=Paper=
{{Paper
|id=Vol-2805/paper12
|storemode=property
|title=Risk Analysis of the Company's Activities by Means of Simulation
|pdfUrl=https://ceur-ws.org/Vol-2805/paper12.pdf
|volume=Vol-2805
|authors=Elena Kuzmina,Oksana Klochko,Nataliia Savina,Svetlana Yaremko,Roman Akselrod,Christine Strauss
|dblpUrl=https://dblp.org/rec/conf/citrisk/KuzminaKSYAS20
}}
==Risk Analysis of the Company's Activities by Means of Simulation==
https://ceur-ws.org/Vol-2805/paper12.pdf
Risk Analysis of the Company's Activities by Means of
Simulation
Elena M. Kuzmina1[0000-0002-0061-9933], Oksana Klochko3[0000-0002-6505-9455],
Nataliia B. Savina2[0000-0001-8339-1219], Svetlana A. Yaremko1[0000-0002-0605-9324],
Roman B. Akselrod4[0000-0001-7643-7194], Christine Strauss5[0000-0003-0276-3610]
1Vinnitsa Institute of Trade and Economics Kiev National Trade and Economic
University, Vinnytsia, Street Soborna 87, Ukraine
lenakuzmina@ukr.ner, svitlanа_yaremko@ukr.net
2The National University of Water and Environmental, Rivne, Ukraine
n.b.savina@nuwm.edu.ua
3Vinnytsia State Pedagogical University named after Mykhailo Kotsiubynsky,
Vinnytsia, Ostrozkoho Street 32, Ukraine
klochkoob@gmail.com
4Kyiv National University of Construction and Architecture, Kyiv, Ukraine
akselrod.knuba@ukr.net
5University of Vienna, Vienna, Austria
christine.strauss@univie.ac.at
Abstract.The use of simulation methods and modern information technologies
increases competitiveness, management efficiency and eliminates possible risks
in the company's activities. The use of the Monte-Carlo method is promising in
simulation. The basis of the classical Monte-Carlo method is to obtain a large
number of implementations of a random process, which is formed so that the
probabilistic characteristics (mathematical expectations, probability of some
events, probability of the trajectory in a certain area, etc.) are equal to the prede-
termined value of the problem. Construction of the model using this method
should be based on the distribution of random variables in the studied process.
The set of implementations can be used as some artificially obtained statistical
material processed by methods of mathematical statistics. The author's devel-
opment was the application in the classical Monte-Carlo method of generating
samples of random variables with uniform and triangular distribution, as well as
risk analysis of the company and forecasting for the future with greater proba-
bility using modern means of automating complex calculations based on high-
level programming languages. The software implementation of the advanced
Monte-Carlo method is performed using high-level object-oriented Python lan-
guage tools that allow you to automate all stages of application of the Monte-
Carlo method and store the results in a database. Strategic planning support
tools based on computer simulation provide an opportunity to reflect complex
nonlinear interactions in the business, assess the consequences of the implemen-
tation of various scenarios or predict further developments in the company.
Copyright © 2020 for this paper by its authors. This volume and its papers are published under
the Creative Commons License Attribution 4.0 International (CC BY 4.0).
Keywords:information technologies, simulation, Monte Carlo method, proba-
bilistic characteristics, risks.
1 Introduction
At the present stage of economic development, information technology (IT) can be
considered an attribute of a successful company. Creating an effective IT application
system in a company is one of the aspects of ensuring its competitiveness and avoid-
ing risk. Modern simulation technologies, including economic systems, are needed to
understand the causal relationships in economics, planning, forecasting, decision
making, and more. With the help of simulation, you can answer various questions that
arise when deciding on changes in the processes occurring in the business: how to
change the profitability of the business; what changes that have already taken place
will affect the productivity of technological equipment and personnel; what additional
investments the company needs to make; what will be the payback period of the in-
vestment. Simulation allows you to test different ideas by reproducing them in a com-
puter model, which is much cheaper than conducting many tests and bug fixes on real
processes [2,3,4].
Today, simulation is a powerful analytical tool based on modern information tech-
nology, including object-oriented programming, Internet solutions, powerful graph-
ical shells for modeling and interpretation of initial simulation results, multimedia
tools, etc. [1,2]. Today, simulation is seen as a mandatory step in making important
management decisions in companies that are actively implementing modern IT in
their activities, and this contributes to the adoption of sound strategic management
decisions. Strategic planning tools based on computer simulation provide an oppor-
tunity to reflect complex nonlinear interactions in the business, assess the conse-
quences of various scenarios or predict the further development of
the company [5,6,7].
2 Initial prerequisites and problem statement
One of the most powerful methods of analyzing economic systems is simulation,
which is the process of conducting experiments with mathematical models of complex
real-world systems using information technology. Computer simulation involves
building a model using specialized software. Computer experiments with a certain
degree of probability describe the patterns of functioning of real systems and objects.
To apply this method to research, create a simulation system that includes a simula-
tion model, as well as internal and external mathematical software. Then enter the
required input data and observe the changes in indicators, which in the process of
modeling can be analyzed and subjected to statistical processing. The range of appli-
cations of computer simulation is extremely wide - from specific forms of business to
the simulation of the economy as a whole [8,9,10].
The main areas of use of simulation in economic objects are:
─ forecasting the development of national economies;
─ development and implementation of information systems for various purposes;
─ training and personnel management.
The methods of computer simulation play an extremely important role in the intro-
duction of information technology in the management of companies, in the creation of
information systems of economic and organizational management. The strategy for
the development of modern information systems in companies, in particular decision
support systems, should provide analysis of the formulation and solution of this class
of problems [1,3, 11]:
─ analytical - calculation of the necessary indicators and statistical characteristics of
business activity on the basis of retrospective (turned back) information from data-
bases;
─ data visualization - visual graphical and tabular display of available information;
─ acquisition of knowledge - determining the relationships and interdependencies of
business processes based on existing information;
─ simulation - conducting computer experiments with mathematical models that
describe the behavior of complex systems. Tasks of this class are used to analyze
the possible consequences of a decision (analysis such as "What if? ...");
─ management synthesis - determination of permissible control actions that ensure
the achievement of goals;
─ optimization - based on the integration of simulation, management, optimization
and statistical methods of modeling and forecasting.
Today, computer simulation plays an important role in the process of automation
of the company as a whole. This work involves the following steps:
1. Engineering - building a model of the company;
2. Stage of reengineering - implementation of analysis and improvement of the mod-
el;
3. Management stage - monitoring the company's work within the created model.
At the same time, various methods of analysis are used, in particular, such as func-
tional-cost analysis, simulation modeling.
All over the world, simulation has become widespread in the study of complex sys-
tems and objects due to important advantages [1,3]:
1. It is possible to answer many questions that arise in the early stages of design and
pre-design of systems, avoiding the use of trial and error, which involves signifi-
cant costs [11].
2. The method makes it possible to study the peculiarities of the functioning of the
system under any conditions, including those that are not implemented in field ex-
periments. The parameters of the system and the environment can be varied within
extremely wide limits, reproducing an arbitrary situation.
3. It becomes possible to predict the behavior of the system in the near and distant fu-
ture, extrapolating to the model the results of industrial tests. In this case, the data
obtained earlier are supplemented through the application of a statistical approach.
4. Simulation models of technical and technological systems and devices make it pos-
sible to reduce their testing time many times over.
5. Using the method of simulation, you can artificially quickly and in large quantities
to obtain the necessary information that reflects the course of real processes, avoid-
ing expensive and often impossible field tests of these processes.
6. The simulation model is an extremely flexible cognitive tool capable of reproduc-
ing arbitrary both real and hypothetical situations.
7. Implementing simulations on a computer is often the only real way to solve such
problems.
However, it should be noted that the method of computer simulation, despite all its
advantages and versatility, is not always acceptable, because the calculations on simu-
lation models require significant money and time. Computer simulation as a method
of solving complex problems should be used under the following conditions:
─ unsuitability or lack of analytical methods for solving problems;
─ complete confidence in the successful creation of a simulation model that ade-
quately describes the studied system (process), in particular that it will be possible
to collect all the necessary information about the simulated system (process),
providing a reliable simulation of real situations on a computer;
─ the ability to use the process of building a simulation model for a preliminary study
of the system being modeled, in order to develop recommendations for improving
the conditions of its operation.
Creating a simulation model designed to study the problems of organizational
management, includes: study of the existing functional system, analysis of a hypothet-
ical functional system, design of an advanced system. However, the successful solu-
tion of these problems of simulation is possible only on adequate models. Therefore,
when studying complex economic systems on simulation models, the adequacy of the
model to real objects should be established first. In case of inadequacy of the model,
the results are unreliable, and the decisions made on their basis are erroneous. Ade-
quate simulation model mathematically and logically with a certain degree of approx-
imation reflects the studied system. The logical elements of the model correspond to
the operations performed in reality, and the mathematical description determines the
functions implemented in the real system. Probabilistic operators of an adequate
simulation model reflect the random nature of the events of the real system. Endoge-
nous parameters of the model with the appropriate input factors should be informa-
tive, ie to give credible messages about the system [15,16].
The future is questionable and therefore risky from a business point of view. When
making business decisions, these risks must be assessed. In other words, there is a
problem of decision-making under conditions of risk, when the parameters and varia-
bles are random variables (eg, cost of production, market share, total sales in future
periods can not be determined accurately). If so, will the risky measure be profitable?
There are several ways to explore aspects of risk (uncertainty).
The first way is to use the analytical capabilities of the what if scenario approach,
which allows you to explore alternative situations by modifying the model and identi-
fying the effects of change. Although this approach is suitable for studying the effects
of changes in one or two variables or obtaining a specific response based on the as-
sumptions of the company's management, it is not the most effective for risk analysis.
The second way is to evaluate the best and worst cases. Under this approach, esti-
mates are created taking into account the most favorable and unfavorable conditions
that each input variable could have. Optimistic values are set for the best case and
pessimistic values for the worst. In the real world, not all variables acquire their best
values at the same time as their worst. Although the study of critical situations is very
useful, but this approach does not lead to a set of situations that can really be ex-
pected.
The third way is to use Monte-Carlo simulation. The Monte-Carlo method is one of
the powerful tools for analyzing real economic systems. The basis of this method,
including stochastic simulation, is the synthesis, as well as methods of sensitivity
analysis and scenarios. The Monte-Carlo method is a numerical method based on
obtaining the number of implementations of a random process, which is formed so
that the probabilistic characteristics (mathematical expectations, the probability of
some events, the probability of the process trajectory in some area, etc.) are equal to
certain values of the problem. The Monte-Carlo method is based on the simulation of
a mass process by subtracting its course, in which random oscillations are determined
by drawing lots or a table of random numbers. Economic experiment can be replaced
by statistical tests of the economic process model. The construction of this model can
be based on the distribution of random variables in the studied process.
The Monte-Carlo method is based on the method of statistical tests. Its essence is
that the test result depends on the value of some random variable distributed accord-
ing to a given law. Therefore, the result of each individual test is random. A funda-
mental feature of the method is that it guarantees high quality statistical estimates
only with a very large number of tests that cannot be performed without the help of a
computer.
3 Presentation of the main results of the research
The key words in the concept of simulation are "selective experiments". A large num-
ber of tests are created in a sample experiment. Due to the uncertainty, the result of
each test may differ from the results of other tests. In simulations, sample experiments
are performed on a computer model, thus allowing many tests to be performed with
little material cost (as opposed to field experiments).
When solving a problem that contains one or more random variables, you must
have a rule for deciding what values each random variable will take. The most effec-
tive way to do this is to assign values according to the probability distribution and
consider them as values that actually took place. Because the simulation is a sample
experiment, this process is repeated many times (for example, 1000 times). Each time
we refer to a random variable, we select a value from the probability distribution and
use it to determine the result, ie we choose the value of the random variable so that
the frequency of occurrence of individual values is related to the probability distribu-
tion.
The simulation procedure in summary consists of the following steps:
1. construction of a simulation model that determines uncertainty and risks;
2. performing experiments on a computer, repeating them according to the model
many times. Each time getting one possible scenario;
3. conducting statistical analysis of experimental data;
4. interpretation of the obtained statistical results for making the optimal decision.
The software implementation of the Monte-Carlo method solves the model prob-
lem many times with different combinations of values of values, each time selected
from the corresponding probability distributions, which were previously specified.
The results of these experiments are statistically analyzed and the output is statistical
results. These results can be interpreted as risks included in the decision. For example,
you can find that there is a 10% chance that the internal rate of return will exceed
25%, or with a probability of 0.9 you can be sure that it will exceed 14%.
The computer implementation of the simulation model involves its repeated appli-
cation, using different combinations of randomly selected values using probability
distributions. The aim is to obtain information not only on the average expected value,
but also on the distribution of probabilities of possible outcomes (to know the risks).
The computer implementation of the Monte-Carlo method involves the user speci-
fying the number of iterations to be performed or the number of default iterations to
be performed (for example, 100 iterations). Once the system has entered the simula-
tion mode, you need to select and enter into the system:
─ variables to be analyzed;
─ data output format (eg histogram, frequency distribution);
─ periods for which you want to get printed results.
As a rule, if an error is made when entering the parameters of the Monte Carlo
model into the system, the system provides certain options for its correction.
Typically, simulations end with one or more probability distributions for each vari-
able and certain columns. The output of the Monte-Carlo method is organized in the
following sequence: table of normal approximation, frequency table, descriptive sta-
tistics (mean value, standard deviation, asymmetry, steepness, etc.), histogram.
The essence of the Monte-Carlo method is as follows [4]:
For the desired value of m we find such a random variable X, the mathematical ex-
pectation of which is equal to m, M(X)=m.
For this purpose, we calculate n independent values of m1, m2,…, mn of the ran-
𝑚𝑚 +𝑚𝑚 +…+𝑚𝑚𝑛𝑛
dom variable m; evaluate the mathematical expectation as 𝑀𝑀(𝑋𝑋) ≈ 1 2𝑛𝑛 .
Since the sequence of equally distributed random variables in which there are
mathematical expectations obeys the law of large numbers, then for n → ∞ the arith-
metic mean of these quantities coincides in probability to the mathematical expecta-
tion, ie, for large n quantities M(X)≈m.
The error of the Monte-Carlo method is estimated as 𝑂𝑂(1/√𝑛𝑛), decreases slowly,
depends on the variance and does not depend on the dimension of the problem.
The application of the Monte-Carlo method is carried out by generating a sample
of a uniformly distributed random variable, as well as generating a sample of a quanti-
ty having a triangular distribution [4,5].
The uniform law of distribution of a continuous quantity X on the segment [a, b] is
characterized by a constant probability density on this segment and is equal to zero
outside it. For a uniform distribution law, the probability density has the form [4, 5]:
0, 𝑖𝑖𝑖𝑖 𝑥𝑥 < 𝑎𝑎;
1
𝜑𝜑(𝑥𝑥) = �𝑏𝑏−𝑎𝑎 , 𝑖𝑖𝑖𝑖 𝑎𝑎 ≤ 𝑥𝑥 ≤ 𝑏𝑏;
0, 𝑖𝑖𝑖𝑖 𝑥𝑥 > 𝑏𝑏.
Mathematical expectation and variance of a random variable X are calculated by the
𝑎𝑎+𝑏𝑏 (𝑏𝑏−𝑎𝑎)2
formulas, respectively: 𝑀𝑀(𝑋𝑋) = 2 , 𝐷𝐷(𝑋𝑋) = 12 .
For a uniform distribution law, the function of a random variable X has the form:
0, 𝑖𝑖𝑖𝑖 𝑥𝑥 < 𝑎𝑎;
x−a
𝐹𝐹(𝑥𝑥) = �𝑏𝑏−𝑎𝑎 , 𝑖𝑖𝑖𝑖 𝑎𝑎 ≤ 𝑥𝑥 ≤ 𝑏𝑏;
1, 𝑖𝑖𝑖𝑖 𝑥𝑥 > 𝑏𝑏.
According to the research task, we also chose a triangular distribution (Simpson dis-
tribution). Because, it is used in cases of lack or limited amount of data, as well as to
build complex distribution laws. This distribution does not provide the opportunity to
independently vary the numerical characteristics of the distribution - mode, median,
mathematical expectation. This distribution is used when adding or subtracting two
random variables that are evenly distributed.
That is, if X1 and X2 are independent random variables having a uniform distribu-
tion law in the interval [a / 2, b / 2], then the random variable X=X1+X2 has a trian-
gular distribution in the interval [a, b].
For the triangular distribution law, the probability density has the form [4, 5]:
Mathematical expectation and variance of a random variable X, distributed by a trian-
gular law, are calculated by the formulas, respectively:
𝑎𝑎+𝑏𝑏 (𝑏𝑏−𝑎𝑎)2
𝑀𝑀(𝑋𝑋) = 2
, 𝐷𝐷(𝑋𝑋) = .
24
For the triangular distribution law, the distribution function of a random variable X
has the form:
0, 𝑖𝑖𝑖𝑖 𝑥𝑥 < 𝑎𝑎;
2(x−a)2 𝑎𝑎+𝑏𝑏
𝐹𝐹(𝑥𝑥) = � (𝑏𝑏−𝑎𝑎)2 , 𝑖𝑖𝑖𝑖 2
≤ 𝑥𝑥 ≤ 𝑏𝑏;
1, 𝑖𝑖𝑖𝑖 𝑥𝑥 > 𝑏𝑏.
Thus, taking into account the peculiarities of the distribution of the studied indicators,
the authors chose uniform and triangular laws of distribution of random variables for
simulation of a particular enterprise using modern tools to automate all stages of cal-
culations.
The action of the proposed method will be considered by example. The initial data
are as follows: the industrial holding company wants to invest 10 million dollars. into
the parent enterprise improvement program, hoping that this program will have a life
cycle of 10 years. The company's management has determined that the key factors for
analyzing the profitability of this proposed investment are: Market size; Selling price;
The company’s market share; Total investment; Salvage value of the investment;
Operating costs; Fixed costs.
All of these metrics are related to the uncertainty that is modeled by the probability
distributions that can be specified. In formulating a forecast, the company knows that
it intends to close the facility if the selling price is lower than the variable cost per
unit of output. In this case, it is necessary to take into account fixed costs.
Fig.1. Algorithm for applying the Monte -Carlo method to predict the company's activities
A generalized algorithm for determining the company's income or the condition of
cessation of production and payback ratio or profit margin is shown in Fig.1. The
algorithm is based on a modification of the Monte-Carlo method of generating sam-
ples of random variables with uniform and triangular distribution.
For the convenience of description, the following notations were introduced in the
algorithm: І_М - Initial Market, the input parameters of which are marked as (a1, a2,
a3); M_G is the Market Growth, which can take values that aredenoted as (b1, b2,
b3), M [m] is the product of I_M and M_G; S_P is the Selling Price, the input param-
eters of which are denoted, as (c1, c2, c3), M_S - Market Share, the value of which is
marked as (d1, d2); I - investment, million dollars. (Investment), the input variables of
which are denoted as (g1, g2, g3); t - the amount of investment; O_C - variable (oper-
ating) costs per unit of output (Operating Cost per unit), the parameters of which are
marked as (u, v, w); F_C - fixed costs, $ thousand (Fixed Cost), whose values are
marked as (x, y, z); R - Revenue income; N_I - net income Net Income; R_R - Net
Income rate of return.
After creating the algorithm, the program code for implementing the Monte
Carlo method was developed to predict the company's activities in the object-oriented
high-level programming language Python [6,7]. A fragment of the listing which,
where the calculation of key indicators is presented in Fig.2.
Fig. 2. A fragment of the listing of the program for the implementation of the Monte Carlo
method
Termination conditions are also programmed. The condition of production shutdown
is expressed by using the built-in Maximum function to determine income. If the sell-
ing price is lower than operating costs, the income is 0; if higher, the income is de-
termined by multiplying the sales volume by the difference between the selling price
and variable (operating) costs.
After developing the program, the initial parameters of all variables were entered
into the program, which for convenience of presentation were summarized in table 1.
Table 1. Functions of distribution of probabilities of expenses and receipts of the company
Index Distribution Parameter values
Initial Market triangular 150 000, 300 000, 84 000
Market Growth triangular 1.04, 1.07, 1.1
Selling Price triangular 420, 570, 610
Market Share homogeneous (uniform) 14 % to 19 %
Investment triangular 8000, 10500, 12500
Operating Cost- triangular 390, 520, 565
perunit
Fixed Cost triangular 300, 350, 410
Salvage Value triangular 4.5, 5.5, 6
After entering the initial data and processing them by the program, indicators of
simulation of net income and profit margins of the company during the forecast peri-
ods were obtained (Fig. 3).
Fig. 3.The results of simulation in the form of a table of frequencies
Analyzing the results of simulation, it can be noted that even in the 10th year, net
income can fluctuate greatly (between losses of more than 300 thousand dollars and
profits of more than 3 million dollars). In addition, the rate of return varies according
to these investment indicators from 0.7 to 673,295.
The graph of the distribution of probabilities of net profit (Fig. 4) showed that the
lowest (with negative values) profit may have a low or highest probability when there
are significant risks of losing investment and when variable (operating) costs exceed
the selling price.
Fig. 4. Graph of the distribution of the probability of net profit
In general, it can be noted that the use of the Monte Carlo method and the triangular
distribution allows you to predict the activities of the enterprisefor future periods with
a certain probability of the ratio of profit and payback.
4 Conclusions
Based on computer simulation, as an effective method of analyzing economic sys-
tems, it is possible to ensure competitiveness and avoid risk in companies of any level
and scale. Making management decisions at risk is always accompanied by subjective
and objective difficulties that are associated with changes in business processes. Stra-
tegic planning support tools based on computer simulation provide an opportunity to
reflect complex nonlinear interactions in the business, assess the consequences of the
implementation of various scenarios or predict further developments in the company.
The synthesized new mathematical model and its software implementation de-
scribe the determination of the company's income or the condition of cessation of
production and the rate of return or rate of return. The application in the classical
Monte Carlo method of generating samples of random variables that have a uniform
and triangular distribution, as well as risk analysis of the company's activities and
forecasting for the future give a greater probability of a correct result. In addition, this
approach is used in cases of lack or limited amount of data, which is also an ad-
vantage of using the proposed method.
References
1. Kuzmina, O.M., Yaremko, C.A.: Pidvyshchennia efektyvnosti upravlinnia biznes-
protsesamy na osnovi imitatsiynogo modeluvannia. Komputerno-integrovani telhnolodii:
ocvita, nauka, vyrobnytsvo. 39: 44-49 (2020). DOI: 10.36910/6775-2524-0560-2020-39-
08.
2. Kuzmina, Elena М., Yaremko, Svetlana А., Ignatovska, Ruslana V., Sichkoc, Tatiana V.,
Smolarzd, Andrzej, Smailovae, Saule: Methods and techniques for evaluating effective-
ness of information technology implementation into business processes. Proceedings of
SPIE Vol. 10808. 108081N:1-7 (2018). DOI: 10.1117/12.2500620.
3. Sytnik, V.F. Systemy pidtrymky pryinyattya rishen: navchalui posibnyk. KNEU. Ky-
iv(2004).
4. Klochko, O.V., Klochko, V.I., Potapova, N.A.: Metody optymizatsii v ekonomitsi:
navchalnyi posibnyk. Vinnytska hazeta. Vinnytsia (2013).
5. Klochko, O., Nagayev, V., Klochko, V., Pradivliannyi M., Didukh L. Сomputer oriented
systems as a means of empowerment approach implementation to training managers in the
economic sphere. Inf. Tech. And Learn. Tools 68: 37- 44 (2018).
DOI:10.33407/itlt.v68i6.2484.
6. Brian Jenkins Python: Python programming. A Step-by-Step Guide For Absolute Begin-
ners Kindle Edition. ATS Coding Academy. Soldby: Amazon.com Services LLC (2018).
7. Richard Ozer Python Programming: The Basic, Blackhat, Intermediary and Advanced
Guide to Python Programming. Volume 1. Paperback (2018).
8. Azarova A. O., Zhelyuk N.S.Selection, planning and realization of development strategy
by an enterprise.Actual Problems of Economics №12. pp. 91–100(2010).
9. Azarova A. O., Hil O.V.Basic indices definition of product quality management by means
of correlation-regressive modelling. Actual Problems of Economics.№ 12. pp. 186–191
(2008).
10. Vassilenko, S Valtchev, JP Teixeira, S Pavlov. Energy harvesting: an interesting topic for
education programs in engineering specialities. Internet, Education, Science (IES-2016)
p.p. 149-156 (2016).
11. Zyanko, V. V., Stasyuk, N. L., Dong Xinying Sutnist ta dzherela finansovogo zab-
ezpechennya innovatsiynoyi diyalnosti malih pidpriemstv [Essence and sources of finan-
cial support of innovation activity of small enterprises]. Visnik Vinnitskogo politehnich-
nogo institute. Bulletin of the Vinnytsia Polytechnic Institute, №4, 57-62 (2015).