=Paper=
{{Paper
|id=Vol-3899/paper7
|storemode=property
|title=Mathematical model for digital transformation of business processes in the coordinates of digital marketing
|pdfUrl=https://ceur-ws.org/Vol-3899/paper7.pdf
|volume=Vol-3899
|authors=Olga Pavlova,Eleonora Zabarna,Marharyta Pierkova,Andrii Kuzmin,Sava Kostiuk
|dblpUrl=https://dblp.org/rec/conf/advait/PavlovaZPKK24
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==Mathematical model for digital transformation of business processes in the coordinates of digital marketing==
https://ceur-ws.org/Vol-3899/paper7.pdf
Mathematical model for digital transformation of
business processes in the coordinates of digital
marketing⋆
Olga Pavlova1,*,†, Eleonora Zabarna2,†, Marharyta Pierkova2,†, Andrii Kuzmin1,† and Sava
Kostiuk1,†
1 Khmelnytskyi National University, Instytuts’ka str., 11, Khmelnytskyi, 29016, Ukraine
2 Odesa Polytechnic National University, Shevchenka str., 1, Odesa, 65044, Ukraine
Abstract
This research introduces a mathematical model designed to optimize the digital transformation of business
processes in the domain of digital marketing. The model incorporates critical variables such as the degree
of digital transformation, audience engagement, technology integration, and the effectiveness and cost of
marketing strategies. Experimental data illustrate that higher levels of digital transformation, combined
with advanced technology use and maximized audience engagement, significantly, enhance business
outcomes, including increased revenue and conversion rates. The model provides a structured approach for
businesses to evaluate and improve their digital marketing strategies, ensuring effective resource allocation
and data-driven decision-making. By aligning digital marketing activities with transformation goals,
companies can achieve optimal results and efficiency. This study lays the groundwork for further
exploration and real-world application of the model to validate and refine its utility in practical business
environments.
Keywords
Digital transformation, marketing optimization, data-driven strategies, mathematical model 1
1. Introduction
Digital transformation is the integration of technology into an organization to create value and
competitiveness. By its content, digital transformation goes beyond digitization, i.e. the conversion
of analog data into digital format and the introduction of digital technologies in various contexts.
Due to the degree of interconnectedness and various accelerations that require organizational
change, digital transformation should be seen as a challenge and an opportunity for organizations to
achieve core business competencies, succeed in rapidly changing environments, the speed of change
refers to a multitude of phenomena, ranging from the acceleration of technological innovation to the
need for speed in dealing with changing customer and partner demand or unexpected events. Among
the main advantages of digital transformation, the following can be highlighted: customers are six
times more likely to try a new product or service from their favorite brand; customers are four times
more likely to recommend their favorite brand to their friends, relatives and acquaintances;
customers are twice as likely to make a purchase with their favorite brand, even when a competitor
has a better product or price. In addition, loyal customers buy 90% more often and spend 60% more.
According to Gartner [1], 91% of businesses are engaged in some form of digital initiative, and 87%
of senior business leaders say digitalization is a priority. Gartner also admits that 56% of CEOs say
AdvAIT-2024: 1st International Workshop on Advanced Applied Information Technologies, December 5, 2024, Khmelnytskyi, Ukraine - Zilina,
Slovakia
∗ Corresponding author.
† These authors contributed equally.
pavlovao@khmnu.edu.ua (O. Pavlova); zabarna@op.edu.ua (E.Zabarna); margaret.p@ukr. net (M. Pierkova); andriy1731@gmail.com
(A. Kuzmin); kostiuk.s@khmnu.edu.ua (S. Kostiuk)
0000-0003-2905-0215 (O. Pavlova); 0000-0002-2659-5909 (E. Zabarna); 0009-0005-6489-225X (A.Kuzmin); 0009-0009-1134-5956
(S.Kostiuk)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
digital improvements have increased revenue. According to Statista [3], in 2023, spending on digital
transformation (DX) is projected to reach 2.15 trillion U.S. dollars. By 2027, global digital
transformation spending is forecast to reach 3.9 trillion U.S. dollars (Figure 1).
Figure 1: Spending on digital transformation technologies and services worldwide from 2017 to 2027
(in trillion U.S. dollars) [3].
Therefore, the purpose of this research is the analysis of modern trends in the development of
information technologies and the processes of marketing digitization, as well as the determination
of the advantages of using single-page digital applications in the field of digital marketing.
2. State-of-the-art
Electronic commerce is the fastest growing segment of retail today. Every year, there are more
buyers on the Internet. Eight years ago, there were 1.5 billion people, and according to the results of
2023 – 2.64 billion [4]. At the same time, the market volume is also increasing. In Ukraine, the e-
commerce market reached almost $5 billion in 2023 [5].
Digital transformation for retail trade includes automation of processes and digitization of data,
as well as the use of cloud technologies for their storage [6]. In addition, you can improve the user
experience of the buyer with the help of advanced analytics, augmented and virtual reality, artificial
intelligence. It is also possible to pay for goods through biometric POS terminals using face
recognition technology [2]. Compared to the past, when shopping on the Internet was done almost
exclusively by young people aged 18 to 23 years, now goods and services are also ordered online by
users in other age categories, from 25 to 45 years. Another trend is the increasing popularity of
shopping via smartphones due to their mobility and convenience, while laptops or desktops are
becoming less popular.
The main task of platforms for digital marketing is to create conditions for attracting customers,
satisfying their requests and making sales [5]. However, platforms involved in the marketing
function must meet the following requirements in order to be flexible and sustainable:
1. Scalability, which determines the effectiveness of attracting investment in a potentially in-
demand product with growth potential – for digital business processes, this will mean the
ability to withstand a rapid increase in traffic and be ready for modifications and adjustments;
2. Ease of integration with various tools (from Internet acquiring to CRM and other systems);
3. Sociality - taking into account the specifics of work and the possibility of integrating one's
work into social networks and influencers;
4. Compatibility with new technologies, in particular such as artificial intelligence (AI), machine
learning, AR/VR, large databases, etc.;
5. Security - the ability to protect personal data.
3. Related works
The research [7] uses general and special methods of cognition: content analysis to substantiate the
use of quantitative indicators for evaluating marketing effectiveness; induction and deduction for
the development of a mathematical approach to evaluating the effectiveness of digital marketing of
territories; analysis and synthesis to coordinate projects under conditions of a dynamic
transformation of marketing processes.
The study [8] aims to examine the challenges and opportunities in the digital transformation of
MSMEs, as well as effective technology management strategies.
The work [9] conducted qualitative research in the form of in-depth interviews with managers
working for companies operating in different Italian industries.
This research [10] intends to develop a conceptual framework investigating how IT-related
resources, namely IT advancement (ITAD) and IT alignment (ITAG), utilization relates to digital
marketing capabilities (DMCs) development, which in turn improves business performance (BP), as
well as how digital orientation (DO) and technological turbulence (TT) moderate these effects.
The research [11] aims to analyze the use of CRM systems for the development and
implementation of communication strategies for digital brand management and Internet marketing
based on the experience of EU countries.
The research [12] investigated several digital technologies, including the Metaverse, artificial
intelligence, blockchain, virtual reality, and augmented reality. It is of the utmost importance for
businesses to be able to compete in digital and virtual environments within the context of digital
transformation to thrive in an increasingly competitive world.
The study [13] findings revealed eight topics that collectively represent the essential features of
data economy in the current literature, namely:
1. Data Security.
2. Technology Enablers.
3. Business Implications.
4. Social Implications.
5. Political Framework.
6. Legal Enablers.
7. Privacy Concerns.
8. Data Marketplace.
The study resulting model may help researchers and practitioners to develop the concept of data
economy in a structured way and provide a subset of specific areas that require further research
exploration.
The studies [14] address the global phenomenon of digital transformation and its impact on the
field of sport marketing.
The work [15] validates our theoretical model using 215 responses from a survey with
Bangladeshi organizations and tests the research hypotheses using structural equation modelling.
The paper [16] examined the emergence of value creation during digital transformation. The
authors used case studies to gather empirical evidence of the phenomenon from an organizational
perspective. The study tried to closely link theory and practice by identifying the mechanisms that
determined the paths of value creation in 11 companies that had taken concrete steps toward digital
transformation.
The study [17] further examined the mediating effects of digital transformation strategy and
organizational innovation on the relationship between digital technology usage and firm
performance.
The purpose of [18] is discovering the stages, protocols, ways and instruments of becoming the
industry 5.0 through the prism of innovation, technology in management of industry and business,
and introducing the features that define the new quality of smart industry, smart business, and smart
services among which modularity, interoperability, virtual reality.
The paper [19] investigates if and how DT changes relationship dynamics and collaboration
efficiency in SCs and distributed manufacturing networks through information sharing and jointly
used digital technologies.
The study [20] examines the sustainable adoption of innovative digital technologies (DTs) within
digital transformations. The data for this study were collected from 760 stakeholders through a
questionnaire survey and analyzed using SPSS software (Version 27). This study’s results underscore
the significance of considering the efficiency of the transformation process and the long-term
sustainability outcomes for organizations.
The work [21] aims to identify how owners or senior managers of MSMEs can initiate a
sustainable digital transformation project. A systematic literature review was carried out, including
59 publications from 2019 to 2023.
Thе study [22] examines the sustainable adoption of innovative digital technologies (DTs) within
digital transformations. The data for this study were collected from 760 stakeholders through a
questionnaire survey and analyzed using SPSS software (Version 27). This study’s results underscore
the significance of considering the efficiency of the transformation process and the long-term
sustainability outcomes for organizations. The findings of the analysis clarify that integrating
sustainability principles and DT has a positive impact on the effectiveness of the transformation, as
indicated by environmental, social, and economic performance indicators.
The research [23] aims to analyse the impact of digital transformation on business models and
competitive advantage. This is a literature review that uses a qualitative approach, which implies
that data will be analysed and interpreted using information and text obtained from various sources.
The study [24] has focused on the pharmaceutical sector of Karachi (Pakistan) to examine the
impact of product, process, marketing, and organizational innovations on firm performance. It also
examined the moderating role of environmental turbulence.
In [25] the features of the work of agricultural entrepreneurship and mechanisms for their
support in the context of global challenges, the implementation of strategic goals of European
integration and martial law are presented. It is noted that farms need to optimize business processes
based on digitalization in order to obtain maximum profit and rational use of natural resources. This
correlates with the goals presented in the "Strategy for the Development of the Sphere of Innovation
Activity for the Period up to 2030", "National Economic Strategy for the Period until 2030".
In [26] we propose the digitalization using Web-cartography for logistical infrastructure and for
the volunteering tasks in the conditions of military conflict in Ukraine. Also in [26] we consider the
possibility of generating digital content by the AI-based systems and conduct the analysis of the
existing systems.
4. Mathematical model
To develop a mathematical model for the digital transformation of business processes in the context
of digital marketing, we'll create a framework that considers key variables influencing the
effectiveness and efficiency of digital marketing activities.
This model will focus on how digital transformation impacts business outcomes through digital
marketing efforts. To maximize business outcomes (such as revenue, customer engagement, and
conversion rates) through the optimization of digital marketing processes influenced by digital
transformation.
Let us identify key variables that influence digital marketing:
• B: business outcome (e.g., revenue, engagement, conversion rate).
• D: degree of digital transformation (a factor representing how much a business has adopted
digital technology).
• Mi: digital marketing components or strategies, where i=1,2,…,n (e.g., SEO, content
marketing, social media, email campaigns, PPC).
• Ci: cost associated with each marketing component Mi.
• Ei: effectiveness of each marketing component Mi (influenced by digital transformation).
• A: audience engagement (interaction level of the audience with digital marketing campaigns).
• T: technology level used in digital marketing (e.g., use of AI, automation, analytics tools).
The business outcome B is a function of the effectiveness and efficiency of digital marketing
components, technology integration, audience engagement, and the degree of digital transformation
can be defined by the formula 1:
𝐵𝐵 = 𝑓𝑓(𝐷𝐷, 𝑀𝑀1, 𝑀𝑀2, … , 𝑀𝑀𝑀𝑀, 𝐶𝐶1, 𝐶𝐶2, … , 𝐶𝐶𝐶𝐶, 𝐴𝐴, 𝑇𝑇). (1)
This function can be expressed as:
𝑛𝑛 𝑛𝑛
𝐵𝐵 = � 𝐸𝐸𝐸𝐸(𝑀𝑀𝑀𝑀, 𝐷𝐷, 𝐴𝐴, 𝑇𝑇) − 𝑖𝑖 = � 𝐶𝐶𝑖𝑖 . (2)
𝑖𝑖=1 𝑖𝑖=1
Here, Ei (Mi,D,A,T) represents the effectiveness of the i-th marketing component influenced by
the degree of digital transformation, audience engagement, and technology integration. The total
business outcome is the sum of the effectiveness of each component minus the associated costs.
The effectiveness Ei of each digital marketing component depends on the degree of digital
transformation D, audience engagement A, and the technology level T:
𝐸𝐸𝐸𝐸 = 𝑔𝑔(𝑀𝑀𝑀𝑀, 𝐷𝐷, 𝐴𝐴, 𝑇𝑇), (3)
where:
• Mi: marketing component’s inherent effectiveness.
• D: degree of digital transformation (ranging from 0 to 1, where 1 represents full
transformation).
• A: engagement level of the audience (can be measured through metrics like click-through
rates, interactions, and conversions).
• T: technology level or technological capability in use (ranging from 0 to 1, where 1
represents full integration of AI, automation, etc.).
A possible formulation for Ei can be denoted by the formula 4:
𝐸𝐸𝐸𝐸 = 𝛼𝛼𝛼𝛼𝛼𝛼 ⋅ 𝐷𝐷 ⋅ 𝐴𝐴 ⋅ 𝑇𝑇, (4)
where:
• α is a scaling factor representing the impact of digital transformation on the marketing
component.
• D, A, T are factors that amplify the effectiveness based on their respective levels.
The cost associated with each marketing component Ci could be modeled as:
𝐶𝐶𝐶𝐶 = 𝛽𝛽𝛽𝛽 ⋅ 𝑀𝑀𝑀𝑀 + 𝛾𝛾𝛾𝛾 ⋅ 𝑇𝑇, (5)
where :
• βi: cost per unit of the marketing component.
• γi: additional cost per unit of technology used for each component.
The objective is to maximize the business outcome B while considering constraints on budget and
resource allocation. We denote the equation 6 for this:
𝑛𝑛 𝑛𝑛
𝑚𝑚𝑚𝑚𝑚𝑚
𝐵𝐵 = �(𝛼𝛼𝛼𝛼𝛼𝛼 ⋅ 𝐷𝐷 ⋅ 𝐴𝐴 ⋅ 𝑇𝑇) − �(𝛽𝛽𝛽𝛽 ⋅ 𝑀𝑀𝑀𝑀 + 𝛾𝛾𝛾𝛾 ⋅ 𝑇𝑇) (6)
𝑀𝑀𝑀𝑀, 𝑇𝑇
𝑖𝑖=1 𝑖𝑖=1
Subject to:
𝑛𝑛
� 𝐶𝐶𝐶𝐶 ≤ Budget;
𝑖𝑖=1
0 ≤ 𝐷𝐷, 𝐴𝐴, 𝑇𝑇 ≤ 1.
The interpretation of the given above formulas is the following:
• Digital transformation (D): as digital transformation increases (closer to 1), the effectiveness
of each marketing component increases, reflecting a more efficient and optimized use of
digital technologies.
• Audience engagement (A): high levels of engagement (A→1) maximize the impact of digital
marketing efforts.
• Technology integration (T): advanced technology use (closer to 1) amplifies the efficiency of
digital marketing but comes with higher costs.
The proposed mathematical model provides a framework for optimizing digital marketing
strategies as businesses undergo digital transformation.
The focus is on balancing costs, audience engagement, and technology integration to maximize
business outcomes. It can help to measure the level of digitalization of businesses, i.e., their
marketing components and business outcome.
5. Experiments & discussion
To provide experimental data using the proposed mathematical model for the digital transformation
of business processes in digital marketing, we would typically need to perform an experiment or
gather real-world data that fits the parameters outlined in the model.
A proposed experimental setup and hypothetical data for demonstrating the model includes the
following parameters:
• Degree of digital transformation (D): measured on a scale from 0 (no digital transformation)
to 1 (full digital transformation).
• Digital marketing components (Mi): components like SEO, PPC campaigns, content
marketing, social media marketing, etc.
• Audience engagement (A): measured using metrics like click-through rate (CTR), conversion
rate, or user interaction levels, normalized between 0 and 1.
• Technology level (T): the extent of technology adoption (e.g., automation, AI) used in the
digital marketing strategy, also on a scale from 0 to 1.
• Cost (Ci): the cost associated with implementing each marketing component and technology
level.
The method of the experiment consists of the following steps:
1. Collect data from various businesses at different stages of digital transformation and with
varying marketing strategies.
2. Measure key business outcomes (e.g., revenue, conversion rates) alongside audience
engagement metrics.
3. Compile a table with the collected data and measurement results (table 1).
Table 1
Experiment data
Experiment D A T Marketing Cost (Ci) Business outcome
ID component (Mi) (B), UAH
1 0,2 0,3 0,1 SEO (0,5) 5000 15000
2 0,4 0,5 0,4 PPC (0,7) 8000 25000
3 0,6 0,6 0,5 Social Media (0,8) 10000 40000
4 0,8 0,7 0,6 Content Marketing 15000 60000
(0,9)
5 1 0,9 0,9 Integrated 200001 90000
Campaign (1,0)
The data that had been collected are the following:
• Experiment ID: represents different businesses or trials under different levels of digital
transformation;
• D: degree of digital transformation, increasing from 0.2 to 1.0;
• A: audience engagement, based on interaction and conversion metrics;
• T: technology level, indicating the extent of technology integration in the marketing
strategies;
• Marketing component (Mi): various components like SEO, PPC, social media, and content
marketing, with effectiveness values;
• Cost (Ci): the cost associated with each strategy and technology level;
• Business outcome (B): calculated as per the model to show the return (e.g., revenue) achieved
for each configuration.
Analysis and interpretation of the experiment: the model suggests that as businesses increase
their degree of digital transformation (D) and integrate more technology (T), while also optimizing
audience engagement (A), the business outcomes (B) significantly improve. The experimental data
demonstrates that:
1. Low transformation levels. Experiment 1, with a low digital transformation level (D=0.2),
results in a lower business outcome, despite the implementation of an SEO strategy. The
minimal technology integration (T=0.1) and low audience engagement (A=0.3) limit the
effectiveness of the campaign.
2. Moderate transformation levels. In Experiment 3, with a higher D value of 0.6 and increased
audience engagement (A=0.6), the business outcome improves significantly. This shows that
higher transformation levels positively influence marketing effectiveness.
3. High transformation Levels. Experiment 5, which reflects full digital transformation (D=1.0),
high audience engagement (A=0.9), and a high technology level (T=0.9), achieves the highest
business outcome. The integrated marketing approach (combining various strategies) and
advanced technology implementation maximize the efficiency of the marketing efforts,
yielding the highest return.
6. Conclusions
The research presents a mathematical model for the digital transformation of business processes
within the realm of digital marketing. The model integrates key variables such as the degree of digital
transformation, audience engagement, and technology level to predict business outcomes, such as
revenue and conversion rates.
The experimental data demonstrates that increasing levels of digital transformation and
technology integration, when aligned with effective digital marketing strategies, result in significant
improvements in business performance.
The results show that businesses undergoing digital transformation can optimize their marketing
efforts and maximize returns by strategically enhancing audience engagement and adopting
advanced technologies like AI, automation, and data analytics. The model provides a framework for
companies to evaluate and refine their digital marketing approaches, ensuring resource-efficient and
data-driven decisions that align with their digital transformation goals. Ultimately, this research
offers a foundation for further exploration and real-world validation of the proposed model, enabling
businesses to fine-tune their strategies and achieve improved business outcomes as they progress
through their digital transformation journey in the dynamic environment.
Declaration on Generative AI
During the preparation of this work, the authors used Grammarly in order to: grammar and spelling
check; DeepL Translate in order to: some phrases translation into English. After using these
tools/services, the authors reviewed and edited the content as needed and take full responsibility for
the publication’s content.
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