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1. Introduction

The complication of social structures and relations, which are increasingly based on modern digital technol- ogies, continues to cause an exponential increase in data flows, highlights the question of the effective functioning

of a digital enterprise. The importance of the processes that are going through has allowed us to raise the question of the formation of a new type of information infrastructure, where relations regarding the production, processing, stor- age, transmission and use of a growing amount of data are becoming dominant. Data become the basis of economic

PROCESSES OF MANAGING INFORMATION INFRASTRUCTURE OF A DIGITAL ENTERPRISE IN THE FRAMEWORK OF THE

«INDUSTRY 4.0» CONCEPT

K . A n d r i u s h c h e n k o Doctor of Economic Sciences, Professor*

E-mail: [email protected] V . R u d y k Doctor of Economic Sciences, Associate Professor Department of Finance, Banking and Insurance State Agrarian and Engineering University in Podilia Shevchenka str., 13, Kamianets-Podilsky, Ukraine, 32300 O . R i a b c h e n k o Doctor of Juridical Sciences, PhD, Professor Department of Administrative Law and Process and Customs Security

National University of the State Fiscal Service of Ukraine Universytetska str., 31, Irpin, Ukraine, 08201 M . K a c h y n s k a PhD, Associate Professor Department of Administrative Police Activity Kharkiv National University of Internal Affairs

Lva Landau ave., 27, Kharkiv, Ukraine, 61080 N . M a r y n e n k o Doctor of Economic Sciences, Associate Professor

Department of Economics and Finance Ternopil Ivan Puluj National Technical University Ruska str., 56, Ternopil, Ukraine, 46001 L . S h e r g i n a PhD, Associate Professor*

V . K o v t u n PhD, Associate Professor*

М . T e p l i u k PhD, Senior Lecturer*

A . Z h e m b a PhD, Associate Professor Department of International Economic Relations Natіonal Unіvеrsіty of Watеr and Еnvіronmеntal Еngіnееrіng Soborna str., 11, Rivne, Ukraine, 33028

O . K u c h a i PhD Department of Tourism and Physical Education Kyiv National Linguistic University Velyka Vasylkivska srt., 73, Kyiv, Ukraine, 03150

*Department of Economics and Entrepreneurship Kyiv National Economic University named after Vadym Hetman Peremohy ave., 54/1, Kyiv, Ukraine, 03057 Проведено дослідження процесу управ-

ління інформаційною інфраструктурою цифрового підприємства в межах концепції

«Індустрія 4.0». Визначено, що сучасні циф- рові технології викликають експоненціаль- не зростання потоків даних, для ефектив- ного функціонування яких постає питання трансформації класичного підприємства в цифрове. З'являються нові моделі веден- ня бізнесу, мережеві структури, що ґрун- туються на колективних методах вироб- ництва і споживання, трансформують традиційні ринкові відносини і вимагають вироблення нових рішень в галузі управлін- ня цифровим підприємством. Зазначено, що використання всіх елементів (мобільність;

соціальність; BPM; система електронного документообігу; ERP фінанси та облік; Big Data & Analytics, бізнес-аналітика) сучас- них інформаційно-комунікаційних тех- нологій дозволить підвищити продуктив- ність та цінність підприємств. Визначено, що інформаційно-комунікаційні технології дозволяють ефективно взаємодіяти між собою в певних галузях виробництва та забезпечують оптимізацію будь-яких біз- нес-процесів за допомогою консьюмеріза- ції. Ідентифіковано сучасні тренди розвит- ку цифрового підприємства та окреслено передумови до впровадження цифровізації у бізнес-простір. Структуровано складові елементи процесу управління інформацій- ною інфраструктурою цифрового підпри- ємства, на базі чого запропоновано модель процесу управління інформаційною інфра- структурою. Обґрунтовано цілі цифрової інфраструктури, які зазначені: в підвищен- ні швидкості прийняття рішень, збільшен- ні варіативності процесів в залежності від потреб та особливостей клієнта, зниженні кількості залучених до процесу співробіт- ників. Поглиблено методичні основи проце- су управління інформаційною інфраструк- турою цифрового підприємства в умовах концепції «Індустрія 4.0»

Ключові слова: процеси управлін- ня, інформаційна інфраструктура, циф- рове підприємство, цифрова економіка, Індустрія 4.0

UDC 338.2

DOI: 10.15587/1729-4061.2019.157765

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analysis, explores the patterns of functioning of modern socio-economic systems. At present, it is not the fact of owning any resource that becomes important at the enter- prise, but the availability of data about this resource and the ability to use them for the purpose of planning its activities.

There is significant potential for the use of modern digital technologies in the activities of enterprises. It is important to pay attention to such aspects as the use of modern com- puting equipment, software, and the availability of qualified specialists. It is necessary to take into account that digital enterprises have significant potential to accelerate innova- tion processes, therefore the indicators of investments in the development of a digital enterprise are an important factor in its competitiveness in modern conditions.

New business models emerge, network structures based on collective methods of production and consumption trans- form traditional market relations and require the devel- opment of new solutions in the field of digital enterprise management. Further development of the digital enterprise is important for the entire economy of the country as a whole. Many governments, predicting such changes, are increasingly seeking to develop the process of managing the information infrastructure of a digital enterprise within the framework of the concept “Industry 4.0” concept. Modern national digital strategies address issues of economic devel- opment, the creation of innovative enterprises, increasing employment, the formation of an effective public sector.

Today, the “Industry 4.0” concept is becoming more and more popular. The term “digital enterprise” was suggested by the Director of MIT Media Lab in Being Digital, which was published in 1996 [1]. Undoubtedly, the process of tran- sition of the enterprise to the “Industry 4.0” concept is quite complex and requires the formation of an information infra- structure, which includes the use of all elements of modern information and communication technologies, in turn, will increase the productivity and value of enterprises. Given the modern course and amount of data generated in modern enterprises, it is very difficult for employees to cope with the relevant information flows, as opposed to information and communication technologies. In turn, information and com- munication technologies allow to effectively interact with each other in certain industries, which allows to optimize any business processes by creating an environment equipped with measuring equipment.

Information infrastructure is defined by four key trends – socialism, mobility, analytics and clouds (so- cial-mobile-analytics-cloud – SMAC) – IDC calls the “third platform” [2], Gartner speaks of the “Nexus of forces”) [3].

Each of these trends, taken separately, is just a technology, but together they form a powerful tool for digital transfor- mation. At first, the corresponding four trends were used in the consumer market (B2C) and caused consumerization. It is proposed to consider consumerization as an active use of personal mobile access to a computer network by employees of the company, whose share prevails over corporate devices of information and communication technologies. Subse- quently, the consummation manifested itself in a corporate (B2B), becoming the basis for the transition to a digital enterprise. At the same time, it is advisable to note that the Internet of Things (IoT) makes it possible to collect data for analytical systems – using embedded sensors and turning on smart devices in different control loops.

Thus, it can be noted that the fourth industrial revolu- tion is manifested in a series of waves:

– a digital consumer who enjoys a more interactive and personalized experience thanks to SMAC (social, mobile, analytical and cloud technologies);

– a digital enterprise that uses SMAC technology to optimize the value of corporate functions that organize in- teraction in the enterprise to increase productivity;

– digital operations in which companies are indeed re- building their business using artificial intelligence, robotics, cognitive computing and the industrial Internet of things,

”said Pierre Nanterme, CEO Accenture, at the World Eco- nomic Forum in Davos [4].

Sociality, mobility, analytics and cloud technologies are the basis on which a digital enterprise is formed, but the fact of using the corresponding tools does not render the enter- prise digital. Therefore, of course, enterprises will have to rebuild their information infrastructure in accordance with the requirements of the digital world.

The formation of an information infrastructure is a process that is initiated and occurs under the influence of external factors, among which the most important is posi- tive customer experience [5]. Partners and customers of the enterprise require a high level of availability of information about the work of the enterprise, in particular its services and products. Providing this level of user access is only possible with the use of technologies that can aggregate and process data and then pass it on to customers and partners.

It is a positive customer experience that allows enter- prises not only to remain in the market, but also to increase their presence on it. Achievement of the relevant results is closely connected with the increase in operational efficiency, which is achieved in the process of building the information infrastructure. According to IDC (an international research and consulting company that studies the global informa- tion technology and telecommunications market), the global expenditures on building an information infrastructure – hardware, software and services – reached 1.3 billion USD in 2017. Expenditures are expected to nearly double by 2021, when the total amount spent on digitization on a global scale exceeds 2.1 billion USD [6].

The MIT Sloan research (international business school at the Massachusetts Institute of Technology) shows the impor- tance of both directions of the formation of the information infrastructure – technological and management [7]. Thus, the company successfully introduced new technologies and advanced management methods, showed an average of 26 percent higher profitability compared with competitors.

Those who chose exclusively the introduction of technical innovations and retained the old bureaucratic management style, as a result were in the red – the yield is 11 percent lower than the leaders.

To succeed in this new world, enterprises will have to change in all directions, being engaged in the formation of the information infrastructure of production and business processes, since only their convergence will ensure the trans- formation of the information enterprise into the modern world according to the “Industry 4.0” concept.

2. Literature review and problem statement In the research environment, there is an active theo- retical discussion about a clear interpretation of the terms:

“digital economy”, “digital enterprise”, “virtual factory”, “In- dustry 4.0”, “deserted production”, “additive technologies”.

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And this is not surprising, since the process of digitalization of the economy is a relatively new phenomenon. Virtually all spheres of human life (economic, social, political, cultural, social, and others) were altered to varying degrees by the discoveries and development of information computer tech- nologies [8]. However, changes in recent years allow many researchers to assert that a new stage of informatization, the name of which is “digital economy”, is starting.

In [1], the use of the term “digital economy” was due to the intensive development of information and communica- tion technologies and the beginning of the second-generation informatization process. Leading consulting company The Boston Consulting Group (Boston, USA) notes [9] that for some countries, the digital economy is a logical continuation of the evolutionary development of the digital ecosystem and the ability to fully realize that very “creative economy”, “new economy” – a system of interconnection “links where the line between online and offline becomes conditional, and the lev- el of involvement of the state, business and citizens reaches 100 percent. This is the near future for the leading countries.

But for those countries that seek rapid development digitali- zation is an opportunity to preserve real competitiveness as well as sustainability in the long term.

It should be emphasized that the development of the in- formation technology sector is accompanied by the growing role of the “digital enterprise” as a key component of the digitalization process of the economy. The term “digital enterprise” does not have an unambiguous definition in the economic literature and is debatable in nature.

In work [10] it is noted that a digital enterprise is an organization capable of quickly adapting to rapidly chang- ing environmental conditions, including on the basis of a proactive forecast of the development of the situation in the future. In [11], the implementation of the “digital enterprise”

model is based on technological innovations, among which cloud computing, big data, mobility and social networks are primarily distinguished. Thus, a traditional enterprise turns into an organization with “digital thinking”, overcoming the path of digital transformation. And the product offered by such an enterprise also becomes digital.

The author [12] notes that the concept of a digital en- terprise implies a complete restructuring of the business, including manufacturing, customer relations, management methods, based on the widespread use of digital technolo- gies. The basis of digitalization is the global technological trends in information technology, the cumulative effect of which causes digital transformation. In the works [13, 14] it is noted that for the implementation of a digital enterprise, new models of business organization are needed, allowing to create enterprises whose activities will be based on process- ing and analyzing data based on the development strategy.

This is what will contribute to the continuous operational development of the enterprise in the changing conditions of the surrounding world, as well as early preparation for future reorganization based on accurate forecasts provided by new information technologies. Modern market conditions re- quire enterprises to make operational management decisions to determine production volumes, elect target markets for product sales [15].

The forum [16] on the strategy, technology and practice of managing a digital enterprise DigEnForum proposes the definition of a digital enterprise as an organization that uses information technology as a competitive advantage in all areas of its business: manufacturing, business process-

es, marketing, and customer interaction. That is why, the primary task of implementing the process of digitization of enterprises should be a general audit of production activities, which will reveal additional competitive advantages. Such advantages may include: cost reduction, saving resources, improving quality, efficiency and reliability, developing customer feedback, switching to other products and, finally, changing the business model.

Leading consulting company Accenture (Dublin, Ire- land) notes that a digital enterprise offers the opportunity for new operating models and business processes, platforms for connected products, analytics and teamwork to increase productivity [17]. It is advisable to note that the business processes of a digital enterprise are nothing more than au- tomation based on the wide use of information technologies.

However, the full implementation of automation is very expensive and often useless. After all, total automation, as a result of which all the problems and drawbacks existing at the enterprise are also automated, not only will not bring the expected positive result, but also strengthen the problematic aspects.

PwC (consulting company) connects the term “digital enterprise” with the “Industry 4.0” concept, focusing pri- marily on changing the sphere of industrial production [18].

It should be noted that PwC’s research focuses more on investments that will be focused on digital technologies – sensors and communication devices, as well as programs and applications – production management systems (PMS). In addition, in this study, the conditions for the formation of the phases of the fourth industrial revolution (Industrial Inter- net of Things) are not given. This means that traditional en- terprises are not able to plan the training of their employees and the procedure for the implementation of organizational changes in their enterprises. This problem can be solved by attracting, retaining and training the specialists of the so- called “digital generation”. It is this highly qualified staff ca- pable of working in a dynamic digital ecosystem, optimally adapting to changes in current activities and in continuous development.

McKinsey & Company (an international consulting company specializing in solving problems related to stra- tegic management) considers the most difficult part of the digital transformation, namely the cultural changes necessary to transform an enterprise into digital [19]. It should be noted that digital transformation will drastically change the social landscape. In order to prevent fatal mass technological unemployment, you need to create a social ecosystem of flexible implementation of technologies for their social design, as well as radically reform the education system and the labor market.

Any digital technology is based on infrastructure. Thus, Capgemini Consulting (a consulting company in the field of management and information technology) and MIT Sloan School of Management conducted research and analyzed more than 400 large companies in various industries, in understanding the essence of the term “digital enterprise”.

According to the results of the study, a digital enterprise is considered as an organization with an expanded range of services, an organization that offers customers revolution- ary digital solutions, including an integrated personalized service based on the collection of various data integrated by the information infrastructure [20].

It should be noted that the existence of a separate infor- mation infrastructure for each individual enterprise with

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its own standards, methods and algorithms is an inefficient and short-sighted solution that can lead to the chaos and disorder of the digitalization process of enterprises of the same industry. That is why an important task of the digital transformation of modern enterprises is the development and implementation of a unified information-analytical in- frastructure to support management decision-making in the framework of digitalization of the economy.

3. The aim and objectives of research

The aim of research is determination of the need and features of the management process of the information infra- structure of a digital enterprise in the context of the “Indus- try 4.0” concept, which ensures an increase in the operating efficiency of companies and the convergence of technologies.

To achieve this aim, the following objectives are solved:

– to identify the constituent elements of the manage- ment process of the information infrastructure of a digital enterprise;

– to propose a model for managing the information infra- structure of a digital enterprise;

– to explore the possibility of using the methods of general management theory for solving specific problems of managing the information infrastructure of a digital enter- prise in the context of the “Industry 4.0” concept.

4. Components and methods of researching the features of the information management processes of

a digital enterprise

4. 1. The investigated constituent elements (external and internal) of the information infrastructure of a digital enterprise

Among enterprises that have transformed into digital, it is worth noting: the high-tech industry, banks and re- tail – right now receive the greatest benefits from digital transformation. If to consider the field, from the point of view of the conservatives, they include insurance compa- nies that care about reducing risks and prevent them from innovating.

In the last place of the digital maturity rating: pharma- ceuticals, industrial production and production of consumer goods – they have yet to build a digital transformation model that will ensure the formation of an information in- frastructure.

The fact of using technology does not make an en- terprise digital. Enterprises still have to rebuild their information infrastructure to meet the requirements of the digital world.

Digital transformation does not mean that enterprises need to abandon all of their existing software and implement new ones. The development goes along the path of modern- ization of corporate systems. Analysts consulting company Gartner noted that in China, the cost of corporate applica- tion software in 2018 will amount to 5.1 billion USD. United States, which is 18.9 percent increase compared with 2017 [21]. But in the context of new challenges, known technolo- gies require rethinking.

The constituent elements on which a digital enterprise is built include:

– Mobility. The number of connected devices in 2016 was 64 billion USD. And by 2020 will reach 208 billion USD (based on research and consulting company specializing in information technology markets – Gartner) [21]. All employ- ees and customers, not just managers, have become mobile, so for managing a digital enterprise, we need new mobile applications with enhanced functionality. The Internet of Things, which are essentially the development of mobile technologies, will have a greater impact. Service industries and B2C markets, primarily retail, are already experiencing another wave of mobilization, which takes their interaction with consumers to a new level;

– BPM (business process management), Workflow, Col- laboration. Business processes. An enterprise will never be able to create a qualitatively new “digital” product, adapting social and mobile technologies, while not avoiding a radi- cal optimization of internal processes. Enterprises need to transform and efficiently organize work within the company before engaging in more customer-oriented and introducing advanced technologies. In doing so, the transformation will require BPM tools;

– ECM (Enterprise content management), EDMS (electronic document management system). Internal and external documents can be both a factor in the growth of efficiency and a brake if the requirements of documenta- tion are contrary to the requirements of the business. Re- strictions, imposed by law, obliging enterprises to use only paper documents, are largely removed. But the syndrome of learned helplessness remained: enterprises are not morally ready to say goodbye to paper in order to switch to digital formats of interaction. In this direction, much work should be done to change the corporate culture, whereas technical solutions for all tasks already exist.

In addition, the key to the formation of the information infrastructure will be not so much the automated work on structured workflow as the integration of the management capabilities of unstructured enterprise content with ana- lytics capabilities;

– ERP (Enterprise Resource Planning), finance and ac- counting. Capgemini Consulting analysts call the ERP a digital transformation driver. But only this will be a new generation of ERP, meeting the principles of Design for Digital (design for digital). The goal of this restructuring is responding as quickly as possible to the demands of consum- ers and brings the product to the market, that is, production must be flexible, adaptive and practically personal – because the requests from each client are individual. This can be achieved by using a stack of SMAC technologies (social, mo- bile, analytical and cloud technologies) in the development of ERP platforms;

– Big Data & Analytics, business analytics. Big data give impetus to the formation of information infrastruc- ture, opening up new opportunities, new customers, new markets. Business intelligence has become a tool for deci- sion-making, which is used not only by advanced special- ists, but also by business leaders at various levels. Moving to a digital enterprise also means data growth. Information from social networks, various external sources and, mainly, various sensors gets into the control loop, since produc- tion also switches to digital format. In connection with the growth of data volume and complexity, the systems of semantic analysis and artificial intelligence will be in demand;

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– Sociality – knowledge and people management. The sphere of marketing in the digital space is also transform- ing towards greater detail and personalization of the offer to customers – and this requires an in-depth study of the available information using knowledge management tech- nologies. Despite all the advances in automating business processes, people with intuition, skills and abilities remain a key factor in the success of a digital enterprise; therefore, traditional personnel management systems are transformed into talent management, employee training and develop- ment. Sociality makes the company “flat” – that is, destroys the vertical hierarchy, allowing everyone to communicate directly. The corresponding trend will inevitably lead to the spread of new management concepts based on network management principles instead of command and control. For example, Facebook audience is 20.6 billion people per month (data for 1 quarter of 2018) [22]. Those who have experience of social interaction on the Web will surely bring it into their working relationships.

4. 2. Digital enterprise information infrastructure management

A general approach to solving control problems in com- plex systems is described in terms of the modern theory of optimal control [23, 24]. At the same time, the state space of control objects is introduced, which is defined by a set of exogenous variables

{

1, ,...2 n

}

Х= x x x and endogenous variables

{

1, ,...2 m

}

. Y= y y y

The trajectory of the control object in the state space is described by a system of differential equations.

( ) ( ) ( ) ( ) ( ) ( ),

Y t =A t Y t⋅ +B t X t⋅ +W t (1) where W(t) – the vector of disturbing influences, including errors of state estimation,

( )

dimW t = ×m 1.

Thus, the rate of change of endogenous variables at each point in time is determined by the value of endogenous vari- ables at that point in time and the compatible control action of exogenous variables.

The control problem is to find the control law X(t), which minimizes the functional

( ) ( )

0 T

( ) ( )

T

( ) ( )

0

d ,

T

J U t =

Y t QY t   + X t RX t  t (2) where Q – the weight matrix, which reflects the difference in the essence of endogenous variables dimQ m m= × , R – the matrix characterizing the level of expenditures on investing exogenous variables, dimR m m= × .

The traditional approach to solving the problem (1), (2) is searching for control that is optimal on average. In this control, it is found, determined by the ratio [25–27]:

( ) ( ) ( )

.

X t = −C t Y t (3)

Relation (3) implements the universal control law in systems with negative feedback. In this ratio

( )

1 T

( ) ( )

,

C t =R B t S t ⋅ (4)

and S(t) – the solution of the Riccati equation

( ) ( ) ( ) ( )

( ) ( ) ( )

T 1

T

( ) ( ) ( ) ( )

( )

( ) ( ) ( ) ( ) .

T

S t S t A t A t S t S t B t R B t S t Q

S t A t A t S t S t B t C t Q

= − ⋅ − ⋅ +

+ ⋅ ⋅ ⋅ − =

= − ⋅ − ⋅ + ⋅ − . (5)

Substituting (3) into (1), let’s obtain

( ) ( ) ( )

( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ).

Y t A t Y t B t C t W t W t A t B t C t Y t W t

= ⋅ + ⋅ ⋅ + =

= − ⋅ + (6)

The nature of further research is essentially determined by the properties of a random process of disturbances affect- ing the system. The assumption of Markov perturbations is natural. As is known [27], this assumption does not impose serious restrictions on the adequacy of the corresponding mathematical models, since the extension of the dimension of the state vector is almost always the non-Markov process can be transformed into a Markov process. The next step in the specification of the disturbing effect is to set the density distribution of the amplitude of this process. With reference to the central limit theorem, let’s assume that this density is Gaussian with a zero mean vector and a known perturbation correlation matrix. Such a process is uniquely determined by two deterministic functions: the law of change in the average values of the components of the vector of perturbations and the law of change of the elements of the matrix of the cor- responding covariances. When a Markov Gaussian process passes through a linear dynamic system, its properties are preserved [28]. This means that if W(t) is a Gaussian process, then the process at the output of the system has the same property. In [27], a relation is obtained for calculating the average value of the control quality criterion:

( ) ( ) ( ) ( )

(

T

)

0

1 d ,

2

T

J= Sp QK t

+ ⋅R C t K t C t⋅ ⋅ t (7) where K t

( )

=<Y t Y t

( ) ( )

T > – covariance matrix of the components of the state vector.

The complexity of directly calculating the quality con- trol criterion is largely determined by the difficulties in solv- ing the Riccati equation [26]. In general, this equation does not have an exact solution, which makes it expedient to find an approximate solution of the control problem. Such a solu- tion can be obtained if it is assumed that all the functional el- ements in the relation (5) are constants. The corresponding situation in practice appears when, when making a decision on the change of exogenous variables, it can be compared with the duration of its implementation (or less). Moreover, as is known [25, 26], there is an established solution to the Riccati equation, in which the elements of the matrix S are also constants. Then equation (5) takes the form:

1 0,

T T

SA A S SBR B S Q

− − + − =

so

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Thus, the resulting matrix system containing m2 alge- braic equations. Of these equations, only m (they are located on the main diagonal of the matrix system) has a meaningful meaning and their solution forms the desired control. The re- maining m2mequations have a trivial zero solution, of no interest. Each of the m informative equations contains only one unknown and therefore they can be solved independent- ly. In this case, the i-th equation has the form:

2 0,

i i i i

s +p s + =v i=1,2,..., ,m (8)

2

1

2 i ,

i n

ij

j j

p a

b

=

= −

δ 2

1

,

i

i n

ij

j j

v q

b

=

= −

δ

1,2,..., .

i= m

Hence, choosing a positive root, let’s obtain

2

2

1 2

2 2

2

1 1

2 2

1 1 1

2 4

1 1 ,

i i i

i i n

ij

j j

i i

n ij n ij

j j

j j

n ij

i i

n ij j j

j j

p p a

s v

b

a q

b b

a q b

b a

=

= =

=

=

= − + − = +

δ

+ + =

 

 δ  δ

 

 

=  + + δ  δ

∑ ∑

∑ ∑

1,2,..., .

i= m (9)

Substituting (9) into (4):

1

1 1 1 11 12 1

2 2 2 21 22 2

2

1 1

1 0 ... 0

0 ... 0 0 ... 0 ...

0 1 ... 0

0 ... 0 0 ... 0 ...

2 ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ...

0 0 ... 0 0 ... ...

0 0 ... 1

n n

m m m m m mn

n

s a s b b b

s a s b b b

s a s b b b

 δ

     

     

      δ

− ⋅ + ⋅

     

     

     

 δ

11 12 1

21 22 2

1 2

1 1 1 1

2 2 2 2

...

...

... ... ... ...

...

0 ... 0 0 ... 0 0 ... 0

0 ... 0 0 ... 0 0 ... 0

... ... ... ... ... ... ... ... 2 ... ..

0 0 ... 0 0 ...

m m

n n mn

m m

b b b

b b b

b b b

s q s a

s q s a

s q



   

   

  ⋅ ×

   

   

 

 

 

   

   

   

× + = − ⋅

   

   

   

1

1 11 1 12 1 1

2 21 2 22 2 2

2

1 2

11 1 12 2 1

12 1 22 2

1 0 ... 0

... 0 1 ... 0

...

. ... ... ... ... ... ...

... ... ... ...

0 0 ... ...

0 0 ... 1

...

...

n n

m m m m m m m mn

n

m m

s b s b s b s b s b s b

s a s b s b s b

b s b s b s

b s b s b

 

δ 

 

   

 

     

  + ⋅ δ ×

   

 

   

     

 

 δ 

 

×

1 1

1 11 1 12

1 2

1 1 1

2 2

2 21 2 22

2 2 2 2

1 2

1 1 2 2

...

0 ... 0 0 ... 0

...

0 ... 0 0 ... 0

... ... ... ... ... ... ... ... 2 ... ... ... ...

... .

... 0 0 ... 0 0 ...

n n

n

m m

n

n n mn m m m m

s b s b s b

q s a

s b s b s b

s q s a

b s b s b s q s a

δ δ δ

     

     

  + = − ⋅ + δ δ δ

     

     

     

1 2

1 2

11 1 12 2 1 1 1 1

12 1 22 2 2 2 2 2

1 1 2 2

.. ... ...

...

... 0 ... 0 0 ... 0

... 0 ... 0 0 ..

... ... ... ... ... ... ... ... 2

... 0 0 ...

m m m m m mn

n

m m

m m

n n mn m m

s b s b s b

b s b s b s q s a

b s b s b s q s a

b s b s b s q

 

 

 

 

  ×

 

 

 

 

 δ δ δ 

 

   

   

   

× + = − ⋅

   

   

   

2

1 1 2 1

2

1 1 2 1

1 1 1

2

2 1 2 2 2

2 1 2 2

1 1 1

2

1 2 2

1 2

1 1 1

...

. 0 ...

... ... ... ...

... ... ... ...

0 0 ...

...

n n n

j j j j mj

m

j j j j j j

n n n

j j j j mj

m

j j j j j j

m m n n n

mj j mj j mj

m m m

j j j j j j

b b b b b

s s s s s

b b b b b

s s s s s

s a b b b b b

s s s s s

= = =

= = =

= = =

δ δ δ

 

 

  + δ δ δ

 

 

 

δ δ δ

∑ ∑ ∑

∑ ∑ ∑

∑ ∑

2

1 1 2 1

2

1 1 1 1 2 1

1 1 1

1 2

2 1 2 2 2

2 2 1 2 1 2 2

1 1 1

2 ...

0 ... 0

0 ... 0 2 ...

... ... ... ...

... ... ...

0 0 ...

n n n

j j j j mj

m

j j j j j j

n n n

j j j j mj

m

j j j j j j

m

b b b b b

s sa q s s s s

q b b b b b

q s s s sa q s s

q

= = =

= = =

 

 

 

 

 

  +

 

 

 

 

 

 

− −

δ δ δ

 

  − −

 

+ = δ δ δ

 

 

 

∑ ∑ ∑

∑ ∑ ∑

2

1 2 2

1 2

1 1 1

0.

...

... 2

n n n

mj j mj j mj

m m m m m m

j j j j j j

b b b b b

s s s s s s a q

= = =

 

 

 

 

 

  =

 

 

 

 − − 

 δ δ δ 

∑ ∑ ∑

(7)

Finally, substituting (10) in (3), let’s obtain the desired equation:

1 11 1 21 2

1 1 1

1 1

2 12 1 22 2

2 2

2 2 2

1 1 2 2

...

... .

... ...

... ... ... ...

...

m m

m m

n m

n n mn m

n n n

b s b s b s

x y

b s b s b s

x y

x y

b s b s b s

 

 δ δ δ 

 

   

 

     

 = − δ δ δ ⋅ 

     

   

     

 

 δ δ δ 

 

(11)

The control problem is solved differently if the control goal is stabilization of the selected system state. In this case, the relation (1) takes the form:

( ) ( ) ( ) ( ) ( ) 0.

A t Y t⋅ +B t X t⋅ +W t = (12) In the particular case when the parameters of the system do not change in time, relation (12) is simplified to the form:

0.

A Y B X W⋅ + ⋅ + = (13) The obtained matrix equation in expanded form is a sys- tem of linear algebraic equations, the distinguishing feature of which is that the equation of this system simultaneously contains sets of endogenous and exogenous variables, for example,

11 1 12 2 1 11 1 1 1

21 2 22 2 2 21 1 2 2

1 2 2 2 1 1

... ... 0,

... ... 0,

... ... ... ... ... ... ... ... ... ... ... ... ...

... ... 0.

m m n n

m m n n

m m mm m m mn n m

a y a y a y b x b x q

a y a y a y b x b x q

a y a y a y b x b x q

+ + + + + + =

+ + + + + + =

+ + + + + + =

(14)

Using (14), let’s express the endogenous variables through exogenous.

Moreover, if the matrix A is non-degenerate, then

1 1 ,

Y=A BX A W CX U = + C A B= 1 , U A W= 1 . (15) IfM U

[ ]

=0, then the relation (15) is simplified to the form:

.

Y CX= (16)

The obtained ratio allows for given matri- ces A, B and vector W to calculate the value of the set of endogenous variables Y depend- ing on the values of exogenous variables X.

The technology of further analysis of the original system of equations depends on whether the model is identified. A model is called identified if, using a known matrix C, using matrices 15 and 15, the matrices A and B can be uniquely calculated. Otherwise, the model is considered identified. Finally, if identification is possible in several ways, then the model is non-identifiable.

A simple feature of the identified model is formulated as follows.

Let nj, mj – respectively, be the number of endogenous and exogenous variables in the j-th equation of system (1). The model is iden- tifiable if for each equation of the system the inequality is satisfied

j j 1,

m m− ≥nj=1,2,..., .m

If a model is identified, then an indirect least squares method (ILS) can be used to analyze it. If the system of equations (1) is over-identifiable, then the two-step least squares method (TLS) is used to analyze the model. The technology of directly solving the problem in both cases is well known [28]. Therefore, we illustrate it with a simple example without detailed explanations.

As part of this study, an analysis was made of factors influencing one of the key elements on the basis of which a digital enterprise is built – sociality – knowledge and people management, using statistical data. The study of the influ- ence of factors carried out by building a mathematical model, allows to give a quantitative assessment of the deterministic relationship between factors.

Since the object of research is a complex system, the construction of isolated regression equations is not enough to describe this system and further explain the mechanism of its functioning. A change in one variable does not occur without changing the others; therefore, the problem arises of describing the structure of relations between variables by a system of so-called simultaneous equations.

The structural form of the research model contains en- dogenous and exogenous variables. In particular, the classi- fication of variables into endogenous and exogenous depends on the theoretical concept of the adopted model; in the study, the variables in some models are endogenous, and in others – exogenous variables [29].

In assessing the dynamics of development and prospects for attracting Ukrainian enterprises to the “Industry 4.0”

concept, let’s propose to highlight key indicators that will provide a definition:

– exogenous changes that change directly as a result of the implementation of measures of regulatory state influence due to:

– the number of employees involved in the implementa- tion of research and development;

– the ratio of the number of doctors of science in the total number of employees involved in the implementation of research and development;

– the ratio of the number of employees involved in the implementation of research and development;

1

11 12 1 1

21 22 2 2

1

2

1 2

1

11 21

1 1 1

12 2

1 0 ... 0

... 0 ... 0

0 1 ... 0 ... 0 ... 0

... ... ... ... ... ... ... ...

... ... ... ...

... 0 0 ...

0 0 ... 1

...

m T m

n n mn m

n m

b b b s

b b b s

C R B S

b b b s

b

b b

b b

 

δ 

     

     

 δ     

= =   ⋅    ⋅ =

 

 δ 

 

δ δ δ

δ

=

1 11 1 21 2

1 1 1

1

2 2

22 12 1 22 2

2

2 2 2 2 2

1 2 1 1 2 2

...

0 ... 0

... 0 ... 0 ...

... ... ... ...

... ... ... ... ... ... ... ...

0 0 ...

... ...

m m

m m m

m

n n mn n n mn m

n n n n n n

b s b s b s

b s b s b s b s

s

b b b s b s b s b s

  

   δ δ δ

    

    

 δ δ  ⋅ = δ δ δ

   

   

 

 

δ δ δ  δ δ δ

  

. (10)





 

 

 

 

 

 

(8)

– the ratio of PhDs (candidates of science) to the total number of employees involved in the implementation of re- search and development;

– the proportion of scientific and technical (experimen- tal) development in the total expenditure on the implemen- tation of research and development;

– the proportion of enterprises performing research and development;

– endogenous changes, which, in response to the dy- namics of external endogenous factors and with different intensity influencing each other, reflect the result of the development of science due to:

– the volume of scientific and technical works performed;

– sources of financing innovation activities of industrial enterprises;

– introduction of innovations at industrial enterpri- ses [30].

In the course of the study, the development of digital entrepreneurship and globalization processes of world re- structuring, a model of the process of managing the infor- mation infrastructure of a digital enterprise was developed.

Key components in it were selected the following exogenous factors, namely:

– х1 – the number of employees involved in the imple- mentation of research and development by categories, which is proposed to be determined by the ratio Number of employ- ees – total, with a 7-year lag. The presence of lag is manifest- ed in the fact that the х1 value calculated for 2010–2017 was used in the construction of the SVEM.

– х2 – the ratio of the number of doctors of science in the total number of employees involved in the implemen- tation of research and development in categories reflect- ing the renewal of the labor potential of the country in science;

– х3 – the ratio of PhDs (PhD), to the total number of employees involved in the implementation of research and development by categories;

– х4 – the proportion of scientific and technical (exper- imental) developments in the total amount of expenditures for research and development by type of work;

– х5 – the proportion of enterprises performing research and development.

Also selected is a set of endogenous variables that, in response to the dynamics of exogenous factors, reflecting the result of the development of science:

– у1 – the volume of completed scientific and scientific and technical works;

– у2 – the volume of sources of financing innovation activities of industrial enterprises;

– у3 – the volume of innovation in industrial enterprises.

Taking into account that endo- and exogenous variables have a simultaneous interaction, the model is constructed in the form of a system of interrelated equations:

1 10 12 2 11 1 13 3 14 4 1

2 20 21 1 22 2 23 3 25 5 2

3 30 32 2 32 2 34 4 35 5 3

, , . y b b y a x a x a x y b b y a x a x a x y b b y a x a x a x

= + + + + + ε

 = + + + + + ε

 = + + + + + ε

The structural form of the model on the right side contains for endogenous variables, the coefficients bik and exogenous variables – the coefficients aij, which are called the structural coefficients of the model. All variables in the model are expressed in deviations from the average level that is, x means x–xav, and y means y–yav, respectively. Therefore, the free term in each equation of the system is absent:

1 12 2 11 1 13 3 14 4 1

2 21 1 22 2 23 3 25 5 2

3 32 2 32 2 34 4 35 5 3

, ,

. y b y a x a x a x y b y a x a x a x y b y a x a x a x

= + + + + ε

 = + + + + ε

 = + + + + ε

Using the OLS for estimating the structural coefficients of the model gives combined and inconsistent estimates, and therefore, to determine the structural coefficients of the model, its structural form is transformed into the reduced form of the model.

The reduced form of the model is a system of linear func- tions of endogenous variables from exogenous:

1 11 1 12 2 13 3 14 4 15 5 1

2 21 1 22 2 23 3 24 4 25 5 2

3 31 1 32 2 33 3 34 4 35 5 3

ˆ ,

ˆ ,

ˆ ,

y x x x x x u

y x x x x x u

y x x x x x u

= δ + δ +δ + δ + δ +



= δ + δ + δ + δ + δ +

 = δ + δ + δ + δ + δ +

where δij – coefficients of the reduced form of the model; ui – the residual for the reduced form.

The form shows the form of the model is no different from the system of independent equations, the parameters of which are traditionally estimated by the method of least squares. Accordingly, one can estimate δij, and then estimate the value of endogenous variables through exogenous ones.

It should be noted that the reduced form of the model, although it allows to obtain the values of the endogenous vari- able through the value of exogenous variables, but is analyti- cally inferior to the structural form of the model, since it lacks estimates of the relationship between endogenous variables.

Taking into account the calculated data in Table 1, the development trend of the information infrastructure of a digital enterprise in the “Industry 4.0” concept is visually presented (Fig. 1–3), with the construction of a polynomial trend line that grows with the coefficient of determination R2=0.9752, which is close to 1.

Table 1 Model of development of information infrastructure of a digital enterprise in the “Industry 4.0” concept

Years x1 x2 x3 x4 x5 y1 y2 y3 y1 model y2 model y3 model

2010 182484 11974 46685 4343 996 9867 8046 2043 10856 -874 2044

2011 175330 11677 46321 4499 1080 10350 14334 2510 7929 1626 2376

2012 164340 11172 42050 4781 1196 11253 11481 2188 11694 5738 1913

2013 155386 11155 41196 5489 1639 11781 9563 1576 12829 8115 1470

2014 136123 9983 37082 5153 1755 10951 7696 1743 11535 12726 1733

2015 122504 9571 32849 6583 2040 12611 13814 1217 12232 17412 2077

2016 97912 7091 20208 6744 2458 13814 23230 3489 13904 24814 3521

2017 94274 6942 19219 7292 2170 23230 9118 1831 22877 27721 1462

(9)

5. The results of the application of new technologies and techniques for managing the information infrastructure of

a digital enterprise

Since all equations of the system are not identified, TLS is used to estimate the structural coefficients of each equation.

At the first stage, the reduced form of the model was found by the method of least squares in the MS Excel envi- ronment:

Fig. 1. Trends in the development of the information infrastructure of a digital enterprise in the “Industry 4.0” concept

Fig. 2. Dynamics of influence of factors on the information infrastructure of a digital enterprise in the “Industry 4.0” concept

Fig. 3. The results of the simulation of factors influencing the information infrastructure of a digital enterprise in the “Industry 4.0” concept

y = 94,499x4- 1563,6x3+ 8802,2x2- 18584x + 21842 R² = 0,9752

-10000 0 10000 20000 30000 40000 50000 60000

1 2 3 4 5 6 7 8 9

Proportion of the volume of scientific and technical works

Proportion of sources of financing innovation in industrial enterprises Polynomial (specific) weight of the volume of scientific and technical works

14334

11481 9563

7696

13814

23230

9118

0 5000 10000 15000 20000 25000

2010 2011 2012 2013 2014 2015 2016

Proportion of the volume of scientific and technical works

Proportion of sources of financing innovation in industrial enterprises

2376

1913

1470 1733

2077

3521

1462

0 500 1000 1500 2000 2500 3000 3500 4000

2011 2012 2013 2014 2015 2016 2017

Proportion of innovation in industrial enterprises

Proportion of innovation in industrial enterprises, model

1 1 2 3 4 5 1

2 1 2 3 4 5 2

3 1 2 3 4 5 3

0,491 0,091 2,499 4,258 0,431 ,

6,769 10,089 7,520 9,027 7,32 ,

22,721 0,622 9,588 21,941 42,816 .

y x x x x x u

у х х x x x и

y x x x x x u

= − − + + +

 = − + + + +

 = − + + − + − +

Посилання

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