=Paper=
{{Paper
|id=Vol-2870/paper113
|storemode=property
|title=Intelligent Management System for Ecological Innovative Enterprises
|pdfUrl=https://ceur-ws.org/Vol-2870/paper113.pdf
|volume=Vol-2870
|authors=Mykola Odrekhivskyі,Uliana Kohut,Ulyana Kostyuk
|dblpUrl=https://dblp.org/rec/conf/colins/OdrekhivskyKK21
}}
==Intelligent Management System for Ecological Innovative Enterprises==
https://ceur-ws.org/Vol-2870/paper113.pdf
Intelligent Management System for Ecological Innovative
Enterprises
Mykola Odrekhivskyіa, Uliana Kohuta and Ulyana Kostyukb
a
Lviv Polytechnic National University, 12 S. Bandera St, Lviv, 79000, Ukraine
b
Ivano-Frankivsk National Technical University of Oil and Gas, 15 Karpatska St, Ivano-Frankivsk, 76000,
Ukraine
Abstract
The purpose of the scientific work is to study problems of eco-oriented management and design
of intelligent management systems for ecological innovative enterprises. The approaches to
formation of the eco-oriented management process are studied. These approaches investigation
additionally proofs the importance for modern business conditions to design the management
model that provide economic as well as environmental and social efficiency of enterprises. At
the same time, the problems of an intelligent system organizational design are relevant for eco-
oriented management and using of artificial intelligence approaches in order to optimize
management decisions. A system model of an intelligent system of eco-oriented management
for innovative enterprises has been developed to improve their environmental efficiency,
sustainability and safety, as well as to improve resource and socio-economic efficiency. Based
on the system model, the organizational structure of the intelligent management system of
ecological innovative enterprises has been developed. It will make it possible to design,
construct and restructure the intelligent management systems of ecological innovative
enterprises as a whole and their units in to adapt them to modern business conditions. The study
of ecological sustainability of enterprises based on its integral index was tested. The
methodological basis of the investigation is a set of general and special methods of scientific
researches. The implementation of these methods is caused by the goal and logic of problems
solving for eco-oriented management and design the system of eco-oriented management that
are based on the using of environmental innovations. Markov chain theory was used as a
mathematical tool to evaluate efficiency of eco-oriented management. Based on this
mathematical tool, the software for evaluation and prediction of state of eco-oriented
innovative enterprises development was presented and tested for adequacy. The prediction
results can be used to support managerial decision-making, developed software can be
incorporated into the structure of the intelligent management system of ecological innovative
enterprises and applied for the study of ecological sustainability of enterprises.
Keywords 1
Eco-oriented management, system, innovative enterprise, ecological, economic and social
efficiency, sustainable development
1. Introduction
The extremely unsatisfactory environmental situation in Ukraine and in the world demands for the
search for new approaches to enterprises management, focused on minimizing negative impact on the
environment and ensuring sustainable development. Different forms and ways of improving production
COLINS-2021: 5th International Conference on Computational Linguistics and Intelligent Systems, April 22–23, 2021, Kharkiv, Ukraine
EMAIL: Mykola.V.Odrekhivskyi@lpnu.ua (M. Odrekhivskyi); Uliana.I.Kohut@lpnu.ua (U. Kohut); kostyuk_u@ukr.net (U. Kostyuk)
ORCID: 0000-0003-3165-4384 (M. Odrekhivskyi); 0000-0002-3847-2762 (U. Kohut); 0000-0001-8826-8084 (U. Kostyuk)
©️ 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)
and economic activities based on introduction of eco-innovations serve s a basis of sustainable
development. Under such circumstances, it is urgent to develop an appropriate of intelligent
management systems (IMS) for ecological innovative enterprises (EIE) to ensure rational decisions
regarding environmental, economic sustainability and security of individual economic entities and the
country as a whole. The designing of the IMS EIE, use of artificial intelligence elements in the system
functioning to optimize management, formation of a system of criteria and indicators to evaluate the
system efficiency are considered as important problems.
Eco-oriented management (EOM) of innovative activities at all organizational levels of national
innovation systems is an urgent issue in the current conditions of international socio-economic
development. EOM generates and activates all enterprise resources to achieve economic goals,
interrelated with purposes of sustainable nature management and development. At present, EOM is
becoming the central subsystem of the management system; whereas operation of all other subsystems
(personnel, financial, etc.) is based on the principles sustainable nature management and environmental
protection [1].
2. Literature review
Eco-oriented management has been the subject of research by many scientists. In particular,
Yasnolob I. notes that as a part of a general management system, an environmental management system,
based on a system-environmental approach, ensures correlation of all management functions according
to sustainable development concept and environmental justice principles [2]. The purpose of enterprise
EOM is to minimize or prevent the negative impact of technological processes on the environment. It
can be implemented by modernization of existing technological processes or by their replacement with
innovative, environmentally-oriented processes [3].
In a broad sense, EOM can be defined as a type of management, mainly oriented at formation and
development of ecological production, ecological culture and life sphere. This type of management
should be considered as a complex and perspective consideration of ecological problem as a part of the
economic policy of enterprises [1]. EOM shall be implemented with continuous interaction of all
economic entities and combine the ecological strategy goals and management methods that are most
relevant to the ecological and economic development of society as a whole. EOM covers macro-, meso-
and micro-levels of environmentally sound management [4], it shall consider the environmental impact
and modern approaches to innovative development regulation at all levels of economic systems
organization.
The principles of an efficient ecological management system include [2]:
target permanency;
acquisition of high quality and safe components of production, technologies, machinery, etc.
Process improvement and compliance with ecological management system requirements;
use of leadership as a method of production quality assurance and safety;
cooperation of managerial staff with employees;
motivation to self-improvement and professional development of the personnel;
the support of ecological management system by chief executive officers.
However, the problems of a mechanism formation for eco-oriented management of innovative
enterprises are not sufficiently addressed and need further research, development and implementation
in compliance with requirements and challenges of industry 4.0.
EOM at the level of innovative enterprises (IE) can be ensured by development of an appropriate
eco-oriented management system (EOMC). EOMC can promote IE to maintain and strengthen its stable
position at the market, form and meet eco-oriented consumer needs, respond adequately and promptly
to changes in the environment, provide sustainable development. Changes in the environment, high
competition and intensive development of eco-oriented demand force IE leaders to reorganize and
improve the organizational and economic mechanism of IE management to provide IE eco-oriented
activities to get, on the one hand, their profit, and on the other, preserve the environment and human
health. That is, nowadays, all IE shall become ecological, by ecological innovating enterprise (EIE) we
mean an enterprise of various organizational and legal forms, engaged in eco-innovation activities,
focused on the production of environmental products (provision of environmental services) in various
fields life. The EIE business strategy is aimed at profit earning with a focus on environmental
conservation and sustainable development [5].
EIE can be described as follows [6]: these are nature-oriented IE, providing wildlife habitat
conservation , eco-tourism and other nature-related activities using economic and human resources to
improve the environment; manufacturers of innovative eco-technologies - production of such
technologies is under the impact of legislative pressure on communities or industrial enterprises to
reduce their environmental, water, air and soil load; providers of innovative ecological management
services are aimed at consultations of companies on use of environmental skills as a source of
competitive advantage; manufacturers of eco-friendly innovative products, differentiated from existing
products due to better ecological life-cycle indices as compared with existing ones.
EIE identification criteria are based on [7, 8]: Compliance with principles of socially responsible
innovative business; consideration of changes in the increasing (but not dominating) significance of
environmental factors; environmental conservation as an integral part of IE management and marketing
system; achievement of economic, social and environmental impact by introduction of innovative
technologies using natural resource potential. That is, EIE shall adhere to sustainable innovative
practices to minimize negative social and environmental consequences, obtain the optimal corporate
performance, and be responsible for sustainable development in products, services, processes and
business models [9].
3. Methods
The methodological basis of the investigation is a set of general and special methods of scientific
researches. The implementation of these methods is caused by the goal and logic of problems solving
for eco-oriented management and design the mechanism of eco-oriented management that are based on
the using of environmental innovations, greening the activities of innovative enterprises for ensuring
the sustainable development. The obtained scientific results are based on the implementation: a
systematic approach, logical analysis and synthesis for researching the reference sources to determine
approaches for the problem solving of forming IMS EIE; structural design methodologies for the
analysis of various aspects of IMS as a complex organizational and economic system that implements
eco-oriented management of EIE; methods of multilevel and multi-stage decomposition of IMS for
construction of its model; the concept of hierarchical management and methods of functional analysis
of IMS, for determination of the multiplicity of its functions, the heterogeneity of structural elements at
all levels of the hierarchy, the diversity of forms of existence throughout the life cycle of EIE;
formalization methods - economic-mathematical models of queuing theory, methods of hierarchical
structures theory, set-theoretic models, differential equations, models of Markov processes - for
quantitative evaluation, comparative analysis and forecasting of EIE states in general and its structural
components; graphical method - for a visual representation of the dynamics and statics of the
development of EIE or their structural units; decision-making methods - for decision-making on EIE
states and the choice of methods for managing these states; methods of cognitology - for development
the organizational structure of intellectual IMS. These aspects will allow the design, construction and
reconstruction of IMS EIE in general and their units with the purpose of their adaptation to modern
business conditions.
4. Results and discussion
4.1. Intelligent management system designing for EIE
It is important to decide on the strategic vector of EIE development to form IMS EIE. For this, it is
relevant to perform: structural analysis of the IMS EIE as a complex system and consider its results; to
use quantitative evaluation, comparative analysis and prediction of EIE conditions in general and its
structural elements; functional consideration of IMS EIE, determined by the multiplicity of functions,
heterogeneity of structural elements, variety of forms of IE life cycle. That is, the analysis of IMS EIE
various aspects as a complex system, implementing IE eco-oriented management, it is recommended to
provide by multilevel and multi-stage decomposition of its model [10].
Analysis of systems, using decomposition methods, allows to break down their models into
subsystems and determine their structure and functions. The complexity that generated decomposition
and aimed efforts of scientists to get further knowledge about certain aspects of phenomena, also caused
the problem of the studied components integration into a complex system - the problem of synthesis
[11, 12]. Synthesis involves use of integration methods to reproduce a system by its functional elements
(subsystems) to study processes of these functions implementation. That is, analysis and synthesis
methods can serve as a basis for the methodology of IMS EIE formation and provide IE adaptive
capacity to solve problems of sustainable development, caused by modern environmental challenges
[13, 14].
Thus, it is proposed to use decomposition methods for formation of IMS EIE (S) [15, 16]. The system
model of IMS S, according to decomposition methods, will have the form as shown in Fig. 1, where SS1
is a subsystem for diagnostics of EIE current state and their environment; SS2 is a subsystem for
evaluation and prediction of EIE states; SS3 is a subsystem to support decision-making on EIE states;
SS4 is a decision support subsystem on selection of main effects on EIE; SS5 is a subsystem for
simulation of EIE states; SS6 is a subsystem for implementation of main effects on EIE. E is a set of
elements of each subsystem, from SS1 to SS6; V is a set of indicators inherent in set E elements; V1 is a
subset of names for the indicators characterizing states of subsystems; V2 is a subset of values of
indicators, changing over time; W is a set of states whose elements are determined by values of
indicators from subset V2, according to their names from subset V1, at a fixed moment in time - set T; F
is a set of functions (actions, operations), providing transition of subsystems from the initial state to the
main purpose of subsystems functioning for EIE management; G is a set of purposes for subsystems
functioning; R is a set of relations, containing subsets of the relations between the sets themselves and
between each set elements.
The following types of relations are observed between these sets of system model of IMS EIE: R1
(E,Vj) – correspondence relation that puts into correspondence to each sample of set E a sample of Vj,
that is, from V1j і V2j; R2 (V1j,V2j) – correspondence relation between a given indicator name and its
specific values at time moment t; R3 (Vj,W) – relation, which puts into correspondence to each element
of set Vj пa subset of values of set W elements at time moment t; R4 (W,F) – relation of order that sets
the sequence of functions (actions, operations) in the process of achieving main goal G0.
S
SS1 SS2 SS3 SS4 SS5 SS6
R
E V T G
W F
GE GV1 GV2 GW GF GG
Figure 1: Decomposition model of intelligent management system for ecological innovative
enterprises
Source: own elaboration.
The goal, in turn, can be formed as a requirement for achievement of specific values of indicators or
states of performance for subsystems of IMS EIE and effective performance of certain functions of IMS
EIE as a whole. That is, when simulation IMS EIE, it is necessary to distinguish such mandatory sets
of components that would ensure the model completeness (1), where i = 1,2,…, N, N = 6.
PM E SS1 , E SS2 , E SS3 , E SS4 , E SS5 , E SS6 ,V SS1 ,V SS2 ,V SS3 ,V SS4 ,V SS5 ,V SS6 ,W SS1 ,W SS2 ,W SS3 ,W SS4 ,W SS5 ,W SS6 ,
F SS , F SS , F SS , F SS , F SS , F SS , G SS , G SS , C SS , G SS , G SS , G SS , R SS , R SS , R SS , R SS , R SS , R SS
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
R( SS1 , SS 2 ), R( SS1 , SS3 ),..., R( SSi , SSi 1 ),..., R( SSi 1 , SSi ),..., R( SS N , SS N 1 ). (1)
The above patterns of structuring and functioning of IMS EIE subsystems are the initial rules for
allocation of a system of elements and its model attributes. Regarding completeness of the mechanism
system model, consideration is required at the upper levels of decomposition relative to the following
objects:
Е Е SS1 , Е SS2 , E SS3 , Е SS4 , E SS5 , E SS6 . (2)
SS SS SS SS SS SS
During decomposition of set E elements, for each element ( E 1 , E 2 , E 3 , E 4 , E 5 , E 6 ) from set
(2), it is proposed to select the entire set of system components – {V,Z,W,F,G,R}. Next decomposition
of elements (2) and their components depend on the analysed subsystem type SSі, where і = 1,2,…,6.
Hierarchy of structuring is a common feature. It can be formalized by a description in a theoretical and
multiple language in the form of a relation tree, which can be an abstract level of a hierarchical model
of subsystems, where the units of their characteristics and the mutual relations are specified. Here we
propose a six-stage decomposition that can be represented as a model (Fig. 1), where the first stage is
represented by graph ( GЕ ) – graph of elements, the second ( GV 1 ) – indicators graph, the third ( GV 2 ) –
graph of indicator values, the fourth ( GW ) – graph of states, the fifth ( GF ) – graph of functions (actions
and operations), the sixth ( GG ) – tree (graph) of goals functioning of the IMS EIE. That is, the presented
six-stage decomposition can set the rules for IMS EIE system model formation.
For graphical representation of IMS EIE (S) hierarchical levels it is proposed to perform three-level
and two-stage decomposition and build a system S model in the form of three-level structure using
system (macro), subsystem (meso) and micro-level (element level). That is, system S model is proposed
to be presented in the form of a graph, where, after the first stage of system S decomposition as a
complex system (macro-level), the second (meso) levels can accommodate hierarchical structures of all
system S components, in our case, these are the following subsystems: SS1, SS2, ... , SS6. Elements of
sets E SS1 , E SS2 , E SS3 , E SS4 , E SS5 , E SS6 (graph GЕ ) indicate the second stage of system S decomposition and,
accordingly, to the third (micro) level of system S hierarchical structure. Similarly, further
decomposition of all elements of set E of system S is performed, if they can be regarded as complex
hierarchical structures.
The evaluation of system S efficiency can be performed based on the evaluation of EIE functioning
efficiency, in particular, on results of economic, environmental, scientific, technical, social, resource,
organizational and managerial types of efficiency, etc. [17-20]. At the same time, the focus will be on
a high level of economic and environmental efficiency, which is a priority.
That is, next graph ( GV 1 ) is indicators graph and the third ( Gv 2 ) is a graph of indicator values can
represent, for example, a graph of EIE performance and, accordingly, a graph of performance. Based
on EIE performance values, it is possible to analyse efficiency of system S functioning of eco-oriented
management of EIE activities in general and its components and to make appropriate decisions on this
basis.
The fourth graph (graph GW ) can be represented by EIE development stages and, accordingly,
implementation states of EIE functions, actions and operations and, accordingly, efficiency states EIE
and IMS.
Study of functions, actions and operations of IMS EIE is relevant, contributing to achievement of
the EIE goal, and during decomposition IMS EIE may be the fifth graph (graph GF ). IMS EIE
management functions, actions and operations are proposed to include: collecting, storing, processing
and transmitting management information, forecasting and supporting the adoption and implementation
of management decisions.
A goal tree of IMS EIE decomposition is proposed as the sixth stage (Fig. 2). This tree defines the
main goal of G0 EIE and the ways to achieve it, that is, includes the goals of all elements and subsystems
of EIE, in particular:
G1 – production of intelligent ecological products; G11 – generation of ecological ideas; G12 –
scientific research work; G13 – design work; G14 – pilot work;
G2 – production of innovative ecological products; G21 – transfer of innovative eco-technologies; G22
– technological preparation of ecological production; G23 – ecological production; G24 – marketing;
G0
G1 G2 G3 G4 G5
G11 G31 G41 G51
G21
G12 G22 G32 G42 G52
G13 G23 G33 G43 G53
G14 G24 G34 G44 G54
G35 G45 G55
G46 G56
G36
G57
G58
G59
Figure 2: EIE goal tree
Source: own elaboration.
G3 – ecological training of personnel; G31 – formation of ecological competence of staff; G32 –
training in ecological knowledge; G33 – ecological skills training (operations and operations); G34 –
provision of eco-innovation certificates; G35 – acquiring eco-innovation skills; G36 – study of
educational process and decision making;
G4 – implementation and use of eco-innovation; G41 – resource; G42 – process; G43 – product; G44 –
market; G45 – managerial; G46 – organizational;
G5 – management; G51 – prediction; G52 – goal formation; G53 – planning; G54 – coordination; G55 –
organization; G56 – stimulation; G57 – control; G58 – regulation; G59 – operational management.
IMS EIE analysis, using multilevel and multi-stage decomposition allows to break up IMS EIE
model into subsystems and study the EIE functioning states at different levels of their organization,
IMS EIE structure, its function, actions and operations. It causes the synthesis problem of studied IMS
EIE components, involving use of integration methods to reproduce IMS EIE from its functional
elements to study implementation processes of IMS EIE functions in general to meet present challenges
of EIE development. That is, the analysis and synthesis will allow the design of IMS EIE, IMS EIE
general construction and reconstruction and their subsystems, to adapt IMS EIE to modern business
conditions.
4.2. Structure of the intelligent management system for ecological innovative
enterprises
The tools, required for IMS EIE formation and operation, can be based on object-oriented integrated
and distributed databases and knowledge bases, hybrid expert systems, decision support systems (DSS),
integrated neural networks and fuzzy logic tools. DSS allow you to model and automate decision-
making processes, model and automate EIE organizational management. Distributed artificial
intelligence, integrated intelligent information systems (IIIS) as multi-agent systems [21-23] is the most
suitable class of models for IMS EIE implementation, its structure is presented in Fig. 3.
The structure of decision support subsystems (SS3 and SS4 subsystems) that are capable of decision
making support and explanation include: the first and second generation knowledge subsystems,
knowledge base, user interface, decision making subsystems and explanation. Necessary decisions,
when using IMS EIE, will be made based on expert knowledge, which, respectively, can be highly
qualified specialists in specialized fields of knowledge (knowledge of the first kind), as well as the
knowledge obtained based on a priori information and the research results of EIE activities (knowledge
of the second kind). This knowledge can be formalized and entered into the knowledge base as
knowledge, on its basis SS3 subsystem supports decision-making on the states of EIE activities, SS4
subsystem - main effects implemented by SS6 subsystem.
Managerial decisions on EIE states in general, or any element of their hierarchy, in IMS EIE with
proposed structure can be supported, using Monte Carlo simulation, discrete simulation, system
dynamics and statics [24, 25], digital business models and visual simulation, operations research
(simulation modelling, business games, stochastic programming), decision trees, impact diagrams,
fuzzy logic tools, agent and multi-agent simulation [26-29].
Study of dynamic and static characteristics of real states of EIE development and their efficiency
with subsequent decision-making is performed by means of IMS EIE. Data collection, their initial
processing, to state an environmental problem, is performed using SS1 subsystem - diagnosing
subsystem of EIE states. The storage and collected data processing and further evaluation and prediction
of EIE states and their efficiency are performed using SS2 subsystem. If real studies fail to be
implemented, then it is proposed to use virtual information from the information block and modulate
virtual states and business processes of EIE using SS5 subsystem. It will promote further evaluation and
prediction of possible states, make situational decisions and implement them using SS6 subsystem. If
ecological problem is well-structured, then mathematical methods are used to process environmental
information about it and subsequent choice of management decisions, and if the problem is poorly
structured or unstructured, expert judgement is proposed to prepare options [30-32] and evaluations.
To evaluate and predict EIE states in general or their components, it is proposed to use a
mathematical tool of Markov chain theory; applying systems of differential equations of Kolmogorov
type. Based on this mathematical tool the corresponding software was developed and tested in the study
of petroleum products concentration on biogeocenosis elements around wells operated in Boryslav-
Skhidnytske oil deposit [33, 34]. This mathematical tool can also be used to study IE environmental
friendliness of before and after introduction of eco-innovations, allowing to evaluate their efficiency.
Decision support subsystem on main effects
Decision support subsystem on EIE state (SS3) (SS4)
Knowledge base Knowledge base
Accumulation of Accumulation of Tool
Tool knowledge of the knowledge of
of conclusions 1st kind the 1st kind of conclusions
Accumulation of Accumulation of Decision
Decision knowledge of
explanation knowledge of the the 2nd kind explanation
2nd kind
Expert Expert
User interface User interface
Database
Evaluation and prediction subsystem Modeling subsystem
of EIE states of EIE states and business processes (SS 5)
and their efficiency (SS 2)
Information block
Evaluation of EIE Prediction of EIE
states states Model bank Model
synthesis
1 - model
Information Information 2 – model Model
processing storage …
presentation
n - model
System interface User interface
...
Diagnosing subsystem (SS1) of EIE states
Diagnosing Data collection Primary information processing
...
Ecological innovative enterprise
...
Subsystem of decision implementation (SS 6)
Formation of main effects Final decision making Decision implementation
Figure 3: Organizational structure of the intelligent management system for ecological innovative
enterprises
Source: own elaboration.
These studies are proposed to be performed based on calculation of integrated ecological indicators
of enterprises [35-37], namely, integral indicator IPEVS, represented as formula (1) [35].
I PEVS 7 K A KVO K B K Z K BB K ZB K N .; I PEVS 1, (1)
where KA – emission coefficient; KA →1;
KWB – coefficient of discharge into water bodies; KWB →1;
KW – waste coefficient; KW →1;
KLP – coefficient of land production capacity; KLP →1;
KWU – waste utilization FACTOR; KWU →1;
KLR – loss ratio of products; KLR →1;
KWH – waste hazard factor; KWH →1.
As information support for calculation of integral indicator (1) and its components, it is possible to
take data from environmental balances and EIE reports.
To study dynamic and static characteristics of the impact of eco-innovation on enterprise activities,
it is proposed to use an integral indicator of their environmental friendliness (ecological sustainability)
(1). Table 1 provides this indicator interpretation [31, 35].
Table 1
Interpretation of integral ecological indicator (ecological sustainability) of enterprises
Stability states Indicator value State description
All ecological issues of enterprise
S5 - absolutely sustainable
0.9…1 production activity are solved
development (very good state, VG)
(considering development prospects)
S4 - high sustainable development Provision of environmental safety and
0.7…0.9
(good state, G) minimizing environmental impact
S3 - sustainable development Payments for environmental pollution
0.5…0.7
(satisfactory state, S) within the established limits
S2 – unstable development (poor
0.3…0.5 Poor ecological sustainability
state, P)
S1 – crisis situation (very poor
less than 0.3 Ecological sustainability is not ensured
situation, VP)
Source: own elaboration based on data from [31; 35].
4.3. Formation of mathematical software for IMS EIE
To evaluate and predict the EIE states of ecological sustainability based on the study of its integral
index, these states are proposed to be presented as a graph with vertices (Fig. 4), identifying the states
(Table 1): S1 – “very poor”; S2 – “poor”; S3 – “satisfactory”; S4 – “good”; S5 – “very good”.
λ 12 λ23 λ34 λ45
S1 λ21 S2 λ 32 S3 λ43 S4 λ54 S5
Figure 4: Graph of ecological sustainability states
This graph can be described by the system of Kolmogorov differential equations (1), and as t → ∞
and dP/dt = 0, by the system of algebraic equations (2), where λi, j are the intensities of the transition
from state i to state j, i, j = 1 , 2,…, 5; i ≠ j; Pi is the probability of i states.
dP1
12 P1 21 P2
dt
dP2
12 P1 (21 23 ) P2 32 P3
dt
(1)
dP3
23 P2 (32 34 ) P3 43 P4
dt
dP4
34 P3 (43 45 ) P4 54 P5
dt
dP5
45 P4 54 P5
dt
The value of transitions from one state to the other, directly affected by eco-innovations, is the
statistical information that can be obtained during the functioning of studied EIE. To evaluate and
predict EIE ecological sustainability state, it is recommended to collect information at the beginning
and at the end of the eco-innovation implementation. For the purpose of automated study of the
dynamics of ecological sustainability states, the numerical solution of the differential equation system
(1) is proposed to be performed by software tools, based on the fourth-order numerical Runge-Kutta
method, included in the structure of the IMS EIE (Subsystem SS 4). An automated study of EIE
ecological sustainability state in static when t → ∞, a dP/dt = 0, is proposed to be performed based on
computer solution of the system of algebraic equations (2) using software developed on the basis of the
Gaussian numerical method. Based on the obtained dynamic and static characteristics of the state of
ecological sustainability of enterprises can make appropriate forecasts and make optimal management
decisions.
12 P1 21 P2 0
12 P1 (21 , 23 ) P2 32 P3 0
(2)
23 P2 (32 34 ) P3 43 P4 0
34 P3 (43 45 ) P4 54 P5 0
45 P4 54 P5 0
The proposed mathematical tool and the developed software to solve systems of differential (1) and
algebraic (2) equations, were tested for relevance in real studies of the state of ecological sustainability
of 100 enterprises in the Western region of Ukraine.. Graph of virtual states of ecological sustainability
is shown in Fig. 5.
Prior to the introduction of eco-innovation, 30 enterprises were in state S1, 40 enterprises were in
state S2, 15 enterprises were in state S3, 10 enterprises were in state S4 and 5 enterprises were in state
S5, that is, the initial values of state probabilities (initial conditions of the studied process) were as
follows:
Р1 = 0.3; Р2 = 0.4; Р3 = 0.15, Р4 = 0.1, Р5= 0.05
3
2
25 30 35 20
S1 S2 S3 S4 S5
2 5 3 1
4
Figure 5: Graph of ecological sustainability virtual states
When solving differential equations system (1), describing the state graph of the integral indicator
of ecological sustainability (Fig. 5) and algebraic equations systems (2), we obtained dynamic and static
characteristics of virtual state probabilities of ecological sustainability, presented in Fig. 6.
P5
P
P2
P3
P4
P1
H – integration step
Figure 6: Dynamic and static characteristics of virtual states of enterprise ecological sustainability
Source: developed by the authors based on own calculations
In this case, state of S5 is most likely, since value of P5 in statics is 0.9342, and P4 = 0.0467, P3 =
0.0093, P2 = 0.0092, P1 = 0.0006. Since S5 is a very good state, characterizing the absolutely sustainable
development of the EIE, it can be considered that most EIE where eco-innovations are implemented,
belong to enterprises where ecological issues of industrial activities are resolved.
Based on the computational experiment, it can be concluded that this mathematical tool and the
software developed on its basis can find application as a mathematical and software IMS EIE to
evaluate, predict and support environmental decision making.
Thus, the proposed approach to designing of IMS EIE, the study of EIE state in general and their
structural elements, goals, efficiency, functions, actions and operations, indicates that IMS EIE should
be considered as a complex system with a set of interdependent elements, their structure, strategic and
operational activities aimed at achievement of EIE interim goals and overarching goals in a market
environment and the constant impacts of a changing environment.
5. Conclusions
Designing of IMS EIE as a complex system is aimed at greening of production and technological
processes of economic entities of different spheres and activities, industries, regions and the country as
a whole in compliance with modern challenges. Use of IMS EIE will allow to make optimal
management decisions on ecological and economic activity and increase the efficiency of enterprises
functioning, increase their environmental and economic security, which is a practical effect of work.
The studied approaches to IMS EIE designing can be widely used for IMS EIE and EIE design,
construction and restructuring in general and their structural elements, to adapt EIE to current economic
conditions.
It is important to formulate criteria to evaluate efficiency of the IMS EIE and use of an integral
indicator for evaluation and prediction of ecological sustainability of enterprises. Approaches to the
study of dynamic and static characteristics of EIE ecological sustainability states, its evaluation and
prediction, are relevant, for further optimal management decisions to improve the IMS EIE functioning
and the EIE as a whole.
6. References
[1] Sadekov A.A. 2002. Mechanisms of ecological and economic enterprise management. Monograph.
Donetsk: Donetsk National University of Economics and Trade named after M. Tugan-
Baranovsky, 311 p.
[2] Yasnolob Ilona, Gorb Oleg, Opara Nadiia, Shejko Serhii, Pysarenko Svitlana, Mykhaіlova Olena,
Mokiienko Tetyana. 2019. The formation of the efficient system of ecological enterprise. Journal
of Environmental Management and Tourism, Vol 9. N 1 (17). (Spring 2019). URL:
http://dspace.pdaa.edu.ua:8080/jspui/bitstream/123456789/5229/1/%D0%A1%D0%9A%D0
%9E%D0%9F%D0%A3%D0%A1.pdf.
[3] Reshetnikova I.L. 2009. Methodical approaches to eco-oriented management of a trading
company. Economy regulation mechanism, N 4. Т. 1, 42-47.
[4] Shylo S.V. 2013. Ecological and economic management of innovation in the agricultural sphere:
organizational aspect. Agroincom, N 10-12, 26-29.
[5] Ching-Torng Lin, Yu-Hsuan Chang, Chuanmin Mi. 2017. Develop Eco-Friendly Enterprise:
Aligning Enablers with Strategy. Sustainability, Vol 9. Issue 4. URL:
https://www.mdpi.com/2071-1050/9/4/570.
[6] Lassi Linnanen. 2002. An Insider's Experiences with Environmental Entrepreneurship. Greener
Management International: The Journal of Corporate Environmental Strategy and Practice, Vol.
Summer, Issue 38, 71-80. URL: https://ssrn.com/abstract=1495532.
[7] Adam Luqmani, Matthew Leacha, David Jessona. 2017. Factors behind sustainable business
innovation: The case of a global carpet manufacturing company. Environmental Innovation and
Societal Transitions, № 24, 94-105.
[8] Coen Bertens, Hidde Statema. 2011. Business models of eco-innovations, 67 p.
[9] Kneipp J., Gomes C., Bichueti R., Frizzo K., and Perlin A. 2019. Sustainable innovation practices
and their relationship with the performance of industrial companies. Revista de Gestаo, Vol. 26. N
2, 94-111. URL: https://doi.org/10.1108/REGE-01-2018-0005.
[10] Andrea Ettekal, Joseph L. Mahoney. Ecological Systems Theory. 2017. URL:
http://dx.doi.org/10.4135/9781483385198.n94.
[11] Agarwal N., Mukkamala R. 2005. Design of complex systems: issues and challenges. URL:
https://ieeexplore.ieee.org/document/1563486.
[12] Andrew P. Sage, William B. Rouse. 2014. Handbook of Systems Engineering and
Management 2nd Edition. Wiley-Interscience, 1504 p.
[13] Rika Preiser, Reinette Biggs, Alta De Vos, Carl Folke. 2018. Social-ecological systems as complex
adaptive systems: organizing principles for advancing research methods and approaches. Ecology
and Society, Vol. 23. No. 4. URL: https://doi.org/10.5751/ES-10558-230446.
[14] Zundong Zhang, Limin Jia, Yuanyuan Chai. 2010. A New Kind Methodology for Controlling
Complex Systems. International Journal of Natural Sciences and Engineering, Vol. 4. No. 8/1369
[15] Nicole Fortin, Thomas Lemieux, Sergio Firpo. Decomposition Methods in Economics. 2010.
Handbook of Labor Economics, No. 4. 118р.
URL: https://www.researchgate.net/publication/46467022.
[16] Nestor Shpak, Mykola Odrekhivskyi, Kateryna Doroshkevych and Włodzimierz Sroka. 2019.
Simulation of Innovative Systems under Industry 4.0 Conditions. Social Sciences. MDPI AG,
Basel, Switzerland, Vol. 8, Issue 7. URL: https://www.mdpi.com/2076-0760/8/7/202
https://doi.org/10.3390/ socsci8070202.
[17] Smol M., Kulczycka J. & Avdiushchenko A. 2017. Circular economy indicators in relation to eco-
innovation in European regions. Clean Technologies and Environmental Policy, Volume 19.
Issue 3 (April 2017), 669–678. URL: https://doi.org/10.1007/s10098-016-1323-8.
[18] Gunarathne, A.D.N. & Peiris, H.M.P. 2017. Assessing the impact of eco-innovations through
sustainability indicators: the case of the commercial tea plantation industry in Sri Lanka. Asian
Journal of Sustainability and Social Responsibility, Volume 2. Issue 1. (September 2017), 41-58.
URL: https://doi.org/10.1186/s41180-017-0015-6.
[19] Katarzyna Tarnawska. 2013. Eco-innovations – tools for the transition to Green economy.
Economics and Management, 18 (4), 735-743.
[20] Tsapuk О. Yu. 2013. System of criteria and indicators for evaluation of innovative development
efficiency. Marketing and innovation management, N 3, 137-145.
[21] Antonescu, M. 2018. Are business leaders prepared to handle the upcoming revolution in business
artificial intelligence? Qual. Access Success, 2018, N 19 (53), 15–19.
[22] Boitnott J. 2019. 7 innovative companies using A.I. to distrust their industries. URL: https://
www.inc.com/john-boitnott/7-innovative-companies-using-ai-to-disrupt-their-industries.html
(accessed on 1 June 2019).
[23] Jaehun Lee, Taewon Suh, Daniel Roy and Melissa Baucus. 2019. Emerging Technology and
Business Model Innovation: The Case of Artificial Intelligence. Journal of Open Innovation:
Technology, Market, and Complexity, 5, 44. URL:
https://www.researchgate.net/publication/334620177.
[24] Aliyev A.G. 2014. Economic-Mathematical Methods and Models under Uncertainty. Apple
Academic Press, 302 p.
[25] De la Fuente A. 2000. Mathematical Methods and Models for Economists. Cambridge University
Press, 836 p. URL: https://www.twirpx.com/file/1180529/.
[26] Ana Paula M. Tanajura, Valdir Leanderson C. Oliveira, Herman Lepikson. 2015. A Multi-agent
Approach for Production Management. Industrial Engineering, Management Science and
Applications, 65-75.
[27] Aradea Dipalokareswara, Iping Supriana, Kridanto Surendro. 2014. An Overview of Multi Agent
System Approach in Knowledge Management Model. International Conference on Information
Technology Systems and Innovation, 2014. URL:
https://www.researchgate.net/publication/268982254.
[28] Dhanashree R. Kamble. 2013. Architectural Review On Multi Agent Knowledge Management.
International Journal of Scientific & Technology Research, Volume 2, Issue 6 (June 2013), 105 –
114.
[29] F. Vendrell-Herrero, G. Parry, O. F. Bustinza, E. Gomes. 2018. Digital business models:
Taxonomy and future research avenues. Strategic Change, Vol. 27, Issue 2. URL:
https://doi.org/10.1002/jsc.2183.
[30] Delgado M., Verdegay J.L., and Vila V. 1993. Linguistic decision making models. International
Journal of Intelligent Systems, Vol. 7, 479-492.
[31] Larysa Cherchyk, Mykola Shershun, Nina Khumarova, Taras Mykytyn, Artur Cherchyk. 2019.
Аssessment of forest enterprises performance: Іntegrating Economic Security and Ecological
Impact. Entrepreneurship аnd Sustainability іssues, Vol. 6, N 4, 1784-1797. URL:
http://doi.org/10.9770/jesi.2019.6.4(17)/.
[32] Singh S., Olugu E. U. and Fallahpour A. 2014. Fuzzy-based sustainable manufacturing assessment
model for SMEs. Clean Technologies and Environmental Policy, Vol. 16 (5), 847-860. URL:
https://doi.org/10.1007/s10098-013-0676-5.
[33] Odrekhivskyy M., Kohut U., Kochan R., Jancarczyk D and Gryga V. 2019. Problems of evaluation
and Forecasting of the Biosystems states. 19th International multidisciplinary scientific
Geoconference SGEM 2019. Nano, Bio, Green and Space: Technologies for Sustainable Future,
(30 June – 6 July, 2019), Albena, Bulgaria. Vol. 19, Issue: 6.1, 859-865.
[34] Odrekhivskyy, M., Kohut, U., Kochan, R., Karpinskyi, V. and Bernas, M. 2019. Problems of
environmental innovation systems design. 19th International multidisciplinary scientific
Geoconference SGEM 2019. Ecology, Economics, Education and Legislation, 30 June – 6 July,
2019, Albena, Bulgaria. Vol. 19, Issue: 5.3, 587-594.
[35] Rudneva H.Y., Zaglada R.Y., Chiechienieva E.R. 2012. Evaluation the ecological Component of
Sustainable development of Coal-mining Industry Enterprises. Bulletin of Zaporizhzhya National
University. Economic Sciences, No. 4 (16), 62 - 68.
[36] Jurgis K. Staniskis, Valdas Arbaciauskas. 2009. Sustainability Performance Indicators for
Industrial Enterprise Management. Environmental Research, Engineering and Management, N 2
(48), 42 - 50. URL: https://www.researchgate. net/publication/49941561.
[37] Hyunkee Bae, Richard S. Smardon. 2011. Indicators of Sustainable Business Practices.
Environmental Management in Practice. Edited by Dr. Elzbieta Broniewicz, 177-206.