=Paper=
{{Paper
|id=Vol-3426/paper25
|storemode=property
|title=Modeling the Development of the Tourism Industry Using the Koba-Douglas Function for Intelligent Management Systems
|pdfUrl=https://ceur-ws.org/Vol-3426/paper25.pdf
|volume=Vol-3426
|authors=Nestor Shpak,Ihor Novakivskyi,Ihor Kulyniak,Viktoriya Kharchuk,Ihor Oleksiv
|dblpUrl=https://dblp.org/rec/conf/momlet/ShpakNKKO23
}}
==Modeling the Development of the Tourism Industry Using the Koba-Douglas Function for Intelligent Management Systems==
https://ceur-ws.org/Vol-3426/paper25.pdf
Modeling the Development of the Tourism Industry Using the
Koba-Douglas Function for Intelligent Management Systems
Nestor Shpak, Ihor Novakivskyi, Ihor Kulyniak, Viktoriya Kharchuk and Ihor Oleksiv
Lviv Polytechnic National University, Stepan Bandera str, 12, Lviv, 79013, Ukraine
Abstract
Modeling the influence of factors on the performance of tourism industry enterprises is very
important for the development of intelligent management systems. This allows us to create
mathematical models that can predict the consequences of various actions and reflect the
relationships between different factors and outcomes. The paper analyzes the dynamics of
growth rates of sales, capital and labor costs and the dynamics of labor productivity and fund
intensity of subjects of the tourism industry of Ukraine, dividing them into three groups
depending on the types of economic activity: the activities of travel agencies, the activities of
tour operators and the provision of booking services. The study was conducted on the basis of
statistical data of the State Statistics Service of Ukraine for the period from 2013 to 2021.
Using the Koba-Douglas function, the influence of factors (capital and labor costs) on the
development of the tourism industry in Ukraine is modeled (the volume of products sold is
selected as the result indicator). It is revealed that for travel agencies, labor has a more
significant impact on the result than capital. For tour operators, the impact on the result of
capital is almost twice as great as labor. For organizations that provide booking services, on
the contrary, the impact on labor results is almost twice as great as capital. Applying
simulation results can help managers of travel companies make decisions based on the
analysis of large amounts of data and statistics, in particular for forecasting sales, production
costs, personnel planning, etc. The built models allow us to determine the optimal
combination of factors of production, which ensures the highest level of efficiency of tourist
enterprises and helps to assess what changes in capital and labor can lead to an increase in the
volume of products sold.
Keywords 1
Tourism, travel agencies, tour operators, booking services, Koba-Douglas production
function, intelligent management systems, capital, labor, volume of products sold, labor
productivity, fund intensity.
1. Introduction
Taking into account the influence of factors on the effectiveness of the development of the tourism
industry, in particular such as labor and capital, is important for effective production management of
travel companies. Capital and labor are the two main factors of production that interact with each
other and affect the effectiveness of production. Taking into account the impact of labor and capital
on production can help determine the optimal balance between these two factors. For example, if a
company has more capital, it can use machines and other means of production more efficiently,
instead of attracting more employees. On the other hand, if production requires a large amount of
MoMLeT+DS 2023: 5th International Workshop on Modern Machine Learning Technologies and Data Science, June 3, 2023, Lviv,
Ukraine
EMAIL: nestor.o.shpak@lpnu.ua (N. Shpak); ihor.i.novakivskyi@lpnu.ua (I. Novakivskyi); ihor.y.kulyniak@lpnu.ua (I. Kulyniak);
viktoriia.y.kharchuk@lpnu.ua (V. Kharchuk); ihor.b.oleksiv@lpnu.ua (I. Oleksiv)
ORCID: 0000-0003-0620-2458 (N. Shpak); 0000-0003-0841-3603 (I. Novakivskyi); 0000-0002-8135-4614 (I. Kulyniak); 0000-0003-4354-
9549 (V. Kharchuk); 0000-0001-7387-6933 (I. Oleksiv)
2023 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
manual labor, then it is necessary to attract enough workers and ensure their efficient operation in
order to ensure high productivity.
The tourism sector as a component of the service sector differs from the manufacturing sector in
terms of providing enterprises with capital and labor. This is evident in the fact that the manufacturing
sector is usually associated with the production of goods and services, while the tourism sector is
associated with the provision of services related to recreation and travel [1]. This can affect the capital
and labor needs that are needed to support industry operations. The tourism industry is often seasonal,
which means that capital and labor needs can change depending on the demand for travel services
throughout the year [2]. The production sector usually does not depend so much on seasonality. The
tourism sector is distributed according to the demand and attractiveness of tourist places, while the
production sector can be concentrated in certain regions. The tourism sector often operates small
businesses such as hotels and restaurants, while the manufacturing sector may have large businesses
such as factories and factories. This is also an important factor that determines the need for a certain
level of providing enterprises with capital and labor.
The dual nature of providing tourism with capital and labor is as follows:
job provision (security) – in tourism, experienced and qualified workers are a key element of
a successful industry. Providing a high-quality workforce and capable managers helps ensure the
quality of service and satisfaction of tourists. In addition, employee security (provision) can be
important for increasing workers’ salaries in the industry, which in turn can support the local
economy and make the tourism industry more attractive to younger generations;
capital security (provision) – in tourism, investment in the development of infrastructure and
services is a necessary condition for ensuring the development and competitiveness of the
industry. For example, the development of a hotel base, the creation of new tourist routes, and the
opening of new businesses may depend on the availability of capital. If the tourism industry is
provided with a sufficient level of capital, it can improve the quality of services and make the
tourism product more attractive to potential customers.
Efficient use of labor and capital can help increase the number of products produced, reduce costs,
and increase the competitiveness of a travel company. Inappropriate use of these factors can lead to
unnecessary costs, reduced product quality, and reduced profitability [3; 4]. Therefore, taking into
account the impact of labor and capital on the efficiency of tourism industry entities, in particular on
the volume of tourist products sold, allows us to increase the efficiency of providing tourist services
and ensure the successful operation of travel companies. In addition, further research on the impact of
capital and labor on the development of the tourism industry can help in studying important factors
that affect the sustainable development of tourism. For example, determining how capital and labor
are effectively used to conserve natural and cultural resources can help reduce its negative impact on
the environment.
Taking into account the above statements, the purpose of our research is to model the dependence
of the development of the tourism industry in Ukraine on factors of production, such as labor and
capital. It is suggested to use the Koba-Douglas production function as a tool. To achieve this goal,
our research is aimed at solving the following problems:
1. Analyze the dynamics of growth rates in the volume of products sold, capital and labor costs
of travel agencies, tour operators and organizations providing booking services.
2. Analyze the dynamics of labor productivity and fund intensity of travel agencies, tour
operators, and organizations providing booking services.
3. Using the Koba-Douglas function, model the impact of factors (capital and labor costs) on the
development of the tourism industry in Ukraine (the resulting indicator is the volume of sales of
products).
2. Related works
Assessment of the impact of factors on the development of the tourism industry is a widely studied
topic in scientific sources. For this purpose, different methods and approaches are used, depending on
the specific task and subject of research. For example, surveys and questionnaires of various
stakeholders, such as tourists, representatives of travel companies, local residents, etc., are used to
investigate their preferences, needs, and impressions of tourist services and infrastructure. The results
of such studies can be used to improve the quality of tourist services and attract new tourists. Thus, by
Chinese scientists Sun Hui et al. [5] the main factors influencing the choice of destination by ski
tourism enthusiasts were investigated through a soft interview, followed by a questionnaire survey;
researcher Zhang Yuanjing [6] conducted an online survey among 350 tourists to identify factors
influencing the tourist experience. In addition, expert assessments are conducted based on the opinion
and experience of representatives of the tourism industry and other experts from various industries to
determine the most important factors influencing the development of the industry.
In the works of scientists, we find the analysis of statistical data and the construction of various
economic and mathematical models of the relationship between various factors and the development
of the tourism industry [7; 8]. Such models include socio-economic and cultural factors such as the
economic situation of the country [8], the standard of living of the population [9], the level of health
and morbidity risks [10], transport infrastructure [11], housing prices in a particular area or market
[12], cultural heritage [13], factors influencing the consumption of tourist online products [14; 15],
etc. Scientists Solyukova Nina, Viegas Cristina and Pinto Patrícia [16] using statistical methods,
correlation and regression analysis analyzed the impact of the company's debt, lack of resources, sales
growth, materiality and size of the firm on the return on assets (ROA), confirming the theory that the
most profitable firms tend to borrow less because they do not need external capital.
Since 2020, the COVID-19 pandemic has affected many economic sectors, including the tourism
industry, not only in Ukraine, but also in other countries [17]. The fact of the impact of the pandemic
on the development of tourism is confirmed in many scientific works [18]. In particular, the Samad I.
scientist [19] studied the role of internal resources and the influence of environmental factors on the
efficiency of small and medium-sized enterprises in the tourism industry. The shift to an asset
reduction strategy is a significant shift for travel companies in light of the global COVID-19 outbreak
[20].
Scientists Faturohman Taufik and Noviandy Rashifa Anita [21] note that the capital structure is
vital for each company, as it has a huge impact on the company’s financial decisions. In particular,
scientists have identified, that size and earnings volatility had significant negative correlations with
net equity. Chambers Nurgul and Cifter Atilla [22] studied the influence of working capital on the
company’s performance in the hospitality and tourism industry and revealed an inverted U-shaped
relationship between working capital and the company’s productivity. A significant amount of
research is aimed at studying the impact of human capital on the development of the tourism industry
[23], and the possibilities of human capital as a key factor in determining the competitiveness of
tourism industry enterprises are considered [24]. Research on the impact of capital and labor on the
development of the tourism market is important for business, government and other stakeholders and
can help solve problems and develop the industry more effectively.
One of the most common functions used to study the relationship between production and the use
of factors of production, such as capital and labor, is the Koba-Douglas function. However, in most
scientific studies, this function is used to analyze productive areas of the economy, such as industry
[25] or agriculture [26], and less is studied for the service sector, such as tourism. However, with the
development of the economy and the growing importance of the service sector, such as tourism,
research on the impact of factors on this area is becoming increasingly important. Therefore, further
research of the Koba-Douglas function for the service sector, in particular for tourism, is an urgent
task. Such studies can be useful for planning and developing tourism development strategies, as well
as for making decisions in the field of tourism.
3. Methods
The current state of the economy creates certain problems in analyzing the dynamics of industry
development. To assess the effectiveness of the mechanisms of functioning of the tourism industry,
mathematical modeling methods are used, which will allow not only to analyze the existing state, but
also to conduct forecasting.
In economics, to determine the mathematical dependence of the amount of output produced on the
amount of factors of production used, such as labor and capital, scientists have adopted the Koba-
Douglas production function, which is named after the economists Koba and Douglas who developed
it in the 1920s. This function shows that an increase in the amount of labor and capital leads to an
increase in production, but the marginal productivity of each additional factor of production
decreases. It also reflects that technological progress can improve production efficiency regardless of
the number of factors of production used.
Mathematical assessment of the effectiveness of the development of the tourism industry using the
Koba-Douglas production function is expressed using the formula:
, (1)
where Р – volume of products produced,
К – amount of capital (assets) involved,
L – amount of labor costs,
α – the Koba-Douglas model coefficient, which indicates which of the factors of production
(capital or labor) has a greater impact on the result. If the coefficient α is greater than 0.5, then capital
has a greater influence on the result, and if the coefficient α is less than 0.5, then labor has a greater
influence on the result. If the coefficient α is 0.5, then capital and labor have the same effect on the
result.
To find the unknowns k, α, and β, the gradient method of the fastest descent for the functional is
used:
, (2)
where J – number of observations over the years.
. (3)
Equally important is the study of deviations from the calculated model during the study period in
order to assess the effectiveness of management both in terms of capital use and labor.
Changes in the economic, socio-political landscape are determined by the following features [27]:
inertia;
subordination to economic laws of development;
classical methods of analysis have strong limitations on application and do not give
sufficiently clear results;
short interval for research;
complexity of using analytical methods.
Therefore, the need to develop effective analysis tools that would take into account such features
of economic processes is being updated.
To analyze the intensity/efficiency of capital and labor use during this period, the following
functionality is constructed:
, (4)
where – capital use intensity coefficients;
– labor intensity coefficients.
The gradient method of the fastest descent is used to find the unknowns: .
The proposed methodology is tested on statistical data published in the public domain by the State
Statistics Service of Ukraine on the website: https://www.ukrstat.gov.ua. To establish the basis for the
preparation and dissemination of statistical information on types of economic activity in Ukraine, the
state classifier DK 009:2010 (classification of types of economic activity KVED-2010) was approved.
The basic principle of KVED is to combine enterprises that produce similar goods or services or use
similar processes to create goods or services (i.e. raw materials, production process, methods or
technologies) into groups. State statistics bodies calculate the main type of economic activity based on
data from state statistical observations in accordance with the statistical methodology based on the
results of enterprises’ activities for the year. To characterize tourism, we will use the statistics of the
KVED-2010, in particular those presented in Section 79 of Section N “Activities in the field of
administrative and support services” [28]. Section 79 is divided into two groups:
79.1 Activities of travel agencies and tour operators. This group includes the activities of travel
agencies, transportation and accommodation in temporary accommodation facilities for tourists and
travelers, organization and conduct of tours that are sold by travel agencies or directly by agents, such
as tour operators. Group 79.1 is divided into 2 classes:
79.11 Activities of travel agencies. This class includes the activities of agencies involved in
organizing trips, tours, and providing short-term accommodation services based on their wholesale
and retail sales to a wide range of consumers or commercial clients [29].
79.12 Activities of tour operators. This class includes organizing and conducting tours that are
implemented through travel agencies or directly by tour operators. The organization of tours may
include: transportation; provision of accommodation; meals; visits to museums, places of historical
and cultural monuments, theater, music or sports events [30].
79.9 Provision of other booking services and related activities.
Taking into account the distribution of subjects of tourist activity by types of economic activity,
which is used in the KVED-2010, further analysis of the dynamics of the development of the tourist
market is carried out for three groups:
activities of travel agencies;
activities of tour operators;
provision of booking services and related activities.
The information source of data on the volume of products sold, capital and labor costs is the
statistical data of the State Statistics Service of Ukraine for the period 2013-2021, which are published
in the section “Economic statistics / Economic activity / Activities of enterprises” [31].
4. Results and discussions
The theoretical concept of our research is based on the choice of a classical model that takes into
account such three basic factors that reflect the activities of tourism industry entities as the volume of
products sold, capital (assets), and labor costs. Time period of the study is from 2013 to 2021. Initial
data are presented for three types of economic activity that characterize the activities of subjects of the
tourism industry of Ukraine, namely: the activities of travel agencies; the activities of tour operators;
the provision of booking services and related activities (Tables 1-3).
Tables 1-3 also show the results of calculating the basic growth rates of sales, capital and labor
costs in relation to the base period – 2013. A graphical representation of the growth rate for travel
agencies is shown in Figure 1, for the activities of tour operators – in Figure 2, and for the provision
of booking services – in Figure 3.
Table 1
Indicators that reflect the activities of travel agencies in Ukraine
Volume of
products Labor costs
(goods, % by Capital, % by of % by Labor Fund
Years
services) 2013 mln. UAH 2013 enterprises, 2013 productivity intensity
sold, mln. UAH
mln. UAH
2013 1323.655 100.00 2202.069 100.00 162.706 100.00 8.135 1.664
2014 913.124 68.99 1165.654 52.93 122.035 75.00 7.483 1.277
2015 1134.863 85.74 1210.410 54.97 154.239 94.80 7.358 1.067
2016 1416.276 107.00 1350.084 61.31 169.948 104.45 8.334 0.953
2017 1530.509 115.63 1673.200 75.98 226.824 139.41 6.748 1.093
2018 1841.803 139.15 2024.089 91.92 248.573 152.77 7.410 1.099
2019 2140.567 161.72 2420.621 109.92 331.893 203.98 6.450 1.131
2020 984.717 74.39 2207.303 100.24 211.686 130.10 4.652 2.242
2021 1867.129 141.06 2008.923 91.23 221.346 136.04 8.435 1.076
Source: Compiled by the authors based on [31]
Table 2
Indicators that reflect the activities of tour operators in Ukraine
Volume of
products Labor costs
(goods, % by Capital, % by of % by Labor Fund
Years
services) 2013 mln. UAH 2013 enterprises, 2013 productivity intensity
sold, mln. UAH
mln. UAH
2013 3937.727 100.00 1960.589 100.00 216.164 100.00 18.216 0.498
2014 2683.723 68.15 2078.432 106.01 183.427 84.86 14.631 0.774
2015 3088.542 78.43 2860.945 145.92 219.776 101.67 14.053 0.926
2016 3845.716 97.66 4095.164 208.87 247.055 114.29 15.566 1.065
2017 4773.367 121.22 3667.749 187.07 347.970 160.98 13.718 0.768
2018 7029.984 178.53 4442.438 226.59 363.687 168.25 19.330 0.632
2019 9736.5312 247.26 6214.208 316.96 536.796 248.33 18.138 0.638
2020 4640.442 117.85 5555.959 283.38 401.481 185.73 11.558 1.197
2021 10928.968 277.55 8255.705 421.08 443.294 205.07 24.654 0.755
Source: Compiled by the authors based on [31]
Table 3
Indicators that reflect the activity of providing booking services in Ukraine
Volume of
products Labor costs
(goods, % by Capital, % by of % by Labor Fund
Years
services) 2013 mln. UAH 2013 enterprises, 2013 productivity intensity
sold, mln. UAH
mln. UAH
2013 266086,2 100.00 806722,8 100.00 35203,6 100.00 7.558 3.032
2014 277473,1 104.28 734278,2 91.02 25748,7 73.14 10.776 2.646
2015 387355,4 145.58 817119,6 101.29 35277,1 100.21 10.980 2.109
2016 441307,1 165.85 739962,5 91.72 46947,4 133.36 9.400 1.677
2017 423900,5 159.31 744345,7 92.27 61449,9 174.56 6.898 1.756
2018 595067,6 223.64 1782491,5 220.95 68641,3 194.98 8.669 2.995
2019 909105,3 341.66 1632840,4 202.40 100061,7 284.24 9.085 1.796
2020 569128,5 213.89 2019447,0 250.33 98388,7 279.48 5.784 3.548
2021 901728,9 338.89 1549717,4 192.10 151091,3 429.19 5.968 1.719
Source: Compiled by the authors based on [31]
Monitoring of the growth rates of indicators that reflect the activities of travel agencies for the
period 2013-2021 shows their decline in 2014, which is due to the occupation of Crimea by the
Russian Federation and its invasion of the territory of the Ukrainian part of Donbas. During 2014-
2019, we observe an upward trend in the analyzed indicators, as Ukraine becomes more attractive for
foreign tourists, as well as the ability of the local population to relax and travel increases. Due to the
spread of the COVID-19 pandemic, a decrease in the values of the analyzed indicators is again
observed in 2020. The growth rate of labor costs exceeds the growth rate of capital, which indicates
that personnel is a key resource in the development of travel agencies.
250
200
150
100
50
0
2013 2014 2015 2016 2017 2018 2019 2020 2021
Volume of products sold Capital
Labor costs of enterprises
Figure 1: Dynamics of growth rates of indicators reflecting the activities of travel agencies in Ukraine
Source: compiled by the authors
450
400
350
300
250
200
150
100
50
0
2013 2014 2015 2016 2017 2018 2019 2020 2021
Volume of products sold Capital
Labor costs of enterprises
Figure 2: Dynamics of growth rates of indicators reflecting the activities of tour operators in Ukraine
Source: compiled by the authors
A similar picture, as with the activities of travel agencies, is observed in the dynamics of growth
rates of indicators that reflect the activities of tour operators: a decrease in 2014 with further growth
until 2019 and a significant drop, which is due to the spread of the COVID-19 pandemic. Growth is
recovering in 2021. However, the activities of tour operators show better results and higher growth
rates than those of travel agencies. Tour operators, unlike travel agencies, tend to deal with more
complex issues related to the organization of tours and package offers, including transportation,
accommodation, meals and excursions. This allows them to offer customers comprehensive services
that include everything they need to travel. Also, tour operators can work with discounts and special
offers from tour operators, which allows them to offer more affordable prices for customers. The
growing popularity of tourism in Ukraine for more comprehensive services offered by tour operators
has led to better results of their activities compared to travel agencies in this period. However, unlike
travel agencies, the growth rate of labor costs is lower than the growth rate of capital, which indicates
that capital is a key resource in the development of tour operators.
500
450
400
350
300
250
200
150
100
50
0
2013 2014 2015 2016 2017 2018 2019 2020 2021
Volume of products sold Capital
Labor costs of enterprises
Figure 3: Dynamics of growth rates of indicators that reflect the activity of providing booking
services in Ukraine
Source: compiled by the authors
The dynamics of activity in the provision of booking services is also demonstrated by similar
trends in the growth rate of indicators, in particular, a decrease in 2014 with further growth until 2019
and a fall in 2020, which is due to the spread of the COVID-19 pandemic and the resumption of
growth in 2021 only in the volume of products sold and labor costs, and capital experienced a
reduction in 2021. As with travel agencies, the growth rate of labor costs exceeds the growth rate of
capital, which indicates that staff is the predominant resource in the development of organizations that
provide booking services. However, as can be seen from Figure 3, the lag in capital growth rates from
the growth rate of labor costs is insignificant, except for 2021.
More information about the dynamics of the development of the tourism industry in Ukraine can
be obtained by studying the ratio of capital use and labor costs to production and sales volumes. In
Figure 4 shows the dynamics of labor productivity (the ratio of volumes of products sold to labor
costs), and Figure 5 – fund intensity (the ratio of capital to the volume of products sold) of travel
agencies, tour operators and organizations that provide booking services.
30
25
20
15
10
5
0
2013 2014 2015 2016 2017 2018 2019 2020 2021
activities of travel agencies activities of tour operators
provision of booking services
Figure 4: Dynamics of labor productivity of travel agencies, tour operators and organizations
providing booking services in Ukraine
Source: compiled by the authors
Labor productivity shows the ratio of the production result to the Labor used. This means that
labor productivity indicates how much of a product or service can be produced per unit of time using
a certain amount of labor. High labor productivity can indicate that employees perform their work
efficiently and use resources such as equipment, materials, and time efficiently. This can have a
positive impact on the profitability of the enterprise, increase wages, and improve the quality of the
product or service [32]. As shown in Figure 4, the labor productivity of tour operators exceeds the
labor productivity of travel agencies and organizations providing booking services. This is due to the
fact that tour operators are usually engaged in creating tours and selling them, which requires fewer
employees compared to travel agencies that provide services for booking hotels, air tickets, transfers
and other similar services. In addition, tour operators usually have a large database of tours that can
be sold, as well as more opportunities in tour planning and travel organization. In addition, tour
operators may have more opportunities for efficient use of information technologies and automated
control systems, which can also provide higher labor productivity.
There is a decrease in the productivity of travel agencies, tour operators and organizations
providing booking services in the period from 2013 to 2020, only in 2021 there is an increase. The
decline in labor productivity in the tourism industry of Ukraine is associated with the influence of
such factors as [33; 34; 35]:
political and economic instability in the country – since 2013, Ukraine has experienced
significant political and economic difficulties, including a political crisis and military operations in
the east of the country;
changes in consumer demand – over the past few years, consumers have become more
demanding and demanding about the quality and price of travel services, which has led to a more
complex and time-consuming process of selling and organizing travel;
competition-the tourism market of Ukraine is quite competitive, with many players in the
market, which has led to the fact that travel agencies and operators are forced to spend more effort
and resources on attracting customers and maintaining a stable business;
technology has evolved and changed rapidly over the past few years, which requires travel
agencies and operators to pay more for software updates, employee training, and other expenses
that also reduce productivity.
However, the measurement of labor productivity should be supplemented with other indicators,
such as product quality, customer satisfaction, employee safety, etc., to ensure a complete assessment
of the performance of tourism industry entities.
4
3,5
3
2,5
2
1,5
1
0,5
0
2013 2014 2015 2016 2017 2018 2019 2020 2021
activities of travel agencies activities of tour operators
provision of booking services
Figure 5: Dynamics of fund intensity of travel agencies, tour operators and organizations providing
booking services in Ukraine
Source: compiled by the authors
Fund intensity characterizes the effectiveness of providing capital to the activities of tourism
industry entities. This means that the enterprise must have a sufficient amount of capital, as well as
ensure the efficient use of this capital. Fund intensity is an important indicator for an enterprise, as it
affects its ability to receive financial resources and develop, so a higher level of fund intensity
provides the enterprise with better conditions for development. As shown in Figure 5, the efficiency
of providing capital to the activities of tour operators and organizations providing booking services
during 2013-2019 was stable; in 2020, we see an increase in the indicator almost twice and a return in
2021 to the value of 2019, due to the impact of the pandemic. Despite the fact that the fund intensity
of travel agencies exceeds the value of the fund intensity of tour operators and organizations
providing booking services, the value of the indicator decreases during 2013-2017; in 2018 and 2020,
we observe an increase in the indicator almost twice and a return in 2021 to the value of 2017.
Along with political and economic instability, Ukraine is characterized by a low level of
investment in the development of the tourism industry. This was the reason for the lack of
infrastructure development, which led to a decrease in the overall efficiency of providing capital to
activities. In general, limited access to loans and other sources of capital, and the lack of an effective
state policy in Ukraine regarding the development of tourism have led to a lack of incentives for
investment in this sector [1; 36].
To model the influence of factors (capital and labor costs) on the volume of products sold in the
tourism industry of Ukraine, we will use the Koba-Douglas function. This function allows you to
evaluate the efficiency of using production resources, as well as understand which factors of
production have the greatest impact on productivity. It allows you to determine the optimal
combination of factors of production, which ensures the highest level of production at minimal costs.
The Koba-Douglas function is an important tool for analyzing and planning the activities of tourism
organizations and developing the tourism industry.
Using formulas (1-4), the following representation of the Koba-Douglas production function for
Ukrainian tourism industry entities is obtained:
for the activities of travel agencies:
;
for the activities of tour operators:
;
to provide booking services:
.
The dynamics of capital and labor efficiency, based on the average model of development of the
tourist market of Ukraine, for travel agencies, tour operators and organizations providing booking
services is shown in Figures 6-8.
140,0
120,0 120,6 121,2
113,9 106,5
105,8 99,9 106,4 99,4
100,0 101,1
100,8 100,4 100,4 101,2 96,9 100,3 92,5 98,1
80,0
60,0 64,1
40,0
20,0
0,0
2013 2014 2015 2016 2017 2018 2019 2020 2021
Capital Labor costs of enterprises
Figure 6: Dynamics of efficiency of capital and Labor use, based on the average model of
development of the tourist market of Ukraine, for travel agencies
Source: compiled by the authors
160,0
140,0 137,9
120,0 122,8 119,1 115,2 115,9
111,1 108,6 108,6
100,0
94,9 87,5 93,7
80,0 90,7
84,8 88,7
77,6 76,2
72,8
60,0 58,1
40,0
20,0
0,0
2013 2014 2015 2016 2017 2018 2019 2020 2021
Capital Labor costs of enterprises
Figure 7: Dynamics of efficiency of capital and Labor use, based on the average model of
development of the tourist market of Ukraine, for tour operators
Source: compiled by the authors
160,0
140,0 140,6
135,3
127,0 120,7 127,5
120,0 118,8 117,0
114,3 104,4
100,0 96,7 102,3 96,3
102,1 100,9 90,0
90,6 93,8
80,0
66,5
60,0
40,0
20,0
0,0
2013 2014 2015 2016 2017 2018 2019 2020 2021
Capital Labor costs of enterprises
Figure 8: Dynamics of capital and labor efficiency, based on the average model of development of
the tourist market of Ukraine, for organizations providing booking services
Source: compiled by the authors
We can conclude that for travel agencies, work with a significant advantage has a greater impact
on the result than capital. For tour operators, capital has almost twice as much impact on the result as
Labor. For booking service organizations, on the contrary, Labor has twice as much impact on the
result as capital.
5. Conclusions
Availability of labor and capital are key factors for the success of the tourism industry, which help
to ensure a high level of service and development of the tourism product. However, as the results of
the study showed, for different subjects of the tourism industry, the level of influence of labor and
capital on the results of their activities is different. Analysis of the dynamics of indicators that reflect
the development of the tourism industry has shown that for travel agencies and organizations
providing booking services, the growth rate of labor costs exceeds the growth rate of capital, which
indicates that personnel is a key resource in the development of organizations. For tour operators, on
the contrary, the growth rate of labor costs is lower than the growth rate of capital, which indicates
that capital is a key resource in the development of tour operators. In general, the activities of tour
operators and organizations providing booking services show better results and higher growth rates
than those of travel agencies.
These results are confirmed by modeling the influence of capital and labor on the volume of
products sold using the Koba-Douglas production function. Models built using the Koba-Douglas
function allow you to assess the efficiency of using production resources, as well as understand which
factors (capital or labor) have the greatest impact on the development of the tourism industry in
Ukraine. It was found that for travel agencies, work with a significant advantage has a greater impact
on the result than capital. For tour operators, capital has almost twice as much impact on the result as
labor. For booking service organizations, on the contrary, Labor has twice as much impact on the
result as capital.
In general, we can state a tendency to increase the volume of products sold by tourism industry
entities, as well as the cost of capital and labor costs, except for periods of exposure to unpredictable
factors (such as the Russian invasion of Ukraine, the spread of the COVID-19 pandemic). This is
confirmed by the growth of absolute and relative performance indicators of travel agencies, tour
operators and organizations providing booking services.
Our research has some limitations. First, among the factors of production, the impact of which was
assessed on the performance of tourist enterprises, only capital and labor costs were studied. At the
same time, a number of factors are not taken into account, such as cultural and social aspects of the
tourism industry, which can significantly affect the choice of tourist destinations and types of
recreation. Second, the Koba-Douglas function involves a constant change in labor and capital
without changing their quality. In other words, the possibility of improving the quality of Labor and
capital is not taken into account, which can lead to changes in the fund intensity or productivity of
enterprises. It also does not take into account possible interactions between factors of production that
may affect the productivity and efficiency of the tourism industry.
The results of modeling the dependence of the development of the tourism industry in Ukraine on
factors of production, such as labor and capital, play an important role for intelligent management
systems. Knowing which factors of production have the greatest impact on the development of the
tourism industry will allow investors and producers of travel services to focus their efforts and
resources on these factors in order to ensure maximum production efficiency. Knowing which factors
of production have the greatest impact on the development of the tourism industry can help managers
predict what changes in these factors may lead to changes in demand for tourism services and how to
develop the tourism industry in the future. The results obtained can also help determine the optimal
level of resource use and ensure maximum production efficiency in the tourism industry.
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