antosz, K., Trojanowski, P., Shramenko,
V. Model of optimization of the parameters of the delivery process in
international traffic. Scientific Journal
of Silesian University of Technology. Series Transport. 2025, 126, 221-235. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2025.126.14.
Natalya SHRAMENKO[1], Agnieszka MERKISZ-GURANOWSKA[2], Justyna TROJANOWSKA[3], Katarzyna ANTOSZ[4],
Piotr TROJANOWSKI[5], Vladyslav SHRAMENKO[6]
MODEL
OF OPTIMIZATION OF THE PARAMETERS OF THE DELIVERY PROCESS IN INTERNATIONAL
TRAFFIC
Summary. The efficiency of
border crossing services depends on a number of parameters, including the scope
of control activities, the number of vehicles to be serviced and the human
resources involved. The paper presents the mathematical model allowing the
optimization of service parameters at the border crossing point. The queuing
theory was implemented due to unbalanced nature of processes. Scientific
interest of the model relates to the optimization of the parameters in
international goods delivery under the conditions of random nature of vehicles
arrival, and with the uneven intensity of servicing vehicles by state
administrative services at the crossing border. The model takes into account
the trade-off between the number of border staff and vehicle handling time. As
a result of the application of the model, the handling process at the
border crossing can be optimized, which will lead to a reduction of delivery
costs in international traffic.
Keywords: simulation model, process parameters,
international freight, border crossing
1. INTRODUCTION
The rapid economic development of countries,
together with the integration process in Europe, is leading to an
intensification of international relations and an increase in the volume of
trade and, as a result, to an increase in the volume of goods, which is
contributing to the development of the transport sector. Transport has a
prominent place in the implementation of trade agreements. Its poor
organization can lead to negative effects on the trade transaction execution.
An incorrect choice of transport, route, packing, and transportation mode can
reduce the quality of the services. The result of deficiencies and mistakes is
the deterioration of the company's image. The combination of the low level of
organization of the delivery of goods raises doubts in the international
community as to the appropriateness of using the services of the carriers of a
given country, and after all, contributes to the decline in the transport
sector's revenues.
In arranging the delivery of goods, consignors,
intermediaries, freight forwarders, carriers, customs officers, insurers, and
representatives of other organizations enter into complex relationships, which
are determined by economic processes, environmental, political and social
factors. In such a constantly changing environment, with a high level of
competition in the transport services market, it is necessary to search for
rational transport routes [1], appropriate technological delivery schemes [2],
introduce innovative forms and methods of organization of the transport
process, and improve existing and develop new promising transport technologies.
The solution of complex tasks requires constant study of issues of ensuring,
regulating, and improving the delivery of goods.
2. LITERATURE REVIEW
The efficient operation of the
logistics system is crucial for various industries and has a direct impact on
the economic development of society [3]. Supply chains are formed with the aim
of reducing shipping costs, reducing transport time and improving the
efficiency of the logistics system in the long term.
In [4] it was stated that the
functioning of the logistics system in a dynamic environment is related to many
problematic situations.
In today's global market,
competition is not between companies, but between supply chains. The best
supply chain is determined by comparing supply chain performance indicators.
The most efficient supply chains operate over a long period of time. The
efficiency of the supply chain is influenced by various internal and external
factors. The optimal selection of the parameters of these factors increases the
efficiency of the supply chain [5].
At present, the increasing
importance of energy issues, rational use of resources and sustainable
development offer great opportunities for the formation of the supply chain. An
optimal supply chain structure is vital to the success of the industry now more
than ever [6].
Supply chain management uses various
optimization techniques to improve the efficiency of the process. To optimize
supply chain networks, mathematical modeling [7], simulation modeling [8], as
well as stochastic optimization [9] can be applied.
Supply chain costs constitute a
significant proportion of the cost of the final product. Therefore, it is
necessary to minimize the costs of the supply chain, which will increase the
efficiency of the delivery process and will contribute to higher profits. At
the same time, supply chain operations are random in nature, which affects
their execution time and, in general, costs. This necessitates the optimization
of supply chain parameters. In turn, the minimization of supply chain
costs will make it possible to form compromise technological solutions at all
stages of the goods delivery process.
The values of technological
parameters of the supply chain affect its effectiveness in the process of
managing the movement of goods between individual links in the chain [10].
These parameters can be taken into account in the mathematical model as
decision variables to determine their best combination in the optimization
process.
Researchers [11] consider the
problem of supply chain design, which is solved using a linear programming
model with mixed integers. The model optimizes various demand scenarios, and
the results obtained are important for designing a supply chain with stochastic
parameters. Thus, when designing a supply chain, it is necessary to assess the
changing demand for products and take consider stochastic parameters.
To solve the problem of optimal
supply chain management, a methodology based on reliable optimization under the
condition of stochastic demand in discrete time is proposed [12]. The proposed
approach includes a wide range of phenomena and requirements, and also takes
into account the capacity of echelons and links.
In [13], a predictive stochastic
gradient method was proposed to improve the efficiency of supply chain
management. In DOI:ng so,
the focus is on developing an efficient multi-stage supply chain using factors
such as cost, time, and risk.
In developing mathematical models
that describe the state of the transport market, a logistics approach is
needed, based on a clear interaction of demand, supply, production, transport,
and distribution of products to achieve the greatest effect [14].
The essence of the logistics concept
is the development of a system for the management of material [15,16] and related information [17], based on logistical
principles and methods [18].
High efficiency in the use of
methods and models in logistics will be achieved if several conditions are met,
among which [19,20]:
-
systemic approach to the problem at hand,
-
scientific validity of the approaches and
models themselves,
-
adequacy of models for the real system,
the objective consideration of subsystem interrelationships,
-
continuity of the model implementation
process.
The reliability of the logistics
system is largely determined by the smooth operation of the transport network
and infrastructure [21-23]. The efficiency of technically sound transport
services depends mainly on the level of organization and management [24,25]. Road transport management is aimed at facilitating the
delivery of goods by road from suppliers to customers, as well as reducing
freight costs and increasing profits.
In the conditions of development of
Industry 4.0 introduction and use of informational, digital and innovative
intelligent technologies in modern transport systems and supply chains is
necessary [26,27].
The results of the research [28]
demonstrated that several enabling technologies such as wireless communication
technology, sensors, positioning technology, and web-based platforms are widely
used in international freight transport.
The process of organizing the
delivery of cargo "just in time" requires a quantitative assessment
of the transportation process and its components.
Thus, efficient supply chain
management is able to ensure permanent competitive advantages of international
transportation. Ensuring effective management of supply chains determines the
need to create new models of optimization of logistics operations and the
organization of interaction and partnership in all links of the logistics
system. At the same time, the stochasticity of certain technological processes,
the random nature of the demand for transport services and the dynamism of the
external environment should be taken into account.
3. PROBLEM STATEMENT
The purpose of this
publication is to select rational technological parameters of the logistic
chain of delivery of goods to improve its functioning. The solution to this problem
will be to minimize the cost of delivering goods in international trade, taking
into account the factor of delivery of goods "exactly on time".
The crossing point
is a complex system consisting of separate elements (subsystems), each of which
performs certain functions in the technological process of crossing the state
border.
The permit
technology determines the types, sequence, content of control operations, and
the procedure for the passage of persons, vehicles, goods, and other property
across the border.
The mathematical
model of goods supply in international traffic takes into account the
specificity of European Union Eastern border, namely Ukrainian border crossing
point, but it can also be used to optimize the functioning of other nodes in the
international traffic.
4. SELECTION OF TECHNOLOGICAL PARAMETERS OF THE
DISTRIBUTION CHANNELS IN INTERNATIONAL TRAFFIC
Crossing the border by people,
vehicles and cargo across the border between Poland and Ukraine is carried out
after border and customs control, and, in appropriate cases, also sanitary,
environmental, veterinary or phytosanitary control or
control related to the export of cultural property from the territory of
Ukraine.
For a system as unbalanced as a
border crossing point, the queuing theory apparatus was applied.
The queuing system makes it possible
to assess the quality of the service system’s functioning under the conditions
of service queues and the uneven nature of the service itself, and will allow
for better management of the processes at the crossing point.
This makes it possible to determine
the optimum value of the performance characteristics of the service system.
The main elements of a queuing
system are as follows:
-
structural indicator of the class and type
of queuing system,
-
traffic flow at the crossing point,
-
service flow.
The functioning of any queuing
system can be represented through all possible states and the intensity of
transition from one state to another. The basic parameters of the operation of
a queuing system are the probability of its condition, i.e., the
possibility of a request in the system –
The intensity of one request is also
an important parameter for the operation of a queuing system
To study the structure of the input
flow of primary statistics, the random time interval between two vehicle
arrivals at a crossing point is considered. The random nature of the input
results in a queue at some points at the input to the system.
In this case, the rate of service
requests is defined as the inverse value of the time interval between incoming vehicles
Service intensity is defined as the
inverse value of the processing time for a single request
After conducting statistical surveys
(the sample size is 500 values), it is determined that the input flow of
vehicles is distributed according to the indicative law.
Given the lack of analytical
dependencies for this type of queuing system, a corresponding graph model of a
three-phase queuing system has been developed.
The Kolmogorov system of equations
defines a quadratic matrix. Changing one of the equations to a normalization
condition
A mathematical model of the choice
of rational technological parameters in international traffic has been
developed as a result of the analysis of the delivery technology in international
traffic and the studies carried out.
The mathematical model is as
follows:
where
The model has two constraints:
1. Carrying capacity of vehicle of
20 t.
2. The limitation system generic
parameter is:
where
where
The loading time shall be determined
as follows:
The time taken to reach the Ukrainian
border is calculated as follows:
The time for crossing the state
border is determined by the formula 16.
Time to destination:
Thus, the mathematical model allows
finding optimal technological parameters of the logistic chain of delivery of
goods in international traffic, namely:
-
costs of the entire international supply
chain R,
-
intensity of service at customs control
-
intensity of service during border control
-
intensity of service during other types of
state control
Through probabilities, the following
calculation parameters can be derived from a queuing system, allowing a more
detailed analysis of the functioning of the logistics chain.
Relative throughput is defined by:
Absolute bandwidth:
The average number of vehicles in
the queue:
The average downtime of the first
phase, i.e., downtime at customs control:
The average downtime of the second
phase, i.e., the downtime during border control, is determined by the formula:
The average downtime of the third
phase, i.e., downtime in other types of state control, is determined by the
formula:
Average waiting time for the
maintenance of one vehicle:
The total time spent by the vehicle
in the system:
5. RESULTS OF MODEL IMPLEMENTATION
The proposed model was implemented
for a border crossing point between Poland and Ukraine.
The considered checkpoint is
classified within the mass service theory as follows:
-
nature of receipt of requests –
stationary,
-
number of requests received at a certain
point in time – ordinary,
-
connections between requirements – without
consequences,
-
behavior of requirements – with unlimited
waiting,
-
method of selecting service requirements –
random,
-
nature of service requirements – random
service time,
-
number of service channels – one channel,
-
number of service stages – three-phase,
-
in terms of the homogeneity of the input
stream of vehicles arriving at the border crossing – non-homogeneous,
-
open system regarding the limitation of
the flow of requirements.
To study the structure of the
incoming flow of vehicles at the border crossing between Ukraine and Poland,
the primary statistic is a random time interval between two arrivals of
vehicles at the checkpoint. The random nature of the receipt leads to the fact
that at certain moments a queue is formed at the entrance of the system.
With equal significance, the
hypothesis that the continuous random variable is distributed according to the
exponential law is verified. The sample size is 500 observations.
The estimate of the parameter of the
admissible exponential law is determined:
Thus, the differential function of
the admissible exponential distribution law is as follows:
Empirical and theoretical
frequencies were compared using the
Thus, as a result of the processing
of statistical data on the intensity of the arrival of vehicles at the border
crossing, the parameters of the distribution law of this random variable were
obtained:
-
mathematical expectation
-
intensity of the incoming flow of vehicles
per hour
-
root-mean-square deviation
-
coefficient of variation
The results of field studies were
analyzed, and it was established that the incoming flow of vehicles at the
border crossing of Ukraine is distributed according to an exponential law.
In the simulation, the following
values of vehicle service intensities at the border crossing were adopted:
-
service intensity during customs control
-
service intensity during border control
-
service intensity during other types of
state control
The vehicle capacity of 20 tons is
accepted for the consignment. The production capacity of the consignor is 3000
tons/year. The vehicle is loaded at the consignor. The productivity of loading
and unloading is 5 tons/ hour.
As the result of model
implementation, the technological parameters of the border crossing of Ukraine
were determined. With a given incoming flow of vehicles of 1,92 vehicles/hour,
the optimal service intensity at the customs point is of 0,255
vehicles/hour, optimal service intensity at the border crossing point is 0,215
vehicles/hour and optimal service intensity when performing other types of
control is 0,2 vehicles/hour.
Simulations allowed to obtain the dependence
of total costs on certain technological parameters. Examples of dependencies
are shown in Figures 1-3.
Fig. 1. Dependence of total costs on
the ratio of the intensity of the incoming flow to the intensity of
servicing vehicles during customs control
The obtained dependencies of total costs on the ratio of the intensity
of the incoming flow of vehicles to the intensity of their maintenance during
border control are shown in Figure 2. With very small values of the ratio of
the intensity of the incoming flow of vehicles to the intensity of servicing
vehicles at the customs point, the total costs are very high, and when passing
some minimum values, with an increase in this ratio, the costs also increase.
Thus, the total costs increase with an increase in the intensity of the
incoming flow and decrease with an increase in the intensity of servicing
vehicles during border control. At the same time, certain values of the
intensity of the incoming flow of vehicles are characterized by certain optimal
values of the intensity of their service when passing border control.
The obtained dependencies of total costs on the ratio of the intensity
of the incoming flow of vehicles to the intensity of their service when passing
other types of control (sanitary, environmental, veterinary, phytosanitary
control, control over the export of cultural property from the territory of
Ukraine, other state types of control) are shown in Figure 3. Dependencies
indicate the presence of optimal values of service intensities when passing
other types of control for the corresponding intensities of the incoming flow
of vehicles.
Fig. 2. Dependence of total costs on
the ratio of the intensity of the incoming flow to the intensity of
vehicle maintenance during border control
The dependence of the absolute throughput on the ratio of the intensity
of the incoming flow to the intensity of service at the customs point was
obtained (Figure 4). With the increase in the intensity of service at the
customs point, the throughput of the checkpoint through the state border
increases.
Based on the analysis and evaluation of the simulation results, the
following recommendations can be made:
- in order
to increase the efficiency of the process of cargo delivery in international
traffic, a close relationship between individual links and coordinated
actions in the links of the logistics
chain are necessary, which will not only reduce costs, but also the waiting
time and excessive downtime of vehicles in the nodes,
- at the
crossing point across the state border of Ukraine, taking into account the
intensity of the incoming flow of vehicles, it is necessary to adjust the
intensity of vehicle servicing by the relevant services (customs, border,
sanitary, environmental, veterinary, phytosanitary control, control related to
the export of cultural property from the territory of Ukraine), which will lead
to the minimization of total costs. For this purpose, it is necessary to change
the number of personnel in service teams depending on the value of the optimal
intensity.
Fig. 3. Dependence of total costs on the ratio of the intensity of the
incoming flow to the intensity of service during other types of control
(sanitary, environmental, veterinary, phytosanitary control, control related to
the export of cultural property from the territory of Ukraine)
Fig. 4. Dependence of the absolute capacity on the ratio of the intensity
of the incoming flow to the intensity of service during
customs control
6. CONCLUSIONS AND PROSPECTS FOR FURTHER
RESEARCH
Based on the analysis of the
delivery technology in international traffic and the statistical processing of
field research data, a mathematical model was developed, based on a systematic
approach and taking into account the costs in the logistics chain of delivery
of goods in international traffic.
The scientific interest of the
presented model is the optimization of the technological parameters of the goods
delivery in international traffic under the conditions of the random nature of
the vehicles’ arrival at the border crossing, and with the uneven intensity of
servicing vehicles by the state administrative services.
The analytical correlation of time
spent by vehicles on waiting for servicing and servicing itself at a crossing
point is obtained by applying the queuing theory.
As a result of the application of
the mathematical model, the handling process at the border crossing can be
optimized, which will lead to a reduction of delivery costs in international
traffic. The model takes into account the trade-off between the number of
border staff and vehicle handling time.
The model was implemented on the
example of the border crossing between Poland and Ukraine. The optimal values
of the parameters were obtained: intensity of service at the customs
checkpoint, intensity of service at the border crossing and intensity of
service by other services.
Performed simulations allowed to
identify dependencies that enable to assess the nature of changes in costs and
technological parameters depending on the intensity of the incoming flow of
vehicles and the intensity of vehicles servicing by various administrative
services at the border crossing point.
The presented mathematical model of
goods supply in international traffic allows optimization of service parameters
at the border crossing point, but it can also be used to optimize the
functioning of other nodes in the logistic chain of goods supply.
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Received 03.06.2024; accepted in revised form 05.09.2024
Scientific
Journal of Silesian University of Technology. Series Transport is licensed
under a Creative Commons Attribution 4.0 International License
[1] Lviv Polytechnic National University,
Department of Transport Technology, Stepana Bandery Street, 12, 79000 Lviv,
Ukraine. Email: nshramenko@gmail.com. ORCID: https://orcid.org/0000-0003-4101-433X
[2] Poznan University of Technology, Faculty of Civil and Transport Engineering, pl. M. Sklodowskiej-Curie 5, 60-965 Poznan, Poland. Email: agnieszka.merkisz-guranowska@put.poznan.pl. ORCID: https://orcid.org/0000-0003-2039-1806
[3] Poznan University of Technology,
Faculty of Mechanical Engineering, pl. M. Sklodowskiej-Curie
5, 60-965 Poznan, Poland. Email:
justyna.trojanowska@put.poznan.pl. ORCID: https://orcid.org/0000-0001-5598-3807
[4] Rzeszow University
of Technology, Faculty of Mechanical Engineering and Aeronautics, al. Powstańców Warszawy 12, 35-959 Rzeszow,
Poland. Email: katarzyna.antosz@prz.edu.pl. ORCID:
https://orcid.org/0000-0001-6048-5220
[5] West Pomeranian
University of Technology in Szczecin, Faculty of Maritime Technology and Transport, al.
Piastów 17,
70-310 Szczecin, Poland. Email:
piotr.trojanowski@zut.edu.pl. ORCID: https://orcid.org/0000-0001-8869-0656
[6] Baden-Württemberg
Institute of Sustainable Mobility, Hochschule Karlsruhe
University of Applied Sciences, Moltkestraße, 30,
76133 Karlsruhe, Germany. Email: vladyslav.shramenko@bw-im.de. ORCID: https://orcid.org/0000-0002-3551-6942