МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВУ ЗАГАЛЬНИХ ПОКАЗНИКІВ БАЗОВОЇ СИСТЕМИ АДМІНІСТРАТИВНОГО МЕНЕДЖМЕНТУ НА РЕЗУЛЬТАТИ ДІЯЛЬНОСТІ ПІДПРИЄМСТВА (ОРГАНІЗАЦІЇ, УСТАНОВИ)
Вступ. Нині перед керівництвом постає завдання: які управлінські новації необхідно враховувати, реалізуючи адміністративні рішення, щоб забезпечити стійкий розвиток юридичної особи для здобуття конкурентних і репутаційних переваг.Проблематика. Розроблення наукового способу оцінювання загальних показ...
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| Date: | 2026 |
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Science and Innovation| _version_ | 1868294495874842624 |
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| author | MINENKO, M. HUSAK, Yu. MASHTALIR, V. SHOVKOSHYTNYI, I. MINENKO, L. MARCHENKO, A. |
| author_facet | MINENKO, M. HUSAK, Yu. MASHTALIR, V. SHOVKOSHYTNYI, I. MINENKO, L. MARCHENKO, A. |
| author_institution_txt_mv | [
{
"author": "M. MINENKO",
"institution": "The National Defense University of Ukraine"
},
{
"author": "Yu. HUSAK",
"institution": "The National Defense University of Ukraine"
},
{
"author": "V. MASHTALIR",
"institution": "The National Defense University of Ukraine"
},
{
"author": "I. SHOVKOSHYTNYI",
"institution": "The National Defense University of Ukraine"
},
{
"author": "L. MINENKO",
"institution": "The National Defense University of Ukraine"
},
{
"author": "A. MARCHENKO",
"institution": "The National Defense University of Ukraine"
}
] |
| author_sort | MINENKO, M. |
| baseUrl_str | https://scinn-eng.org.ua/ojs/index.php/ni/oai |
| collection | OJS |
| datestamp_date | 2026-06-17T11:30:40Z |
| description | Вступ. Нині перед керівництвом постає завдання: які управлінські новації необхідно враховувати, реалізуючи адміністративні рішення, щоб забезпечити стійкий розвиток юридичної особи для здобуття конкурентних і репутаційних переваг.Проблематика. Розроблення наукового способу оцінювання загальних показників базової системи адміністративного менеджменту (різновиду інформаційно-комунікаційної системи, базису раціонального отримання очікуваних підсумків праці), зважаючи на досягнення у роботі, потенціал адміністративних документів, фактори внутрішнього та зовнішнього середовища, норми впроваджених управлінських новацій.Мета. Науково обґрунтувати математичну модель, яка відображає вплив загальних показників базовоїсистеми адміністративного менеджменту на результати діяльності підприємства (організації, установи),із визначенням характерних функціональних взаємозв’язків між складовими елементами останньої.Матеріали й методи. Досліджено джерела та використано методи математичного моделювання, аналізу та синтезу, графічний, діалектичний, економічного моделювання, системно-структурного та структурнофункціонального аналізу.Результати. Використовуючи формули, схеми і моделі, доведено ефект впливу загальних показниківдосліджуваної системи на результати роботи юридичної особи. Окреслено умови результативності застосування такої управлінської новації. Вперше формалізовано процес керування юридичною особою для оцінювання осібної адміністративної ваги визначених показників означеної базової системи у відповідномусередовищі функціонування.Висновки. Результати підтвердили значення всіх загальних показників організації праці та базової системи адміністративного менеджменту. Запропоноване сприятиме подальшому пристосуванню математичних моделей до умов роботи конкретної юридичної особи і напрацюванню методики, що унормує використання розробленого та стане вагомим засобом гарантування конкурентних і репутаційних переваг. |
| doi_str_mv | 10.15407/scine22.03.080 |
| first_indexed | 2026-06-18T01:01:16Z |
| format | Article |
| fulltext |
ISSN 2409-9066. Sci. innov. 2026. 22(3)80
© Publisher PH “Akademperiodyka” of the NAS of Ukraine, 2026. Th is is an open access article
under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Citat ion: Minenko, M. A., Husak, Yu. A., Mashtalir, V. V., Shovkoshytnyi, I. I., Minenko, L. M., and
Marchenko, A. O. (2026). Mathematical Modelling of the Impact of General Indicators of the Basic
Administrative Management System on the Performance of an Enterprise (Organization, Institu-
tion). Sci. innov., 22(3), 80—94. https://doi.org/10.15407/scine22.03.080
https://doi.org/10.15407/scine22.03.080
MINENKO, M. A. (https://orcid.org/0000-0002-7492-3196),
HUSAK, Yu. A. (https://orcid.org/0000-0002-3423-2112),
MASHTALIR, V. V. (https://orcid.org/0000-0002-8132-217X),
SHOVKOSHYTNYI, I. I. (https://orcid.org/0000-0001-9245-4111),
MINENKO, L. M. (https://orcid.org/0000-0003-0249-9856),
and MARCHENKO, A. O. (https://orcid.org/0000-0002-1268-8012)
The National Defense University of Ukraine,
28, Prospekt Povitryanykh Syl, Kyiv, 03049, Ukraine,
+380 44 271 0780, nuou@mod.gov.ua
MATHEMATICAL MODELLING OF THE IMPACT
OF GENERAL INDICATORS OF THE BASIC
ADMINISTRATIVE MANAGEMENT SYSTEM
ON THE PERFORMANCE OF AN ENTERPRISE
(ORGANIZATION, INSTITUTION)
Introduction. Contemporary management faces the challenge of determining which managerial inno-
vations should be systematically integrated into administrative decision-making in order to ensure the
sustainable development of a legal entity and to secure stable competitive and reputational advantages.
Problem Statement. Th ere is a need to develop a scientifi cally grounded approach to assessing the
overall performance of the Basic Administrative Management System (BAMS), considered as a type of
information and communication system that facilitates the rational achievement of expected results,
while taking into account organizational performance outcomes, administrative documentation prac-
tices, environmental factors, and the implementation of managerial innovations.
Purpose. Th e purpose of this study is to provide the scientifi c substantiation of a mathematical mo del
that captures the impact of the general indicators of the Basic Administrative Management System on the
performance of an enterprise (organization, institution), while identifying the characteristic functional
interrelationships among its constituent elements.
Materials and Methods. Th e research draws upon a comprehensive review of relevant scholarly sour-
ces and applies mathematical modelling, analytical and synthetic methods, graphical modelling tech-
niques, economic modelling approaches, and systems-based analytical frameworks.
81ISSN 2409-9066. Sci. innov. 2026. 22(3)
Mathematical Modelling of the Impact of General Indicators of the Basic Administrative Management System
Results. Th e study has demonstrated, through the use of formulas, diagrams, and formalized models, the infl uence
of the system’s general indicators on organizational performance outcomes. Th e conditions required for the eff ective
implementation of this managerial innovation have been identifi ed and conceptually justifi ed. Furthermore, the ma-
nagement process of a legal entity has been formally represented and analytically structured in order to evaluate the
administrative signifi cance of the identifi ed indicators within the operational environment.
Conclusions. Th e fi ndings have confi rmed the substantive signifi cance of the general indicators of labor organiza-
tion and of the Basic Administrative Management System as determinants of organizational performance. Th e pro-
posed approach enables the adaptation of mathematical models to the institutional and operational conditions of a
specifi c legal entity and supports the development of a methodological framework for their practical application as an
analytical instrument for achieving sustainable competitive and reputational advantages.
Keywords: basic administrative management system, information and communication system, general indicators of
administrative performance, managerial innovations, mathematical modelling, administrative decision-making, sus-
tainable development, competitive and reputational advantages.
Any enterprise (organization or institution) cons ti-
tutes a systemic entity in which numerous informa-
tional, technological, technical, social, and huma-
nitarian processes operate relatively autonomously
while simultaneously interacting with one another.
These processes also encompass the administration
of organizational development and growth. Mana-
gers are therefore required to regularly analyze or-
ganizational performance outcomes, systematical-
ly evaluate and account for the behavior of envi-
ronmental factors influencing their activities, and
consider existing constraints and recommenda-
tions that have been agreed upon with stakehol-
ders and formally approved through internal orga-
nizational regulatory (administrative) documents.
At the same time, it is important to recognize that
these formal regulations define and institutionalize
the substantive and methodological potential of the
general indicators (elements and subsystems) of the
Basic System of Administrative Management (he-
reinafter referred to as BSAM). This system estab-
li shes the foundational framework for the effecti-
ve functioning of the overall organizational mana-
gement system of a particular legal entity [1, 2].
Given the above, whenever an operational or
production problem arises, administration beco-
mes an integrated task within the process of pre-
paring, adopting, and implementing an administ-
rative decision. Such integration is necessary to
ensure the rational resolution of the problem un-
der the prevailing conditions and to facilitate the
most effective coordination and direction of syner-
gistic influences, whether through mechanisms
of enforcement or motivation.
In this context, the authors have analyzed scien-
tific studies devoted to issues of mathematical mo-
deling, which has made it possible to clarify the
functional potential of the general indicators of
BSAM (hereinafter referred to as general indica-
tors of activity administration) [3, 4]. In particu-
lar, study [5] presents the principles of the theory
of multi-level hierarchical systems and proposes
specific classes of hierarchical structures, inclu-
ding strata, layers, and echelons. These structures
differ in the principles governing the relationships
among elements within the same level and in the
degree of intervention that higher hierarchical
levels may exert in organizing interactions and re-
lationships among elements at lower levels.
However, the provisions of this theory allow on-
ly the description of the process of constructing
abstract mathematical models of complex hierar-
chical systems. Therefore, they require a certain
degree of methodological adaptation in order to
adequately represent the BSAM model. A similar
conclusion can be drawn regarding [6].
In addition, studies conducted by researchers
who have explored the application of mathemati-
cal modeling within the theory of enterprise ma-
nagement have also been systematically exami-
ned [7, 8]. At the same time, the contemporary
foundations of management theory and practice,
82 ISSN 2409-9066. Sci. innov. 2026. 22(3)
Minenko, M. A., Husak, Yu. A., Mashtalir, V. V., Shovkoshytnyi, I. I., Minenko, L. M., and Marchenko, A. O.
as well as the theoretical principles and applied
aspects of administrative management, have been
carefully taken into account [9—11].
Study [12] investigates mathematical models and
methods of personnel management which, within
the management cycle, operationalize administ-
rative management decisions through processes
of staff selection, placement, and professional de-
velopment. The theory of Markov processes cons-
titutes the basis of the mathematical apparatus,
allowing a complex management system to be re-
presented as a queuing system. However, the sys-
tem of administrative management cannot be ade-
quately represented by such a model without int-
roducing a number of simplifying assumptions
and substantial analytical constraints.
Furthermore, the work of M. A. Kukhar deser-
ves particular attention. Based on the methodo-
logical framework of category theory, the resear-
cher has proposed conceptual models for the imp-
lementation of decision-support systems within
multi-level administrative governance structures.
These models make it possible to formally repre-
sent domain-specific knowledge within decision-
support systems designed to address specific ma-
nagerial tasks and decision-making scenarios [13].
Among foreign studies available in open access,
there are also contributions in which mathe ma tical
modeling is characterized as a professional and ana-
lytical task within administrative mana ge ment. In
particular, C. Telles has proposed a ma the matical
heuristic model for analyzing informa tion flows wi-
thin administrative workflow systems [14]. In turn,
J. Tick and A. Tick have investigated simulation mo-
deling approaches for workflow processes that ref-
lect administrative governance activities. The pur-
pose of such simulations is defined as conducting
dynamic analysis of workflow models, identifying
operational bottlenecks, and optimizing the alloca-
tion and utilization of organizational resources [15].
At present, the theory and practice of administ-
rative management continue to evolve and expand.
Within this context, the BSAM concept has been
introduced and conceptually articulated [16]. The
tasks of administration have been specified, their
interrelationships with the functional responsi-
bilities of staff members have been theoretically
substantiated, and the structure and scope of in-
ternal organizational regulatory (administrative)
documents have been systematically characteri-
zed [1]. Some studies have been devoted to impro-
ving the indicators of administrative enforcement
and motivational influence, identifying the posi-
tive applied potential of these mechanisms, and
analyzing the impact of comprehensive digitali-
zation on existing management systems, particu-
larly within the defense sector [2].
In summary, it should be emphasized that only a
limited number of researchers have focused spe-
cifically on the development of mathematical mo-
dels in the field of administrative management. The
application of mathematical modeling for assessing
the influence of the general indicators (ele ments
and subsystems) of the BSAM on the effectiveness
of the overall organizational management system of
an enterprise (organization or institution), as well as
on the performance outcomes of the organization
as a whole, has not yet been sufficiently investigated.
This circumstance further confirms the relevance,
scientific significance, and timeliness of the research
objectives pursued by the authors of this article.
The purpose of this study is to provide a scien-
tific substantiation of a mathematical model that
reflects the influence of the general indicators of
the BSAM on the performance results of an en-
terprise (organization or institution), while iden-
tifying the characteristic functional relationships
that emerge among its constituent elements.
One of the key methodological approaches app-
lied in this study is mathematical modeling. At the
outset, it should be emphasized that in order to en-
sure a reliable and analytically grounded assess-
ment of the consequences of administrative inf-
luence — whether exercised through enforcement
mechanisms or motivational incentives — imple-
mented through the general indicators of activity
administration and through the BSAM as an integ-
rated system, on the effectiveness of the perfor-
mance of a particular enterprise (organization or
institution), its structural units, or individual staff
83ISSN 2409-9066. Sci. innov. 2026. 22(3)
Mathematical Modelling of the Impact of General Indicators of the Basic Administrative Management System
members, it is necessary to employ the mathema-
tical methods of management theory [7].
To accomplish this objective, the management
system must initially be conceptualized as a set
con sisting of two components:
the subject of management, that is, the head, ad-
ministration (management apparatus), a col le gial
or collective statutory body, or a manager (here-
inafter referred to as the controlling subject (CS));
the object of management, that is, a staff mem-
ber, a structural unit, or an enterprise (organi-
zation or institution) (hereinafter referred to as
the controlled object (CO)).
Under these conditions, the management process,
which includes feedback, can be represented as a set
of actions, operations, and procedures involving di-
rect or indirect influence of the controlling subject
(CS) on the controlled object (CO). This process is
car ried out in order to achieve the desired performan-
ce outcomes within clearly defined timeframes, with
the rational use of resour ces, given previous achie-
vements as well as internal and external circums-
tances that may exert direct or indirect influence.
In addition, particular importance is attributed
to the general indicators of activity administra-
tion, which are duly agreed upon with stakehol-
ders and approved by internal organizational re-
gulatory (administrative) documents. The official
significance of such documents characterizes the
substantive and methodological foundational po-
tential of labor administration within a specific le-
gal entity and objectively defines the duties, rights,
and responsibilities of each participant involved
in the corresponding process [1] (Fig. 1).
During the implementation of the management
process, the state of the controlled object (CO)
changes continuously over time. Therefore, the
general expression for the vector of its state ( )x t
,
after the implementation of an administrative de-
cision, can be represented as follows [7, 8]:
( )
( ), ( ) ,
dx t
f x t u t
dt
(1)
where: ( )x t
is the state vector of the controlled
object (CO) based on previously obtained perfor-
mance results; ( )u t
is the vector of administrati ve
decisions adopted by the controlling system (CS).
Further, the authors have conducted a step-by-
step analysis of the influence of the general indi-
cators of activity administration and BSAM as a
whole, as well as the factors that objectively deter-
mine the real state of the controlled object (CO)
following the implementation of an administra-
tive decision.
Thus, the influence of CS on CO relates to the
processes of organizing purposeful work to achie-
ve a defined Goal. This Goal must necessarily cor-
respond to the Values, Vision, Mission, Outlook,
and Policy of a particular legal entity. However,
the Goal may change over time and may be adjus-
ted depending on previous achievements, inter-
nal conditions (including actual capabilities), the
external situation, and the formal guidelines of
current regulations.
In this context, it should be understood that
goals, structure, tasks, technology, personnel, and
resources constitute a group of internal environ-
ment factors (hereinafter — IE). At the same ti me,
the following elements — consumers, suppliers,
competitors, government authorities, infra struc-
tu re, legislative acts, trade unions (parties and
other public organizations), the system of econo-
mic relations within the state, and neighboring
or ganizations — are factors of the external envi-
ronment of direct effect (hereinafter — EEDE).
Meanwhi le, international events, the international
environment, scientific and technological prog-
ress, political cir cumstances, socio-cultural con-
ditions, the level of technology and equipment,
the specifics of international economic relations,
and the state of the economy form the list of fac-
Fig. 1. General flowchart of the management process
Source: compiled by the authors based on the results of
the study using [7].
Controlling
subject
(subject
of management)
Controlled
object
(object
of management)
Administrative
decisions
Previous status
of the object
u(t)
x(t)
84 ISSN 2409-9066. Sci. innov. 2026. 22(3)
Minenko, M. A., Husak, Yu. A., Mashtalir, V. V., Shovkoshytnyi, I. I., Minenko, L. M., and Marchenko, A. O.
tors of the external environment of indirect effect
(hereinafter — EEIE) [9].
In addition, it should be emphasized that each
CS, while performing the official duties delegated
to them, carries out a continuous function of ad-
ministrative management, namely the preparation,
adoption, and implementation of administrative
decisions [8]. An appropriate administrative deci-
sion, according to established criteria, is selected
from a set of possible administrative decisions,
which represents a certain collection of alternatives
regarding the influence of the CS on the CO. Such a
set may contain either a limited or an unlimited
number of alternatives. From this set, taking into
account the objective and subjective circumstances
of the production problem, including previously
obtained performance results, the possible beha-
vior of factors of the external environment of direct
and/or indirect effect (EEDE and/or EEIE) and in-
ternal factors, and — most importantly — the stan-
dardized guidelines of the general indicators of the
BSAM, a rational decision is chosen. This choice
aims to ensure the best operational mode, enabling
the effective, timely, and successful achievement of
the established Goal [developed by the authors
based on research results using sources [3 and 8].
To evaluate potential options for solving a pro-
duction problem and to select the optimal one,
Officially approved conceptual and methodological guidelines
for the core BSAM indicators of an enterprise (organization or institution)
Influence of previously obtained
performance results
Changes in the behavior
of external environment factors
of direct and/or indirect effect
Establishing the set of possible
administrative decisions:
development of decision criteria;
information processing and analysis;
analysis and preparation of decision
alternatives
Identification
of the operational
problem:
situation analysis;
formulation
of the goal
(objectives)
Controlled object
(object of manage-
ment)
Administrative
instruments of direct
or indirect influence
Adoption
of the appropriate
administrative decision
option:
discussion of possible
alternatives
selection
of the optimally
adapted option
formal documentation
of the decision dra
Administrative
decision
of the control-
ling subject
(subject
of manage-
ment)
Changes in the behavior
of internal environment factors
Information on the state
of the controlled object (object
of management)
Corrective actions in the event
of deviations from established
criteria
Implementation of the administrative decision:
◆ development of measures
◆ establishment of implementation deadlines
◆ designation of responsible executors
◆ resource allocation and support
◆ communication of the decision to executors
◆ administrative support of implementation and monitoring of execution
Fig. 2. Visualized scheme of the process of preparation, adoption, and implementation of administrative decisions
Source: compiled by the authors based on research results using [9—11].
85ISSN 2409-9066. Sci. innov. 2026. 22(3)
Mathematical Modelling of the Impact of General Indicators of the Basic Administrative Management System
not a single criterion but several criteria are used,
which help to perform a rational selection. In this
case, a multicriteria problem is solved.
In this way, the selected criteria make it possib-
le to realistically assess the content-methodologi-
cal potential of the restrictions and recommenda-
tions of the general indicators of the BSAM, as
well as the influence of the controlling subject and
the possibilities for productive and effective per-
formance of the controlled object.
A visualized scheme of the process of prepara-
tion, adoption, and implementation of adminis-
trative decisions is presented in Fig. 2.
The actions, operations, and procedures (Fig. 2)
are regulated by internal guidelines. In addition,
their effectiveness depends on previously obtai ned
performance results, the behavior of factors of the
external environment of direct and/or indirect ef-
fect, and changes in factors that determine the
state of the internal environment. However, it is
precisely the official guidelines that characterize
the actual general indicators of the BSAM of a par-
ticular legal entity.
In practice, such a system is considered a gua-
ran tee of the stable effectiveness of the general
organizational management system and a foun-
dation for the implementation of organizational
innovations, including certification for complian-
ce with Technical Regulations and/or Standards
and the requirements of one of the Business Ex-
cellence models, for example: Australian, Ameri-
can, Euro pean, Ibero-American, Indian, Singapo-
rean, or Japanese [16].
This is explained by the fact that, from a practi-
cal and legal perspective, the BSAM — as a type
of information and communication systems — re-
presents an officially structured set of relatively se-
parate but interdependent general content-metho-
dological indicators (elements and subsystems)
of activity administration. Through professionally
organized cross-cutting subsystems of Commu-
nication with Stakeholders and Record-Keeping
and Documentation of Activities, and through
formally legalized documents — such as the Char-
ter; File Classification System (Records Schedu le);
Staffing Schedule; Organizational Management
Struc ture; Regulation On Remuneration; Internal
Labor Regulations; Instructions, including those
on Occupational Safety, Fire Safety, and Occupa-
tional Hygiene and Industrial Sanitation, etc.; Re-
gulations On Information Policy and On Struc-
tural Units; Job descriptions and, based on them,
signed Contracts and Employment agreements —
these elements, through the professional imple-
mentation of sequential and continuous func-
tions of the administration (management appara-
tus) and the use of appropriate resource potential
(including digitalization and, especially, inno-
vative digital tech nologies and means of infor-
mation and communication security), serve the
effective and timely achievement of the estab-
lished Goal(s).
These goals correspond to the adopted Values,
Vision, Mission, Outlook, and Policy, as well as to
the situationally selected development strate gy(ies)
and the organizational and legal form of econo-
mic activity. They do not contradict the norms of
the approved Collective Agreement and Corpo-
rate Ethics Code, the chosen laws, principles, and
management methods, and they also facilitate cer-
tification processes for compliance with Techni-
cal Regulation(s) and/or Standards, or the appro-
priate implementation of one of the international-
ly recognized Business Excellence models.
As a result, they ensure a regime of reliable, high-
quality, rational, productive, and effective activity
within the environment of the global economy and
total digitalization. When necessary, they also form
the basis for a profitable level of practical excel-
lence and, above all, act as a guarantee of the ef-
fectiveness of the general organizational manage-
ment system of a particular legal entity and, con-
sequently, its sustainable development and ability
to achieve the desired level of competitive and re-
putational advantages [developed by the authors
based on research results using sources [1, 16].
Thus, it can be stated that the proper appro val
of the general indicators of the BSAM, which oc-
curs through the official development of internal
organizational administrative documents, plays
86 ISSN 2409-9066. Sci. innov. 2026. 22(3)
Minenko, M. A., Husak, Yu. A., Mashtalir, V. V., Shovkoshytnyi, I. I., Minenko, L. M., and Marchenko, A. O.
a key role in the regulated influence of the con-
trolling subject on the controlled object. The se
documents are associated with the optimally
adapted selection and effective application of app-
ropriate administrative instruments of direct or
indirect ac tion for resolving a specific produc-
tion situation.
The above-mentioned approach enables the go-
ver ning body of a particular enterprise (organiza-
tion or institution) — by using the available re sour-
ce poten tial and applying modern management
innovations, especially one of the internationally
recognized models of business excellen ce — to
en sure effective goal-setting aimed at the sus tai-
nab le, rational, timely, and effective achievement
of the defined Goal(s).
At the same time, this allows the organization
to become a real leader in a particular field of ac-
tivity, taking into account the possible behavior of
factors of the external environment of direct and/
or indirect effect, as well as objective changes in
the factors influencing the state of the internal en-
vironment [2, 16] (Fig. 3).
For a more detailed representation of the gen-
eral scheme of the management process (Fig. 1),
it is presented taking into account the analysis of
the specific features of the process of preparation,
adoption, and implementation of administrative
decisions (Fig. 2), as well as the model for ensuring
sustainable development and achieving the desi-
red advantages of a leader (Fig. 3) in the relevant
field of activity (Fig. 4). Here: B is the module ge-
External environment factors of direct and/or indirect effect
Achievement of desired competitive and reputational advantages
Es
ta
bl
ish
m
en
t o
f a
n
eff
ec
tiv
e
or
ga
ni
za
tio
n-
w
id
e
m
an
ag
em
en
t s
ys
te
m
Form
ati
on an
d su
sta
inab
le
deve
lopmen
t o
f a
n en
ter
pris
e
(orga
niza
tio
n or in
sti
tutio
n)
Management of the enterprise (organization or institution)
Certification for compliance with a Technical Regulation and/or relevant Standard(s)
Implementation of an internationally recognized Business Excellence model
External environment factors of direct and/or indirect effect
e
nt
er
pr
is
es
(o
rg
an
iz
at
io
n
or
in
st
itu
tio
n)
Official conceptual
and methodological
development of the core
indicators of the BSAM
Selection and application of appropriate
administrative instruments of direct
or indirect influence
Internal environment factors (including
the provision of necessary resources)
Fig. 3. Visualized model for ensuring sustainable development and achieving desired competitive and reputa-
tional advantages by an enterprise (organization, institution)
Source: compiled by the authors based on the results of the study using [1].
87ISSN 2409-9066. Sci. innov. 2026. 22(3)
Mathematical Modelling of the Impact of General Indicators of the Basic Administrative Management System
ne rating the appropriate parameters of influence
of the controlling system on the controlled object
in response to changes in the behavior of internal
environment factors (IEFs), which are formed
under the influence of the factors illustrated in
Figs. 2 and 3; A is the module accounting for the
transformation parameters of the CO state after
the implementation of an administrative decision
produced by the CS, aimed at resolving the oper-
ational or production problem, while taking into
account the factors shown in Figs. 2 and 3; ( )t
is
the vector of influence of the internal environment
factors (IEFs) of the enterprise (organization or ins-
titution), whose state is determined, among other
things, by the factors presented in Figs. 2 and 3;
( )t
is the vector of influence of external system and
operational environment factors (see Figs. 2 and 3).
Considering the analysis of factors presented in
Figs. 2 and 3, it can be concluded that any administ-
rative decision adopted by the CS (Figs. 1 and 4)
is determined by the following expression:
( ) ( ) ( ) ( ) ( ),u t A t x t B t t
(2)
where: A(t) = ||akj|| is the transformation matrix
of the BSAM that converts one state vector of the
controlled object (CO) into another by multiply-
ing its coordinates with the values of the previous
coordinates. This matrix represents the transition
of the CO state, based on the influence of previous-
ly obtained performance results ( )x t
, to the subse-
quent moment in time after the implementation
of an administrative decision, given the factors
illustrated in Figs. 2 and 3; akj are the elements of
the transformation matrix (coordinates charac-
terizing rotation, translation, scaling, and inclina-
tion of the CO state vector based on previously
obtained results) of the BSAM; B(t) = ||bkj|| is the
decision-generation matrix of the controlling sys-
tem (CS), which determines the administrative
decision, taking into account the influence of the
factors depicted in Figs. 2 and 3; bkj are the ele-
ments of the decision-generation matrix (coordina-
tes characterizing rotation, translation, scaling, and
inclination of the vector ( )t
representing the CS
administrative decision); k = (1, …, n), j = (1, …, m)
is the number of elements in the rows and columns,
respectively, of the matrixes ||akj|| and ||bkj||.
Given expressions (1) and (2), the vector ( )x t
at
the subsequent moment in time is calculated using
a differential equation that characterizes the ad-
mi nistrative management process of the legal en-
tity, effectively incorporating the previously ana-
lyzed processes depicted in Figs. 2 and 3:
( )
( ) ( ) ( ) ( ) ( ).
dx t
A t x t B t t t
dt
(3)
Reproducing the complete set and precise se-
quence of the general indicators of the BSAM, as
well as assessing their role, significance, and the
specifics of their interdependence, increases the
demands on its functional-mathematical consis-
tency. To ensure the reliability of results, it is ne-
cessary to strive for a balance between two rather
complex tasks:
1. Accurately reflecting the general indicators
of the established BSAM, which determine the
vector of the primary purposeful influence of the
CS on the CO, are considered during the imple-
mentation of administrative decisions (Fig. 2), fa ci-
litate the timely and rational achievement of Goals,
and form the basis for the ongoing development
of the legal entity (Fig. 3);
2. The complexity of the functional-mathemati-
cal construction of its analogue.
Fig. 4. Structural scheme of the management process
over time t, taking into account the processes of prepa-
ration, adoption, and implementation of administrative
decisions, as well as ensuring sustainable development
and achieving the desired competitive and reputational
advantages by an enterprise (organization, institution)
Source: compiled by the authors based on the results of
the study using [3, 4, 7, 8, 15].
Controlling subject BSAM
Controlled
object
X
B
A
x(t)
v(t)
δ(t) u(t) + δ(t)
A(t)x(t)
B(t)v(t)
88 ISSN 2409-9066. Sci. innov. 2026. 22(3)
Minenko, M. A., Husak, Yu. A., Mashtalir, V. V., Shovkoshytnyi, I. I., Minenko, L. M., and Marchenko, A. O.
Successfully addressing these tasks allows clai-
ming that the set problem (hereafter referred to
as the “task”) has been solved. Modeling is advi-
sable to carry out in three stages [3, 4, 8]:
Stage I: The process of organizing work is recom-
mended to be assessed from the perspective of
systems analysis. At this stage, we immediately
present a model of the legal entity’s BSAM, which
illustrates how the idea of initiating a business
emerges and, subsequently, how all the general
indicators of administrative activity are gradual-
ly formed, usually in four stages (Fig. 5).
Fig. 5. Visualized model of the basic administrative management system of the enterprise (organization, institution)
Source: compiled by the authors based on research results using [1, 16].
Values
Vision
Mission
Vision
Policy
Goal (Objectives)
Functions. Tasks
Development Strategy
Organizational and Legal Form
of Business Activity
Charter. Extract from the Unified State Register
of Legal Entities and Individual Entrepreneurs
Records Retention Schedule (File Classification Schedule)
Staffing Schedule Organizational Management Structure
(and other organizational work structures)
Regulation on Remuneration (Compensation Policy)
Internal Labor Regulations
Occupational Health and Safety Instruction. Fire Safety Instruction.
Occupational Hygiene and Industrial Sanitation Instruction
Regulation on Information Policy
Regulations on Structural Units
Job Descriptions Employment Agreements (Labor Agreements). Contracts
Subsystem of Work Planning, Budgeting, and Resource Provision
Subsystem of Organization, Operational Support, Monitoring, and Regulation of Activities
Subsystem of Activity Motivation. Regulation on Discipline
Corporate Ethics Code
Collective Agreement
Managerial Innovations. Technical Regulation. Standards
Business Excellence Model
Laws, principles, and methods of management
Subsystem
of Com
m
unications
with Stakeholders
Su
bs
ys
tem
of
R
ec
or
d-
Ke
ep
in
g
an
d
D
oc
um
en
tat
io
n
of
A
ct
ivi
tie
s
Stage I
Stage II
Stage III
Stage IV
External environment
of direct or indirect effect
89ISSN 2409-9066. Sci. innov. 2026. 22(3)
Mathematical Modelling of the Impact of General Indicators of the Basic Administrative Management System
Considering the presented model (Fig. 5) and
recognizing the conceptual and methodological
significance of each general indicator of administ-
rative activity for the object of study selected, the
second stage of modeling can be carried out:
Stage II: At this stage, it is necessary to abstract
from the specific nature of the general indicators
in the visualized BSAM model and focus on the
algorithms for solving the task we have posed. In
other words, to ensure systematic re presen ta-
tion of the foundational object of stu dy, estab-
lished mathematical tools should be emp loyed,
including both classical methods (nu me rical me-
thods, differential equations theory, op timiza-
tion, etc.) and modern approaches using com-
putational algorithms (fuzzy logic, neural net-
works, genetic algorithms, etc.) [3, 4, 7, 8, 14, 15].
Stage III: At this stage, it is appropriate to inter-
pret the previously obtained solutions to the
task: to verify whether they provide the most
accurate representation of the BSAM as the es-
tablished object of study and of the functional-
mathematical construction of its analogue. The-
se actions should serve to validate the results,
identify new hidden properties, and reveal in-
terconnections. If the obtained results do not
pass the verification stage, it is necessary to re-
turn to the previous stages and adjust or revise
the input data for the proposed mathematical
model (3), which forms the basis of the func-
tional-mathematical model [4, 14].
Despite these procedures, it is important to ob-
jectively consider that determining the approp ria-
te place and role of each general indicator of the
BSAM (Fig. 5) occurs sequentially and/or in pa ral-
lel through the meaningful development of their
administrative potential. As noted, these actions,
operations, and procedures follow four relatively
distinct, logically interconnected, and mutually
complementary stages.
Particular attention should be paid to the for-
mation of the Subsystem for Communication with
Stakeholders and the Subsystem for Record-Keeping
and Documentation of Activities. A key feature of
the development of these subsystems is that the
initiation of administrative work in their creation
coincides with the inception of the idea to estab-
lish the legal entity. The completion of filling the se
general indicators occurs upon the formal trans fer
of official documents concerning the entity’s acti-
vities to the archive, following its liquidation or reor-
ganization, in accordance with regulations [1, 11].
The deline ated stages of administrative activity
in an enterprise (organization, institution) invol ve
the development, coordination with key stakehol-
ders, and formal official approval of the complete
set of current internal organizational regulatory
documents. These documents conceptually and me-
thodologically define the actual place and role of
each general indicator of the BSAM, both indivi-
dually and in relation to others, as well as the opti-
mal and adapted use of digitalization resources [1].
At the same time, it should be understood that
general indicators such as Values, Vision, Mission,
Outlook, Policy, Goal(s), Functions, Tasks, Develop-
ment Strategy(ies), and the Organizational-Legal
Form of Management by the governing body of a
specific legal entity may, if necessary, be forma-
lized in one or more official documents, such as
the Charter or other acts. Under certain circum-
stances, the formation of subsystems for Commu-
nication with Stakeholders and Record-Keeping and
Documentation of Activities requires regular up-
dates to the corresponding regulations. However,
in any case, to ensure sustainable development
and achieve the desired level of competitive and
reputational advantages, the significance of each
individual general indicator of the BSAM (Fig. 5)
remains essential [2, 16].
This analysis serves as the foundation for const-
ructing a functional-mathematical model that jus-
tifies a unified approach to the conceptual develop-
ment of the general indicators of the BSAM (Fig. 5).
Accordingly, taking into account the features of the
overall management process scheme (Fig. 1), the
related processes (Figs. 2 and 3), and, under these
conditions, the time-based management process
(Fig. 4), and — most importantly — the stepwise
formation of the BSAM’s general indicators for the
legal entity (Fig. 5), we can develop a functional
90 ISSN 2409-9066. Sci. innov. 2026. 22(3)
Minenko, M. A., Husak, Yu. A., Mashtalir, V. V., Shovkoshytnyi, I. I., Minenko, L. M., and Marchenko, A. O.
schematic of the model as an analogue of the se-
lected object of study.
This schematic is presented as a sequential, step-
wise structure, where at each stage (N = I, II, III, IV)
of administrative activity, the implementation of
the expression (3) described above is required.
This expression indeed characterizes the continu-
ity of the management process within the enter-
prise (organization, institution) (Fig. 6).
Thus, at Stage N = I (Fig. 6), where 11 BSAM in-
dicators are formed (see Fig. 5), the vector of in-
ternal environment factors (IE) serves as the input
for module BI (see Fig. 4). This vector generates
the parameters of enforcement or motivation of
the controlling system on the controlled object in
response to changes in the behavior of internal
factors, which may be determined by the elements
shown in Figs. 2 and 3.
In turn, the object XI, which is being managed
at Stage N = I (Fig. 6), under the influence of the
adopted administrative decision and taking into
account the corresponding BSAM indicators for
Stage I I
ix
,
i = 1, …, 11 (see Fig. 5) and the beha-
vior of external business environment and/or ope-
rating environment factors I
(see Fig. 4), forms
the state vector of the CO after the implementa-
tion of the administrative decision: I I,0( ,0, 0).x x
The module for accounting of parameters AI trans-
forms the state of the CO I
ix
in accordance with
the directives established by internal organizatio-
nal official documents, using the appropriate set of
acts, actions, procedures, and operations of direct
or indirect administration. This transformation also
takes into account the behavior of relevant factors
(Figs. 2 and 3) to ensure the legal entity’s sustai-
nable development and the attainment of desired
competitive and reputational advantages [1, 16].
Next, at Stages N = II, III, and IV (Fig. 6) —
whe re the following BSAM indicators are formed
(Sta ge II: five indicators; Stage III: five indicators;
BI XI
AI
BII XII
AII
BIII XIII
AIII
BIV XIV
AIV
Stage I
Stage II
xI, i = 1, ..., 11i
xI = (xI, 0, 0, 0)vI
ϕI, ϕI
1 2
δI
xII, i = 1, ..., 5i
xII = (xI, xII, 0, 0)vII
ϕII, ϕII
1 2
δII
Stage III xIII, i = 1, ..., 5i
xIII = (xI, xII, xIII, 0)
vIII
ϕIII, ϕIII
1 2
δIII
Stage IV xIV, i = 1, ..., 3i
xIV = (xI, xII, xIII, xIV)
vIV
ϕIV, ϕIV
1 2
δIV
Note: In Fig. 6, all vectors are, by default, considered time-dependent, with time denoted as t in Figs. 1 and 4 and
in the expressions; represents the vector of internal influence at the corresponding stage N; I II III IV, , ,x x x x
are the
state vectors of the BSAM after the completion of Stages I, II, III, and IV, respectively.
Fig. 6. Functional schematic of the model as an
analog of the operating basic administrative
management system of the enterprise (orga-
nization, institution)
Source: compiled by the authors based on re-
search results using [1, 3, 4, 7, 8, 16].
91ISSN 2409-9066. Sci. innov. 2026. 22(3)
Mathematical Modelling of the Impact of General Indicators of the Basic Administrative Management System
Stage IV: three indicators; see Fig. 5) — the process
of generating the state vector of the controlled
object XN, aimed at the establishment and deve-
lopment of a given legal entity, is again carried out
under the enforcement or motivational influence
of directives established by internal organizational
regulations. This process is repeated for each cor-
responding group (x
i
II, i = 1, …, 5; x
i
III, i = 1, …, 5;
x
i
IV, i = 1, …, 3), respectively, given the influence
of external business environment and/or opera-
ting environment factors II III IV, ,
(see Fig. 4), as
well as the factors depicted in Figs. 2 and 3 [1, 16].
Next, at Stages N = II, III, IV (Fig. 6), where the
following BSAM indicators are formed — Stage II:
five indicators; Stage III: five indicators; Stage IV:
three indicators (see Fig. 5) — the process of gene-
rating the CO state vector XN, for the purpose of
building and developing a given legal entity, is
again carried out under the enforcement or moti-
vation of directives established by internal regula-
tions. This process is repeated for each corres pon -
ding group (i = 1, …, 5 for Stage II; i = 1, …, 5 for
Stage III; i = 1, …, 3 for Stage IV), taking into ac-
count the influence of external business envi-
ronment and/or operating environment factors
II III IV, ,
(see Fig. 4), as well as the factors depic-
ted in Figs. 2 and 3 [1, 16].
Moreover, at the output of each N stage of the
functional schematic model, the actual influence
of the Record-Keeping and Documentation of Ac-
tivities
1
N
and Communication with Stakeholders
2
N
subsystems (Fig. 6), which are approved by se-
parate regulations, is necessarily taken into ac-
count [1]. The resulting outcome is the CO state
vector of the BSAM, based on the previously ob-
tained performance results ( )x t
(see Fig. 6), which
characterizes the management process of the le-
gal entity. The absence (or disregard) or underes-
timation of the role of even a single general indi-
cator of administrative activity (Fig. 5) reduces
the accuracy of determining the overall vector of
the state of the operating BSAM. This may lead to
an increase in organizational entropy and, conse-
quently, to a decrease in the efficiency and effec-
tiveness of the work of individual staff members,
structural units, and the enterprise (organization,
institution) as a whole. Ultimately, it may prevent
its sustainable development and become one of
the main reasons for failing to achieve the desired
competitive and reputational advantages [16].
For this reason, and considering that the mana-
gement process of an enterprise (organization, ins-
titution) — given the specific features of the pro-
cesses of preparation, adoption, and implementa-
tion of administrative decisions (Fig. 2), as well as
the processes ensuring sustainable development
and the attainment of the desired competitive
and reputational advantages (Fig. 3) — is conti-
nuous, expression (3) should appropriately be writ-
ten, taking into account Fig. 6, as a system of diffe-
rential equations. In this system, each differential
equation describes the process of administrative
management at Stages I, II, III, and IV of the for-
mation of the BSAM indicators:
I
I I I I
1 2
I I I I
II
II II II II
1 2
II II II
II I I
III
III III
( )
( ) ( ) ( ) ( )
( ) ( ) ( ), (0) (0) (0,0,0,0),
( )
( ) ( ) ( ) ( )
( ) ( ) ( ),
(0) (0) ,0, 0, 0 ,
( )
( ) ( )
dx t
A t x t t t
dt
B t t t x x
dx t
A t x t t t
dt
B t t t
x x x
dx t
A t x t
dt
III III
1 2
III III III
III II II
I
IV IV IV IV
1 2
IV IV IV
IV III III
( ) ( )
( ) ( ) ( ),
(0) (0) 0, ,0, 0 ,
( )
( ) ( ) ( ) ( )
( ) ( ) ( ),
(0) (0) 0, 0, , 0 .
t t
B t t t
x x x
dx t
A t x t t t
dt
B t t t
x x x
(4)
Thus, the overall state vector of the BSAM after
the completion of the four stages of forming its
indicators, (IV),x
is described by the following
equation: IV
I
(IV) (0) ( )i
i
x x x t
, (5)
92 ISSN 2409-9066. Sci. innov. 2026. 22(3)
Minenko, M. A., Husak, Yu. A., Mashtalir, V. V., Shovkoshytnyi, I. I., Minenko, L. M., and Marchenko, A. O.
where: (0)x
is the BSAM state vector at time t = 0;
IV
I II III IV
I
( ) ( ) ( ) ( ) ( )i
i
x t x t x t x t x t
; ( )ix t
are
functions representing the change in the BSAM
state at the i-th stage.
Thus, expression (4) may be considered the star-
ting point for the mathematical formalization and
evaluation of the applied influence of each BSAM
general indicator, as well as other internal and ex-
ternal factors, on the management process of a
particular enterprise (organization, institution), its
structural units, and staff members, taking into
account the defined stages of formation of a given
legal entity (Fig. 5). At the same time, expression (5)
describes this process as the sum of the contribu-
tions ( )ix t
at each stage, і = І, …, IV. This makes it
possible to confirm that disregarding even a sing-
le general element or subsystem of the BSAM —
which formally and purposefully, through concep-
tual and methodological provisions, ensures enfor-
cement and/or motivation toward safe, coor dinated,
rational, productive, effective, and timely work —
as well as ignoring existing factors of direct and/
or indirect influence, may lead to an imbalance in
the overall organizational management system and
make it impossible to ensure sustainable develop-
ment or achieve the desired competitive and repu-
tational advantages of the legal entity. In other words,
this confirms that any existing internal organiza-
tional regulatory (administrative) act — including
provisions On Record-Keeping and Documenta-
tion of Activities
1
N
and On Communication with
Stakeholders
2
N
— formally obliges every staff ma-
nager of a particular enterprise (organization, ins-
titution), during the preparation, adoption, and
implementation of administrative decisions (Fig. 2),
to unequivocally take into account the concep-
tually and methodologically defined standards,
rules, and recommendations of each general indi-
cator of the BSAM (Fig. 5), which have been duly
coordinated with stakeholders and officially app-
roved, in order to support the organization’s con-
tinuous development and the achievement of lea-
dership in a given field of activity (Fig. 3).
In addition, managers must also take into ac-
count [1]:
the influence of previously obtained performan-
ce results ( )x t
;
changes in the behavior of internal environment
factors, including available resources and those
that may be timely mobilized ( );t
the projected state and possible changes in the be-
havior of factors of the external business environ-
ment and/or the operating environment ( ).t
At the same time, if an enterprise (organization,
ins titution) is certified for compliance with a Tech-
ni cal Regulation and/or Standard, or has implemen-
ted one of the internationally recognized Bu si ness
Excellence models, this also necessitates the intro-
duction of appropriate amendments and additions
to the content of the existing internal regulations.
Moreover, it should not be overlooked that, in
a specific operational situation, the choice of the
required configuration of administrative instru-
ments of direct or indirect action also depends on
the conceptual and methodological potential of the
existing internal organizational regulatory (admi-
nistrative) documents.
Thus, administrative acts of direct action —par-
ticularly organizational acts —are essentially in-
ternal regulations that define the foundations of
administration for any legal entity. The effective-
ness of directive or reference acts, as well as the
actions, operations, and procedures involved in
organizing work (of both direct and indirect natu-
re), also directly depends on the quality and subs-
tance of the general indicators (elements and sub-
systems) of the BSAM [1].
CONCLUSIONS
1. A functional mathematical model has been de-
veloped to describe the influence of the BSAM
general indicators, considered as a type of infor-
mation and communication system, on the per-
formance results of an enterprise (organization,
institution).
2. The enterprise management process has been
formalized in the form of a system of differential
93ISSN 2409-9066. Sci. innov. 2026. 22(3)
Mathematical Modelling of the Impact of General Indicators of the Basic Administrative Management System
equations (4—5), which describes the change in the
state of the controlled object depending on: pre-
vious performance results; vectors of influence from
the internal and external environments; adopted
administrative decisions; and the characteristics
of the elements and subsystems of the BSAM.
3. Four stages of forming the BSAM indicators
(I—IV) have been proposed, each characterized
by a corresponding set of managerial parameters
and its own functional influence on the perfor-
mance results of the enterprise (organization, in-
stitution). The systemic nature of the model is en-
sured through the gradual contribution of each
stage — Stage I (organizational and legal), Stage II
(regulatory), Stage III (regulatory and functional),
and Stage IV (strategic development) — to the ove-
rall BSAM effectiveness.
4. Model (5) demonstrates that the complete
or partial omission of at least one BSAM general
indicator in the management process may lead to
a decrease in the integrated efficiency indicator of
the enterprise.
5. The proposed model, as a managerial inno-
vation, may be useful for the practical assessment
of the level of administrative efficiency, forecas-
ting the performance results of a legal entity, and
optimizing the management system of personnel
and resources.
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[in Ukrainian].
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(2019). Mathematical Foundations of Human Resource Managementin the Military Sphere: monograph. (Ed.
I. S. Romanchenko). Kyiv [in Ukrainian].
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pages. https://doi.org/10.1155/2019/4784909
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profile/Andrea-Tick-2/publication/261381192_Business_process_modeling_-_Simulation_of_administrative_
94 ISSN 2409-9066. Sci. innov. 2026. 22(3)
Minenko, M. A., Husak, Yu. A., Mashtalir, V. V., Shovkoshytnyi, I. I., Minenko, L. M., and Marchenko, A. O.
activities/links/569aa02a08ae748dfb0b4e75/Business-process-modeling-Simulation-of-administrative-activities.pdf
(Last accessed: 28.03.2025).
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“KPI,” 16, 242—251. https://doi.org/10.20535/2307-5651.16.2019.182607 [in Ukrainian].
Received 21.07.2025
Revised 02.12.20 25
Accepted 25.12.2025
М.А. Міненко (https://orcid.org/0000-0002-7492-3196),
Ю.А. Гусак (https://orcid.org/0000-0002-3423-2112),
В.В. Машталір (https://orcid.org/0000-0002-8132-217X),
І.І. Шовкошитний (https://orcid.org/0000-0001-9245-4111),
Л.М. Міненко (https://orcid.org/0000-0003-0249-9856),
А.О. Марченко (https://orcid.org/0000-0002-1268-8012)
Національний університет оборони України,
проспект Повітряних Сил, 28, Київ, 03049,Україна,
+380 44 271 0780, nuou@mod.gov.ua
МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВУ ЗАГАЛЬНИХ ПОКАЗНИКІВ
БАЗОВОЇ СИСТЕМИ АДМІНІСТРАТИВНОГО МЕНЕДЖМЕНТУ
НА РЕЗУЛЬТАТИ ДІЯЛЬНОСТІ ПІДПРИЄМСТВА (ОРГАНІЗАЦІЇ, УСТАНОВИ)
Вступ. Нині перед керівництвом постає завдання: які управлінські новації необхідно враховувати, реалі-
зуючи адміністративні рішення, щоб забезпечити стійкий розвиток юридичної особи для здобуття конку-
рентнихі репутаційних переваг.
Проблематика. Розроблення наукового способу оцінювання загальних показників базової системи ад-
міністративного менеджменту (різновиду інформаційно-комунікаційної системи, базису раціонального
отримання очікуваних підсумків праці), зважаючи на досягнення у роботі, потенціал адміністративних до-
кументів, фактори внутрішнього та зовнішнього середовища, норми впроваджених управлінських новацій.
Мета. Науково обґрунтувати математичну модель, яка відображає вплив загальних показників базової
системи адміністративного менеджменту на результати діяльності підприємства (організації, установи),
із визначенням характерних функціональних взаємозв’язків між складовими елементами останньої.
Матеріали й методи. Досліджено джерела та використано методи математичного моделювання, аналізу
та синтезу, графічний, діалектичний, економічного моделювання, системно-структурного та структурно-
функціонального аналізу.
Результати. Використовуючи формули, схеми і моделі, доведено ефект впливу загальних показників
досліджуваної системи на результати роботи юридичної особи. Окреслено умови результативності засто-
сування такої управлінської новації. Вперше формалізовано процес керування юридичною особою для
оцінювання осібної адміністративної ваги визначених показників означеної базової системи у відповідному
середовищі функціонування.
Висновки. Результати підтвердили значення всіх загальних показників організації праці та базової систе-
ми адміністративного менеджменту. Запропоноване сприятиме подальшому пристосуванню математичних
моделей до умов роботи конкретної юридичної особи і напрацюванню методики, що унормує використання
розробленого та стане вагомим засобом гарантування конкурентних і репутаційних переваг.
Ключові слова: базова система адміністративного менеджменту, інформаційно-комунікаційна система,
загальні показники адміністрування діяльності, управлінські новації, математичне моделювання, адмі-
ністративне рішення, стійкий розвиток, конкурентні та репутаційні переваги.
|
| id | oai:ojs2.scinn-eng.org.ua:article-1149 |
| institution | Science and Innovation |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-06-18T01:01:16Z |
| publishDate | 2026 |
| publisher | PH “Akademperiodyka” |
| record_format | ojs |
| resource_txt_mv | scinn-engorgua/3f/f51c9fa8b4ea683dc2edd709309e0b3f.pdf |
| spelling | oai:ojs2.scinn-eng.org.ua:article-11492026-06-17T11:30:40Z МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВУ ЗАГАЛЬНИХ ПОКАЗНИКІВ БАЗОВОЇ СИСТЕМИ АДМІНІСТРАТИВНОГО МЕНЕДЖМЕНТУ НА РЕЗУЛЬТАТИ ДІЯЛЬНОСТІ ПІДПРИЄМСТВА (ОРГАНІЗАЦІЇ, УСТАНОВИ) MATHEMATICAL MODELLING OF THE IMPACT OF GENERAL INDICATORS OF THE BASIC ADMINISTRATIVE MANAGEMENT SYSTEM ON THE PERFORMANCE OF AN ENTERPRISE (ORGANIZATION, INSTITUTION) MINENKO, M. HUSAK, Yu. MASHTALIR, V. SHOVKOSHYTNYI, I. MINENKO, L. MARCHENKO, A. базова система адміністративного менеджменту загальні показники адміністрування діяльності тотальна дигіталізація метод математичного моделювання адміністративне рішення стійкий розвиток конкурентні та репутаційні переваги Вступ. Нині перед керівництвом постає завдання: які управлінські новації необхідно враховувати, реалізуючи адміністративні рішення, щоб забезпечити стійкий розвиток юридичної особи для здобуття конкурентних і репутаційних переваг.Проблематика. Розроблення наукового способу оцінювання загальних показників базової системи адміністративного менеджменту (різновиду інформаційно-комунікаційної системи, базису раціонального отримання очікуваних підсумків праці), зважаючи на досягнення у роботі, потенціал адміністративних документів, фактори внутрішнього та зовнішнього середовища, норми впроваджених управлінських новацій.Мета. Науково обґрунтувати математичну модель, яка відображає вплив загальних показників базовоїсистеми адміністративного менеджменту на результати діяльності підприємства (організації, установи),із визначенням характерних функціональних взаємозв’язків між складовими елементами останньої.Матеріали й методи. Досліджено джерела та використано методи математичного моделювання, аналізу та синтезу, графічний, діалектичний, економічного моделювання, системно-структурного та структурнофункціонального аналізу.Результати. Використовуючи формули, схеми і моделі, доведено ефект впливу загальних показниківдосліджуваної системи на результати роботи юридичної особи. Окреслено умови результативності застосування такої управлінської новації. Вперше формалізовано процес керування юридичною особою для оцінювання осібної адміністративної ваги визначених показників означеної базової системи у відповідномусередовищі функціонування.Висновки. Результати підтвердили значення всіх загальних показників організації праці та базової системи адміністративного менеджменту. Запропоноване сприятиме подальшому пристосуванню математичних моделей до умов роботи конкретної юридичної особи і напрацюванню методики, що унормує використання розробленого та стане вагомим засобом гарантування конкурентних і репутаційних переваг. Introduction. Contemporary management faces the challenge of determining which managerial innovations should be systematically integrated into administrative decision-making in order to ensure the sustainable development of a legal entity and to secure stable competitive and reputational advantages.Problem Statement. There is a need to develop a scientifically grounded approach to assessing theoverall performance of the Basic Administrative Management System (BAMS), considered as a type ofinformation and communication system that facilitates the rational achievement of expected results, while taking into account organizational performance outcomes, administrative documentation practices, environmental factors, and the implementation of managerial innovations.Purpose. The purpose of this study is to provide the scientific substantiation of a mathematical modelthat captures the impact of the general indicators of the Basic Administrative Management System on theperformance of an enterprise (organization, institution), while identifying the characteristic functionalinterrelationships among its constituent elements.Materials and Methods. The research draws upon a comprehensive review of relevant scholarly sources and applies mathematical modelling, analytical and synthetic methods, graphical modelling techniques, economic modelling approaches, and systems-based analytical frameworks. Results. The study has demonstrated, through the use of formulas, diagrams, and formalized models, the influenceof the system’s general indicators on organizational performance outcomes. The conditions required for the effective implementation of this managerial innovation have been identified and conceptually justified. Furthermore, the management process of a legal entity has been formally represented and analytically structured in order to evaluate the administrative significance of the identified indicators within the operational environment.Conclusions. The findings have confirmed the substantive significance of the general indicators of labor organization and of the Basic Administrative Management System as determinants of organizational performance. The proposed approach enables the adaptation of mathematical models to the institutional and operational conditions of aspecific legal entity and supports the development of a methodological framework for their practical application as an analytical instrument for achieving sustainable competitive and reputational advantages. PH “Akademperiodyka” 2026-06-17 Article Article Рецензована стаття Peer-reviewed article application/pdf https://scinn-eng.org.ua/ojs/index.php/ni/article/view/1149 10.15407/scine22.03.080 Science and Innovation; Том 22 № 3 (2026): Science and Innovation; 80-94 Science and Innovation; Vol. 22 No. 3 (2026): Science and Innovation; 80-94 2413-4996 2409-9066 10.15407/scine22.03 en https://scinn-eng.org.ua/ojs/index.php/ni/article/view/1149/325 Copyright (c) 2026 Copyright Notice Authors published in the journal “Science and Innovation” agree to the following conditions: Authors retain copyright and grant the journal the right of first publication. Authors may enter into separate, additional contractual agreements for non-exclusive distribution of the version of their work (article) published in the journal “Science and Innovation” (for example, place it in an institutional repository or publish in their book), while confirming its initial publication in the journal “Science and innovation.” Authors are allowed to place their work on the Internet (for example, in institutional repositories or on their website). https://creativecommons.org/licenses/by-nc/4.0/ |
| spellingShingle | базова система адміністративного менеджменту загальні показники адміністрування діяльності тотальна дигіталізація метод математичного моделювання адміністративне рішення стійкий розвиток конкурентні та репутаційні переваги MINENKO, M. HUSAK, Yu. MASHTALIR, V. SHOVKOSHYTNYI, I. MINENKO, L. MARCHENKO, A. МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВУ ЗАГАЛЬНИХ ПОКАЗНИКІВ БАЗОВОЇ СИСТЕМИ АДМІНІСТРАТИВНОГО МЕНЕДЖМЕНТУ НА РЕЗУЛЬТАТИ ДІЯЛЬНОСТІ ПІДПРИЄМСТВА (ОРГАНІЗАЦІЇ, УСТАНОВИ) |
| title | МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВУ ЗАГАЛЬНИХ ПОКАЗНИКІВ БАЗОВОЇ СИСТЕМИ АДМІНІСТРАТИВНОГО МЕНЕДЖМЕНТУ НА РЕЗУЛЬТАТИ ДІЯЛЬНОСТІ ПІДПРИЄМСТВА (ОРГАНІЗАЦІЇ, УСТАНОВИ) |
| title_alt | MATHEMATICAL MODELLING OF THE IMPACT OF GENERAL INDICATORS OF THE BASIC ADMINISTRATIVE MANAGEMENT SYSTEM ON THE PERFORMANCE OF AN ENTERPRISE (ORGANIZATION, INSTITUTION) |
| title_full | МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВУ ЗАГАЛЬНИХ ПОКАЗНИКІВ БАЗОВОЇ СИСТЕМИ АДМІНІСТРАТИВНОГО МЕНЕДЖМЕНТУ НА РЕЗУЛЬТАТИ ДІЯЛЬНОСТІ ПІДПРИЄМСТВА (ОРГАНІЗАЦІЇ, УСТАНОВИ) |
| title_fullStr | МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВУ ЗАГАЛЬНИХ ПОКАЗНИКІВ БАЗОВОЇ СИСТЕМИ АДМІНІСТРАТИВНОГО МЕНЕДЖМЕНТУ НА РЕЗУЛЬТАТИ ДІЯЛЬНОСТІ ПІДПРИЄМСТВА (ОРГАНІЗАЦІЇ, УСТАНОВИ) |
| title_full_unstemmed | МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВУ ЗАГАЛЬНИХ ПОКАЗНИКІВ БАЗОВОЇ СИСТЕМИ АДМІНІСТРАТИВНОГО МЕНЕДЖМЕНТУ НА РЕЗУЛЬТАТИ ДІЯЛЬНОСТІ ПІДПРИЄМСТВА (ОРГАНІЗАЦІЇ, УСТАНОВИ) |
| title_short | МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВУ ЗАГАЛЬНИХ ПОКАЗНИКІВ БАЗОВОЇ СИСТЕМИ АДМІНІСТРАТИВНОГО МЕНЕДЖМЕНТУ НА РЕЗУЛЬТАТИ ДІЯЛЬНОСТІ ПІДПРИЄМСТВА (ОРГАНІЗАЦІЇ, УСТАНОВИ) |
| title_sort | математичне моделювання впливу загальних показників базової системи адміністративного менеджменту на результати діяльності підприємства (організації, установи) |
| topic | базова система адміністративного менеджменту загальні показники адміністрування діяльності тотальна дигіталізація метод математичного моделювання адміністративне рішення стійкий розвиток конкурентні та репутаційні переваги |
| topic_facet | базова система адміністративного менеджменту загальні показники адміністрування діяльності тотальна дигіталізація метод математичного моделювання адміністративне рішення стійкий розвиток конкурентні та репутаційні переваги |
| url | https://scinn-eng.org.ua/ojs/index.php/ni/article/view/1149 |
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