Article citation information:
Matyja, T.,
Stanik, Z., Włodkowski, K. A method of generating customer requests in a
car rental simulation model. Scientific Journal of Silesian
University of Technology. Series Transport. 2024, 123, 191-208. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2024.123.9.
Tomasz MATYJA[1],
Zbigniew STANIK[2],
Krzysztof WŁODKOWSKI[3]
A METHOD OF GENERATING CUSTOMER REQUESTS IN A CAR RENTAL SIMULATION
MODEL
Summary. Optimization
of business processes and policies in a car rental company is an ongoing topic.
Especially that each of these companies operates in slightly different local
conditions and external environments. Testing new optimization algorithms is
best done with simulation methods. A comprehensive rental simulation model can
be built, for example, using the SimEvents library of the Matlab/Simulink
environment. The paper focuses on the problem of preparing a sequence of
customer requests in the short-term car rental system, necessary to carry out
simulations in the SimeEvents environment. It was assumed that these data may
come from the real world, or they may also be artificial data. A method of
generating artificial sequences of customer requests and the structure of input
data necessary to carry out this process have been proposed. The use of machine
learning to build models that transform real data in such a way that it can be
randomized was also tested.
Keywords: short-term
car rental, client’s requests, machine learning, SimEvents
1.
INTRODUCTION
Car
rental companies can operate according to different business models [14]. Most
often, a registered customer orders the service via the company's website or
the application on the phone. The vehicle is released at one of the company's
stations (offices), or, if there is such an option, the vehicle is delivered to
the indicated address. The return of the vehicle can take place at the same
station (two-way, round trip), at another station (one-way trip), or at the
address indicated. In the case of car sharing, it is frequently possible to
leave the vehicle anywhere (free-floating car sharing) [6].
In
connection with the activities of car rental companies, there are many
interesting logistical and decision-making problems. A significant issue is
making decisions about accepting or rejecting vehicle bookings to ensure
maximum use of the fleet and customer satisfaction. The most popular and
frequently researched concern in the literature is the problem of optimal
relocation of vehicles [14]. Vehicle relocation aims to balance the demand and
supply of cars in a specific location. Relocation can be based on the operator,
then it is carried out by the rental staff. Another way is relocation based on
users, encouraged to do so by proposed discounts or clients, who are
appropriately selected at the stage of the decision to accept a reservation.
Another problem is maintaining the size of the vehicle fleet that is optimal
for the current needs. Supplementing it by purchasing new cars from
manufacturers (“fleeting”) or resale of cars after a certain period
of use (“de-fleeting”) [8].
Simulation
research allows for the search for new algorithms for the functioning of the
vehicle rental system in order to increase the efficiency of processes [12, 13].
The problem of relocation is most often considered as a flow optimization
issue. Among other things, a mathematical programming-oriented approach and a
simple linear model based on integer flow variables [2], time expanded network
(time-space network) [4, 5], Petri nets [3] are used. Models based on event
simulations [9] are suitable for simulating the processes taking place in a car
rental company.
In
the future, the authors plan to develop a simulation model representing the
functioning of car rental companies, using event-driven simulation technology.
This model would enable testing of various sales policies, algorithms
optimizing customer and vehicle flows, algorithms for making short-term
decisions, e.g., in the field of vehicle relocation, as well as other processes
occurring in this type of enterprise.
The
article focuses on the issue of developing a rental customer request generator
that could be implemented in a rental model built using the SimEvents library
of the Matlab/Simulink environment [11]. Such a generator is one of the most
important elements of the car rental modelling system. At the stage of
designing the generator, it is necessary to formulate basic assumptions
regarding the functioning of the rental company and to decide on the data
structure describing a typical customer request.
Simulations
always require input. The correctness of the results depends on their quality,
and therefore, such data should be objective and reliable. Real-world data is
the most desirable, but it is usually difficult to obtain. Real data in some
cases may be biased. The disadvantage of real data is also that they are static
(deterministic), i.e., they do not change. Statistical analysis of real data
allows detecting trends and estimators of parameters necessary to generate
artificial data, e.g., parameters of probability distributions. Based on the
statistical analysis of real data, an artificial data generator can be built.
Such data will be similar to real data, but at the same time, will not be
identical to it. Artificial data can also be random. Data artificially
generated based solely on arbitrary assumptions and estimates, without a
thorough analysis of real data, may be unreliable.
In
the work, an analysis of real-world data obtained from a company dealing with
short and medium-term vehicle rental was carried out. On this basis, a scalable
method for generating artificial data was proposed. In addition, the
possibility of using machine learning to generate such data was tested. In
accordance with the idea suggested in paper [1], the following were used:
Gaussian mixture model to generate the times of customer notification, start of
vehicle rental, vehicle return; a model of a binary classification tree to
generate vehicle delivery and return stations.
2.
CUSTOMER REQUEST GENERATOR
2.1.
The general idea of a vehicle rental simulation model
It
is assumed that the company deals in the short-term rental of passenger
vehicles (RAC) for a period of 1 to 30 days. The minimum rental time is one
day. This type of car rental is more interesting than medium-term rental (MTR)
because there is a higher turnover of cars and the likelihood of relocation is
increased. The presented model of the customer request generator can be easily
scaled and adapted to the needs of simulating car rental by the hour in car
sharing systems.
The
company has N stationary stations (offices) where clients can rent and return a
vehicle, located in a specific area. The customer can rent a vehicle at one of
the rental points and then return it at any point (two-way or one-way trip mode
is allowed). If necessary, it is also possible to simulate cases where the
vehicle is delivered or picked up at any location specified by the customer
(free-floating car sharing). Such a virtual station may have a number equal to
zero. The location of all stations as well as locations indicated by the
customer can be described using GPS coordinates.
Client service system Client generation system Reservation system accept Waiting for the rental start Car booking system reject Customer request generator FIFO queue of requests Archiving for later analysis Booking system decision
Fig. 1. Simplified schematic diagram of the rental model
One
day was assumed as the basic unit of time in the model. A day does not have to
be interpreted as the equivalent of 24 hours, it is rather a part of a day - a
working day, corresponding to the opening hours of the rental stations. The
occurrence of each event during the day is described by a fraction of a day.
This allows timing the customer requests and other events that may occur during
the simulation.
The
schematic diagram of the car rental model is shown in Fig.1. The subject of
interest is the subsystem that generates customer requests. An important role
in the model will also be played by the booking subsystem and the customer
service subsystem, which must also include other subsystems, e.g., a subsystem
simulating the use of a car by the customer.
When
booking a vehicle, the customer specifies the start and end date of the rental,
the starting, and ending station and chooses the class of the vehicle.
Optionally, it also provides location coordinates when picking up or returning
a vehicle outside stationary stations.
Car
rental companies offer their customers vehicles in various categories of size
and equipment. They usually use SIPP codes (Standard Interline Passenger
Procedure) so customers can easily compare different models of vehicles. SIPP
or ACRISS (Association of Car Rental Industry Systems Standards) car
classification is a 4-letter code, in which: the 1st character denotes the
vehicle category (size, luxury factor); the 2nd character defines the vehicle
chassis type; the 3rd character defines the transmission and drive; the 4th
character defines the fuel and whether the car has air conditioning or not.
From the customers' perspective, the most important thing is the size of the
car, i.e., how many passengers and how much luggage can be accommodated. The
European fleet is divided into the following categories: mini, economy,
compact, intermediate, standard, full-size, premium, luxury. In each of them,
an additional elite subcategory can be distinguished (e.g., compact elite). The
term elite has been selected by ACRISS to identify a category of vehicle that
is superior to another of equal body size. There is one more category: special.
In total, there will be 17 categories of car sizes [15]. Companies can freely
limit the range of vehicles available to customers, or extend it to a selection
of other car parameters, including even specific brands and models [10]. For
this reason, a variable parameter defining the number of available vehicle
types should be included in the simulation.
2.1. Generator data structures
The
SimEvents library has been equipped with the ability to dynamically generate
events based on assumed probability distributions, for example, exponential
distribution appropriate for customer requests. According to the authors, this
method may not be sufficient if it has considered the volatility of demand for
services over time and the existing trends. For this reason, it was decided to
use the simplest solution consisting in preparing a sequence of customer's
requests in advance, before starting the simulation. This will enable the
simulation to incorporate both real and artificially generated data.
Based
on the general idea of the car rental model described above, the minimum set of
data describing the application of one customer in the form of a vector can be
determined:
|
|
|
(1) |
where:
If
the vehicle is to be delivered to the customer at the address provided, the
data should be supplemented with information about the location of the pick-up
point (when S=0) and/or return of the vehicle (when E=0). These can be, for
example, GPS coordinates in the format
If
historical data are available, there are no obstacles to determining a sequence
of customer requests on their basis, which can be implemented in a model made
in the SimEvents environment.
If the data is to be
generated artificially, it was assumed that the most important factor is the
rental start time, and that it must be generated first.
Then
the request time is generated. It was assumed that the interval between the
request and the start of the rental will have an exponential distribution with
a mean
The
selection of the rental starting point is made randomly based on an arbitrarily
assumed probability distribution:
|
|
|
(2) |
In
the case of generating the end station, we have to deal with conditional
probability. To describe the density of this probability, a square matrix was
arbitrarily selected. The elements of this matrix determine the probability of
choosing the end station number j provided that the starting station was:
|
|
|
(3) |
It
was assumed that the
Exactly
on the same principle, a vector describing the distribution of the probability
density of the vehicle class selection
Generating
location GPS coordinates can be solved in different ways. The easiest way is to
define the boundary ranges of coordinates in the area of operation of the car
rental company and determine the GPS coordinates by two random numbers from a
uniform distribution. Another possibility is to arbitrarily create a
two-dimensional Gaussian mixture model with the components concentrated around
the locations of stationary stations, and randomize locations using this
distribution.
3.
REAL-WORLD DATABASE ANALYSIS
Real-world
data were obtained from a company that conducts both short-term rental (RAC)
and medium-term rental (MTR), lasting from one month to two years. For this
reason, these data are not fully representative of the simulation model being
prepared. However, some regularities can be observed on their basis, which were
then used to prepare the artificial data generator.
The
actual data were properly processed and filtered. Datetime fields were
converted to the time unit assumed in the simulation - one day. The data were
sorted chronologically according to the start time of the reservation. In a few
cases, records with missing information were rejected or corrected.
Fig. 2. Schedule of customer requests, start, and end of rental
|
Fig. 3. Intervals between successive rental start
times |
|
Fig.
2 shows the time distribution of customer requests, rental start and end times.
According to the assumptions of the model, the basis is the booking start time
line (black). Around this line are the booking request time (red line) and
booking end time (blue line). The selected fragment of the graph is shown enlarged.
It is visible that the company allows to book cars even several months in
advance. In the initial phase, most of the notifications concerned medium-term
rentals. Later, both short-term and medium-term rentals were serviced.
Intervals between successive rental start events are shown in Fig. 3. At the
beginning, they are even several days long, then these times shorten
significantly below the value of 0.5 of the contractual working day. The daily
demand for vehicles shows seasonality with a clear upward trend (Fig. 4).
Refusals to accept vehicle reservations accounted for slightly more than 6% of
all applications.
Interestingly,
customers most often chose Monday as the vehicle release day and Friday as the
return day (Fig. 5). For short-term rentals, the most likely rental duration
was 5 days. The company rents a lot of vehicles on a medium-term basis (Fig. 6).
The company provided several stations where the customer can rent or return a
car.
|
Fig. 5. Vehicle rental and return probabilities by
day of the week |
|
Fig.
7 shows how the number of vehicles rented in individual company offices was
distributed, and similarly the number of vehicles returned. The matrix of
conditional probability distributions of returned cars is graphically presented
in Fig. 8. Only a small percentage of customers dropped off the vehicle at a
different office than they picked it up. For this reason, the probability
values on the diagonal are dominant.
|
Fig. 7. Number of vehicles borrowed (probability
distribution) and returned by rental office number |
Fig. 8. Probability distributions of returning the
car to a specific office provided it was rented from this or another office |
The
last analysed issue was the structure of the fleet of cars chosen by customers.
The company uses the ACRISS classification. Based on the classification code,
the histogram shown in Fig. 9 was created. Then, the percentage share in the
rental of individual types of cars was calculated. The largest group are
vehicles in the compact class (Fig. 10).
|
Fig. 9. Number of vehicles by classification code |
|
4.
ARTIFICIAL DATA GENERATOR
Since the obtained real data turned out to be insufficient,
an attempt was made to generate artificial data, assuming that the vehicles are
rented for a short time. The starting day was January 1, 2023 (important due to
the later calculation of the days of the week). The time horizon was set at two
years (730 days). Efforts were made to reproduce the regularities noticed
during the analysis of real data as best as possible.
|
Fig.
11. Generated number of cars per day |
Fig.
12. Daily averaged interval between clients |
As mentioned earlier, it is best to
begin generating the start of the rental times. It can be difficult to directly
determine the sequence that describes rental start times. Therefore, first, the
number of vehicles to be rented each day was generated. The appropriate data
series were obtained by adding together four time series: trend, weekend cycle,
seasonality, and noise.
It was assumed that the trend
will be modeled by a polynomial of the type
Finally, the data series obtained
is overwritten, at selected points of the timeline, with arbitrarily adopted
values - holiday impacts. If negative values occur in the series as a result of
the addition operations, they are reset to zero.
The results of generating the
number of vehicles for each day are shown in Fig. 11. The reciprocal of the
number of vehicles allows determining the average daily interval between
customers (Fig. 12). If the number of vehicles is zero, then the interval is
infinite. This case is marked with a red asterisk in the figure.
In the next step of the method,
for each day, based on the average daily interval between customers, customer
requests are generated using exponential distribution. The first interval
obtained in this way is randomly shortened - the event moves closer to the
beginning of the day. Subsequent intervals are generated until the sum of all
of them exceeds the time of one day. The last interval is discarded because it
corresponds to an event that would occur on the following day. In this way, a
sequence of intervals between successive customer notifications is created,
which allows the generation of rental start events throughout the expected time
of the simulation, i.e., up to the 730th day. Intervals generated in this way are shown in Fig. 13.
Fig. 13. Intervals between successive rental starts
The cumulative sum of the intervals determines the
occurrence of successive rental start events on the time axis. By subtracting
the randomly generated intervals between the start and request, the request
time is obtained. Similarly, by adding the length of the rental time, the
rental end time was calculated. It was assumed that the mean value of the
intervals between the request and the start of the rental is
Fig. 14. The time of the events: request, start and
end of the rental
|
Fig.
15. Pdf for start station |
Fig.
16. Pdf matrix for end station |
|
|
|
Fig.
17. The results of random selection the starting station;
on the left – cumulated; on the right – distribution over time
Generating further customer request data (the place of
rental start and rental end) requires arbitrary determination of the density
probability for the starting point and the matrix of conditional probabilities
for the rental end point. In the case of the starting point, it was assumed
that the probability values change every 90 days (Fig. 15). In the case of the
rental end point, one density probability matrix graphically shown in Fig. 16
was used. It was assumed that a two-way rental was the most likely. The results
of the starting point randomization are shown in Fig. 17. The results of the
randomization of the rental termination points based on the probability density
(Fig. 16) are shown in Fig. 18. The bars in Fig. 16 and Fig. 18 are not
identical, but very similar.
Fig. 18. The results of random selection the end
station (transformed to probability density)
Generating the type of vehicle selected by the
customer during the booking is done in the same way as above, using an
arbitrarily selected probability distribution.
Fig. 19. Results of random selection of the
locations outside stationary stations
In order to generate artificial
locations indicated by customers, a nine-component bivariate Gaussian mixture
distribution with equal mixing proportions was prepared. The mean values of the
distributions were the GPS coordinates of stationary car rental stations. It
was assumed that the radius served by the station with numbers 2,6,7,8 was 0.5
degrees of latitude (just over 50 km), while for the remaining stations it was
only 0.3 degrees. This was taken into account by specifying the values of the
elements of the covariance matrix, which was diagonal.
Fig. 19 shows stationary station
placement (red circles), the probability distributions function of location
selection, and randomly generated locations. This method of generating
locations has an advantage over randomization from uniform distributions
because it considers customer behaviour. Customers are aware that their order
will be rejected if they choose a location too far from existing stationary
stations.
5.
GAUSSIAN MIXTURE MODEL
In the search for tools for prediction and possible
forecasting of data for the car rental simulation model, mathematical models
dedicated to time series and machine learning models were tested. Analyzing
real data, e.g., daily demand for vehicles based on customer request (Fig. 4)
or adequate artificial data (Fig. 11), it can be seen that these are time
series having such features as trend and seasonality. Unfortunately, it was not
possible to obtain satisfactory results using SARIMA (Seasonal Auto Regressive
Integrated Moving Average) econometric models [7]. The residual errors of the
tested models were too large for both real and artificial data.
Based on work [1], a Gaussian mixture model (GMM) was
used to predict times (
Fig. 20. Event times from GMM
On the basis of the trained GMM
model with the use of artificial data, values of time events were then randomly
generated. Not all values generated in this way met the imposed constraints
The generation results are shown
in Fig. 20. For comparison, the original time course of the rental start times
has also been plotted. It is apparent that the GMM data have slightly different
forms than the original data. This may adversely affect the preservation of
trend and seasonality features present in the original data. The consequences
of selecting a shorter or longer data sequence than the original data are
explained in Fig. 21. Then the number of events in the analysed period changes.
At the same time, the GMM is quite stable even though the generated data
sequences are slightly different (Fig. 22). This feature can be used to test
the sensitivity of the simulation model to input data.
|
Fig.
21. Influence of the data series length |
Fig.
22. Several series of data randomly selected from the GMM |
|
Fig.
23. Intervals between customers |
Fig.
24. Vehicles per day |
Based on the start times generated from the GMM,
graphs of intervals between customers (Fig. 23) and the number of vehicles each
day (Fig. 24) were reconstructed. To evaluate the GMM data, it would be
necessary to compare these plots with their counterparts for artificial data
(Fig. 13) and (Fig. 11). There is a similarity in the values and time course of
the functions, but they are generally different data.
The procedure was repeated for real-world data. The
results are presented in Fig. 25 and Fig. 26 (comparison of event times)
and Fig. 27 (daily demand for vehicles). Based on the comparison of Fig. 25
with Fig. 2, it can be concluded that the structure of booking times (more -
early bookings) and rental termination times (more - longer rental times) has
changed significantly. In real-world data, there were both very long and very
short periods at the same time. The GMM model clearly averaged them out.
Fig. 25. GMM trained with real-world data
|
Fig. 26. Time course of several series of
random data |
Fig. 27. Daily demand for vehicles |
6.
CLASSIFICATION TREES
Based on artificially generated data (
In the case of the first tree, the input variable
(also known as predictor) was the rental start time
|
|
|
Fig. 28. Rental starting point prediction results
using a trained classification tree;
on the left – the number of inquiries depending on the office number;
on the right – the number of queries spread over time
|
|
|
Fig. 29. Rental endpoint prediction results;
on the left – only one input variable
For the second tree, the output
variable was the booking endpoint. Two variants were tested. The first one
considers only one input variable: start time. In the second, there were two
input variables: reservation start time and starting point. It
appears that the second variant better reflects the fact that the
probability of choosing the end point is conditioned by the choice of the
starting point. The prediction results are shown in Fig. 29. They should be
compared with the simulation results shown in Fig. 16, where it was assumed
that the dominant rental method is the two-way variant (the values on the
diagonal of the probability density matrix are then dominant). The analysis of
the data obtained from the prediction showed that the probability of one-way
rental increased at the expense of the two-way probability. Interestingly, the
case with one input variable (start time) gives better results because the
probability values on the diagonal are higher (Fig. 29 left).
7. CONCLUSIONS
The
method of preparing a sequence of requests from car rental customers proposed
in the work can be used both in the case of having a real database and in the
case of generating artificial data. The
sequence of requests will be a set of necessary information to generate events
in the model made in the SimEvents environment.
The obtained real-world data are
not representative for short-term rental. However, their analysis allowed to
detect certain regularities and observe seasonality and trends. For example,
the specific days of the week when the rental starts and ends, or the specific
length of the rental. While developing the method of generating artificial
data, efforts were made to reproduce the most characteristic features of real
data. The proposed method of generating artificial data is easy to modify and
to scale it to the case of renting per hour. Unfortunately, artificially
generated data is usually too regular. In the developed method, it can be tuned
by increasing the noise level.
An
alternative to the proposed method of generating artificial data may be the use
of machine learning models: trained Gaussian mixture models and trained binary
classification trees. However, the tests of these models for the available data
showed some disadvantages, discussed in the text of the article. Briefly
summarizing the results of testing machine learning models, it can be said that
they can distort trends and cyclicality existing in the input data. This was
particularly evident in the case of GMM training with real-world data. In the
real data, there were bookings with very short or very long advance times. The
GMM matching algorithms averaged these values, and consequently bookings with
very short advance times disappeared. The averaged advance time for all
bookings has increased. The same was true for the duration of the rental.
Initially, short 5-day rentals and long rentals, almost two years long,
dominated. After the transformation to GMM, short-term rentals almost
disappeared.
Despite some disadvantages,
machine learning models can be a source of fresh artificial random data
obtained on the basis of other data.
References
1.
Brendel Alfred Benedikt, Christian Rockenkamm,
Lutz M. Kolbe. 2017. „Generating Rental Data for Car Sharing Relocation
Simulations on the Example of Station-Based One-Way Car Sharing”. In: Proceedings of the 50th Hawaii International
Conference on System Sciences: 1554-1563. Hilton Waikoloa Village,
Hawaii, USA, January 4-7, 2017. ISBN: 978-0-9981331-0-2.
2.
Carlier Aur´elien, Alix Munier Kordon,
Witold Klaudel. 2014. „Optimization of a oneway carsharing system with
relocation operations”. In: 10th International
Conference on Modelling, Optimization and SIMulation MOSIM 2014. Nov
2014, Nancy, France. hal-01294548.
3.
Clemente M., M.P. Fanti, A.M. Mangini, W.
Ukovich. 2013. “The vehicle relocation problem in car sharing systems:
Modelling and simulation in a Petri net framework”. In: Application and Theory of Petri Nets and
Concurrency. PETRI NETS 2013. Lecture Notes in Computer Science 7927:
250-269. Edited by J.M. Colom, J.
Desel. Springer, Berlin,
Heidelberg. DOI: 10.1007/978-3-642-38697-8_14.
4.
Conejero J. Alberto, Cristina Jordán, Esther
Sanabria-Codesal. 2014. „An Iterative Algorithm for the
Management of an Electric Car-Rental Service”. Journal of Applied
Mathematics 2014 (Article ID 483734): 1-11. DOI: 10.1155/2014/483734.
5.
Fink A., T. Reiners. 2006. „Modelling and
solving the short-term car rental logistics problem” Transportation Research Part E: Logistics and Transportation Review
42(4): 272-292. DOI: 10.1016/j.tre.2004.10.003.
6.
Jorge D., G. Correia. 2013. „Carsharing
systems demand estimation and defined operations: A literature review”. European Journal of Transport and
Infrastructure Research 13(3): 201-220. DOI: 10.18757/ejtir.2013.13.3.2999.
7.
Milenković
Miloš, Libor Švadlenka, Vlastimil Melichar, Nebojša
Bojović, Zoran Avramović. 2018.
„SARIMA modelling approach for railway passenger flow forecasting”.
Transport 33(5): 1113-1120. ISSN:
1648-4142. DOI:
10.3846/16484142.2016.1139623.
8.
Nair R., E. Miller-Hooks, 2011. „Fleet
management for vehicle sharing operations”. Transportation Science 45(4): 524-540. ISSN: 0041-1655. DOI:
10.1287/trsc.1100.0347.
9.
Repoux Martin, Burak Boyacı, Nikolas
Geroliminis. 2015. „Simulation and optimization of one-way car-sharing
systems with variant relocation policies”. In: 94th Annual Meeting of the Transportation Research Board At:
Washington D.C.
10.
Turoń K., A. Kubik, F. Chen. 2022.
„What Car for Car-Sharing? Conventional, Electric, Hybrid or Hydrogen
Fleet? Analysis of the Vehicle Selection Criteria for Car-Sharing
Systems”. Energies 15: 4344.
11. SimEvents
User’s Guide. 2022. MathWorks Inc.
12.
Wang H., R. Cheu, D.H. Lee. 2010. „Dynamic
relocating vehicle resources using a microscopic traffic simulation model for
carsharing services”. In: Computational
Science and Optimization (CSO), 2010 Third International Joint Conference
2010(1): 108-111. DOI: 10.1109/CSO.2010.98.
13. Wang
Yuxuan, Feng Huixia. 2020. „Optimization and Simulation of Carsharing
under the Internet of Things”. Hindawi
Mathematical Problems in Engineering 2020 (Article ID 4873048): 1-8. DOI:
10.1155/2020/4873048.
14.
Yang Y., W. Jin, X. Hao. 2008. „Car rental
logistics problem: A review of literature”. In: Service Operations and Logistics, and Informatics, 2008. IEEE/SOLI
2008. IEEE International Conference on Volume 2. DOI: 10.1109/SOLI.2008.4683014.
15. ACRISS.
„Car Codes”. Available at: https://www.acriss.org.
Received 02.12.2023; accepted in
revised form 12.03.2024
Scientific Journal of Silesian University of Technology. Series
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[1] Faculty of Transport and Aviation Engineering, The Silesian University
of Technology, Krasińskiego 8 Street, 40-019 Katowice, Poland. Email:
tomasz.matyja@polsl.pl. ORCID: https://orcid.org/0000-0001-6364-619X
[2] Faculty of Transport and Aviation Engineering, The Silesian University
of Technology, Krasińskiego 8 Street, 40-019 Katowice, Poland. Email:
zbigniew.stanik@polsl.pl. ORCID: https://orcid.org/0000-0003-1965-4090
[3] MM Cars Renta Sp. z o.o., Lotnisko
81 Street, 40-271 Katowice. Email: k.wlodkowski@mmservicelease.pl. ORCID:
https://orcid.org/0009-0001-0063-3233