Assessment and Forecasting of the Environmental Sustainability Statuses of Innovative Enterprises in the Context of Sustainable Development

Abstract

The aim of the research is to improve approaches to assessing and predicting the environmental sustainability of innovative enterprises (IEs) for their sustainable development. The concept of environmental sustainability is defined, and the mechanism for managing it at IEs is developed. To implement the system of methods, models, principles, functions, actions, stages, and operations of the proposed management mechanism of the IE’s environmentally sustainable development, intelligent environmental monitoring, and a set of indicators for assessing and forecasting the status of an IE’s environmental sustainability were developed. It is proposed to evaluate the statuses of environmental sustainability of IEs on the basis of expert assessments of indicators and the developed scoring system and to forecast them using Markov chains described by the system of Kolmogorov differential equations and the corresponding system of algebraic equations. The proposed methodology was tested on the environmental sustainability analysis of Enzym Company (Lviv, Ukraine) in 2017–2021. The results of the study allow us to objectively assess the statuses of environmental sustainability of the enterprise and determine their probability, as well as its directions of sustainable development and ways of introducing innovative eco-technologies.

1. Introduction

Sustainable development is the driving force of the XXI century as automation was to the XX century and steam was to the XIX century. Moreover, since the adoption of the Sustainable Development Goals (SDGs) by the UN in 2015 [1,2], it has become a key concept of the global agenda. The SDGs have critical importance as they are aimed at protecting the environment, eradicating poverty, and ensuring prosperity for humanity. However, the worldwide progress in achieving them faces multiple challenges and thus remains insufficient [3,4,5,6,7,8,9,10,11].

Achieving the SDGs by 2030, particularly Goal 9, “Industry, Innovation, and Infrastructure”, and Goal 12, “Responsible Consumption and Production”, requires (due to global environmental problems and the overpopulation of the planet in combination with an uncertain and dynamic modern high-tech competitive environment) understanding of the key influencing factors and urgent global action at different levels, starting from the enterprise level [12,13,14,15,16,17,18].

The World Economic Forum’s Global Risks Report 2025 [19] shows that escalating geopolitical, environmental, societal, and technological challenges significantly threaten global stability and progress. State-based armed conflict is identified as the most pressing immediate global risk for 2025; misinformation and disinformation remain top short-term risks for the second consecutive year; other leading short-term risks include extreme weather events, societal polarization, cyber-espionage, and warfare; while technological risks related to misinformation, disinformation, and adverse outcomes of AI technologies dominate in the long-term estimate. Environmental risks are prevalent in the longer-term outlook, with extreme weather events, biodiversity loss and ecosystem collapse, critical change to Earth systems, and natural resource shortages leading the 10-year risk rankings. The fifth environmental risk in the top 10 is pollution, which also dominates in the short term. Its ranking expresses recognition of the serious ecosystem and health impacts of different types of air, water, and land pollutants.

Significant efforts nowadays are directed at intensifying innovation activity, concentrating resources on scientific and technological progress, intellectualizing business processes of enterprises, and creating an innovative environment that can ensure their sustainable development. However, there are still significant gaps in the research and development of effective approaches to assessing and forecasting the environmental sustainability of enterprises (described in detail in Section 2 and Section 5). All this makes the study on managing the innovative enterprises’ (IEs) environmental sustainability particularly relevant.

Thus, the aim of the research is to improve approaches to assessing and predicting the environmental sustainability of innovative enterprises (IEs) for their sustainable development through designing a mechanism for managing the environmental sustainability of innovative enterprises; creating a system of intelligent environmental monitoring of the environmental sustainability of enterprises; and elaborating on indicators, methods, and tools for assessing and predicting future statuses of environmental sustainability based on the assessment of the current ones.

This will help enterprises to make more effective management decisions for ensuring their competitiveness and environmentally sustainable development and to explore and develop actionable strategies for enterprises to contribute effectively to achieving the Sustainable Development Goals (SDGs), with a particular focus on Goal 9, “Industry, Innovation, and Infrastructure”, and Goal 12, “Responsible Consumption and Production”, by 2030.

The novelty of the research lies in the development and application of a comprehensive methodological framework for assessing and forecasting the environmental sustainability of innovative enterprises (IE). This research bridges gaps in the existing literature by providing a robust methodological foundation for evaluating and forecasting environmental sustainability while offering actionable strategies for innovative enterprises to enhance their ecological and economic performance.

2. Literature Review

2.1. Environmental Sustainability and Innovations

Environmental sustainability is the ability of an environmental system to maintain its structure and functions under the influence of internal and external factors. At least two main levels of sustainability can be distinguished: macro-level (country, region, city) and micro-level (enterprises, towns, regional areas) [20,21]. The environmental sustainability of an enterprise should be understood as its ability to develop while ensuring compliance with environmental protection rules and regulations.

Environmental sustainability is one of the most important characteristics of innovative enterprises (IEs) as they operate in an unstable environment. If the development of an IE is environmentally sustainable, it is competitive and has advantages in introducing innovative products, obtaining investments and loans, selecting suppliers, and recruiting qualified personnel. At the same time, an IE does not come into conflict with the ecosystem and, accordingly, with status and society as a whole, as it cares for the environment, saves resources, pays taxes, fees, and charges, and pays decent wages and dividends in a timely manner and in full. The higher the level of environmental sustainability of an IE, the more competitive and independent from changes in the external environment it is, which requires its effective management.

Enterprises must constantly innovate to develop sustainably [22]. The authors of [23,24,25,26] consider the importance of environmental innovations for sustainable development of small and medium-sized enterprises. SMEs, in general, play an important role in creating GDP and ensuring the sustainable development of the economy on an eco-intensive basis. The authors of [27] investigate sustainable development and innovations of 233 SMEs in Taiwan and develop a business model for more sustainable and environmentally friendly functioning. Shukla [28], based on the study of Indian firms, suggests the adoption of eco-innovation strategies. Many studies [29,30,31,32,33,34,35,36,37] are devoted to the implementation of environmental innovations and investments in eco-oriented development of firms in China, since it is among the largest polluters in the world. At the same time, the EU countries are global leaders in compliance with and development of sustainable development standards [38].

Different determinants and factors influencing enterprise’s innovative and sustainable development (firm’s knowledge, production, and market innovation capabilities; dynamic capability; decision-making and planning; investments and economic policy; stakeholder engagement; social aspects; circular economy implementation; business environment; and environmental requirements and regulation) were analyzed in [39,40,41,42,43,44,45].

The authors of [46] address the principles of sustainable entrepreneurship. If businesses are not aware of their contribution to sustainable development activities, the practical implementation of this concept cannot be carried out. Sustainable development is understood as knowledge and ethical potential. The development of such potential is achieved by businesses through innovation.

The problems of managing environmental sustainability and sustainable development of enterprises are addressed in many studies [29,47,48,49,50,51]. The nature, main tasks, and advantages of introducing environmental innovations and eco-oriented management, key aspects of enterprise management in the context of sustainable development, are studied. The authors of [23] examine technological and managerial innovation as the dual keys to achieving environmental sustainability. They consider the role of environmental innovations in minimizing industry’s environmental impact.

2.2. Environmental Sustainability Management of Enterprises

It is reasonable to manage sustainable development using the appropriate mechanism as a set of successive and coordinated methods and tools applied by the management entities for the targeted development of enterprises [52]. The authors describe the information system for ensuring the management mechanism of an enterprise’s sustainable development and classify the information flows circulating in the management mechanism of an enterprise’s sustainable development.

The authors of [53] examine the relationship between information systems (IS), competitive advantages of an enterprise, and environmental sustainability. The results show that the sustainable competitiveness of enterprises is improved by the synergy between IS and other resources within firms. Green IS initiatives not only improve environmental sustainability but also enhance sustainable competitive advantages [54]. However, sustainable development of an enterprise in the conditions of permanent changes is provided only by an effective system of external and internal control [55].

As a part of the general management system, environmental management based on the system-environmental approach ensures the correlation of each management function according to the principles of sustainable development and environmental justice [56].

In [57], modeling is used to assess the level of an enterprise’s sustainable development based on expert assessments in the competitive space model. The parameters for the model were grouped and evaluated by these main components: economic sustainability and competitiveness of the enterprise; social responsibility (degree and efficiency of implementation of ideas of socially responsible business in economic activity); and environmental efficiency of the enterprise (the ratio of the result to resources used, the level of implementation and effectiveness of eco-friendly programs, projects, etc.).

Environmentalists and governments use eco-innovation strategies to pursue economic growth, prevent environmental degradation, augment welfare, and address societal challenges [28]. It is essential, though, to quantify the actual effect of sustainability strategies of companies by identifying their sustainable patents and associating them with company characteristics [28]. In general, in the era of environmental awareness, eco-oriented culture must be the main habit and focus of management. A growing number of business leaders commit to integrating eco-orientation into their corporate culture [29,58,59].

The process of forming an effective mechanism of sustainable development of industrial enterprises can be divided into five blocks: (1) assessing the aggregate potential of the enterprise, determining indicators or factors characterizing the strength of the company, sources, capabilities, funds, reserves, resources, etc.; (2) setting of sustainable development goals; (3) setting of factors, methods, tools, and principles of sustainable development; (4) assessment of the level of stability; (5) adaptation of managerial decisions and adjustment of the goals, functions, principles, and methods in accordance with the level of sustainability identified in the evaluation phase [60].

Considering the need for sustainable development of enterprises and the requirement of the dual carbon goals of carbon peaking and carbon neutrality, the environment, social responsibility, and governance (ESG) management and green technology innovation of enterprises are in the spotlight [61].

2.3. Environmental Sustainability of Enterprises and SDGs Achievement

The need to ensure sustainable development and environmental sustainability of enterprises on the basis of the introduction of environmental innovations in the context of achieving the SDGs has been widely researched. In particular, the study [62] proves the need to invest in clean technologies and accelerate the transition to renewable energy sources, such as solar and wind energy and hydropower, in order to meet the goals of sustainable development. This study, examining the Kuznets environmental curve hypothesis for 17 MENA countries in 1990–2020, investigated the symmetric and asymmetric effects of energy consumption and economic growth on CO₂ emissions. The results show that an increase in energy consumption leads to environmental degradation, and a decrease in energy consumption leads to environmental improvement in MENA countries.

Research [63] highlights the relationship between sustainability performance and productivity management in the logistics industry and proves that sustainability performance management is a necessary strategic management tool.

The authors of [64] argue that with increasing global problems and citizen awareness of sustainability issues, policymakers are under more pressure than ever to factor sustainability into innovation policy. They emphasize the need to integrate it into small businesses and social enterprises, which will lead to better results for people and the planet in general.

The authors of [65] prove that corporate reputation and shareholder value may be at risk for organizations that cannot demonstrate a rational position on sustainable development. Specific challenges faced by organizations include the selection of appropriate products, processes, and life cycle assessment methods; changing the mindset of employees and other stakeholders; and, perhaps most importantly, creating new business models in general.

The paper [66] identifies a set of industry drivers and key factors (introduction of foresight, emergence and convergence of new technologies, and internationalization) for developing future innovation scenarios, taking into account current and future prospects. These factors, in the form of a three-dimensional structure, describe the way to develop future scenarios for the implementation of sustainability-oriented innovations for international New Technology-Based Firms.

The authors of [67] carry out a predictive assessment of the effectiveness of innovative environmental protection technologies using a clustering procedure based on the use of a scoring system of expert evaluation. The conducted clustering provides reasonable recommendations on the feasibility of financing an eco-innovation project based on predictive expert assessments.

Study [68] substantiates the effectiveness of using artificial intelligence to reduce carbon emissions. It is shown that artificial intelligence, the Internet of Things, and digitalization help reduce energy consumption, material waste, and carbon emissions, significantly improving the results of sustainable development. Industrial intelligence relies on green technological innovations, modernization of the industrial structure, and energy intensity to realize carbon reduction. However, the effectiveness of these technologies is ensured together with strategies that balance economic, environmental, social, and political aspects [68,69].

As we can see, scientists, who have been actively researching this topic over the past decades, looked at its various aspects and researched different areas. However, what is common in their works is the emphasis on:

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The importance of implementing environmental innovations in the context of the SDGs;

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The need to invest in clean technologies;

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Ensuring competitive advantages, environmental, social, and economic effects through the introduction of environmental innovations;

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The need to develop and implement environmental innovation strategies to ensure economic growth and prevent environmental degradation;

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The importance of integrating eco-orientation into the corporate culture of enterprises;

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The importance of assessing and forecasting the environmental sustainability of innovative enterprises.

Thus, the importance and necessity of studying and formulating approaches to solving the above problems from the standpoint of environmental, economic, and social efficiency in the context of achieving the Sustainable Development Goals (primarily SDG 9 and SDG 12) are undeniable.

However, all the above-mentioned analyzed studies still do not sufficiently cover the following:

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The mechanism for managing the environmental sustainability of innovative enterprises;

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The system of intelligent environmental monitoring of the environmental sustainability of enterprises, their networks, and territorial entities;

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Methods and tools for predicting future states of environmental sustainability based on the assessment of the current ones.

Thus, based on the literature review, it can be concluded that elaboration of approaches to innovative enterprise’s environmental sustainability management (in particular assessment and forecasting of its status) in order to ensure their competitiveness and environmentally sustainable development is relevant and meets the modern challenges.

3. Materials and Methods

As stated above, there are gaps in the current research on the sustainability of IEs in terms of predicting future states (statuses) of environmental sustainability based on the assessment of the current ones.

It should also be noted that the indicators of ecological sustainability are probabilistic in nature and cannot be clearly measured using accurate methods and tools. Accordingly, the states of the ecological sustainability of IE and the transitions from one state to another are also probabilistic in nature. Therefore, to predict future states of the ecological sustainability of IE based on the assessment of current ones, it is proposed to present these states and the transitions between them in the form of Markov chains, as a Markov random process with discrete states and discrete time, and describe them by a system of Kolmogorov differential equations [70].

A Markov chain is a stochastic model describing a sequence of possible states where the probability of each state depends only on the previous one. It has been proven as one of the most versatile and powerful tools in mathematical modeling due to its many advantages: simplicity, ability to handle uncertainty (including incomplete and probabilistic information), flexibility, memoryless feature, and out-of-sample forecasting accuracy (ability to predict complex dynamic spatial patterns with high reliability). Therefore, they are particularly useful for environmental sustainability analysis, where changes are often nonlinear, depend on random factors, and are difficult to predict by traditional means.

This method is widely used in different fields, including research on ecology and sustainability [70,71,72,73,74,75,76,77,78,79,80] (even though it has some pitfalls [61,62,63,81]), in particular, for analyzing ecology/ecosystems [72,76,82], animal behavior [70,71,73,75,77,83], geographical issues [74,80], sustainability [79,80], etc. The authors of [76] review the vast range of hidden Markov models for applied ecological research (including assessing ecological states) and provide a tutorial on their implementation and interpretation. They argue that these models “can facilitate inferences about complex system state dynamics that might otherwise be intractable by formally disentangling state and observation processes based on simple but powerful mathematical features that can be used for many ecological phenomena”.

In comparison with other mathematical tools (e.g., regression models, system dynamics, or fuzzy logic), Markov models are particularly appropriate for predicting the states of environmental sustainability of enterprises because of the following:

• Simplicity of modeling with minimal data (e.g., while regression models require a large number of precise input variables and their relationships, for Markov chains it is enough to know only the transition probabilities between states).
• Dynamic modeling of transitions between states (e.g., while many models (especially deterministic ones) assume fixed states without a clear transition logic, the Markov approach naturally describes how an enterprise moves between levels of environmental sustainability over time).
• Probabilistic nature of changes (e.g., while some methods such as system dynamics or linear programming are often based on exact cause-and-effect relationships, the Markov chain allows for uncertainty, which is typical in the field of ecology, where many variables (policy changes, climate, public pressure) are random).
• Minimum assumptions on dependencies (e.g., while regression analyses often require linear (or other) relationships between variables, Markov models do not require them, as they are based only on the probability of transition from one state to another).
• Possibility of long-term forecasts (e.g., while optimization or factor analysis methods can be effective for short-term decisions, Markov chains are easily adaptable to modeling future states 5, 10, or even 50 steps ahead—and allow us to estimate which state is most likely in the long term (stable distribution)).
• Flexibility in representing complex systems (e.g., one can add more states, include external events (extended Markov processes), or even use hidden Markov chains if the real state of the system is observed indirectly (for example, by indicators)).

Accordingly, the chosen methodology of structural modeling and a set of relevant methods used in the research are presented in

Table 1. Research methods used, their characteristics, and application.

№	Methods	Characteristics	Application in the Research
1	Analytical	A tool for studying the peculiarities and specifics of intra-system interaction, including results of abstraction, simplification, and formalization	Description of the statuses of environmental sustainability of IEs by the system of Kolmogorov differential equations and the corresponding system of algebraic equations
2	Cognitive science	Methods of building logical and cognitive models	Building an intelligent environmental monitoring of IEs
3	Expert evaluation	A method of scientific and technical forecasting of the future development of an object built on expert opinions	Assessment of the statuses of environmental sustainability of IEs and their corresponding indicators by using a scoring system
4	Markov chains	Markov random processes with discrete states and discrete time	Presentation of IEs’ environmental sustainability statuses
5	Structural design	A set of rules and procedures for building a functional model of the research object	Building a functional structure of the intellectual environmental monitoring of IEs
6	Synthelectics	Methods of collaborative thinking, synthesis of natural and artificial intelligence	Synthesis of natural and artificial intelligences in intelligent environmental monitoring

.

Thus, the research methodology is as follows: the analytical method allowed to describe the states of IE environmental sustainability by the system of Kolmogorov differential equations and the corresponding system of algebraic equations, which is the mathematical basis for intelligent environmental monitoring; the method of expert assessments on the relevant indicators allowed assessing the statuses of environmental sustainability of IE on the basis of a scoring system; the presentation of the statuses of environmental sustainability of IE is based on Markov chains—a Markov random process with discrete states and discrete time; the data of expert assessments were collected and accumulated in a database, and processed by the corresponding subsystem of intelligent environmental monitoring, which is a complex human-cyber-physical system and functions through the use of logical and cognitive models and by synthesizing natural and artificial intelligence. The processed data of expert assessments of the statuses of environmental sustainability of the IP were presented in the form of dynamic and static characteristics of the probabilities of these states, on the basis of which better management decisions can be made and implemented.

The proposed methodology was tested on Enzym Company PrJSC (Lviv, Ukraine). The company operates systems of environmental management (ISO 14001:2015) and energy management (ISO 50001:2018) [84,85]. One of its most effective environmental solutions was the installation of heat energy recuperators. In 2004–2024, the company implemented a unique, large-scale, innovative complex of wastewater treatment. Capital investments in the sewage treatment plants for 2004–2014 amounted to EUR 9 million, and in 2015 an additional anaerobic technological line (worth EUR 2.5 million) was installed for deepening wastewater treatment. As a result, biological (oxygen-free) methods of wastewater treatment ensure the formation of biogas, which is an alternative to natural gas and covers about 60% of the energy needs of the enterprise. In 2021, the company started the next stage of modernization of the sewage treatment system, which is still ongoing. Therefore, for the study, we chose the period of 2017–2021, when the results of the main completed stage of the innovation project were already notable. In accordance, during this period 84 observations of the environmental sustainability of Enzym Company were conducted, and their results became input data for the testing of the proposed methodology.

Further presentation of the results of the research is conditioned by a sequential description of the stages of the developed mechanism of management of innovative enterprises’ environmental sustainability, with an emphasis on assessment and forecasting of its status.

4. Results

The mechanisms for managing the IE’s environmentally sustainable development constitute a comprehensive system of methods, functions, and means of management based on the characteristics and principles of management through which environmental sustainability processes are organized, controlled, and regulated. According to the results of [24,31,44,46,48,51,52,61], the main components of the mechanism for ensuring and managing the environmental sustainability of innovative enterprises should include the following:

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Developing an integrated system for stimulating, supporting, and regulating environmentally sustainable innovation activities;

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Increasing resources for the implementation of environmental innovation projects;

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Developing a range of environmental innovation projects;

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Participating in targeted international, national, regional, and anthropological environmental programs and innovative projects;

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Motivating employees to develop environmentally sustainable innovation activities;

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Developing criteria for selecting potential opportunities for R&D of the enterprise for the production of competitive innovative environmental products;

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Developing indicators to assess dynamics and statics of environmentally sustainable development of the enterprise and make corresponding managerial decisions.

When creating a mechanism for managing the environmentally sustainable development of an IE, a strategy, goals, functions, principles, and methods of IE management should be set out, and the subject and object of management should be determined [24,25,86].

Development of environmentally oriented innovation strategies for an innovative enterprise should be based on an eco-oriented methodology and relevant provisions. The basic assumption is that innovation strategies form a system with hierarchically interconnected elements. This system should be in line with global trends of environmentally oriented development and, accordingly, the development of the national economy, combining macro-, meso-, micro-, and nano-levels in cooperation with foreign countries. The environmentally oriented business strategy is aimed at profit earning with a focus on sustainable development [24,25]. The main goal of the mechanism for managing the IE’s environmentally sustainable development is to improve its competitiveness as well as environmental safety and sustainability [87].

This goal can be achieved through the proposed mechanism of management of innovative enterprises’ environmental sustainability. Further presentation of the results of our research will actually be conditioned by a sequential description of its stages, where the assessment and forecasting of environmental sustainability statuses are the most important ones (Figure 1).

While creating a mechanism for managing the IE’s environmentally sustainable development, it is important to not only identify and manage the statuses of the IE’s environmental sustainability but also to determine the impact of these statuses on the financial and economic prospects of the IE’s development, which are suggested to be analyzed in the following stages [88]:

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Comprehensive assessment of the efficiency of environmental management during the life cycle of IE, its adaptivity, and investment attractiveness: analysis of capital and current environmental costs; analysis of the effectiveness of environmental measures.

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Analysis of the economic efficiency of environmental protection activities.

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Information support for the company’s management and other stakeholder groups to make and implement optimal management decisions.

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Analysis of environmental risks and quality of management decisions related to environmental management processes and introduction of resource-saving technologies and technologies for waste utilization and recycling.

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Assessment of the efficiency of environmental taxation and other environmental obligations.

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Modeling, evaluation, and forecasting of environmental and economic processes and their impact on the long-term sustainable development of the enterprise.

These stages of analysis are particularly relevant due to the objective need to conduct a comprehensive analysis of the performance of IEs through environmental indicators in order to maintain their environmental sustainability and implement energy-efficiency measures and environmentally friendly technologies [89].

Herewith it is important to determine the results of environmental protection activities. The environmental result is determined by a reduction in the level of harmful substances in the IE’s ecosystem and the goods produced by IEs in the course of their operation and entering various environmental systems. The eco-result is measured in terms of natural goods [90]. The economic result achieved through the implementation of environmental protection measures can be expressed as [91]: the cost of registered fixed assets for environmental protection purposes; additional profit received from the use of technological waste in production; additional profit received from the sale of utilized technological waste of production; and reducing environmental payments for the use and pollution of natural resources.

The proposed management mechanism is based on the relevant principles, in particular: consistency, flexibility, adaptability, information content, planning, normativity, self-organization, self-development, transformability, purposefulness, irreversibility, rational use of natural resources, optimality, and efficiency.

To implement the system of the mentioned methods, principles, and stages of the mechanism for managing the IE’s environmentally sustainable development, we suggest applying intelligent environmental monitoring [20]. It is a system of tools for systematic monitoring, collection, storage, processing, and analysis of information on the statuses of IE’s ecosystems, their assessment and forecasting, and support for making and implementation of appropriate decisions on managing these statuses.

Talking about the management of IE’s ecosystems in a broad sense, we should first of all keep in mind the management system, where the presence of components A, B, and C in its structure is a necessary but not sufficient condition for its effective functioning (Figure 2). Entity A is an ecosystem or an entity subject to management; B is an intelligent information system—an entity that implements function F1—the function of reflecting the statuses of entity A and forms the control function F2; and C is an entity that implements function F2 in order to control the behavior of entity A.

Entity A is an ecosystem, an information status of which is characterized by aggregate information about its statuses. That is, the management entity A is characterized by the information status Ia—a certain aggregate information, the components of which at a fixed point in time include descriptions and values of the main indicators of the behavior of entity A. Then, a certain status Ib of the computer memory will be a reflection of the information status Ia in entity B, which can be an intelligent information system as a human-cyber-physical system. The function defined as F1 (A) = Ib or F1: Ia → Ib will be a reflecting function. The control function F2 can be represented at a certain fixed time interval by a set of interrelated actions defined on information Ib, such that F2 (Ib) = Ia’, where Ia’ is the information status of entity A obtained as a result of the implementation of the control function F2.

The functional purpose of entity B in the general logical organization of the IE’s ecosystem management system is such that the implementation of the reflecting function F₁ should cover the process, the components of which include collecting information about the statuses of the ecosystem, storing the necessary information, and processing it according to some target algorithms in order to reflect the information status Ia of entity A in entity B and support decision-making. The control function F₂ is based on the results of reflecting the information status of the IE’s ecosystem, forming decision options, supporting decision-making, and transferring decisions to the person who makes the final decision. After that, the process of supporting the implementation and the actual implementation of the ecosystem management decisions takes place. Therefore, the control process in the ecosystem management system should be carried out in three stages: reflection of the information status of the IE’s ecosystem—implementation of the reflecting function F₁; support for decision-making and the making of relevant decisions—formation of the control function; support of the implementation and actual implementation of the decisions made—implementation of the control function F₂.

Therefore, the mechanism for managing the IE’s environmentally sustainable development, in our opinion, should include methods, models, and tools for the analysis of: (1) internal and external factors of IEs and management of their business processes and their environmental friendliness; (2) the phases of the IEs’ life cycles and their provision with resources; (3) the efficiency of the use of resources and making adequate decisions; and (4) the status of environmentally sustainable development of IEs in general, their business processes, actions, operations, etc., as well as making and implementing optimal management decisions.

Today, international integration of IEs, their clustering, social partnership, innovative cooperation, diversification of business processes, compliance with the quality of management systems in general, management of potential resources, risks, and development, and the use of information and communication technologies are particularly relevant. This allows us to see the process of the IE’s functioning in the long term and in interaction with the external environment, as well as contributes to the preparation of various scenarios for the development of IEs [86]. Thus, by promoting environmental sustainability, flexibility, and adaptability of IEs to the challenges of today, their need for natural resources can be significantly minimized. The latter dictates the need to systematically assess and forecast the status of environmental sustainability of IE.

To assess and forecast the statuses of the IE’s environmental sustainability and to support more effective decision-making, the chosen indicators are summarized in

Table 2. Environmental sustainability indicators and their characteristics. (source: developed by the authors based on [20,90]).

№	Indicators	Characteristics of the Indicators
1	Volume of toxic waste	Volume of toxic waste—the amount of waste containing harmful substances (mercury, lead, cadmium, and other heavy metals) that can harm human health or the environment
2	Volume of production emissions	Volumes of pollutants or their mixtures released by enterprises into the atmosphere
3	Efficiency of low-waste technologies	Efficiency of production of products, in which a part of raw materials and supplies is transformed into waste
4	Efficiency of resource-saving technologies	Efficiency of resource-saving technologies that ensure absolute and relative reduction in material, technical, and energy resources
5	Volume of primary waste	The amount of waste generated directly during production
6	Degree of recycling of primary waste	The extent to which waste is used as a secondary raw material and its processing to recover useful components as fully as possible
7	Efficiency of energy-saving technologies	Efficiency of energy-saving technologies used in production and vehicles
8	Volume of natural resources used	Volume of natural resources utilization of the territorial unit
9	Quality of workplaces	The quality of a unit of the production structure, which contains a part of the space of the production unit that is required for the labor operation and is equipped with material and technical means used in the process
10	Efficiency of environmental protection measures	The efficiency of measures to maintain the optimal state of the natural environment and eliminate damage from anthropogenic and man-made impacts

.

To analyze these indicators, expert assessment and a scoring system are suggested, as environmental sustainability indicators are diverse in nature, mostly uncertain and probabilistic, and cannot be clearly measured by precise methods and tools.

The statuses of the IE’s environmental sustainability (

Table 3. Statuses of environmental sustainability of innovative enterprises. (source: developed by the authors).

Statuses of Environmental Sustainability (SES)	Symbols	Total Points (SP)	Points (P)	Indicators of Environmental Sustainability
Very high environmental sustainability	SES1	80 < SP ≤ 100	8 < P ≤ 10	Very low volumes of toxic waste
			8 < P ≤ 10	Very low production emissions
			8 < P ≤ 10	Very efficient low-waste technologies
			8 < P ≤ 10	Very efficient resource-saving technologies
			8 < P ≤ 10	Very low volumes of primary waste
			8 < P ≤ 10	Very high degree of recycling of primary waste
			8 < P ≤ 10	Very efficient energy-saving technologies
			8 < P ≤ 10	Very low use of natural resources
			8 < P ≤ 10	Very high quality of jobs
			8 < P ≤ 10	Very efficient environmental protection measures
High environmental sustainability	SES2	60 < SP ≤ 80	6 < P ≤ 8	Low volumes of toxic waste
			6 < P ≤ 8	Low production emissions
			6 < P ≤ 8	High efficiency of low-waste technologies
			6 < P ≤ 8	High efficiency of resource-saving technologies
			6 < P ≤ 8	Low volumes of primary waste
			6 < P ≤ 8	High degree of recycling of primary waste
			6 < P ≤ 8	High efficiency of energy-saving technologies
			6 < P ≤ 8	Low use of natural resources
			6 < P ≤ 8	High quality of jobs
			6 < P ≤ 8	High efficiency of environmental protection measures
Satisfactory environmental sustainability	SES3	40 < SP ≤ 60	4 < P ≤ 6	Permissible volumes of toxic waste
			4 < P ≤ 6	Permissible production emissions
			4 < P ≤ 6	Satisfactory efficiency of low-waste technologies
			4 < P ≤ 6	Satisfactory efficiency of resource-saving technologies
			4 < P ≤ 6	Permissible volumes of primary waste
			4 < P ≤ 6	Satisfactory degree of recycling of primary waste
			4 < P ≤ 6	Satisfactory efficiency of energy-saving technologies
			4 < P ≤ 6	Permissible volumes of use of natural resources
			4 < P ≤ 6	Satisfactory quality of jobs
			4 < P ≤ 6	Satisfactory efficiency of environmental protection measures
Low environmental sustainability	SES4	20 < SP ≤ 40	2 < P ≤ 4	High volumes of toxic waste
			2 < P ≤ 4	High production emissions
			2 < P ≤ 4	Low efficiency of low-waste technologies
			2 < P ≤ 4	Low efficiency of resource-saving technologies
			2 < P ≤ 4	High volumes of primary waste
			2 < P ≤ 4	Low degree of recycling of primary waste
			2 < P ≤ 4	Low efficiency of energy-saving technologies
			2 < P ≤ 4	High volumes of use of natural resources
			2 < P ≤ 4	Low quality of jobs
			2 < P ≤ 4	Low efficiency of environmental protection measures
Very low environmental sustainability	SES5	0 ≤ SP ≤ 20	0 ≤ P ≤ 2	Very high volumes of toxic waste
			0 ≤ P ≤ 2	Very high production emissions
			0 ≤ P ≤ 2	Very low efficiency of low-waste technologies
			0 ≤ P ≤ 2	Very low efficiency of resource-saving technologies
			0 ≤ P ≤ 2	Very high volumes of primary waste
			0 ≤ P ≤ 2	Very low degree of recycling of primary waste
			0 ≤ P ≤ 2	Very low efficiency of energy-saving technologies
			0 ≤ P ≤ 2	Very high volumes of use of natural resources
			0 ≤ P ≤ 2	Very low quality of jobs
			0 ≤ P ≤ 2	Very low efficiency of environmental protection measures

) and, accordingly, transitions from one status to another, are probabilistic in nature.

Therefore, in order to predict future statuses on the basis of the assessment of the current ones, it is suggested to present them in the form of Markov chains, i.e., a status graph (Figure 3), and to describe them using the system of Kolmogorov differential Equation (1) [85,87], where P_i—probabilities of i–x statuses; λ_ij—intensity of transition from the state i to the state j; i, j = 1, 2, …, 5—sequential numbers of states.

$$\begin{array}{c}{dP}_1/dt={-(\lambda }_{12}+{\lambda }_{13}+{\lambda }_{14}+{\lambda }_{15})·P_1+{\lambda }_{21}{·P}_2+{\lambda }_{31}·P_3+{\lambda }_{41}·P_4+{\lambda }_{51}·P_5;\\ {dP}_2/dt={{\lambda }_{12}{·P}_1-(\lambda }_{21}+{\lambda }_{23}+{\lambda }_{24}+{\lambda }_{25})·P_2++{\lambda }_{32}·P_3+{\lambda }_{42}·P_4+{\lambda }_{52}·P_5;\\ {dP}_3/dt={\lambda }_{13}{·P}_1+{\lambda }_{23}·P_2{-(\lambda }_{31}+{\lambda }_{32}+{\lambda }_{34}+{\lambda }_{35})·P_3+{\lambda }_{43}·P_4+{\lambda }_{53}·P_5;\\ {dP}_4/dt={\lambda }_{14}{·P}_1+{\lambda }_{24}·P_2+{\lambda }_{34}·P_3{-(\lambda }_{41}+{\lambda }_{42}+{\lambda }_{43}+{\lambda }_{45})·P_4+{\lambda }_{54}·P_5;\\ {dP}_5/dt={\lambda }_{15}{·P}_1+{\lambda }_{25}·P_2+{\lambda }_{35}·P_3+{\lambda }_{45}·P_{4 }{-(\lambda }_{51}+{\lambda }_{52}+{\lambda }_{53}+{\lambda }_{54})·P_5.\end{array}$$

(1)

Each of the equations of the system of differential Equation (1) describes the change in time of the values of the probabilities of the states Pi (i = 1, 2,…, 5). Solving each of Equation (1) allows us to obtain the dynamic characteristics shown in Figure 4. Therefore, in each equation of the system of differential Equation (1), to the left of the equal sign, the derivatives of the probabilities P_i of the i statuses (i = 1, 2,…, 5) dependent on time t are provided, and to the right, the sums of the products of the intensities of transitions λ_ij from state i to state j (i, j = 1, 2,…, 5; i ≠ j) and the probabilities of the states P_i are provided. If the arc of transitions (Figure 3) leaves the i-th status, then λ_ij is taken with a minus sign; if it enters the i-th status, it is taken with a plus sign. The number of equations in the system corresponds to the number of statuses (5 in our case).

Thus, the formed system of differential equations describes the dynamics of changes in the probabilities of states P_i, and when t → ∞ and dP/dt = 0, the system of differential equations is transformed into a system of algebraic equations that enables calculating the values of the probabilities of states P_i in the stationary mode and making appropriate predictions.

The corresponding system of algebraic Equations is as follows (2):

$$\begin{array}{c}{-(\lambda }_{12}+{\lambda }_{13}+{\lambda }_{14}+{\lambda }_{15})·P_1+{\lambda }_{21}{·P}_2+{\lambda }_{31}·P_3+{\lambda }_{41}·P_4+{\lambda }_{51}·P_5=0;\\ {{\lambda }_{12}{·P}_1-(\lambda }_{21}+{\lambda }_{23}+{\lambda }_{24}+{\lambda }_{25})·P_2++{\lambda }_{32}·P_3+{\lambda }_{42}·P_4+{\lambda }_{52}·P_5=0;\\ {\lambda }_{13}{·P}_1+{\lambda }_{23}·P_2{-(\lambda }_{31}+{\lambda }_{32}+{\lambda }_{34}+{\lambda }_{35})·P_3+{\lambda }_{43}·P_4+{\lambda }_{53}·P_5=0;\\ {\lambda }_{14}{·P}_1+{\lambda }_{24}·P_2+{\lambda }_{34}·P_3{-(\lambda }_{41}+{\lambda }_{42}+{\lambda }_{43}+{\lambda }_{45})·P_4+{\lambda }_{54}·P_5=0;\\ {\lambda }_{15}{·P}_1+{\lambda }_{25}·P_2+{\lambda }_{35}·P_3+{\lambda }_{45}·P_{4 }{-(\lambda }_{51}+{\lambda }_{52}+{\lambda }_{53}+{\lambda }_{54})·P_5=0.\end{array}$$

(2)

The values of the intensities of transitions λ_ij from a status i to a status j (i, j = 1, 2,…, 5; i ≠ j), obtained in the process of monitoring the IE’s environmental sustainability, can be represented as a matrix Λ (3).

$$\Lambda =\left(\begin{array}{c}0 {\lambda }_{1_2} {\lambda }_{1_3} {\lambda }_{1_4} {\lambda }_{1_5}\\ {\lambda }_{2_1} 0 {\lambda }_{2_3} {\lambda }_{2_4} {\lambda }_{2_5}\\ {\lambda }_{3_1} {\lambda }_{3_2} 0 {\lambda }_{3_4} {\lambda }_{3_5}\\ {\lambda }_{4_1} {\lambda }_{4_2} {\lambda }_{4_3} 0 {\lambda }_{4_5}\\ {\lambda }_{5_1} {\lambda }_{5_2} {\lambda }_{5_3} {\lambda }_{5_4} 0\end{array}\right)$$

(3)

As mentioned above, based on 84 observations of the environmental sustainability of Enzym Company (Lviv, Ukraine), the following results were obtained: Enzym was in status SES₁ (very high environmental sustainability) 3 times, in status SES₂ (high environmental sustainability)—7 times, in status SES₃ (satisfactory environmental sustainability)—17 times, in status SES₄ (low environmental sustainability)—30 times, and in status SES₅ (very low environmental sustainability)—27 times.

The values of statuses’ probabilities obtained as a result of the expert assessment of the environmental sustainability of Enzyme Company are summarized in

Table 4. The values of probabilities of the environmental sustainability statuses of Enzym Company.

Statuses		Years
		2017	2018	2019	2020	2021
		The Values of Probabilities of the Statuses
1	Very high environmental sustainability (P1)	0.036	0.071	0.111	0.154	0.198
2	High environmental sustainability (P2)	0.083	0.115	0.148	0.177	0.202
3	Satisfactory environmental sustainability (P3)	0.202	0.240	0.254	0.253	0.245
4	Low environmental sustainability (P4)	0.357	0.312	0.272	0.237	0.206
5	Very low environmental sustainability (P5)	0.322	0.262	0.215	0.179	0.149
Σ·Pi		1	1	1	1	1

.

The company’s environmental sustainability was changing over the period of research (2017–2021) due to the implementation of the above-mentioned eco-innovation project. The intensity of transitions λ_ij from a status i to a status j (i, j = 1, 2,…, 5; i ≠ j) of matrix (3), thus, acquired the actual values and is represented as the matrix Λ (4).

$$\Lambda =\left(\begin{array}{c}0 5 3 0 0\\ 1_9 0 3 0 0\\ 9 2_3 0 2 3\\ 0 0 2_5 0 1\\ 0 0 1_1 { 1}_3 0\end{array}\right)$$

(4)

To assess and predict the statuses of environmental sustainability of Enzym Company, the system of differential Equation (1) and the system of algebraic Equation (2) were solved using the Runge–Kutta method of the 4th order to solve the system of differential equations and the Gauss method to solve the system of algebraic equations. Thus, the dynamic and static characteristics of the probabilities P_i of the statuses of environmental sustainability SES_i, where i = 1, 2, 3, 4, 5, were obtained (Figure 4), where P (vertical axis) is the probability of states and H (horizontal axis) is the integration step, which is identified with time. It should be noted that the presented dynamic characteristics converge to static ones, and at each integration step, Σ Pi = 1; therefore, the calculation results can be considered reliable. The reliability of the calculations is checked at each integration step, built into the software.

Based on analyzing the dynamic and static characteristics of the probabilities of Enzyme’s environmental sustainability statuses P_i, a conclusion can be made that SES₁ (very high environmental sustainability (corresponding P₁)) is the most likely status in the long term. This indicates that the implementation of the mentioned eco-innovation project was successful.

It should be noted that the results of the study, obtained through the expert evaluation and summarized in Table 4, at the first steps of integration, basically coincide with the values obtained as a result of the computational experiment, which confirms the adequacy of the calculation model and the reliability and robustness of the results obtained. That is, this model adequately describes the states of environmental sustainability of Enzyme Company (Lviv, Ukraine) and can be widely used to assess and predict the statuses of environmental sustainability of other IEs.

Based on the same mathematical tools, but for different purposes/tasks, in 2016/2018 we also conducted a study of the environmental sustainability of 100 enterprises in the western region of Ukraine [20] and a study of the concentration of oil products in areas (elements of biogeocenosis) around wells operated at the Boryslav oil field [92]. And in 2016/2020, the pollution levels of territorial entities in the Lviv region (Ukraine) were assessed, which led to the conclusion that the largest emissions of pollutants into the air are generated by enterprises supplying electricity, gas, steam, air conditioning, and coal mining [87]. The above-mentioned research provided an opportunity to make better management decisions to ensure the environmental sustainability of the analyzed enterprises and help eliminate the negative impact of anthropogenic factors on the environment of the region.

However, when working with large amounts of environmental information, the proposed research methodology needs to be supplemented with other mathematical tools (big data theory, cloud computing, etc.), which may be the subject of further research.

5. Discussion

In the research, environmental sustainability is considered as the ability of an ecological system to maintain its structure and functions in the process of influence of internal and external factors. Since IEs operate in an unstable external environment, sustainable development is considered to be their most important characteristic. If an IE’s development is environmentally sustainable, it is competitive and has advantages in introducing innovative products, obtaining investments and loans, selecting suppliers, and recruiting qualified personnel. The higher the level of environmental sustainability of an IE, the more independent it is from changes in the external environment, which necessitates an effective management mechanism to ensure environmental sustainability.

The environmental sustainability management mechanism is presented as a system of methods, functions, and means of management based on the characteristics and principles of management, through which the processes of environmental sustainability are organized, controlled, and regulated. The main purpose of such a mechanism is to increase the level of competitiveness, environmental safety, and sustainability of enterprises. This is proposed to be carried out in accordance with the stages of managing the eco-sustainability of IEs. In addition, it is considered relevant not only to study the statuses of IEs’ eco-sustainability and their management but also to determine the impact of these statuses on the financial and economic prospects of IEs’ development in general.

It is worth noting that some other studies also propose methods for analyzing and forecasting the environmental sustainability states/statuses of enterprises, but they focus more on forecasting based on historical data rather than on the assessment. In particular, the study [93] analyzes the state of China’s environmental sustainability using a modified Ecological Footprint (EF) method that takes into account the freshwater ecological footprint, improves the energy ecological footprint, and changes the equivalence ratio and yield ratio. Then, linear autoregressive integrated moving average (ARIMA) models and nonlinear artificial neural network (ANN) models are used to predict future environmental security. The researchers in [94,95] study the impact of innovative business models on the environment in the context of the digital economy. The research [95] examines the environmental impact of implementing circular business models through 29 semi-structured interviews and 39 survey responses of business developers, managers, product designers, and consultants from more than 10 industries. The results show that while most respondents measure the impact of their current business models, they do not predict the future impacts of their cyclical business ideas prior to the implementation. The study [96] proposes a statistical model of the ecological and economic state of an enterprise using a synthesis of econometrics and multidimensional forecasting methods that ensure the correlation of the obtained indicators, taking into account the mutual proportionality with respect to the dynamic characteristics of environmental sustainability factors within the framework of the sustainable development paradigm. Using the least squares method, the interdependence of environmental and economic indicators of enterprise sustainability is shown as follows: the costs of capital repairs of fixed assets for environmental protection; labor costs, including contributions to the social needs of employees involved in environmental protection; operational environmental costs; sales revenue; and profitability of production and sales. The research [97] forecasts the environmental sustainability states of companies based on three performance indicators: resource use assessment, emissions assessment, and environmental innovation assessment. A forecasting model is proposed that is best suited when the available data sets are small. A trigonometric gray forecasting model is used, where the GM (1, 1) model is first used for forecasting, and later an error forecasting model is built based on the trigonometric residual forecasting model.

A significant result of our study can be considered the implementation of a system of methods, models, principles, functions, actions, and operations of the mechanism for managing the eco-sustainable development of IE through the use of intelligent environmental monitoring as a system of tools for managing the IE’s eco-sustainable development. These methods (see Table 1) are focused on systematic monitoring, collection, storage, processing, and analysis of information on the states of IE ecosystems, their assessment and forecasting, and making and implementing appropriate decisions on management.

Also of scientific interest is the assessment of statuses, which is proposed to be carried out on the basis of expert assessments, the essence of which is the use of a scoring system for determining the states of environmental sustainability and their corresponding indicators. For forecasting, the statuses are represented in the form of a Markov chain, a status graph (Figure 3), and are described by a system of Kolmogorov differential equations. This mathematical toolkit was tested in the analysis of the environmental sustainability of the Enzym company (Lviv, Ukraine). We believe that the implementation of the proposed mechanism for ensuring the ecologically sustainable development of IEs will contribute to the implementation of SDGs, especially SDG 9 and SDG 12.

The results of the study can be as well of practical importance for both business and politics. Indeed, there are many examples of environmentally oriented activities among international corporations: many of them implement specialized environmental policies and publish environmental guidelines and codes of conduct to ensure product and production safety. For example, Ford Corporation sees the main goal of its environmental policy in reducing carbon dioxide emissions by improving the environmental friendliness of its car engines. In general, in the United States, environmentally friendly technologies have similar volumes of venture capital investment to information and new technologies. In China, such venture capital investments have more than doubled in recent years, accounting for 19% of total investment. China, the largest energy consumer and CO₂ emitter, has developed various carbon emission reduction policies. The European Commission has also developed a plan to reduce greenhouse gas emissions in the EU by at least 55% by 2030 compared to 1990 levels. According to the International Labor Organization (ILO), the environmental technology industry in Germany will grow 4 times from its current level by 2030 and will account for up to 16% of total industrial production [98,99,100].

Canada has many startups in the environmental innovation sector and strong government support, and eco-innovation enterprises are intensively created and developed due to digital technologies. For example, Canada’s Corporate Environmental Innovation (CEI) initiative is a partnership-based government project aimed at accelerating innovation and improving the environmental performance of companies. The CEI brings together industry, the financial sector, academia, non-governmental organizations, and governmental bodies [101]. Over the past five years, the Canadian technology ecosystem has been ranked in the annual Global Cleantech 100, a prestigious list of startups and emerging companies that have the best opportunities to grow, develop their technologies, and overcome the climate crisis. In 2022, this list included 13 Canadian firms (second only to the USA), nine of which are part of the MaRS portfolio [102].

6. Limitations

The research has several limitations and, accordingly, future directions for its improvement, in particular regarding the selected mathematical and software tools. Firstly, the selected system of indicators for analyzing the efficiency of the functioning of IEs is limited to ten indicators. Secondly, to conduct research on the efficiency of the network of IEs and their territorial entities, it is necessary to process large volumes of environmental information, in which regard the proposed mathematical and software tools have limitations (less effective or potentially misleading in the cases of complex systems with long-term dependencies, high-dimensional state spaces, or systems with significant external influences). Therefore, it is advisable to focus further research on a more deeply studied system of indicators of the efficiency of IEs and modern mathematical tools to support the adoption and implementation of management decisions to ensure the sustainable development of IEs, their networks, and relevant territorial entities. This, in particular, includes methods and tools for processing big data, which concerns working with large volumes of environmental information for making management decisions regarding the environmental sustainability of the network of IEs and territorial entities.

The limitations of the study also consist of using data only for Ukraine and its companies. Therefore, in further research, it would be advisable to focus on collecting, storing, and analyzing data on the environmental sustainability of enterprises, their networks, and territorial entities globally.

7. Conclusions

The IE’s environmental sustainability is its ability to maintain its structure and functions under the influence of internal and external factors and to develop sustainably in compliance with the rules and regulations on environmental protection.

The proposed mechanism for managing the IE’s environmentally sustainable development constitutes a comprehensive system of methods, functions, and stages based on the characteristics and principles of management, through which the processes of environmental sustainability are organized, controlled, and regulated. The main goal of this management mechanism is to increase the level of enterprises’ competitiveness, environmental safety, and sustainability.

To this end, a functional structure of IE’s intelligent environmental monitoring is developed, and a methodology for assessing the status of the IE’s environmental sustainability is proposed. To assess, forecast, and manage the statuses of the IE’s environmental sustainability, we suggest (1) systematic monitoring of indicators of the IEs’ environmental sustainability, their actual statuses, and the dynamics of these statuses; (2) assessment of the intensity of transitions from one status to the other one; and (3) forecasting the statuses and decision-making according to them. Expert assessment of indicators is recommended, with experts using a scoring system for determining the statuses of environmental sustainability and corresponding indicators, since environmental sustainability indicators are diverse in nature, mainly uncertain and probabilistic, and cannot be clearly measured by precise methods.

For assessment purposes, the statuses of the IE’s environmental sustainability were represented in the form of Markov chains and described by the system of Kolmogorov differential equations and the corresponding system of algebraic equations.

The methodology was tested by assessing and forecasting the environmental sustainability statuses of Enzym Company (Lviv, Ukraine). This made it possible to evaluate the success of the implementation of its eco-innovation project to ensure its environmentally sustainable development and provide the company with effective tools for optimizing further management decisions.

That is, the results of the study are of great scientific and practical importance, as they allow us to objectively assess the states of environmental sustainability of IEs and determine their probability and directions of sustainable development, including ways to introduce innovative eco-technologies. This research methodology and the results of its implementation can be further applied in scientific circles to study the environmental sustainability of the functioning and development of enterprises, their networks, and territorial entities. This can assist the management of enterprises and territories in making optimal management decisions and in formulating goals, strategies, and policies for their development. Political leaders of territorial entities can include the developed strategy and policy in their program documents for further implementation. However, the methodological basis for assessing and forecasting the environmental sustainability of IEs should be supplemented with a system of objective indicators for a comprehensive assessment of the processes of achieving and maintaining a high level of environmental sustainability of IEs, their networks, and territorial entities to ensure their sustainable development.

Based on the research results, we recommend governments consider implementing policies on:

• better integration of economic and environmental policies in order to achieve a balance between economic growth and environmental sustainability;
• promoting collaboration between public and private sectors in the creation and implementation of environmental policies;
• encouraging investment in sustainable practices, green innovations, and technology through fiscal incentives, subsidies for R&D, and financing ecoprojects;
• more effective environmental regulations by setting clear emission standards and implementing transparent intellectual environmental monitoring;
• investing in sustainable infrastructure to support both environmental sustainability and economic growth;
• increasing public awareness of environmental sustainability and the level of ecological culture.

Thus, further scientific research should be focused on improvement of the following:

-

The system of indicators of environmental sustainability of IEs, their networks, and territorial units;

-

Modern mathematical tools to support the adoption and implementation of management decisions, in particular, methods and tools for processing big data, since it is a matter of working with large amounts of environmental information.