Sustainable Management of Healthcare Settings’ Personnel Based on Intelligent Project-Oriented Approach for Post-War Development

Abstract

The paper considers the transformation of human resource management processes in the healthcare settings of Ukraine in the context of war and the COVID-19 pandemic. It is noted that the unstable and hostile environment of a healthcare setting during times of crisis leads to the need to change the personnel selection and team formation model to increase the adaptability and resilience of human resources involved in the provision of medical care. The key features of the human resource management process in a turbulent environment are the high migration activity of personnel, which leads to the need to reallocate resources, the need to operate under severe financial constraints, and the need to consider personnel as a non-renewable resource when it is impossible to attract additional resources. To ensure the reliability of the functioning of a medical institution, the transformation of human resource management processes should be based on strategic agility and human resource management, organizational resilience as a resource-based capability, corporate sustainability, and transformation of enterprises’ resources, which can be achieved by applying methodological support for resource management in a multi-project environment. Considering a network of medical institutions as a multi-project environment will allow using the methodology of project-oriented resource management, forming adaptive teams in a multi-project environment, to ensure flexible redistribution of resources both within a single institution and within a network of institutions. It is proposed to use formal transformations to manage a medical institution’s human resources. Applying the proposed approach for managing the human resources of a medical institution is considered. The formation of a project team that satisfies the minimum requirements with the maximum value of the team’s qualification score is considered. It is shown that the use of this methodological support made it possible to choose the composition of the project team with a minimum number and a maximum value of the characteristic.

1. Introduction

Healthcare settings in Ukraine are forced to operate in challenging, unstable conditions due to the Russian war and the COVID-19 pandemic.

In order to improve the sustainability of the functioning of healthcare settings, it is necessary to transform the processes of human resource management. At the same time, the transformation should provide strategic flexibility in managing human resources and organizational resilience as a resource-based capability.

Ensuring organizational sustainability can be achieved using agile approaches to management [1,2], ensuring proactive human resource management [3,4].

If, before the start of the medical reform, the staff in healthcare settings was somewhat redundant, then the reform against the backdrop of the emergence of the COVID-19 pandemic led to a shortage of personnel (a shortage of specialists of a particular specialization and qualifications) and the need to transform human resource management processes [5].

In an analysis of changes in the medical environment [6], recruiting trends in 2021–2022 showed the need to reduce personnel costs while tightening the requirements for ensuring sustainable project management [7] against the backdrop of an unbalanced labor market due to migration [8].

Formed teams must be flexible [9], adaptable [10], and resilient [11], comply with the principles of functional redundancy and ensure the organizational sustainability [12] of a medical institution. Since healthcare settings are safety-oriented systems, when forming teams, it is advisable to use specialized methodological tools, e.g., presented in the works of Zachko et al. [13], Golovatyi [14], and Ponomaryov et al. [15]. The presented models of the formation of project teams in security-oriented systems take into account the parameters of candidates’ personal human qualities and professional skills. They improve the efficiency of recruitment. However, the models do not consider the need to ensure the redistribution of resources in a multi-project environment.

Taking into account the cyclical nature of the COVID-19 pandemic and the presence of hostilities on the territory of Ukraine, the task of recruiting personnel for healthcare settings with the possibility of quickly forming teams under given functional and resource constraints is relevant.

The article aims to develop a conceptual framework for transforming human resource management processes in the healthcare settings of Ukraine in the conditions of war and the COVID-19 pandemic, based on the application of methodological support for resource management in a multi-project environment.

The further structure of the paper is as follows: Section 2, namely, current research analysis, provides an overview of up-to-date research connected with the paper. Section 3, Materials and Methods, proposes the scientific hypotheses and tasks, which will be addressed in the paper. Section 4 describes the results obtained within the research. An analysis was made of the functioning of the multi-project environment of medical institutions during the COVID-19 pandemic and hostilities. A model of project resource support in the Backus–Naur notation was built, which made it possible to formalize the requirements for human resources in a multi-project medical environment: the formation of a functionally reserved adaptive resolute team in multi-project no-nonsense healthcare settings was proposed to use the methodology of a project-oriented approach to resource management in a multi-project environment. Section 5 discusses the obtained results. The Conclusions section describes the outcomes, limitations of the study, and future research.

2. Current Research Analysis

Adam et al. [16] describe the experience of changes made to the distribution of human resources in the Center Hospitalier de Universite de Montreal (CHUM) pharmacy department. The issues of crisis management, internal communications, employee stress, reorganization of workplaces and clinical staff, remote work, and schedule management were considered. At the same time, the main changes did not concern the redistribution of duties of medical personnel and were not aimed at improving their work efficiency. The purpose of implementing the changes was primarily to improve the safety of personnel in the context of the COVID-19 pandemic.

A study by Amorim-Lopes et al. [17] proposes a sociotechnical methodology to account for future uncertainty in mathematical programming modeling to aid in planning for health workforce adjustments. The authors propose to create individual scripts and input parameters corresponding to the scripts, which are then used in mathematical programming models. At the same time, the proposed methodology involves experts at all stages: from developing scenarios to interpreting model results.

Paper [18] examines the redeployment of human resources for health care in conjunction with contact tracing and border control in the context of the COVID-19 pandemic in Barbados. The authors propose controlling the population’s contact to avoid overcrowding in medical institutions. However, the proposed approach does not consider the human and financial resources required for contact tracing, testing, and isolation management. The authors of [19] consider the complex use of resources to provide medical care, focusing on distributing doctors and medical beds. The study shows that these distributions are embedded in health systems, i.e., the ratio of doctors to beds varies for treating different diseases. At the same time, it was concluded that the distribution of human resources and beds depends on the region’s funding, and only health policy can influence this.

A study by Hafezalkotob et al. [20] proposes a collaborative game theory approach to mitigate the adverse effects of catastrophic events, minimize the expected level of hospital care, and reduce unwanted costs. At the same time, cooperation between medical centers is considered, not within one institution. Paper [21] analyzes the evolution and use of contactless healthcare services over three different periods: before, during, and after COVID-19. As a result, a conclusion was drawn about the redistribution of human resources for the hybrid provision of services for those medical services that have proven their effectiveness with contactless use. The authors analyze contactless service provision after the COVID-19 pandemic, although it is still ongoing.

Paper [22] is devoted to measures for the development of healthcare teams. At the same time, the main result of introducing such measures is to increase the psychological safety of medical workers. However, the proposed approach does not consider the medical worker’s previous experience and competencies. Paper [23] is based on the concept of intelligent hospitals. It presents an elastic distribution of human resources in medical institutions, focused on the Internet of Things model, capable of tracking the use of hospital rooms by patients and adapting the distribution of medical workers to these rooms to meet the needs of patients. The purpose of the proposed approach is to reduce the waiting time for patients in the queue, i.e., this is a supply and demand management model, and not to increase the efficiency of the use of human resources.

The authors of [24] consider the lean approach to managing human resources in healthcare. Among the main achievements of implementing the lean approach in healthcare institutions, the authors highlight the increase in job satisfaction and work autonomy.

An analysis of works [25,26] showed the need to transform human resource management processes to ensure the stable functioning of companies.

Assisting patients with COVID-19 in Ukraine is currently associated with specific problems that negatively affect the fight against COVID-19:

• War;
• Hostile environment for the functioning of medical institutions;
• Destruction of medical facilities;
• Insufficient supply of medicines to hospitals;
• Lack of the required number of medical staff with the necessary qualifications;
• Uncontrolled population migration;
• Non-compliance with personal protective measures;
• The impossibility of assisting at the primary level in the territories where hostilities are taking place;
• Re-profiling of hospitals.

PMI notes [27] that most companies, in the course of their work, face the problems of implementing projects in an unstable environment; thus, it is advisable to direct efforts towards combining the attributes of adaptability and resilience (persistence). Regarding human resource management, adaptability refers to the team’s ability to respond to changing conditions. With this approach, aspects such as the ability to accept changes and recover from setbacks are taken into account when determining resilience.

Analysis of the impact of COVID-19 on management processes, given in [28], showed that to ensure the viability of an organization, it is necessary to implement opportunity agility and planning agility. Indeed, there might be a positive relationship between the adverse impact of the pandemic on enterprises and their agility. The stronger the impact of the pandemic on the organization, the higher will be the opportunity agility and planning agility.

Table 1. Analysis of models for ensuring adaptability and resilience of project teams.

Task	Ahammad M.F., et al. (2020). [29]	Ambituuni A., et al. (2021) [30]	Anwar A., et al. (2021). [31]	Williams T. A., et al. (2017) [32]	Linnenluecke M. K. (2017) [33]	Lisdiono P., et al. (2022). [34]	Afruzi E., et al. (2020) [35]	Heredia J., et al. (2022) [36]	Song W., et al. (2018) [37]
Strategic agility and human resource management	+			+	+			+
Improvisation, fluidity and flexibility		+
Organizational resilience as a resource-based capability			+	+				+
Organizational sustainability				+	+		+	+
Transformation of enterprises’ resources					+	+	+
Resource management in a multi-project environment							+		+

provides an analysis of models for ensuring the adaptability and resilience of project teams.

Some authors, such as Williams et al. (2017) [32] consider organizational sustainability as the foundation for the development of an organization during a crisis.

Increasing the adaptability and resilience of the project team facilitates the delivery of planned values under given time and financial constraints.

The process of transitioning the project team from the current state to a resource state capable of achieving the desired planned values can be carried out by implementing change management (enablement) [1].

Adaptive approaches are helpful when requirements are subject to high uncertainty and volatility and can change throughout the project’s life, which most accurately characterizes project management during wartime [1,27].

An adaptive approach to human resource management uses iterative and incremental approaches [38,39].

A study of systemic risks and their impact on organizational management was presented by Wever et al. in [40]. Jahn et al. [41] made it possible to form a register of triggers to identify potentially dangerous risks in the medical field.

Federico Trigos and Mario Doria (2021) note that applying the Transdisciplinary Flextime Hiring Method to the service sector is advisable. Applying this method, based on the concept of organizational design, will allow service companies to justify and implement a flexible schedule based on cost reduction and increase employee satisfaction and commitment [42].

Khatun et al. (2021) [43] consider the application of a static and dynamic resource allocation strategy between projects in a multi-project environment. It is proposed to use a dynamic approach to redistribute resources, in which resources are distributed from the shared pool of a multi-project environment.

When forming a staff of medical workers in stable operating conditions, it is advisable to use recruitment methods that allow you to create highly effective teams, considering the organizational structure [44,45].

Podra and Petryshyn [46] focus on the effectiveness of modern human resource management technologies based on the high involvement approach to human resource management—“HIHRM” and “Hay Group” as a tool for evaluating the results of work with human resources.

An analysis of the tasks of personnel management is presented in

Table 2. Analysis of the tasks of human resource management.

Task	Structure	Composition	Description	Source
Structure management	Not determined	Fixed	In the presence of a set of employees with known characteristics (fixed composition), it is required to find the optimal structure of the active system (communications and interactions between employees).	[44,47]
Composition management	Fixed	Not determined	It consists of determining the optimal set of employees of the active system, provided that the structure of the entire active system is set, and the management problem has already been solved.	[42,47]
Fixed composition management	Fixed	Fixed	It consists of the appointment of an optimal incentive system to achieve the best result with a fixed composition and structure.	[48,49,50]

.

The provision of medical services is associated with a number of features that reflect the emerging resource conflicts shown in

Table 3. Resource conflicts arising in healthcare settings.

Type of Conflict	Resource	Influence	Resolution Paths
Lack of healthcare settings in a certain area	material	Inability to provide medical care	Redirection of patients, provision of logistics.
Insufficient number of medical staff	labor	Restriction on the possibility of receiving patients, declining quality of service	Recruitment, consideration of a multi-project environment to attract staff from other medical institutions, external consultation [51,52]
Lack of equipment	material	Restriction on the possibility of receiving patients, declining quality of service	Purchase (leasing) of equipment, contacting other institutions
Limited funding	expenses	Limiting the possibility of receiving patients, reducing the quality of service	Attracting additional funding, volunteer organizations, sponsors
Functional limitations	labor	Prohibition of combining functions, positions, recommendations for combining functions, etc.	Personnel planning subject to constraints [51,52]
Changing staffing requirements	labor	Changing the competency profile of the staff of medical institutions	Personnel planning, taking into account the possibility of redistribution [37].
Psychological conflicts	labor	Functioning under stress: external factors (war, COVID), internal (conflicts in the project team)	Methods for reducing stress levels [53], methods for increasing flexibility [28], developing emotional intelligence [54,55]

.

Changes in the requirements for the staff of medical institutions providing medical care for COVID-19 may occur due to changes in the Cabinet of Ministers of Ukraine decree on the introduction of quarantine [56]. At the time of writing, it depends on:

• the number of cases per 100,000 population (if we consider an oblast, then the quarantine level applies to the entire oblast);
• occupancy in the area of oxygen beds (more than 65%—orange/red zone);
• number of hospitalizations;
• an increase in hospitalizations in 7 days compared to the previous 7 days.

When determining the requirements for candidates for the project team and forming an agreed list of requirements, it is advisable to use the techniques described in [57], adapting them to the functioning conditions of medical institutions in Ukraine.

Thus, the analysis of the current state of research has shown that it is necessary to consider healthcare settings as safety-oriented systems to ensure the sustainable functioning of the healthcare system during the COVID-19 pandemic in war conditions. The task of personnel management remains relevant and can be solved by transforming existing human resource management processes (in particular, building functionally redundant adaptive, resilient teams).

3. Materials and Methods

3.1. Methodology

The paper uses a project-oriented resource management methodology to form adaptive teams in a multi-project environment.

Scientific hypotheses:

Hypothesis 1 (H1).

Considering the network of medical institutions as a multi-project environment operating with a given pool of resources will allow the application of methodological tools for project and program management in human resource management.

Hypothesis 2 (H2).

Recruiting personnel for medical institutions with the ability to quickly form teams under given functional and resource constraints caused by COVID-19 and military operations on the territory of Ukraine can be solved by introducing a project-oriented approach to resource management in a multi-project environment.

Hypothesis 3 (H3).

Using a donor-acceptor approach will ensure the transfer of resources between projects to increase the adaptability and resilience of teams and the viability of a medical institution.

Hypothesis 4 (H4).

Forming an adaptive, functionally redundant team will make it possible to provide both cold and hot backup, ensuring the redistribution of resources within the medical institution and in the district, regional, and national network of medical institutions.

Hypothesis 5 (H5).

In order to reduce the influence of the subjective factor and eliminate the corruption component in the formation of project teams, it is proposed to use a software package to form adaptive functionally redundant teams.

Figure 1 demonstrates the research framework presented for this study.

The paper solves the following tasks:

• Formalization of the recruitment process for healthcare settings;
• Formation of medical teams, taking into account the restrictions on requirements;
• Ensuring that teams become more resilient and adaptive as resource requirements change.

3.2. Conceptual Framework

When forming a staff of medical workers in stable operating conditions, it is advisable to use recruitment methods to create highly effective teams. However, given the Russian war in Ukraine and during the formation of brigades, the following features were revealed:

• a sharp reduction in the number of medical workers (both due to mobilization and migration (internal and external));
• a rapid change in the competence profile of medical personnel, taking into account the territorial sign (decrease in the level of qualification of personnel in Kharkiv due to the migration of highly qualified specialists to the west of Ukraine and abroad, raising the level of qualifications in the west of Ukraine. At the same time, the medical personnel who remained in Kharkiv acquired unique skills in providing medical care and management of patients with COVID-19 through an affordable set of medicines (phase of active hostilities in February-March 2022);
• inability to arrive at the place of work (lack of transport);
• selection of shifts, taking into account the possibility of transporting medical personnel (most of the medical personnel who remained to work in Kharkiv lived in the region, which led to the need to reduce the number of shifts and increase the duration of shifts so as not to expose personnel to the risk of shelling when traveling to and from work);
• lack of differentiation between anesthesia and therapeutic teams due to lack of staff and the inability to ensure the separation of infectious and non-infectious patients. In destroyed hospitals, with an insufficient number of personnel and the need to ensure evacuation to shelters during air raids and shelling, there was a problem in ensuring quarantine restrictions;
• lack of highly specialized doctors in the hospital and the need to involve doctors from other medical institutions for consultation or transport patients for consultation (which contributes to the spread of infectious diseases and nosocomial infections);
• the impossibility of online consultations by family doctors due to lack of Internet access and electricity.

The presence of specific restrictions leads to the fact that when managing personnel in wartime, it is necessary to provide a comprehensive solution to the problems of managing a structure, a composition, and stability of composition.

The limiting factor is a high degree of uncertainty due to military operations in some regions of Ukraine. The number of medical institutions ready to provide medical care and their technical condition (destruction of buildings, damage to critical infrastructure, damage to oxygen lines, energy supply systems, and water supply systems) changed under the influence of a hostile environment, which entails the transfer of patients and changes in the staff of a medical institution.

According to the regulatory framework, teams to work with patients with COVID-19 can only be formed from employees of hospitals where appropriate departments operate. Over the past year, the number of employees in medical institutions in Kharkiv has decreased by 2000 people, so there is not enough staff in ordinary departments. The situation has become even more aggravated considering the hostilities.

According to the National Health Service of Ukraine, anesthesiologists, cardiologists, therapists, nurses, and junior medical staff are needed in COVID teams. In addition, following the order on the organization of measures to minimize the spread of coronavirus disease (COVID-19), during the diagnostics [58], the teams must include a driver and at least one medical worker who is not associated with the provision of emergency medical care. Thus, when forming COVID teams (mobile teams), restrictions on attracting employees to teams following qualification and competence restrictions are significant.

Requirements regarding the level of doctors and their professional competence must be considered when forming medical teams for COVID response since this is a significant limitation for allocating COVID resources to hospitals that can deal with this. In conditions of congestion, it becomes necessary to combine medical workers from different medical institutions in a team.

The network of medical institutions can be represented as a multi-project environment (Figure 2).

Multi-project management is the management of a group of projects, programs, and portfolios of projects carried out by one or more industry organizations in a certain period to achieve the industry’s strategic goals or a certain circle of stakeholders [59,60].

With this approach, the i-th project can be the functioning of the i-th medical institution under given resource and time constraints. Since the work is carried out in a hostile environment (COVID-19, military operations), applying a project-oriented approach to human resource management is appropriate and contributes to improving the quality of medical care through the formation of adaptive functionally-reserved project teams.

If decomposition is necessary, it is possible to consider the work of particular areas (departments) as a project (mass individualization).

To formalize the process of determining the requirements for human resources, it is proposed to use the Backus–Naur form. A model of project resource support in the Backus–Naur notation was built, which made it possible to formalize the requirements for human resources in a multi-project medical environment:

<multi-project environments of healthcare settings> ::= <project 1> <project 2> ... <project n>

<multi-project team> ::= <multiproject management team> <project 1 team> <project 2 team> ... <project n team>

<multiproject resource> ::= <multiproject external resource> <multiproject own resource>

<external resource of multiproject> ::= <external resource of project 1> ... <external resource of project i> ... <external resource of project n>

<own resource> ::= <project 1 own resource> ... <project i own resource> ... <project n own resource>

<competency profile of the multi-project team> ::= <competency profile of the multi-project management team> <competency profile of the project team 1>...<competence profile of the project team i>... <competency profile of the project team n> <change trends competency profile of multi-project teams>.

<multi-project resource constraints> ::= <multi-project external resource constraints> <multi-project internal resource constraints> <multi-project temporary resource constraints> <permanent multi-project resource constraints> <resource restrictions>

<multi-project external resource constraints> ::= <project 1 external resource constraints> ... < project i external resource constraints> ... <project n external resource constraints>

<internal resource constraints of a multi-project> ::= <internal resource constraints of project 1> ... <internal resource constraints of project i> ... <internal resource constraints of project n>

<resource restrictions> ::= <combination restrictions> <conflict of interest> <regulatory framework><stakeholder conflict of interest><temporary suspension>.

Under temporary resource constraints in the multi-project environment of healthcare settings in Ukraine, we can consider logistics (restriction in the possibility of attracting employees due to lack of transport communications), suspension for a period of illness, and occupation. Under constant resource constraints, we will consider the regulatory framework of the Cabinet of Ministers of Ukraine and the National Health Service.

When describing an external resource of a multi-project, it should be noted that the issue is not a simple union of external resources of projects since the external resource for the i-th project can be the internal resource for the j-th project. Further detailing of resources will allow taking into account their type, qualifications, load level, etc.

In general, redistributing resources can be solved by applying a donor-acceptor approach to human resource management. In this case, some projects will act as donors for other projects within the same medical institution and within the framework of a multi-project environment.

Using a donor-acceptor approach will ensure the transfer of resources between projects to increase the adaptability and resilience of teams and the viability of a medical institution.

Let us introduce the following notation:

• n is the number of performers;
• m is the number of functions;
• Q = {q₁, q₂, ..., q_n} is a set of performers;
• A = {a₁, a₂, ..., a_m} is a a set of functions.

The modified responsibility matrix C indicates the ability of the performers to implement the relevant functions. The value c_ij indicates the characteristics of the i-th executor in implementing the j-th function. c_ij > 0 if the i-th worker can perform the j-th function with the given characteristic c_ij, c_ij = 0 if the i-th worker cannot perform the j-th function.

A group of performers or a group (denoted by G) is a subset of performers H = {h1, ..., ht} ∈Q that implement a subset of functions F = {f1, …, ft} ∈A.

Two groups G¹ and G² are called H equivalent (denoted by ${\mathrm{G}}^1\hspace{0.17em}\stackrel{\mathrm{H}}{\approx }\hspace{0.17em}{\mathrm{G}}^2$) if H¹ = H². H equivalent types are described using a type representative (composition of the group), formed by the lexicographic ordering of the numbers of performers included in the set H.

The operation of selecting performers that implement the j-th function (A (Q, j)):

A(Q, j) = q₁^jr_1j v … v q_i^jr_ij v … v q_n^jr_nj.

(1)

Definition of groups that do not intersect (⊗):

G¹ ⊗ G² = G¹ χ G², if H¹ ∩ H² = ∅, and G¹ ⊗ G² = G⁰ otherwise.

The operation of selecting groups containing the desired combination of performers (Δ):

G¹ Δ G² = G¹, if H² ∈ H¹, and G¹ Δ G² = G⁰ otherwise.

The paper uses the mathematical apparatus of the project-oriented resource management methodology for the formation of adaptive teams in a multi-project environment [60].

Functional transformation of H-equivalent groups:

Let there be two groups of workers G¹ and G² with a set of workers H = {h₁, …, h_t} and functions F¹ = {f¹₁, …, f¹_t} i F² = {f²₁, …, f²_t} implemented by them. The functional transformation of H-equivalent groups reflects the changes in the functions performed by the performers during the transition of the G¹ group to the G² group, and is described as follows:

Φ(G¹→G²) = (ϕ₁, … ϕ_t),

(2)

where ϕ_i describes the change of functions by the i-th executor (f¹_i→f²_i). If f¹_i = f²_i, then ϕ_I = 0.

The number of performers changing their functions L_ф and changing the characteristics of the group X_ф is determined as follows:

$${\mathrm{X}}_{\mathsf{\Phi }\hspace{0.17em}}=\hspace{0.17em}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{t}}({\mathrm{C}}_{\mathrm{i},{\mathrm{f}}_{\mathrm{i}}^1}}-\hspace{0.17em}{\mathrm{C}}_{\mathrm{i},{\mathrm{f}}_{\mathrm{i}}^2}),\dots {\mathrm{L}}_{\mathsf{\Phi }\hspace{0.17em}}=\hspace{0.17em}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{t}}\mathrm{sgn}(\left|{\mathrm{C}}_{\mathrm{i},{\mathrm{f}}_{\mathrm{i}}^1}\hspace{0.17em}-\hspace{0.17em}{\mathrm{C}}_{\mathrm{i},{\mathrm{f}}_{\mathrm{i}}^2}\right|}).$$

(3)

An adaptive approach to building and changing the work schedule provides for the restructuring of the project plan when various events occur:

• Reducing the availability of the performer;
• The inability of the executor to perform his functions (illness, injury, death, mobilization, migration);
• Limited availability (temporary disability, temporary exceptions);
• Changing tasks;
• Changing the conditions for the functioning of a medical institution;
• Changing deadlines or priorities.

Each action in the project requires resources to implement. Renewable (non-limited resources), non-renewable and limited resources attracted the most significant attention of researchers.

While renewable resources are periodically updated and can be attracted to projects from the external environment (incorporation, outsourcing, outstaffing), and their limited number may vary from one period to another, non-renewable resources are limited within the horizons of the project, and attraction of external resources is not allowed.

Depending on the task being solved, human resources can be considered renewable or non-renewable.

The composition of the team is considered irreplaceable. That is, the analysis of the possibility of solving the problem within the limits of the current composition of the team is carried out. A new H-equivalent group is formed with a new distribution of functions. At the same time, the functional changes in the group must cause the least number of reallocations of functions (schedule adaptations). If the functionality of the team members is “exhausted” and they cannot solve the problem, it is necessary to attract additional resources.

Consider changing functional responsibilities with a constant team composition (for example, when some performers cannot perform certain functions).

Consider a project team consisting of a set of executors H = {h₁, …, h_t}∈Q, which implement the corresponding functions F = {f₁, …, f_t}∈A and are described by the group G^K = q_h1^f1q_h2^f2…q_ht^ft.

The set of performers H = {h₁,…,h_t} included in the project team can implement various functions that correspond to H-equivalent groups. The constructive enumeration of which ∏^k is described as follows:

$${\mathsf{\prod }}^{\mathrm{k}}=\hspace{0.17em}\underset{\mathrm{j}=1}{\overset{m}{\chi }}\mathrm{A}(\mathrm{Q},\mathrm{j}).$$

(4)

The existing restrictions can be represented as follows:

∏⁻ = G⁻₁ v … v G⁻_z,

(5)

where z is the number of groups included in ∏⁻.

The solution of the problem:

• A constructive enumeration of groups is carried out, taking into account the restrictions:

$${\mathsf{\prod }}^{\mathsf{\Phi }}=\hspace{0.17em}\underset{j=1}{\overset{m}{\chi }}\mathrm{A}(\mathrm{Q},\mathrm{j})\hspace{0.17em}\mathsf{\Theta }(\underset{\mu =1}{\overset{z}{\mathrm{v}}}{\mathrm{G}}_{\mu }^{-}) = \underset{i=1}{\overset{s}{{\displaystyle \vee }}} {\mathrm{G}}_i^{\mathsf{\Phi }}.$$

(6)

2.

Functional transformations of H-equivalent groups of the form Φ(Gk→GiΦ) are considered. For each functional transformation, the number of performers is determined, changing their functions Liф and the characteristics of the group Xiф, i =1, …, s, and the preferred option is selected according to the given parameters.

4. Results

4.1. Collecting Initial Data

Resource requirements for hospitals serving COVID-19 patients are determined based on an analysis of the conditions for the functioning of health settings, the level of bed occupancy belonging to a particular quarantine zone of the region, and recommendations from the National Health Service of Ukraine. Correction of resource requirements when solving the problem of forming a project team in a multi-project environment is carried out based on monitoring the current state of the functioning object, taking into account regular resource audits.

4.2. Processing the Data

Let us consider an example.

Input data:

Initial data: 14 team members, 6 functions to be performed within one medical institution.

Task: form a project team that meets the requirements of the tasks with the maximum value of the team’s qualification score.

The modified competency matrix, taking into account the qualification assessment of the project team members, is shown in

Table 4. Modified competency matrix.

Q/A	a1	a2	a3	a4	a5	a6
q1	0	8	0	6	0	5
q2	7	0	0	6	0	0
q3	6	0	4	0	0	3
q4	0	5	0	4	0	0
q5	0	0	5	0	4	4
q6	5	0	6	0	0	4
q7	7	5	0	0	0	0
q8	4	0	3	0	6	0
q9	0	7	0	5	0	8
q10	0	0	8	0	5	0
q11	0	0	7	4	6	0
q12	6	0	0	0	5	0
q13	0	6	0	6	0	0
q14	0	0	0	6	7	0

.

Redundancy requirements are set, provided that one person performs one function:

T₁ = {3, 2, 3, 2, 2, 2}

Table 5. The results of the constructive enumeration of the groups ∏^k.

Function	Option	Quantity	Constructive Enum
a1	q2 q3 q6 q7 q8 q12	20	{1 1 1 0 0 0}, {1 1 0 1 0 0}, {1 1 0 0 1 0}, {1 1 0 0 0 1},{1 0 1 1 0 0}, {1 0 1 0 1 0}, {1 0 1 0 0 1}, {1 0 0 1 1 0}, {1 0 0 1 0 1}, {1 0 0 0 1 1}, {0 1 1 1 0 0}, {0 1 1 0 1 0}, {0 1 1 0 0 1}, {0 1 0 1 1 0}, {0 1 0 1 0 1}, {0 1 0 0 1 1}, {0 0 1 1 1 0}, {0 0 1 1 0 1}, {0 0 1 0 1 1}, {0 0 0 1 1 1}
a2	q1 q4 q7 q9 q13	10	{1 1 0 0 0}, {1 0 1 0 0}, {1 0 0 1 0}, {1 0 0 0 1}, {0 1 1 0 0}, {0 1 0 1 0}, {0 1 0 0 1}, {0 0 1 1 0}, {0 0 1 0 1}, {0 0 0 1 1}
a3	q3 q5 q6 q8 q10 q11	20	{1 1 1 0 0 0}, {1 1 0 1 0 0}, {1 1 0 0 1 0}, {1 1 0 0 0 1}, {1 0 1 1 0 0}, {1 0 1 0 1 0}, {1 0 1 0 0 1}, {1 0 0 1 1 0}, {1 0 0 1 0 1}, {1 0 0 0 1 1}, {0 1 1 1 0 0}, {0 1 1 0 1 0}, {0 1 1 0 0 1}, {0 1 0 1 1 0}, {0 1 0 1 0 1}, {0 1 0 0 1 1}, {0 0 1 1 1 0}, {0 0 1 1 0 1}, {0 0 1 0 1 1}, {0 0 0 1 1 1}
a4	q1 q2 q4 q9 q10 q11 q13 q14	21	{1 1 0 0 0 0 0 0}, {1 0 1 0 0 0 0 0}, {1 0 0 1 0 0 0 0}, {1 0 0 0 0 1 0 0}, {1 0 0 0 0 0 1 0}, {1 0 0 0 0 0 0 1}, {0 1 1 0 0 0 0 0}, {0 1 0 1 0 0 0 0}, {0 1 0 0 0 1 0 0}, {0 1 0 0 0 0 1 0}, {0 1 0 0 0 0 0 1}, {0 0 1 1 0 0 0 0}, {0 0 1 0 0 1 0 0}, {0 0 1 0 0 0 1 0}, {0 0 1 0 0 0 0 1}, {0 0 0 1 0 1 0 0}, {0 0 0 1 0 0 1 0}, {0 0 0 1 0 0 0 1}, {0 0 0 0 0 1 1 0}, {0 0 0 0 0 1 0 1}, {0 0 0 0 0 0 1 1}
a5	q5 q8 q10 q11 q12 q14	15	{ 1 1 0 0 0 0}, { 1 0 1 0 0 0}, { 1 0 0 1 0 0}, { 1 0 0 0 1 0}, { 1 0 0 0 0 1}, {0 1 1 0 0 0}, {0 1 0 1 0 0}, {0 1 0 0 1 0}, {0 1 0 0 0 1}, {0 0 1 1 0 0}, {0 0 1 0 1 0}, {0 0 1 0 0 1}, {0 0 0 1 1 0}, {0 0 0 1 0 1}, {0 0 0 0 1 1}
a6	q1 q3 q5 q6 q9	10	{1 1 0 0 0}, {1 0 1 0 0}, {1 0 0 1 0}, {1 0 0 0 1}, {0 1 1 0 0}, {0 1 0 1 0}, {0 1 0 0 1}, {0 0 1 1 0}, {0 0 1 0 1}, {0 0 0 1 1}

presents the results of a constructive enumeration of ∏^k groups, showing options for the distribution of work by performers, taking into account the requirements for redundancy.

Table 6. Result of constructive enumeration subject to constraints.

No. of Option	q1	q2	q3	q4	q5	q6	q7	q8	q9	q10	q11	q12	q13	q14	Xiф
1	2	1	1	4	6	1	2	3	6	3	3	5	4	5	83
2	6	1	1	2	3	1	2	5	6	3	3	5	4	4	84
3	2	1	1	2	3	6	1	3	6	3	5	5	4	4	84
4	2	1	1	2	3	6	1	5	6	3	3	5	4	4	88
5	2	1	1	2	6	3	1	5	6	3	3	5	4	4	89
6	2	4	1	2	6	3	1	5	6	3	3	1	4	5	90

shows the results of the process of constructing team formation options and the total qualification (s = 90).

A constructive enumeration of groups, taking into account the restrictions of ∏⁻, has the form:

∏^Φ = q₁²q₂¹ q₃¹ q₄⁴ q₅⁶ q₆¹ q₇² q₈³ q₉⁶ q₁₀³ q₁₁³ q₁₂⁵ q₁₃⁴ q₁₄⁵ v q₁⁶q₂¹ q₃¹ q₄² q₅³ q₆¹ q₇² q₈⁵ q₉⁶ q₁₀³ q₁₁³ q₁₂⁵ q₁₃⁴ q₁₄⁴ v q₁²q₂¹ q₃¹ q₄² q₅³ q₆⁶ q₇¹ q₈³ q₉⁶ q₁₀³ q₁₁⁵ q₁₂⁵ q₁₃⁴ q₁₄⁴ v q₁²q₂¹ q₃¹ q₄² q₅³ q₆⁶ q₇¹ q₈⁵ q₉⁶ q₁₀³ q₁₁³ q₁₂⁵ q₁₃⁴ q₁₄⁴ v q₁²q₂¹ q₃¹ q₄² q₅⁶ q₆³ q₇¹ q₈⁵ q₉⁶ q₁₀³ q₁₁³ q₁₂⁵ q₁₃⁴ q₁₄⁴ v q₁²q₂⁴ q₃¹ q₄² q₅⁶ q₆³ q₇¹ q₈⁵ q₉⁶ q₁₀³ q₁₁³ q₁₂¹ q₁₃⁴ q₁₄⁵ == G₁^Φ v … v G₆^Φ.

For each functional transformation, the number of performers is determined, changing their functions L_i^ф and the characteristics of the group X_i^ф, i = 1, …, s.

The optimal variant according to the criterion of total qualification is the distribution variant {2, 4, 1, 2, 6, 3, 1, 5, 6, 3, 3, 1, 4, 5}.

The graph model of the organizational structure of the project team is shown in Figure 3.

As a result of the analysis of changes in resource requirements, new requirements for redundancy were determined:

T₂ = {2, 3, 2, 2, 3, 2}

The results of the redistribution of project team members are shown in

Table 7. Options for redistributing functions to project teams after redistribution.

No. of Option	q1	q2	q3	q4	q5	q6	q7	q8	q9	q10	q11	q12	q13	q14	Xiф
1	2	1	1	2	3	6	2	3	6	5	4	5	4	5	78
2	2	1	1	2	3	6	2	3	6	5	5	5	4	4	79
3	2	1	1	2	3	6	2	5	6	3	4	5	4	5	84
4	2	1	1	2	3	6	2	5	6	3	5	5	4	4	85
5	2	1	1	2	6	3	2	5	6	3	4	5	4	5	85
6	2	1	1	2	6	3	2	5	6	3	5	5	4	4	86
7	2	4	1	2	6	3	1	5	6	3	5	5	2	4	87
8	2	4	1	2	6	3	2	5	6	3	5	1	4	5	87

.

The analysis of the obtained results shows that option number 8 has the largest characteristic (87) with the least number of changes (2).

Graph models of the organizational structure of project teams for these options for the distribution of functions are shown in Figure 4 and Figure 5. The change in the distribution of functions is represented by a dotted line.

The change in the profile of the characteristics of the project team as a result of the reallocation is shown in

Table 8. Changing the profile of project team characteristics as a result of redeployment.

Redistribution Option	Team Performance Profile		Profile Changes	Liф
	Primary	After Redistribution
1	90	78	−12	8
2	90	79	−11	9
3	90	84	−6	6
4	90	85	−5	7
5	90	85	−5	4
6	90	86	−4	5
7	90	87	−3	4
8	90	87	−3	2

.

5. Discussion

The options for building a functionally redundant adaptive team in a multi-project environment of medical institutions are considered. Functional redundancy is provided by considering the stage of requirements definition, taking into account the trends in the competence profile of teams in a multi-project medical environment. Adaptability and resilience are ensured by the possibility of redistributing resources between projects, both within the projects of one institution and between projects of different institutions that form the medical environment.

In the considered example, the human resource management problem is solved, and a command is received that satisfies the redundancy requirement (3, 2, 3, 2, 2, 2). The maximum value of the team’s qualification score corresponds to option number 6 of the function distribution {2, 4, 1, 2, 6, 3, 1, 5, 6, 3, 3, 1, 4, 5}. The use of formal transformations in the formation of the project team showed an increase in the efficiency of the use of human resources in the formation of teams according to the classification of Patanakul and Milosevic [59]; according to the efficiency criteria, the distribution of work between the contractors in the project and the distribution of resources increased the characteristics level of the team (qualification assessment of the team) by 8%.

As a result of the analysis of changes in resource requirements (2, 3, 2, 2, 3, 2), the modeling of the redistribution of performers between jobs was carried out, taking into account the initial distribution. Eight options for the redistribution of performers were found. The change in the profile of the team’s characteristics ranges from −13% (option number 1) to −2% compared to the original allocation of resources. The number of changes (the number of redistributed functions) ranges from 64% for option number 2 to 14% (option number 8) concerning the total number of functional links. Redistribution variant 8 was chosen as the optimal one (the profile of the characteristics of the project team is 90, and the number of changes is 2).

In order to reduce the influence of the subjective factor and eliminate the corruption component in the formation of project teams, it is proposed to use a software package for the formation of functionally redundant adaptive teams: “FRAT building information system” (copyright of Ukrainian Institute of Intellectual Property No. 112096), “Agile multi-project team management” (copyright of Ukrainian Institute of Intellectual Property No. 100715).

6. Conclusions

An analysis was made of the functioning of the multi-project environment of healthcare settings during the COVID-19 pandemic and hostilities. It is proposed to use the Backus–Naur form to formalize the process of determining the requirements for human resources. It is proposed to use the methodology of a project-oriented approach to resource management in a multi-project environment to form a functionally redundant adaptive resolute team in a multi-project group of healthcare settings.

• The scientific novelty of the proposed approach is as follows:
• It is proposed to consider the network of healthcare settings as a multi-project environment with the subsequent application of the methodology of a project-oriented approach to resource management in a multi-project environment.
• A model of project resource support was built in the Backus–Naur notation, which made it possible to formalize the requirements for human resources in a multi-project healthcare environment.
• A method of forming a functionally redundant adaptive resolute team based on formal transformations in a multi-project medical environment is proposed.

The solutions obtained were tested by examples, which showed the method’s effectiveness. It is proposed to use the developed specialized software “FRAT building information system”, and “Agile multi-project team management” to automate the process of human resource management in a multi-project medical environment.

The proposed approach acquires particular relevance in the context of Russia’s military invasion of Ukraine and the post-war reconstruction of Ukraine. Unpredictable changes in energy systems and the uncertainty of available resources dictate the need to implement automated solutions for reallocating resources in critical infrastructure institutions.

Future Research: A promising area of research is the development of instrumental decision-making support in forming a project team with functional redundancy for sustainable project management. The proposed ideas can be used in the flexible transformation of human resource management processes in a multi-project healthcare environment.