Кwilinski Alex


49 
www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

2019 Volume 2 Number 1 (January) 
 

  
COOPERATION AND INTEGRATION PROCESSES AND MODELS IN CONTEXT OF 

DEVELOPMENT OF BRANCHES OF ECONOMY AND TERRITORIES 
 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
 
Abstract. The conditions of enterprise functioning in the agrarian sector have been analyzed. 
It has been proved that cooperation and integration are a basis for the development of the 
agro-industrial complex. The necessity of developing the models of forming and managing 
integration processes of enterprises of the agrarian sphere has been substantiated. The use 
of a multiagent approach to the study of agricultural servicing cooperatives has been 
proposed. The developed models of social and economic systems can serve as a tool for 
their optimization. Such indicators as stability of the system, competitive reliability have 
been used. Approaches to determining the optimal potential of the system, strategies for its 
management have been substantiated. Based on these approaches, a model of the optimal 
policy for updating equipment has been determined. 
Keywords: cooperation, integration, agro-industrial complex, multi-agent structure, social 
and economic systems 
JEL Classification: F15, P13, Q13  
 
Author(s):  
 
Mykola Rohoza 
Poltava University of Economics and Trade, 3, Kovalya Street, Poltava, Ukraine, 36040 
E-mail: rogoza.ne@gmail.com 
https://orcid.org/0000-0002-5654-7385 
 
Vasyl Perebyynis 
Poltava University of Economics and Trade, 3, Kovalya Street, Poltava, Ukraine, 36040 
E-mail: perebyynis@gmail.com 
https://orcid.org/0000-0002-4779-515X 
 
Kseniia Verhal 
Poltava University of Economics and Trade, 3, Kovalya Street, Poltava, Ukraine, 36040 
E-mail: vergal.ks@gmail.com 
https://orcid.org/0000-0001-6611-0489 
 
Citation: Rohoza, M., Perebyynis, V., & Verhal, K. (2019). Cooperation and integration processes and 
models in context of development of branches of economy and territories. Virtual Economics, 2(1), 
49-63. https://doi.org/10.34021/ve.2019.02.01(3) 
 
Received: September 7, 2018. Revised: October 21, 2018. Accepted: December 25, 2018. 
© Author(s) 2019. Licensed under the Creative Commons License - Attribution 4.0 International (CC BY 4.0) 

https://orcid.org/0000-0002-5654-7385
https://orcid.org/0000-0002-4779-515X
https://orcid.org/0000-0001-6611-0489
https://doi.org/10.34021/ve.2019.02.01(3)
https://creativecommons.org/licenses/by/4.0/


50 
www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

1. Introduction 
 
Appraising the situation at the stage of prospects of Ukraine for joining the association with 
the European Union, it has to be admitted that Ukraine’s economy does not fully correspond 
to the EU’s existing economic and technological structure, regional, branch division and the 
level of personnel corps. After all, the use of the potential can stimulate not only complex 
technological export production, but also development of industries, in particular, formation 
of the agro-industrial complex. Obviously, this sector, as a leader of the economy, can 
become one of the system-makers, stimulate development of economic and social processes 
in the respective territories (Chygryn et al., 2018; Czyzewski & Majchrzak, 2017; Czyzewski et 
al., 2018; Ivanov et al., 2016a; 2016b; 2016c; Ivanov et al., 2017; Kharazishvili et al., 2016; 
Lyeonov et al., 2018; Pająk et al., 2016; Yakubovskiy et al., 2017). 
 
Identification of priority sectors affords an opportunity to implement development of other 
supporting industries, which in turn constitutes the basis for development of territories and 
reaching nationwide goals. 
 
The main argument for such a model is self-organization of the economic system, since in 
complex systems, such a phenomenon may be in open non-linear systems which also include 
social and economic systems (SES). However, in this case, it is necessary to regulate 
emergence of stable elements constituting the structure of complex control systems. In the 
SES, the phenomenon of self-organization is also associated with processes of the world 
globalization with simultaneous integration ensuring an increase in exchange of 
technological innovations. At the expense of this, there is formulation of a basis for rapid 
dissemination of uniform international standards of manufacturing methods, necessary 
institutional factors in the political, economic and social spheres allowing to reduce 
differences in development of states and their territories. 
 
In view of the stated above, it is important to study cooperation and integration as a basis 
for the development of the agro-industrial complex, consider servicing agricultural 
cooperatives as a multi-agent structure and model social and economic systems as an 
instrument for their optimization. 
 
2. Literature review 
 
It is evident that the policy of economic development should be built on the processes of 
self-organization of the domestic market which is possible as long as there are active 
processes of cooperation and integration of economic objects. At the same time, the state 
should not only be an observer, but actively participate in monitoring, regulation and 
management of these processes. It has been established that unstable business 
environment having a high level of dynamism affects conditions and generates risks for 
managing economic objects associated with the need for timely response to these changes 
when managing them. Therefore, the key is an ability to predict and implement necessary 



51 
www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

changes that will ensure effective activities in the strategic perspective of both an economic 
object and the national economy as a whole. 
 
Such tools can include analysis of business environment of any economic object, monitoring 
conditions and parameters of such changes while developing social and economic systems of 
territories. In this case, it is necessary to regulate the process of occurrence of stable 
elements in the structure of complex management systems, which will be related to the 
needs of consumers and changes in their behavior. This, in turn, gives grounds to consider 
issues related to management of cooperation and integration processes of developing 
economic entities, branches of the economy and territories (Dinar & Wolf, 1997; Dźwigoł & 
Dźwigoł-Barosz, 2018; Kvilinskyi et al., 2017; Kwilinski, 2018; Lakhno et al., 2018; Lyulyov & 
Pajak et al., 2016; Shvindina, 2017; Sheldon, 2017; Vasylieva et al., 2018; Vernay et al., 2018; 
Wink et al., 2017). 
 
To achieve this, the modern paradigm of the domestic economy functioning was based on 
designing regional programs aimed at regulating development of economic sectors, 
concentration of material, technical, financial and other resources, scientific, technical and 
industrial potential of the country. Herewith, the coordinating of the activities of local self-
government bodies, central and local executive authorities, as well as enterprises, 
institutions, organizations and citizens is envisaged to solve the most important problems 
(Grishova et al., 2013). 
 
Although there are programs of legislative and regulatory state support of economic 
development, the process of self-organization of the domestic market of territories and the 
nation in general remains imperfect and is characterized by a number of shortcomings. In 
particular, they are related to distribution of funds allocated for financial support and 
insufficient funding of direct support measures for the agrarian sector (as a possible system-
creating sector of the national economy). The main disadvantage lies in the fact that the 
provided support is disproportionate and situational, thus excuses are found for ambiguity 
of formulating objectives and results of the programs as well as lack of responsibility for 
their implementation. This is also due to unresolved issues of the regulatory and legal 
framework and termination of a number of state target programs, as a result of which 
certain areas of the state support for agriculture have ceased their existence (Grishova et al., 
2013). 
 
In such conditions, when the problem of providing financial resources is unsolved, the search 
for new forms of support for agro-industrial development becomes especially urgent. They 
should be aimed at forming financial stability of agricultural production. This, in turn, will 
create prerequisites for expanding production volume of competitive agricultural products 
and food security in the country. Emphasizing the role of the agro-industry for development 
of rural areas is necessary when there is a model of the economic development based on the 
priorities of development of certain industries and territories through development of the 
agro-industrial complex as the main industry. After all, this complex of industries provides 
development of other branches of the economy commissioned to manufacture products for 



52 
www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

the agro-industrial complex (machinery, fertilizers, etc.). The said provides their 
development and, respectively, achievement of the main nationwide goals. 
 
The situation is challenging because till the present time, there has not been set up an 
appropriate system of organizational and economic measures and models which would be 
able to ensure effective functioning of the agricultural industry. Discussions about 
methodology of cooperation and integration strategies have been in progress, which 
prevents to harmonize organizational and economic components of the agrarian reform. It 
results in incompleteness of the scientific and theoretical substantiation of completion of the 
agrarian reform in the country. The issues of establishing institutions at the industry level 
that would be capable of solving problems of social and economic development of rural 
territories have not been resolved. 
 
The study is based on the hypothesis of possibility to overcome the crisis phenomena in the 
social and economic development of territories due to processes of cooperation and 
integration in the agrarian sector of the economy. This is possible provided that models of 
development of not only the economy but also corresponding territories are constantly 
being improved. The achievement of this goal has determined the need for solving problems 
on the basis of disclosure of methodological approaches to activities of rural servicing 
cooperatives. It is important to harmonize the complex of organizational and economic 
measures for development of agro-industrial production on the basis of integration 
processes and cooperation. The above mentioned motivates to elaborate methodological 
principles for assessing agro-economic potential and individual components as one of the 
grounds for development of rural areas (Czyzewski & Majchrzak, 2017; Czyzewski et al., 
2018). 
 
In support of this, it is necessary to provide the following statistics: domestic peasant 
households produce 97-99% of potatoes, 80% of vegetables, fruits and berries, about 80% of 
milk and up to 50% of meat. It should be borne in mind that these products are practically 
made by hand by means of a shovel and have no civilized channels of sales. It should be 
noted that fairly tight trends in the marketing of food products are developing worldwide. 
Obviously, Ukraine will not be able to avoid them. This means that small agricultural 
producers who are out of associations, do not have their own capacities of processing 
agricultural raw materials, storage and pre-sale preparation of agricultural commodities will 
not be able to ensure independently their competitiveness and sales at attractive prices. 
Therefore, there is no other way for domestic small-scale farmers than their association 
(Ivanov et al., 2017). 
 
It should also be borne in mind that agricultural holdings constitute a serious problem for 
development of unintegrated and unassociated agricultural commodity producers. In fact, 
they have already monopolized food markets dictating conditions on the markets for 
agricultural raw materials. This is due to the fact that they have no counterweight - there is 
no cooperation, no association of producers. At the same time, agricultural holdings are not 



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www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

motivated to develop social and economic processes in the territories where they operate, 
therefore they do not invest money in this. 
 
It applies not only to agricultural servicing cooperatives, but also to consumer and credit 
cooperatives. It has resulted in one of the highest poverty rates on the continent, especially 
in rural areas, accompanied by unemployment, extinction of the Ukrainian rural territories 
and decline of territorial communities (Ivanov et al., 2017). 
 
Cooperation in the rural territories has always contributed to the development of the 
infrastructure of the agrarian market and social sphere, and it is a complex social and 
economic problem for management. Problems of creating effective conditions, models and 
methods for the development of agricultural servicing cooperatives as an integral part of the 
agro-industrial complex of the state are caused by the following: lack of trained personnel, 
information and educational resources to form organization of the cooperatives themselves, 
lack of a legal form of regular financial support for cooperation development, indefiniteness 
of nonprofit character of agricultural servicing cooperatives, misunderstanding and 
disinclination of agricultural entities and rural communities to cooperate, underestimating 
the essence and benefits of the cooperative model of agrarian entrepreneurship (Vernay et 
al., 2018; Wink, 2017). 
 
3. Methodology 
 
To develop the models for formation and management of integration processes, which can 
be attributed to innovative ones, goals of the subject (a cooperative) must be divided into 
several directions, which are both external and internal. 
 
The external type of tasks of the analyzed management object (a cooperative) should 
include the following: those connected with information security and decrease in 
uncertainty level, formation of working capital and renewal of fixed assets, support of the 
national regional producer, adoption of amendments to the Tax Code, identification of the 
world trends and, on this basis, improvement of management of the agrarian sector of 
Ukraine's economy, in particular, improvement of the state support for development of rural 
territories and the agrarian sector in general, etc. 
 
In other words, creation of a system for effective study, analysis and use of information 
resources is one of the conditions for successful operation of an economic entity (a 
cooperative) under conditions of uncertainty in the competitive environment; it is a 
prerequisite for adoption and assessment of decisions on determination of a strategy for the 
development of servicing cooperation (Ivanov et al., 2017). This provides with an 
opportunity to establish a general methodological framework for the program of 
development of the Ukrainian rural territories on the principles of combining organizational 
and economic factors of development of the agro-industrial sphere. The reason for such 
optimism is the IMF's assessment of the fact that one dollar invested in the agriculture in 
Ukraine yields a return of ten times higher than in Europe. 



54 
www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

 
The internal problem of the cooperation development is recognizing the need for taking into 
account the potential and peculiarities of forming cooperation and integration processes, 
forming an effective integrated structure of horizontal or vertical orientation, its influence 
on the activities and the development of the enterprises belonging to rural servicing 
cooperatives. In the context of globalization influences, such processes have a positive 
impact not only on the state, but also on any territory and object. Vertical integration is 
defined as extending activities and/or controlling an economic object (a cooperative) along 
the technological-distribution-sales chain: a) at the preliminary stage – till there is primary 
production; b) at the next stage - before commodities are sold to the end user. Its purpose is 
to replace market transactions with other forms of contacts (internal operations and 
processes, long-term contracts, etc.). 
 
A vertically integrated structure model in the simplest form is a two-tier hierarchical 
structure consisting of n functionally dependent subsystems and Pm business processes 
where the results of the previous parts of the hierarchy are an input. In this case, all 
subsystems have the right to make decisions on organization of relevant business processes 
within the limits defined by the management system. Under this condition, the hierarchical 
location of the subsystems (a multi-strand structure) is determined by the fact that some of 
the processes are under the influence or managed (partially/completely) by the 
management system. 
 
The following advantages of the vertical integration have been identified (Ivanov et al., 
2017): decreasing the final product price due to elimination of a traditional distribution 
network, increasing competitiveness of enterprises, reducing transaction costs, synergy 
effect of joint activities, reducing prime cost of the final product, forming vertically 
integrated structures. This presents an important stimulus when forming agricultural 
servicing cooperatives, improving relations between agricultural commodity producers, 
enhancing peasants’ well-being. 
 
The main features of management of agricultural cooperatives are defined by the Laws of 
Ukraine "On Cooperation" and "On Agricultural Cooperation". Their main content is as 
follows: a cooperative is managed on the basis of self-government, publicity, participation of 
its members in solving issues of the cooperative. Governing bodies of a servicing cooperative 
are a general meeting and a board. 
 
When modeling, it is necessary to take into account a possibility of participation of each 
association member in management. In this case, a structure of an agricultural servicing 
cooperative as a multi-agent system can be shown as follows (Fig. 1). 
 
In this case (Fig. 1), an integrated structure is represented by a graph consisting of n+1 
vertices. Each of them defines a type of an agent involved in the cooperation. The vertices 
В01 and В02 are, respectively, managing bodies (functions of which are executed by a 
general meeting and a board of a cooperative). It should be noted that the members of an 



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www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

agricultural servicing cooperative have the right to vote and participate in economic 
activities of the cooperative. Therefore, between each agent Bi and other agents 
constituting a cooperative, there is interaction created when the members of a cooperative 
are rendered services provided by its charter. 
 
Since a general meeting of the cooperative members is the supreme governing body of the 
cooperative, the following can be written (1): 
 

    :   ⋃     . (1) 
 
 

B01 B02

Bi

Bi+1

Bn

B1

Bi-1
B2

 
 
Figure 1. A servicing cooperative as a multi-agent system  
Source: formed by the authors. 

 
In this case, each agent Bi has the freedom to make managerial decisions within a defined 
joint strategy and has a controlling influence on the strategy formation. 
 
It should be taken into consideration that a board headed by a chairman is the executive 
body of a cooperative, and there are restrictions on the number of board members 
depending on the number of the cooperative members. Then, you can specify the following 
(2): 
 

    :   ⋃     . (2) 
 
Let us consider features of membership in a servicing cooperative. According to the 
legislation in force, cooperatives are non-profit organizations created to meet economic, 
social and other needs of cooperative members. We introduce the function f(x) as a function 
of satisfying an agent’s needs. According to studies, an agent’s need will be considered a 



56 
www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

desire to move from one current state to another or a desire to maintain the current state 
expressed in an agent's application to meet his needs. So, (3):  
 

    ⋃   * (  )   ( 
 )                + (3) 

 
where  (  ) is a function of satisfaction of an agent's needs at the expense of his own 

resources; 
 (  ) is a function of satisfaction of an agent's needs due to membership in a 

cooperative; 
A is an external agent. 
 

4. Results 
 
Since an integrated system is a social and economic system (SES) and simultaneously is a 
subject and object of economic relations, it is necessary to understand the nature of 
reproductive and transformational processes that lead to the formation of a new structure 
of relations in the market-led economy. In such case, destabilizing and favorable factors 
for functioning of entity mechanisms should be taken into account . A list of the factors is 
rather general and does not reflect fullness of the economic environment. Therefore, a 
more detailed decomposition of various factors of such an environment of the SES as a 
subject of management (Butyrkin, 2003) is required. 
 
To justify methodological foundations in the management mechanisms, it is necessary to 
consider the nature of interaction of a business entity with the external environment, 
components of which also have their own specifics. When modeling organizational 
structures, it is expedient to use a system quality indicator. It should be understood as 
totality of objectively existing characteristics (indicators) relating to the ability of the system 
to perform its function. In this case, quality indicators can include stability of the system, i.e. 
its ability to perform its functions within the specified parameters under the influence of 
external and internal stimuli (first of all, structural changes). The result of its functioning is 
directly related to the achievement of the system goals. 
 
This indicator is directly related to the functioning or movement of the system to change the 
final state of the business-system in a given strategic period (development) (4): 
 

BSBSv
BSBS

ZtZtZR  )()(
0

 .  (4) 

 
The result of functioning of the business system is an absolute indicator demonstrating how 
much the state of the system at the moment differs from the state of the system in the past. 
A volume of commodities manufactured for a certain period, gross expenditures, net profit, 
etc. may be the indicators of the result of system activities. 
 



57 
www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

Naturally, to analyze alternatives of influence on the system activities, it is necessary to 
develop an effective method for the analysis of production and economic activities. 
Efficiency should be the main static characteristic of such a method. This allows us to assess 
the quality of the functioning of the system/entity and, on its basis, to make managerial 
decisions. 
 
The system analysis methods (hierarchy model) have been used for modeling the relations 
between the SES and external subjects (tax administration, government authorities, financial 
and banking system). Herewith, their dependence on economic, political, social, legal 
conditions has been taken into account. The external subjects’ objectives were the criteria 
used in modeling. Therefore, models for adaptation of national economic development in 
the context of a model of the global development are needed. Given the peculiarities of 
Ukraine's economic development, an analysis of impact of the environment on the results of 
activities of the SES can be provided by assessing the potential of the SES. 
 
Herewith, it should be borne in mind that mathematical models may prove to be 
complicated and their solving may prove to be excessively lengthy. Therefore, in order to 
obtain a result, it is necessary to use so-called heuristic methods based on intuitive and 
empirical rules that allow a researcher to improve already-existing solving. 
 
Competitive reliability of any system depends on its ability to form, use and evaluate the 
available potential of all its elements in conditions where external and internal disturbances 
arise (which must be attributed to the nature of devastating effects).  
 
It is possible to establish comp etitive reliability of the SES by means of determining 
the difference of potential states before and after the effect of disturbing 
influences on the system or by determining the difference in assessment of the 
potential use efficiency (5):  
 





m

i

i

kn

tn

k

j

i

m

i

k

t

k

j

xfxfz
1

0

11

0

00

1

)()(  
 
(5) 

 
where k is a set of potential states of the components of the SES; 
m is potential components of the SES; 

0

00

k

t
f )(

i
x , )(0 i

kn

tn
xf  are, respectively, the optimal potential of a separate component 

of the SES at the beginning and at the end of the forecast period;  

Xx  ( Х is a set of admissible potential components of the SES).  
 
The need to determine the optimal potential is relevant to ensuring the model's 
efficiency in assessing the potential of each component of the SES. This is the 
potential of components of the SES, i.e. х, that (6): 
 

)(*)(
00

xfxf
kk

  for all  Xx  . (6) 



58 
www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

Consequently, since the assessment of the potential use efficiency is an estimate 
that matches each potential х with a real number, i.e. it is a function of the variable 
х. In this case, a criterion of efficiency is a basis for determining the assessment. If 
values of у

0
 factors that are not controlled are known, we have the criterion of 

efficiency )(),(
0

xfyxfz  , which is a function of only х and can obviously serve as 

an efficiency assessment .  
 
The model provides efficiency assessment in several ways, depending on the 
availability and the type of the distribution law of a quantity of random or uncertain 
impact factors. It is known that if an indefinite ( or random) factor is a quantity with 
a known distribution law, mathematical expectation of a criterion of efficiency is 
used as an efficiency assessment (7):  
 





k

i

ii
yxfxfz

1

0
),()(   

 

(7) 

 

where iy is a random factor that takes k values with i  probability. 

 
Having determined the assessment of the SES potential, we have an opportunity to establish 
its stability. Its stability is to be determined through reliability. Functioning of all system 
elements depends on its reliability. In relation to the potential of the SES components, this 
means a loss/decrease in not only certain times in specific time periods, but also a 
loss/decrease in its overall potential. In the context of competitive reliability of the SES, in 
case of their quantitative and qualitative accumulation, such violations lead to a failure of 
using the potentials of its components. It also means a decrease in the overall potentials. 
 
Let us use the definition of reliability suggested: 
 





m

i

i
p

1

1  

 

(8) 

 
which depends on the total weight of violations of all elements (components) of the system 
(i = 1, 2, …m): 
 

 ijijip   
 

(9) 

 

where i j  is a number of violations of a j type in i element of the SES potential which 

leads to a decrease in the potential of these elements;  

ij
 is a numerical value of a significant factor (assessment) of j violation in ith element of 

the SES.   



59 
www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

This allows to determine reliability of the system. We measure its efficiency in this way: 
 





k

i

ii
yxfxfz

1

0
),()(   (  ijij1 ). 

 
(10) 

 
When examining the SES, destructive internal influences should be taken into account. Let us 
note that this estimate is applied to the process (potential use) which is repeated many 
times. In rare cases, it does not mean anything. 
 
If for a random у factor, only the area of its possible values (variations interval) is known, in 
this case, it is possible to use so-called guaranteed efficiency assessment (11): 

.),(minmax*)(
*

yxfxfz
YyXx

гг


  
 

(11) 

 
This is also evident in many of the tasks of modeling potential use risk. When a system is 
viewed as a “black box”, an internal structure of which is unknown, it is necessary to observe 
only inputs and outputs of the system (Butyrkin, 2003).  
 
Let us use the methodological approaches suggested in (Ivanov et al., 2017) to determine 
the parameters and state of potential of such an integrated structure as the SES. We assume 

that the physical system S is in the state 00 SS  , where 0S is a set of initial states and is 

controlled by influence of the parameters of the potential. 
 
It should be noted that under the influence of some U potential management, the system 

grades from the initial state 0S  (the state in which the potential of the enterprise is 

characterized by the existing indicators of personnel, production capacities, financial 

possibilities, etc.) into a state kk SS   where kS  is a set of final states (these are the 

indicators of the potential which are necessary to solve the tasks). 
 
In this case, quality of each defined option to manage U potential is characterized by the 
corresponding value of the W(U) function. The task is to find such U* from a set of possible 
management options where the W(U) function takes the extreme (minimum or maximum) 
value of W(U*). In this case, S is called a dynamic system and tasks that are put in this model 
are called dynamic programming tasks. 
 

The state of the dynamic system S on a kth step (k= n,1 ) can be determined by a set of 
numbers (12): 
 

),,...,,(
)()(

2

)(

1

)( k

n

kkk
xxxX   (12) 

 



60 
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Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 

obtained as a result of implementation of uk potential management which ensures 
grading the system S from the state X

(k-1)
 into the state of X

(k)
. 

 
Herewith, we assume that the state X

(k)
, into which the system S graded, depends 

on the particular state X
(k-1)

 and chosen uk management and does not depend in 
what way the system S graded into the state X

(k-1)
. This condition is called the 

condition of lack of aftereffect.  
 
Therefore, if a certain gain Wk(x

(k-1)
,uk) which depends on the state x

(k-1)
 and chosen, 

uk management is provided as a result of implementation of a  kth step, the total 
state of the potential for n steps will be determined by the formula (13):  
 

 





n

k

k

k

k
uxWF

1

)1(
,  

 

(13) 

 
This condition is called the condition of additivity of the objective function.   
 
Whatever the state of the system before the next step is, you should choose a 
management option in this step so that the gain at this step plus the optimal gain at 
all subsequent steps is maximal.  
 
From this principle, it follows that the overall optimal potential management 

strategy U* that equals  **2
*

1
,...,,*

n
uuuU   is determined if the optimal management 

strategy is at the nth step (Wn
*
). Then, it is done on the last two steps (un-1

*
,un

*
), 

next - on the last three steps (un-2
*
,un-1

*
,un

*
) and so on till the first step.  

 
Let us suppose that it is necessary  to determine the optimum replacement policy for 
some equipment for n years. At the beginning of each year, a decision is made 
either to keep the equipment for its further exploitation, or to replace it with the 
new one. We denote the operating surplus of t-year equipment during a year and 

expenses for its maintenance for the same period by  tr  and  tu . Let  ts  be the 
residual value of the sold equipment that operated for t years. Price of new 
equipment remains unchanged and is equal to p. 
 
We introduce the function )(tf

n
, which is an amount of total income for the last n 

years of the planning period, provided that at the beginning of this period there is 
equipment of t age. Let us take into account that the optimal replacement policy is 
chosen. 
 
Replacing an existing car of t age with a new one makes sense when the revenue 
from a new car is bigger than the old one. If )(

1
tf  is the profit at the last stage, 

the ratios (14) and (15) express criteria for choosing a solution :  
 



61 
www.virtual-economics.eu                                                                                ISSN 2657-4047 (online) 

 

Mykola Rohoza, Vasyl Perebyynis, and Kseniia Verhal 
Virtual Economics, Vol. 2, No. 1, 2019 

 










replaceurptS

keeptutr
tf

),0()0()(

),()(
max)(

1
 

 
 

(14) 

 











replacefurptS

keeptftutr
tf

n

n

n
,)0()0()(

),1()()(
max)(

)1(1
 

 
 

(15) 

 

The formulas (14) and (15) establish a connection between the expressions nt  and 1nt  

and are recurring relations that allow to solve the problem with the dynamic programming 
method. 
 
5. Conclusions 

 

The mentioned approaches to modeling and their further analysis in the process of 
organization of a cooperative and integrated structures on the basis of enterprises of rural 
servicing cooperation provide an opportunity to substantiate the strategies of their 
development and increase efficiency of their functioning taking into account trends, 
features, directions of improving management of economic subjects of the agrarian sector of 
the Ukrainian economy, to suggest ways of improving and creating a database to make 
effective management decisions. Herewith, the main goal of forming a modern level of an 
economic object is also provided. Having methodological tools for effective activities in the 
domestic market, it will be able to provide the external market with competitive 
commodities. This, in turn, creates necessary opportunities for growth of the potential of the 
economy of territories. In this case, there is no narrowing of market relations but formation 
of economic objects with modern management technologies. Mechanisms and models of 
interconnected viable processes, cooperation and integration models for development of 
the economy of industries and territories are in accordance with the tasks of constructing a 
model of transition to the development path through finding optimal management methods 
for integration structures of the economy. 
 
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