=Paper=
{{Paper
|id=Vol-2851/paper30
|storemode=property
|title=The Information Technology Use for Studying the Impact of the Project Environment on the Timelines of the Crops Harvesting Projects
|pdfUrl=https://ceur-ws.org/Vol-2851/paper30.pdf
|volume=Vol-2851
|authors=Pavlo Lub,Vitaliy Pukas,Andriy Sharybura,Roman Chubyk,Olga Lysiuk
|dblpUrl=https://dblp.org/rec/conf/itpm/LubPSCL21
}}
==The Information Technology Use for Studying the Impact of the Project Environment on the Timelines of the Crops Harvesting Projects==
https://ceur-ws.org/Vol-2851/paper30.pdf
The Information Technology Use for Studying the Impact of the
Project Environment on the Timelines of the Crops Harvesting
Projects
Pavlo Luba, Vitaliy Pukasb, Andriy Sharyburaa, Roman Chubyka, Olga Lysiuka
a
Lviv National Agrarian University, str. V. Velykogo, 1, Dublyany, 80381, Ukraine
b
Podilsk State Agrarian-Technical University, str. Shevchenka, 13, Kamyanets-Podilsk, 32316, Ukraine
Abstract
The influence of the project’s environment on the start-up time and duration of works in
sugar beets harvesting projects is characterized. The main attention is paid to the
agrometeorological and subject-biological components of the project environment. The usage
necessity of statistical simulation modelling methods for the features consideration of the
project environment influence on works timelines in projects is substantiated. The main
requirements for the statistical simulation model of harvesting projects are given. The main
indicators that should be taken into account in the statistical simulation model of projects to
establish the characteristics of the natural time of project start-up and duration of work are
revealed, as well as assess their overall impact on the value of these projects. The main stages
of the impact study of the project environment and substantiation of management decisions in
crop harvesting projects are identified. The results of computer experiments with a statistical
simulation model of crop harvesting projects according to the impact of the project
environment on the work timing in these projects are processed and summarized. The
distribution of naturally determined time of sugar beet harvesting projects start-ups with a
different planned duration of their implementation has been established. The regularity of
change of mathematical expectation estimations of naturally caused works duration in
projects is given and this indicator is compared with their planned duration. The distribution
of naturally determined works duration in harvesting projects with different planned value is
substantiated. The differential functions of distribution and statistical characteristics
estimation of naturally determined works duration are given. On the example of the task of
the impact consideration of project environment on the timing of the works was proved a
relevance the risk management task in crop harvesting projects. The development necessity
of automated decision support systems is also confirmed.
Keywords 1
Project environment, Observations, IT, mathematical methods of statistics, Modelling,
Support of management decisions, Start-up time, Project, Efficiency.
1. Introduction
A significant part of projects in agricultural production requires consideration of the impact of the
project environment. The project environment is external influences that can change the outcome of
the project compared to its planned value [17, 19]. Such components of the project environment of
crop harvesting (CH) technological systems projects of agricultural crops include agrometeorological
conditions and the reached yield [7, 14, 15]. The continuity and variability over time of these natural
processes leads to the risk of the effectiveness of CH projects and the occurrence of losses.
Proceedings of the 2nd International Workshop IT Project Management (ITPM 2021), February 16-18, 2021, Slavsko, Lviv region, Ukraine
EMAIL: pollylub@ukr.net (A. 1); pukas.ivanna@gmail.com (B. 1); ascharibura@gmail.com (A. 2); r.chubyk@gmail.com (A. 3);
data_2008@ukr.net (A. 4)
ORCID: 0000-0001-9600-0969 (A. 1); 0000-0002-0083-7359 (В. 1); 0000-0001-7329-8774 (A. 2); 0000-0003-1974-2736 (A. 3); 0000-
0001-5121-359X (A. 4)
©️ 2021 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)
Accordingly, to determine the startup time and completion of CH projects, it is necessary to take into
account the patterns of change of the projects environment, which will ensure their implementation
with the highest indexes’ of value [5, 15, 27]. Undoubtedly, such scientific and applied tasks are
related to management and require the use of specific methods and models for their solution [2, 3, 25],
and the use and processing of significant amounts of characteristics data of the project environment
with information technology (IT) using. Thus, the implementation of CH projects requires solving a
scientific and applied problem to improve the efficiency of relevant management processes by taking
into account the impact of the project environment on the timing of their implementation and the
value of projects in general. The solution of these problems requires the creation and use of specific
methods and models of project management. Their construction requires a synergistic combination of
different areas of knowledge – management, operational-subject, technological, mathematical
statistics, simulation and IT.
2. Analysis of Recent Research and Publications
Time management tasks in projects have long been the subject of research in various fields of
industrial production [12, 20, 23] and the national economy [3, 28-30]. In the field of agriculture,
many scientific works are devoted to this task [1, 3, 14, 15, 27], based on a systems approach, use
methods of mathematical statistics [6] and statistical simulation using IT [8, 9, 11, 16, 21]. Known
works in which the tasks of project management for the development of technological systems
involve the justification of rational parameters of specialized machines complexes in accordance with
the planned scope of work and the natural timing of projects [1, 14]. In particular, the configuration
and content of agricultural projects are substantiating by the cost criterion – the minimum unit cost.
To do this, evaluate the rationality of decisions on project management – the consistency impact of
project start-up time (start of work), configuration and content on the work timeliness and economic
indicators of value (efficiency). The analysis of these works convinces of the need for a deeper study
of management decisions on the coordination of project start-up time, content and duration of work,
as well as the configuration of projects (technical equipment).
The aim of the research is to reveal scientific and methodical provisions and results of research
of objective components influence of the projects environment on the time of start-up and works
duration in agricultural crops harvesting projects.
2.1. Results of Research
Implementation of СH projects is based on the well-known project management processes, and
also requires consideration of the impact of the project environment (rate of harvest,
agrometeorological conditions), content (scope of work) and configuration (technical support,
contractors) of projects. Therefore, the determination of the start time (τз) (calendar day) of СH
projects should be performed taking into account that the terms of their completion (τк) coincide with
the corresponding agro-technical terms [27]. In particular, such terms of completion of sugar beet СH
projects are due to the correspondence between their content and configuration, as well as the impact
of the project environment – harvest, continuous change of soil (its physical maturity) in autumn and
the impact of agrometeorological conditions [27, 28]. Then the project will be considered in time, and
the time of its launch will be rational. Note that the completion time (τф) of the soil’s physical
maturity reflects the production situation in which work in the sugar beet harvesting projects are
stopped (due to the beginning of winter), the crop is lost, and the value of projects decreases.
The development of such methods and models of СH project management, which allow to take
into account the peculiarities of the project environment (with probabilistic components) on the
indicators of the value of their implementation requires the use of appropriate databases and
knowledge, statistical simulation methods [9, 10, 13], information technology (IT) and generalization
of the results of computer experiments (Figure 1).
On this basis, there is an opportunity to justify management decisions to improve the efficiency of
project management processes, the development of concepts for the coordination of projects
components for the development of agricultural production and their value in general.
Substantiation of
Observation and IT and
management
database formation Project Modelling
decisions
Project The value of CH
environment Project CH projects
Figure 1: The main stages of the study of the project environment impact and substantiation of
management decisions in the CH projects
To determine τз it is necessary to have a database on τф, as well as to know the duration of work
(tр) in СH projects:
=p
S
=1
n
(1)
tp = ,
Wд
where Snγ – the area of the γ-th field, which forms the content of the СH projects with р-th their total
number, hа; Wд - daily rate of works in СH projects, ha/day.
Thus, the start time τз of the СH projects must be determined so that all work is completed before
the event τф, then the equality – τк = τф will be ensured. Abstracting from the influence of the
agrometeorological component of the project environment τз can be defined ideally as the time
difference between the calendar day τф and the duration of work tр. However, in production
conditions, the time of completion of τк projects of СH is characterized by the probability due to the
influence of agrometeorological component:
τк = f(τз, Wд, Sn, Σtн). (2)
where Σtн – the total duration of non-rainy intervals during the implementation of projects, days.
Information on Σtн can be obtained from official data of agrometeorological stations [1].
The probable character of the CH projects completion time τк complicates its accurate forecasting.
Therefore, for any planned (defined) time of launch τз of projects there is only a certain probability
that specialized works will be completed at the moment τф and the condition – τк=τф will be fulfilled.
This feature of CH projects is due to the probabilistic influence of the project environment –
agrometeorological allowed fund time for the implementation of works in projects.
The objective reason for such stochasticity is also the influence of non-rainy intervals (tн), which
leads to an increase in the duration tр of the corresponding works in the projects and the risk of their
timeliness. Occurrence of non-rainy intervals tн presupposes the need to shift the start time τз of CH
projects at an earlier date by the total duration of non-rainy intervals – Σtн. Accordingly, the actual
duration tр of work in CH projects will increase in direct proportion, which reflects the objective need
to develop methods and models for content and time management in these projects.
It should be mentioned that the daily rate of works Wд in CH projects is also characterized by
variability. These rates are determined by the productivity of beet harvesters [18, 22, 26], as well as
organizational and technological forms of relevant work [1, 14, 15, 27]. Seeing that the productivity
of the beet harvester depends on the fields and the state of the crop grown characteristics, the pace of
work in the projects of CH will be variable.
As for the state of the grown crop, in particular sugar beets, this state changes objectively and not
only before the launch of the CH projects but also during their implementation. The pattern of
changes in this project environment component state is characteristic of each individual field Snγ,
which is included in the content of the CH projects. At the time of their launch, this state is different.
Knowledge of the regularity of its change to the event τз as well as its significance at the time of τз
allows you to predict this state (yield) for any time of work in these projects [7]. The ability to predict
this condition is the basis for assessing potential losses from premature or untimely work. If they are
performed prematurely, losses will occur due to a shortage of potential yield [7], which could grow to
τф [27]. In the case when works in CH projects are performed late (before the onset of frost, or τф) part
of the area with the achieved harvest of sugar beets remains unharvested, and therefore the crop
grown on them is lost completely. The possibility of estimating crop losses due to premature and
untimely execution of works makes it possible to assess the risks of CH projects, and thus justify
management actions to minimize them. This is achieved through knowledge of the patterns of change
in the state of the biological component (sugar beet harvest) of the project environment during the
relevant calendar period.
Having data on the timeliness of work in the CH projects there is a possibility of cost estimation of
crop costs due to their early or undeveloped implementation. To assess (forecast) these costs, it is
necessary to know the number of crop losses, their market value, material and technical costs, as well
as the cost of time to work on these projects. Cost estimation is performed according to known
methods [24].
Quantitative assessment of the timeliness of work in the CH projects with the appropriate technical
support is carried out on the basis of modelling the impact of agrometeorological and subject-
biological components of the project environment on the course of work in these projects. Given the
probabilistic nature of many components, the model of CH projects should be statistical and
simulation [9, 10, 13], which would reproduce the features of their interaction. It is the repeated
(iterative) reproduction of works in projects that makes it possible to reflect and take into account the
probabilistic components and determine the estimates of statistical characteristics [6] of the main
indicators of the CH projects value.
Considering the key points of statistical simulation, which allow determining the number of works
in the CH projects. Generating in the calendar time model (τф) the completion of the physical maturity
of the soil (or the occurrence of frosts in the autumn-winter period) at which work in the projects of
CH is completed allows you to set an "extreme point" to record the timeliness of work. For each
iteration of the model, the value of τф allows setting CH τз. To do this, determine the duration of tр in
projects. Under favourable agrometeorological conditions (tн = 0 days) the duration of tр is found by
formula (1). For this purpose, the daily rate (Wд) of works in CH projects for the γ-th field is
determined, which depends on many factors: 1) configuration (Кγ) and relief (ργ) of the field; 2) yield
of sugar beets (Uγ); 3) technical support of CH projects (Тн); 4) organizational and technological
forms of their implementation (TЛ); 5) the daily duration of harvesting (tд):
Wдγ = f(Kγ, ργ, Uγ, Tн, TЛ, tд). (3)
Without resorting to the methodological principles of determining (forecasting) the daily rate of
work Wд for many fields with sugar beet harvest [18, 22, 26], note that the value of Wд is taken as the
average for all fields and is determined by statistical simulation modelling of project-technological
works.
The availability of statistical models of τф, tн and clear intervals (tп) for the autumn-winter period,
as well as knowledge of the daily rate Wд of works is the main database for statistical simulation of
sugar beet projects and forecasting of terms τз. In particular, the start time τз of projects for a known
value of τф, in this case, will be determined by the formula:
зi = фі − (t р + tн ).
i іj (4)
j
where і, j – the indices of the multiplicity of the implementation of CH projects in the model and the
values of the non-rainy period of the autumn-winter period.
Thus, the analysis of the preconditions for the formation of the start time τз of the CH projects
shows that for a constant duration tр is determined by three probabilistic components – the time of
completion τф physical maturity of the soil, as well as the duration of non-rainy (tп) and rainy (tн)
intervals. Given this, the "scatter" of the values of the probabilistic value of τз will be larger compared
to the values ф [25]. This means that the risk of making an incorrect decision on the start time τз of
CH projects increases compared to the accuracy of forecasting the time of completion τф of physical
maturity of the soil in the autumn-winter period.
Taking into account the impact of the agrometeorological component on the work in the CH
projects makes it possible to objectively establish the statistical change patterns in their functional
indicators of efficiency. In particular, to take into account the impact of this component of the project
environment, the relevant observational data were collected, systematized and processed. Based on
the processing of observation reports (TСХ-1, KM-1) of the Volodymyr-Volyn meteorological station
on the condition of the upper layers (0-2, 2-10 cm) of the soil (for the period of 45 years – 1971-
2016), time and volume of precipitation rain (for 16 years – 2000-2016) formed empirical data (for
the calendar period from September 1 to November 30): 1) the duration of the naturally allowed daily
fund of time to perform work in the СН projects; 2) the duration of the naturally allowed time fund
for these works during the autumn period; 3) the time of rain in the context of the day.
Empirical data are processed by known methods of mathematical statistics [6], as a result the
theoretical distributions of probabilistic quantities are substantiated. The obtained statistical
regularities are the basis for the reflection of the simulation model of the project environment impact
on the timeliness of work in virtual projects of CH [13].
Thus, the method of performing production observations on the impact of agrometeorological and
biological-subject components of the project environment is based on the results of specially
organized observations of the meteorological station. On this basis, a retrospective set of indicators
was obtained and their mathematical processing was performed, which made it possible to form an
exhaustive list of statistical regularities to take into account time constraints on work in CH projects in
their statistical simulation model.
The method of works modeling in projects is to reflect the impact of natural processes on the
timing of their implementation, as well as to reflect the daily course of beet harvesting [18, 22, 26],
which are performed adaptively to the continuous growth of sugar beetroots, their maturation, and
physical maturity under the stochastic influence of agronomic conditions autumn period.
It is well known that due to such a biological feature of sugar beet root formation as an increase in
their weight and sugar content in the autumn, it is quite economically motivated to harvest at the latest
calendar dates [27]. However, due to the stochasticity of agrometeorological conditions, the
timeliness of work in CH projects will be characterized by risk [15].
That is why the time fund for the implementation of these works must be coordinated with natural
processes, to perform simulation modelling of the impact of the project environment on the value of
CH projects, to use the appropriate database and IT. To reveal the relationship between the duration tр
of the work in the projects and the natural time of their beginning ( зп ), as well as to assess the risk
зп , we performed a statistical simulation of the development of weather conditions in the autumn. In
particular, зп it was determined for four variants of the planned duration of tр – 5, 10, 15 and 20 days
(Figure 2).
The analysis of distributions indicates of the зп a significant variation of this probabilistic value,
which is 60 days. Accordingly, in practice it is quite difficult to accurately predict τз at which work in
the CH projects will be performed with the provision of the condition – τк = τф. This feature of the
impact of the project environment determines the significant relevance of risk management tasks in
CH projects and the development of automated decision support systems.
It should also be noted that due to the influence of non-rainy intervals, the duration of tр will
increase. This impact of the project environment also increases the probability of losses in CH
projects. Our computer experiments made it possible to establish the influence of the
agrometeorological component of the project environment on the "extension" of the duration of work
tр in projects compared to their planned value (Figure 3).
The obtained regularity of mathematical expectation estimates M [t пp ] for different tр in CH
projects (Figure 3) confirms the hypothesis that for relatively large values of tр duration the influence
of agrometeorological component of the project environment on the timeliness of work will be more
negative.
This phenomenon also causes a downtime of technical support at rainy intervals and affects the
risk of timely work in projects. In particular, the value of the correlation coefficient – r = 0.999 states
a close relationship between M [t пp ] and tр.
It is also established (Figure 4) that the increase in the planned duration tr leads to an increase in
the scatter of the probabilistic quantity t pп .
0.30
M [ з.15
п
] =284 day; (tр=15 days) M [ з.10
п
] =291 day; (tр=10 days)
M [ з.20
п
] =276 day; (tр=20 days) M [ з.5
п
] =299 day; (tр=5 days)
0.25
0.20
Frequency, Рі
0.15
0.10
0.05
0.00
240 250 260 270 280 290 300 310 320 330
Calendar terms d, days
Figure 2: Distribution of naturally determined time of sugar beet harvesting projects start-up with
different planned duration of their implementation: M [ з.5 п
], M [ з.10
п
], M [ з.15
п
], M [ з.20
п
] – the
estimation of the naturally determined time mathematical expectation of the CH projects start-up
for different (5,10,15 and 20 days) planned (tр) their implementation
45
Estimates of mathematical expectation of naturally
40
determined duration of works М[tпр], days
M [tpп ] = 1.5238∙tр - 0.9413
35
30
25
20
15
10
5
0
10 15 0 20 5 25 30
Planned duration of works tр, days
Figure 3: Regularity of estimations of mathematical expectation of naturally caused duration ( M [tpп ] )
of works in СH projects (in comparison with its planned value)
In particular, the study of the results of statistical simulation relatively t pп , allowed to establish that
their empirical distributions are consistent with the theoretical law of Weibull distribution.
0.45
1
0.40
0.35
2
0.30
3 4
Frequency, Рі
0.25
0.20
0.15
0.10
0.05
0.00
0 5 10 15 20 25 30 35 40 45 50 55
п
Naturally determined duration of work t , days зб
Figure 4: Distribution of naturally determined duration ( t pп ) of works in СH projects with different
planned value (tр): 1 – 5 days; 2 – 10 days; 3 – 15 days; 4 – 20 days
Table 1
Differential functions of distribution and estimation of statistical characteristics of naturally caused
duration of works implementation in CH projects
Estimates of statistical
Planned characteristics
Differential distribution function
duration of M [tpп ]
(Weibull)
works tр, days , [tpп ]
day
tp.5
п
−5
0,079
t п − 5 1,079
f (t ) = 0,498
п
exp −
2,169 2,169
p.5
5 7,12 0,939
p.5
tp.10
п
− 10
0,154
t п − 10 1,154
10 f (t
п
) = 0,258 4,472 exp − p.10 14,27 0,879
p.10
4,472
tp.15
п
−15
0,451
t п −15 1,451
15 f (t п
) = 0,19 7,624 exp − p.15 21,91 0,698
p.15
7,624
tp.20
п
− 21
0,528
t п − 21 1,528
20 f (t п
) = 0,161 9,492 exp − p.20 29,55 0,664
p.20
9,492
The obtained data sets were processed by the methods of mathematical statistics, which together
with the application of Pearson's χ2 criterion made it possible to substantiate the differential
distribution functions t pп (Table 1). Thus, taking into account the impact of the project environment
(agrometeorological and subject-biological components) on the start-up and end dates of work in the
CH projects plays an important role in assessing the risk of their timeliness. On this basis, the risk of
losses in projects, the consistency of the start time, production area and parameters of technical
support of projects is assessed, and then their value is determined. The generalization of tasks for the
CH projects convinces that agricultural enterprises are interested in starting their implementation in
the late calendar period at which the crop yield is maximum, as well as to perform of projects work in
the shortest possible time. However, shifting project start times to late calendar periods increases the
likelihood of delays in harvesting, frost damage to root crops, and reduced the project efficiency.
Simultaneously, reducing the duration of work in these projects requires powerful technical support
and leads to significant costs [24]. To solve this problem, it is necessary to reconcile the start up time
of project and the culture production area with the technical support parameters of the respective
projects. However, the choice of CH projects start up time with a known duration of work will allow
to ensure their timeliness only with a certain level of probability. If the work is performed for a long
time, there will objectively be a larger "scatter" of the distribution values of the naturally determined
time of project start (Figure 4). This indicates that ensuring the timeliness of work in projects will be
less likely, and thus increase the likelihood of losses and reduce the value of projects. Disclosure of
the methodology of taking into account the impact of the project environment at the start up time of
CH projects is aimed at identifying the criteria and function of the goal, as well as defining
requirements for modelling techniques and establishing statistical patterns of functional indicators of
relevant projects. The establishment of these patterns is the basis for testing the hypothesis that
improving the efficiency of project management can be achieved by coordinating the interaction of its
components, in particular, on the criterion of minimum specific total cost. The combined impact of
agrometeorological and biological-subject components of the project environment of the СH is
characterized by stochasticity and objectively forms the naturally determined terms of its
implementation. Taking into account of this feature makes it possible to assess the timeliness of the
relevant work in the projects for a given area of sugar beet and technical support. Substantiated
distributions and statistical regularities of influence of agrometeorological and biological-subject
components allow to reflect objectively a course of works in projects of CH in their statistical
simulation model. The development of this model and the performance of computer experiments
make it possible to obtain functional indicators of the efficiency of the relevant work, and thus to
reconcile the time of their beginning and the production area of sugar beets with the parameters of
technical support.
2.2. Conclusions and Prospects of Further Researches
The objectives specificity of the study necessitates a combination of production observations and
computer experiments, which are aimed at system-event reflection of the impact of
agrometeorological and biological-subject components of the project environment of CH on the
timeliness of their implementation. Uncontrollability and stochasticity of basic events that affect the
course of work, necessitate the consideration of functional indicators in probabilistic terms. The
development of methods and models of CH project management that allow to take into account the
probabilistic components of the project environment requires the use of appropriate databases and
knowledge, methods of statistical simulation, IT, computer experiments and generalization of their
results. This makes it possible to decisions substantiate for the efficiency increase of projects
management, as well as to form programs for the development of technological systems for
harvesting crops. The use of IT in the study of the project environment impact on the start-up time
and duration of work in the projects of CH allows performing statistical simulation of these works and
obtaining objective results of computer experiments. On this basis, establish patterns of change in the
value of projects with the appropriate technical support (configuration), start-up time and crop
harvesting area (content). The analysis of the established distributions of the naturally conditioned
time of start-up of CH projects indicates a significant variation of this probabilistic value (60 days)
(Figure 2). Therefore, in practice it is quite difficult to predict the time of project launch at which the
relevant work will be performed on time. This feature of the project environment impact, determines
the significant relevance of risk management tasks in СH projects and the development of automated
decision support systems. Due to the influence of the project environment, there is also a risk of the
duration of work increasing in CH projects and increasing the likelihood of losses. Our computer
experiments allowed us to establish the influence of the projects environment on the "extension" of
the duration of work compared to its planned value (Figure 3). For a relatively longer planned
duration of works, the impact of the project environment on the timeliness of work in the CH projects
will be more negative. In particular, the study of the results of statistical simulation on the variability
of the natural work duration in the projects of CH, allowed establishing (Figure 4) that their empirical
distributions are consistent with the theoretical Weibull distribution law (Table 1). The choice of CH
projects start up time with a known duration of work will allow to ensure their timeliness only with a
certain level of probability. If the work is performed for a long time, there will objectively be a larger
"scatter" of the distribution values of the naturally determined time of project start (Figure 4).
3. Acknowledgements
All studies were performed on a self-financing basis, with the non-commercial assistance of the
agrometeorological monitoring station and with the support of researchers. The research and results
presented in the materials of the article are performed and summarized in co-authorship of several
people. In particular, the collection and processing of agrometeorological data for the conditions of
the Volodymyr-Volyn region of the Volyn region was performed by co-authors Lub P.M. and
Pukas V.L. The formation of the database and its processing by methods of mathematical statistics
was performed by Sharybura A.O. and Lysiuk O.V. The creation of a statistical simulation model of
weather conditions that affect the technological processes of sugar beets harvesting in the autumn,
thanks to the joint work of Lub P.M., Pukas V.L. and Chubyk R.V. They also performed statistical
simulation, summarized the results and formulated conclusions. Processing of simulation results was
also carried out by Sharybura A.O. and Lysiuk O.V.
We thank the meteorological station located in Volodymyr-Volynskyi, Volyn region for
cooperation, clarity and systematization in providing access to the results of observations of
agrometeorological processes and the achievement of crop yields.
Thanks also to Lviv National Agrarian University for providing technical equipment and research
laboratories to develop the program code of the statistical imitation model of virtual CH projects and
performing computer experiments.
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