A Continuous Monitoring and Reallocation Method for Successful Decisions in Change Management

Abstract

Businesses and organizations often struggle to cope in a rapidly changing and competitive environment, requiring changes with increasing frequency and complexity. The evolution of information systems has enabled direct access to information and data, which can be utilized for the effective implementation of changes. This usually requires managing resistance to change, which is often presented by employees. The aim of this study is to address the problem of change management in order to limit the decline in overall performance during the critical period of change and to accelerate the implementation of change. This study provides a new innovative approach to managing employee resistance during the change process based on a continuous monitoring and reallocation algorithm. The proposed method introduces the idea of solving the human resource allocation problem by continuously readjusting staff allocation during the change process. The Hungarian algorithm is used to optimize assignments. In this way, the resistance of each employee is taken into account regularly, and the assignment can be altered in the early stages of change. The new method is mathematically formulated and described in detail through an algorithm, which is then used in experiments. The proposed method of frequently reallocating human resources to tasks leads to better overall performance and improves decision making during change processes. The experimental results show that the new approach significantly increases the total performance by up to 124% when compared to existing change management approaches and reduces the time required to achieve the desired state by up to 20%. Thus, the enhanced management of human resistance to change provides distinct advantages over traditional methods by ensuring more dynamic, timely, and adaptive resource allocation during the change period, ultimately leading to successful decision making and sustainable change management.

1. Introduction

Organizations and businesses often make changes to deal with challenges and improve their performance and effectiveness [1,2]. However, these changes are often unsuccessful. About 70% of changes are not completed on time or are abandoned [2,3,4]. Many models and methods have been proposed for managing change, and most of them have a defined sequence of steps for successful management [5,6,7]. One of the most important factors for the success or failure of a change is the behavior of employees, especially their resistance to the change process. Employees who are affected by an upcoming change can experience emotional turmoil [8,9,10,11]. Thus, many unsuccessful attempts to implement changes are due to such behaviors in employees [12,13,14]. Individuals have different typical reactions to changing situations: while some accept change, others tend to resist it [15]. Employee performance and resistance to change (RtC) are related to the type of work provided [16,17]. Human resources can play a decisive role in the success of an organization, especially in the case of an upcoming change. It is important for managers to seek the most effective means of optimizing the use and distribution of available resources across different services or systems in order to optimize certain functions related to performance and productivity. The significance of human resource allocation has been recognized in numerous business sectors [18].

The original version of the assignment problem concerns the allocation of n resources to n activities in order to minimize the cost or maximize the benefit with the following constraints: each resource should be used in only one activity, and each activity should use only one resource. When human resources are being allocated, the problem is known as the human resource allocation problem (HRAP) [18]. In the change management literature, the methods proposed for decision making are based on qualitative and quantitative controls for the collection of information, including through questionnaires and interviews, personnel training, and technical briefings, as well as the means of communication to prepare for change, the selection of people who will be the agents or leader of the change, and so on [6,19,20].

Arazmjoo and Rahmanseresht [21] presented a dynamic meta-heuristic model of effecting organizational change, which involves smoothly directing and routinizing change according to the specific situation relevant to every change attempt. The system model of organizational change proposed by Maes and Hootegem [22] views organizational change not as a linear process but, instead, as a multidimensional mechanism.

McDermott et al. [23] present a practical approach to assessing organizational readiness and maturity for continuous improvement, identifying areas of strength that can serve as cornerstones of an initiative, as well as areas that would benefit from further development. The study by Srivastava and Agrawal [24] examines employees’ turnover intentions in the context of resistance to change, analyzing the mediating role of burnout and the moderating role of perceived organizational support in this relationship.

These methods are very time-consuming, meaning that RtC is not addressed in a timely manner, possibly resulting in the abandonment or incomplete implementation of changes. Consequently, there are several research gaps in the literature:

• Existing models do not consider real-time adaptation to employee resistance during the change process.
• Current methodologies that incorporate communication through interviews, seminars, and technical briefings are time-consuming, which makes them unable to address RtC in a timely manner. This frequently results in change failure.
• Current methods treat human resource allocation as a fixed process, without considering the dynamic nature of employee behavior or resistance during change.

The main innovation of the proposed method is that the staff allocation is readjusted at regular intervals during the process of change. In this way, the RtC of each employee is taken into account during the change period, and consequently, decisions regarding the assignment of personnel can also be made. This process is expected to reduce the frequency of failures in organizational changes. Thus, the research objectives are as follows:

• Develop a dynamic resource allocation model that continuously adjusts based on the real-time monitoring of employee performance.
• Ensure that resources are allocated effectively throughout the change process.
• Evaluate the effectiveness of real-time interventions and monitoring in addressing RtC, reducing the likelihood of abandonment or incomplete implementation of organizational changes.
• Compare the proposed dynamic change management model with the traditional static model in terms of their ability to manage RtC and improve the success rate of change initiatives.

The rest of this paper is organized as follows. In Section 2, a literature review is presented, including the state of the art in change management models and human resource allocation problems. The proposed method is described in Section 3, which includes a description of the problem and the proposed method application. Experimental results and a discussion are presented in Section 4. Section 5 provides the conclusions and limitations.

2. State of the Art

2.1. Change Management Models

The contemporary literature contains a number of models and strategies that aim to optimize the introduction and management of changes. Historically, the first change management model was proposed in 1947 by Kurt Lewin, who described the change management process in three stages, “Unfreeze”, “Change”, and “Freeze”, as shown in Figure 1. The first stage includes recognizing the willingness to change. In this stage, there is a balance between forces that resist change and those that are positive toward change. The process of change has not started, so these forces are not yet apparent. The second stage is the process of “Change” that will lead to the new state. Here, the conflicting forces emerge. Initially, the forces that resist the change overcome the driving forces that are positive. All necessary actions to reduce RtC must be taken. The third stage is “Freeze”, encompassing the consolidation of the change and stabilization in the new situation [25,26].

Beer et al. [27] presented a six-step management model of effective change, including reorganizing employee roles, responsibilities, and relationships to solve specific business issues by breaking them into smaller units with clearly defined goals. In the final stage, the change must be monitored and adjusted. Kotter and Schlesinger [10] proposed an eight-step change management model that is also highly relevant to successfully implementing organizational change. The steps that must be followed are described in detail, emphasizing the preparation for, participation in, and acceptance of the change by employees. The ADKAR model focuses on people’s adaptation to change rather than the change itself. ADKAR is an acronym for Awareness, Desire, Knowledge, Ability, and Reinforcement, the five tangible and concrete outcomes that people need to achieve for a change to be sustainable [28,29]. All of the above models follow a linear sequence of steps from the initiation of the change to stabilization and the establishment of the new situation. There are also approaches that consider the importance of taking action before the upcoming change. According to these methods, training, readiness for change, communication of change, and commitment to change play important roles [6,8,30,31,32].

2.2. Human Resource Allocation Problem

The first algorithmic solution to the assignment problem was developed and published by Kuhn [33] with the so-called Hungarian method. The name was given in honor of two Hungarian mathematicians who inspired Kuhn [33] in the implementation of the algorithm. The original version of the assignment problem is concerned with allocating n resources (persons) to n activities (tasks) so as to minimize the cost or maximize the benefit, subject to the constraints that one resource is used in a single activity and that each activity uses only one resource. The optimal solution is the one that minimizes the total cost, as defined in Equation (1). The HRAP is an adaptation of the assignment problem when the number of tasks to be assigned is equal to human resources [18]. The mathematical model of the assignment problem is as follows:

$$\mathrm{Minimize}\sum _{i=1}^n\sum _{j=1}^n{c}_{ij}{x}_{ij}$$

(1)

subject to the constraints

$$\sum _{i=1}^n{x}_{ij}=1\forall j=1,\dots ,n$$

(2)

$$\sum _{j=1}^n{x}_{ij}=1\forall i=1,\dots ,n$$

(3)

$$x_{ij}=\{\begin{array}{cc}1& \mathrm{if}\mathrm{worker}i\mathrm{is}\mathrm{assigned}\mathrm{to}\mathrm{task}j\\ 0& \mathrm{otherwise}\end{array}$$

(4)

where n is the total number of tasks and workers, i is the index of the worker ($i=1,2,\dots ,n$), j is the index of the task ($j=1,2,\dots ,n$), and $c_{ij}$ is the cost of task j when worker i is assigned. Both indexes $i,j$ end at n because the number of workers is equal to the number of tasks.

The importance of the optimal solution to the human resource allocation problem has been widely studied in the literature, and various mathematical models and algorithms have been proposed. Several approaches to solving the HRAP in different real-life scenarios are presented by Bouajaja and Dridi [18]. There are exact methods, branch-and-bound algorithms, dynamic programming, linear programming, and the Hungarian method [34,35]. When the above methodologies cannot achieve solutions accurately and relatively quickly due to the high dimensions of these problems, researchers opt for heuristics or meta-heuristic algorithms [36], Tabu search [37], simulated annealing [38], algorithms inspired by nature, especially by ant colonies (ant colony optimization) [39,40], and hybrid algorithms [41]. These algorithms are applied in various fields, such as production management [36,42], healthcare systems for the allocation of nursing staff [43,44], project management [45,46], organization maintenance management [47], hotel unit management [48,49], education [35], and the military [50]. Panagiotopoulos et al. [51] introduced and tested a Nurse Reallocation (NuRe) method for addressing and managing nurses’ resistance during Electronic Health Record (EHR) implementation. The results of the experiments show that the early stages are the critical time frame for the hospital manager to reallocate nurses [51].

3. The Continuous Monitoring and Reallocation (CoMoRe) Method

3.1. Problem Description

The problem that we attempted to solve in this work concerns the management of employee resistance to change. Although the change is intended to improve performance through the transformation of the business, we usually see the opposite. This happens in many cases because the expected change is not fully implemented as a result of strong resistance to transformation efforts. The process of change is described by a change curve in the literature [5]. First, there is a sharp drop in employee performance, and then it takes a significant amount of time for the desired result to be achieved. In many cases, this drop and the corresponding time can be so critical that the change plan is ultimately abandoned.

The NuRe method [51] is the first attempt to extend the classic idea of the HRAP by incorporating continuous monitoring. During the period of change, the manager continuously monitors staff performance and decides when to perform a single reallocation of staff to tasks. This reallocation reduces the overall resistance of nurses to using a new health information system.

The proposed continuous monitoring and reallocation (CoMoRe) method extends the idea of the NuRe method by continuously readjusting staff allocation throughout the process of change at regular time intervals. In this way, the RtC of each employee is taken into account regularly, and the assignment can be altered in the early stages of change. It is posited that through implementing this regular readjustment, the task performed by each worker will be optimized for maximum performance. Although the idea of continuous monitoring and reallocation can be applied to all change management problems, in the following, it is applied to a simple problem governed by the following constraints:

(a)

Every task is assigned to only one worker.

(b)

Every worker is assigned to only one task.

In addition, the following assumptions are made:

(a)

Each worker will be able to carry out all available tasks.

(b)

Each worker has an initial known performance for each task.

(c)

The resistance presented by each worker during the change period follows the change curve model [5].

More specifically, suppose there is a business that wants to make a change in a process that includes n jobs carried out by n workers. The business aims to be the most productive and utilize human resources to achieve the greatest overall performance. This can be accomplished by optimizing staff allocation. When the change process begins, individual performance will change due to the effect of resistance to change. The goal of the business remains the same. In addition, the business wants to minimize the time required for change implementation and achieve a positive effect on overall performance. The formulation of this problem is based on the mathematical model of the HRAP. The objective function includes the performance $\left(Pij\right)$ of each employee $\left(i\right)$ in each task $\left(j\right)$. This objective function should be maximized to achieve the best performance. The mathematical model of performance is formulated in the following.

Proposed mathematical model—objective function:

$$\mathrm{Maximize}\sum _{i=1}^n\sum _{j=1}^n{P}_{ij}{x}_{ij}$$

(5)

where $Pij$ is the performance when worker i is assigned to task j, subject to the following constraints:

$$\sum _{i=1}^n{x}_{ij}=1\forall j=1,\dots ,n$$

(6)

$$\sum _{j=1}^n{x}_{ij}=1\forall i=1,\dots ,n$$

(7)

$$x_{ij}=\{\begin{array}{cc}1& \mathrm{if}\mathrm{worker}i\mathrm{is}\mathrm{assigned}\mathrm{to}\mathrm{task}j\\ 0& \mathrm{otherwise}\end{array}$$

(8)

3.2. Description of the Proposed Method Application

Initially, when the change begins, the first allocation will apply Equation (5) and achieve maximum performance by allocating each employee to a specific task. After this point, RtC will emerge and begin to affect the performance of the workers. The innovative idea of the proposed method is that it considers changes in performance at regular intervals and optimally reassigns human resources. Thus, the RtC of each employee is considered during the change, and the overall performance is improved with this reallocation. Performance is considered time-dependent and can be described by Equation (9) [51]:

$$P_{ij}(t+1)=P_{ij}\left(t\right)-R_{ij}\left(t\right)$$

(9)

where $R_{ij}\left(t\right)$ is RtC at time t, $P_{ij}\left(t\right)$ is performance at time t, and $P_{ij}(t+1)$ is performance at time $t+1$.

In order to apply the proposed method, the following steps should be followed:

Step 1:

The initial values of performance ($P_{ij}\left(t\right),t=0$) achieved by each worker and for each task are defined in a matrix of size $n\times n$.

Step 2:

The allocation of workers to tasks is optimized through the implementation of the Hungarian algorithm. This approach results in the maximum total performance according to Equation (5).

Step 3:

The total performance is calculated as the sum of performance values for optimal pairs $i,j$, as determined in step 2.

Step 4:

The values of resistance to change ($R_{ij}\left(t\right)$) that are presented by each worker for each task are calculated and stored in a matrix of size $n\times n$.

Step 5:

The new values of performance ($P_{ij}\left(t\right),t=t+1$) are recalculated using Equation (9).

Step 6:

If the change period (T) is not complete, steps 2-6 are repeated with the new matrix values.

Step 7:

When the change period (T) is complete, the allocation of workers to tasks is optimized through a final implementation of the Hungarian algorithm. This maximizes total performance according to Equation (5).

Step 8:

Finally, based on the optimal allocation (determined in step 7), the total performance is calculated as the sum of performance values for optimal pairs $i,j$.

The flowchart for this algorithm is shown in Figure 2, and the pseudocode follows as Algorithm 1.

Algorithm 1 CoMoRe.

1: Initialize $P_{ij}(t=0)$   2: repeat   3:      OptimalAllocation = HungarianAlgorithm($P_{ij}\left(t\right)$)   4:      TotalPerformance = 0   5:      for all $(i,j)$ in OptimalAllocation do   6:            TotalPerformance += $P_{ij}\left(t\right)\ast x_{ij}$   7:      end for   8:      $R_{ij}\left(t\right)$ = CalculateResistance()   9:      for $i=1,\dots ,n$ do 10:            for $j=1,\dots ,n$ do 11:                 $P_{ij}(t+1)=P_{ij}\left(t\right)-R_{ij}\left(t\right)$ 12:            end for 13:      end for 14:      $t=t+1$ 15: until  $t=T$ 16: OptimalAllocation = HungarianAlgorithm($P_{ij}(t=T)$) 17: TotalPerformance = 0 18: for all $(i,j)$ in OptimalAllocation do 19:      TotalPerformance += $P_{ij}(t=T)\ast x_{ij}$ 20: end for

4. Experiments and Results

Appropriate experiments were designed and carried out to verify the efficiency of the proposed CoMoRe method. This section presents the graphical and numerical results of experimental testing. The application of the method is studied, and the advantages that arise from the experimental results are analyzed. The developed simulation program uses the Python programming language in the Scientific Python development environment (Spyder) on Anaconda Navigator.

According to change models, human behavior varies. As presented in Section 3, it starts with denial, which gradually grows and then manifests as increasing resistance. Then, acceptance slowly begins, and finally, the performance significantly increases.

The experiments involved a hypothetical company that is implementing a change. In the first experiment, the company uses 10 workers for 10 corresponding tasks ($n=10$). In the second experiment, the number of workers and tasks are increased to $n=100$ in order to study the performance and time for larger values. The period of change, in which human behavior in response to change was simulated, was split into 15 intervals ($T=15$) for both experiments.

The performance values are measured as a percentage of the maximum initial performance, which is always assumed to be 100%. Figure 3 [51] shows the simulated curve obtained with the change management model, which reflects simulated human behavior in the phase of change. Although the simulated curve in Figure 3 shows the typical behavior of employees in a period of change, the specific values of performance are not always constant. This uncertainty in performance values was modeled in the experiment by applying a symmetric triangular probability distribution to the values of performance and by repeating the experiment numerous times by using these random performance values. The triangular distribution was selected because for the phenomenon described by the change curve, only the average performance decline is known, having been derived from many observations in the past. It is also known that these changes are not abrupt, i.e., the standard deviation of the distribution is relatively small, and the values become less probable as we move away from the mean. Furthermore, all tailed distributions are rejected because they could lead to negative performance, which is not expected for this phenomenon. Thus, the triangular distribution is the easiest and best way to describe the uncertainty in resistance to change.

Figure 3 also presents (in green) the random performance values when the simulation was repeated 100 times. The performance change simulation procedure presented in Figure 3, which shows the performance distribution during the change process, was used as the ground-truth change curve in the following experiments and is named the Classical Change Management Model (CCMM).

Based on the simulation of the CCMM change curve (Figure 3), employee behavior was simulated in this experiment using the parameters in

Table 1. Limits of resistance in triangular distribution (red indicates positive resistance; green indicates negative resistance).

TIME (t)	0	1	2	3	4	5	6	7
Resistance limits	[0,20]	[0,44]	[0,30]	[0,18]	[0,14]	[0,12]	[0,8]	[-]
TIME (t)	8	9	10	11	12	13	14	15
Resistance limits	[0,−8]	[0,−12]	[0,−20]	[0,−22]	[0,−30]	[0,−34]	[0,−34]	[-]

[51], which shows the minimum and maximum values of resistance for every time interval, from t = 0 to t = 15. The interval limits are considered the lower and upper limits of the triangular distribution, which provided random values for resistance that were used during repetitions of the experiments. Red indicates that the resistance values are positive, meaning employees have a negative attitude toward the change. Green indicates “negative resistance”, which, in fact, means employees have a positive attitude toward the change. By using these resistance values and Equation (9), the corresponding performance values can be calculated for the next interval of time.

4.1. First Experiment: Algorithm Implementation

The application of the algorithm starts at time $t=0$, along with the initiation of the change period. Following the algorithm flowchart presented in Figure 2, in step 1, a $10\times 10$ performance matrix $P_{ij}$ contains the initial values. These values are randomly selected from the range between 90% and 100% based on assumption (a) in the problem description in Section 3.1 (each worker will be able to carry out all available tasks). Consequently, each worker’s performance in each possible task takes random values from 90 to 100 as an initial condition of the algorithm application. An example of such random values is shown in

Table 2. Initial performance matrix $P_{ij}(t=0)$ for each employee and task.

Performance (${\mathit{P}}_{\mathit{ij}}\mathbf{(}\mathit{t}\mathbf{=}\mathbf{0}\mathbf{)}$)
Human	Tasks ($\mathit{j}$)
Resources ($\mathit{i}$)	1	2	3	4	5	6	7	8	9	10
1	97	91	90	93	91	96	97	97	96	98
2	98	99	96	95	96	92	99	94	99	90
3	94	93	90	94	96	94	95	92	99	90
4	99	92	97	97	97	94	90	91	95	99
5	92	97	90	90	99	91	97	94	98	92
6	94	91	94	95	97	91	94	92	96	97
7	98	95	91	99	94	98	98	99	94	98
8	98	94	98	95	92	95	97	90	91	98
9	93	92	90	90	95	93	94	97	95	96
10	95	97	91	97	90	90	95	93	93	91

.

In step 2, the Hungarian algorithm is employed to identify the task that each employee will perform to achieve the overall maximum performance. The optimal human resource allocation is demonstrated in Table 2. The bold numbers correspond to the optimal allocation.

The third step of the algorithm is to calculate the total performance at $t=0$ according to the optimal human resource allocation.

Table 3. Optimal allocation at $t=0$.

Human Resources (i)	Tasks (j)	Performance (${\mathit{P}}_{\mathit{ij}}\mathbf{(}\mathit{t}\mathbf{=}\mathbf{0}\mathbf{)}$)
1	7	97
2	2	99
3	9	99
4	1	99
5	5	99
6	10	97
7	6	98
8	3	98
9	8	97
10	4	97
Total Performance		980

simplifies Table 2 by presenting only the optimal allocation of human resources to tasks, the corresponding performance values of the workers, and the total performance, which is calculated as the sum of all performance values. In a hypothetical scenario where all ten workers exhibit maximum performance levels in all tasks, the maximum total performance would be 1000 ($100\times 10$). However, in this example, the optimal allocation results in a total performance of 980.

At this point, the resistance to change is not yet apparent, and the calculated total performance is the initial state of the algorithm. This optimal allocation and the corresponding total performance will be used as the starting point for both the proposed method and the CCMM to facilitate a fair comparison between the two methods.

In step 4, the resistance to change emerges, leading to a reduction in employee performance. A $10\times 10$ resistance matrix ($R_{ij}$) is created for each employee and task, with random values in the range from 0 to 20, according to Table 1, for $t=0$. An illustrative example of these random values is provided in

Table 4. Resistance matrix for each employee and task.

Resistance (${\mathit{R}}_{\mathit{ij}}\mathbf{(}\mathit{t}\mathbf{=}\mathbf{0}\mathbf{)}$)
Human	Tasks ($\mathit{j}$)
Resources ($\mathit{i}$)	1	2	3	4	5	6	7	8	9	10
1	10	0	6	5	12	11	3	17	17	7
2	7	1	11	2	6	16	17	16	16	17
3	10	1	14	18	6	15	6	7	6	7
4	10	17	6	7	15	12	1	11	9	2
5	15	16	16	15	9	13	4	14	3	10
6	2	14	2	9	1	1	5	13	0	1
7	2	1	1	14	11	12	1	7	5	11
8	11	10	11	9	0	17	4	15	15	1
9	8	5	13	17	7	10	3	19	1	17
10	3	6	2	12	15	15	14	5	18	2

.

Subsequently, in step 5, a new performance matrix for the next time interval (t = 1) is calculated using Equation (9). Steps 2 to 6 will be repeated until the end of the change period (t = 15). In all these iterations, the Hungarian algorithm is used to reallocate human resources to tasks, and the total performance is calculated again. New resistance matrices are created with random values in a range according to Table 3, from $t=1$ to $t=14$. A new performance matrix is calculated in every iteration according to Equation (9).

In step 7, when the change period ends (t = 15), the Hungarian algorithm is used one last time to reallocate human resources to tasks. Finally, in step 8, the total performance is calculated according to the last human resource reallocation.

The main innovation of the proposed method (CoMoRe) compared to the CCMM is that it monitors and provides decisions for reallocating human resources to tasks during the change period. On the contrary, the classical method keeps workers in the same initial positions throughout the change period, so it cannot take advantage of new information about people’s ability to accept change during the change period.

An example of reallocations during the iterative process (from t = 0 to t = 14) is shown in

Table 5. An example of reallocations during algorithm iterations.

Time (t)	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Human	Tasks ($\mathit{j}$)
Resources ($\mathit{i}$)
1	7	4	6	6	6	10	10	10	7	7	7	7	7	7	7
2	2	2	1	4	4	4	4	4	4	4	4	4	4	4	4
3	9	5	9	9	9	9	9	9	9	9	9	9	9	9	9
4	1	3	10	5	3	3	3	3	3	3	3	3	3	3	3
5	5	7	8	10	10	7	7	7	10	10	10	10	10	10	10
6	10	6	4	3	2	2	2	2	2	2	2	2	2	2	2
7	6	1	7	7	7	6	6	6	6	6	6	6	6	6	6
8	3	10	5	8	8	8	8	8	8	8	8	8	8	8	8
9	8	9	2	2	5	5	5	5	5	5	5	5	5	5	5
10	4	8	3	1	1	1	1	1	1	1	1	1	1	1	1

. For example, worker 2 ($i=2$) initially works at task 2 at $t=0$ and $t=1$ and then works at task 1 at $t=2$ and at task 4 from $t=3$ until the end of the change period. The employees that perform a specific task can also be observed. For example, task 2 ($j=2$) is initially performed by worker 2 at $t=0$ and $t=1$, then by worker 9 at $t=2$ and $t=3$, and finally, by worker 6 from $t=4$ until the end of the change period. Reallocations are more frequent in the early stages. Bold numbers in Table 5 indicate when human resources remain at the same task until the end of the change period.

4.2. First Experiment’s Results and Analysis

In order to test the proposed CoMoRe method, we ran the algorithm repeatedly, trying to minimize the possibility that the results were influenced by random values. These random values were used for the initial state of the performance and resistance matrices used during the iterations. Starting with 100 repetitions, the algorithm was also repeated 1.000, 10.000, and 100.000 times. The average performance was calculated for each case. The results of 10.000 repetitions were not significantly different from those of 100.000 repetitions, so there was no need to further increase the number of repetitions. Figure 4 compares the average results of the CoMoRe method with the results of the CCMM based on the classical change curve.

Table 6. Comparison of total performance results for 100, 1.000, 10.000, and 100.000 repetitions between the proposed CoMoRe method and the CCMM method for 10 workers and tasks ($n=10$).

Total Performance
Repetitions	100		1.000		10.000		100.000
Time ($\mathit{t}$)	CCMM	CoMoRe	CCMM	CoMoRe	CCMM	CoMoRe	CCMM	CoMoRe
0	981	981	981	981	981	981	981	981
1	885	932	887	933	887	933	886	933
2	666	820	671	818	672	819	671	819
3	521	707	526	707	526	708	526	708
4	434	634	441	632	441	634	441	633
5	369	575	376	573	376	575	376	575
6	312	524	321	522	321	524	321	524
7	277	491	287	489	286	491	286	491
8	277	491	287	489	286	491	286	491
9	311	525	322	524	321	526	321	526
10	365	579	377	579	377	581	376	581
11	459	670	473	675	472	676	472	676
12	562	775	578	780	577	782	576	781
13	707	921	724	925	722	926	722	926
14	877	1082	889	1091	887	1091	886	1091
15	1046	1246	1054	1255	1051	1256	1051	1256

summarizes the corresponding arithmetic values used to create the curves in Figure 4.

Figure 4 and Table 6 show that the CoMoRe method achieves a higher total performance than the CCMM method, and the advantages are obvious. The graphical representation and corresponding arithmetic values indicate that the total performance with the CoMoRe method is better at all time intervals of change. Moreover, the drop in total performance is much lower. As shown in Figure 4a–d, both methods start from the same value, which is the average total performance for 100, 1.000, 10.000, and 100.000 repetitions, respectively. As observed in these figures, the improvement occurs mainly during early time intervals and is maintained until the end of the change period. Another useful observation from the curves is that when using the CoMoRe method, the total performance is always significantly better than that obtained with the classical method; this improvement in performance favors a commitment to change and reduces the likelihood that the change process will be abandoned, which is often observed in companies and organizations when performance drops to significantly low levels.

Table 6 shows that in all experiments (100, 1.000, 10.000, and 100.000 repetitions), the average total performance starts ($t=0$) at a value of 981 in both methods. From t = 1 to t = 7, the overall performance for the proposed CoMoRe method begins to be significantly better than that for the CCMM method. At t = 7, the lowest total performance has a value of 491 for CoMoRe versus 286 for the CCMM. This is the most critical point in the change process. At the next time step, the performance starts to increase. At t = 14 for 100.000 iterations, the total performance for the proposed CoMoRe method is 1091 and has exceeded the initial total performance (981), while the total performance for the CCMM is less than the initial total performance, with a value of 886. Thus, the new desired state that improves performance over the initial state is reached in a shorter time.

Table 7. Comparison of Total Performance Improvement for 100, 1.000, 10.000, and 100.000 repetitions between CoMoRe and CCMM methods for 10 workers and tasks ($n=10$).

	Total Performance Improvement
	Repetitions	100	1.000	10.000	100.000
	0	0.00%	0.00%	0.00%	0.00%
	1	5.27%	5.25%	5.28%	5.30%
	2	23.12%	21.95%	21.99%	22.01%
	3	35.83%	34.33%	34.52%	34.43%
	4	46.10%	43.31%	43.56%	43.52%
	5	55.87%	52.28%	52.66%	52.66%
	6	68.07%	62.65%	63.15%	63.09%
Time$\left(t\right)$	7	77.54%	70.75%	71.51%	71.44%
	8	77.54%	70.75%	71.51%	71.44%
	9	68.85%	63.01%	63.69%	63.65%
	10	58.40%	53.64%	54.30%	54.36%
	11	46.04%	42.77%	43.40%	43.38%
	12	37.85%	34.90%	35.49%	35.47%
	13	30.21%	27.79%	28.33%	28.33%
	14	23.35%	22.75%	23.07%	23.07%
	15	19.08%	19.03%	19.52%	19.45%

compares the Total Performance Improvement (TPI) in percentage between the two methods at all time intervals. The Total Performance Improvement is defined as follows:

$$TPI={\displaystyle \frac{T{P}_{CoMoRE}-T{P}_{CCMM}}{T{P}_{CCMM}}}\times 100$$

(10)

where $T{P}_{CoMoRE}$ and $T{P}_{CCMM}$ denote the total performance with the CoMoRe and CCMM methods, respectively.

As presented in Table 7, the lower total performance at time t = 7 and t = 8 is approximately 71% higher for the CoMoRe method compared to the CCMM method. As a result, the plans for change are more likely not to be rejected in the early stages, something that usually happens in the change management process. From the above data, it is evident that a specialist change process manager has the tools to deal with the RtC effect as a consequence of change and make optimal decisions. The CoMoRe method provides the manager with information that can serve as an early warning about the process of change over time, enabling the timely reallocation of human resources to achieve a successful change. Generally, a continuous evaluation of change is achieved using the CoMoRe method.

Figure 5 shows the average number of employees that will need to be reallocated during the change process (these results were produced in the experiment with 100.000 repetitions). At the early stages of change, when the RtC is high, the reallocation frequency is higher to avoid a significant drop in performance. Afterward, fewer adjustments have to be made, and the number of reallocations decreases over time. Another interesting result in Figure 5 is that human resources are allocated to their most productive positions at about the halfway point (t = 8) of the total change period, and no further reallocation is required.

4.3. Second Experiment: Algorithm Implementation

In the second experiment, the hypothetical company uses 100 workers for 100 corresponding tasks ($n=100$) in order to evaluate the effectiveness, efficiency, and computational complexity of the proposed CoMoRe method on a more extensive dataset. The change period, in which human behavior in the change phase was simulated, remained at 15 intervals ($T=15$). Following the same process as in the first experiment, the algorithm was applied for 100, 1.000, 10.000, and 100.000 repetitions. The results of the total performance obtained using the CoMoRe and CCMM methods are compared in

Table 8. Comparison of total performance results for 100, 1.000, 10.000, and 100.000 repetitions between the proposed CoMoRe method and the CCMM method for 100 workers and tasks ($n=100$).

Total Performance
Repetitions	100		1.000		10.000		100.000
Time ($\mathit{t}$)	CCMM	CoMoRe	CCMM	CoMoRe	CCMM	CoMoRe	CCMM	CoMoRe
0	9900	9900	9900	9900	9900	9900	9900	9900
1	8941	9766	8949	9767	8950	9767	8950	9767
2	6773	9198	6795	9198	6802	9197	6800	9197
3	5320	8454	5343	8458	5352	8458	5350	8458
4	4472	7838	4495	7844	4501	7843	4500	7843
5	3822	7318	3845	7325	3851	7327	3850	7326
6	3274	6859	3294	6869	3300	6870	3300	6870
7	2921	6548	2943	6560	2950	6561	2950	6560
8	2921	6548	2943	6560	2950	6561	2950	6560
9	3269	6941	3294	6949	3300	6950	3300	6950
10	3819	7582	3845	7588	3850	7589	3850	7588
11	4767	8759	4794	8766	4800	8766	4800	8765
12	5823	10,070	5846	10,072	5849	10,070	5850	10,070
13	7269	11,946	7301	11,946	7299	11,945	7300	11,945
14	8924	14,088	8947	14,088	8951	14,087	8949	14,087
15	10,581	16,198	10,595	16,192	10,602	16,192	10,600	16,190

.

Table 8 shows that in all experiments (for 100, 1.000, 10.000, and 100.000 repetitions), the average total performance starts (t = 0) with an initial value of 9900 in both methods. From $t=1$ to $t=7$, the overall performance obtained with the proposed CoMoRe method begins to be significantly better than that achieved with the CCMM method. At $t=7$ (for 100.000 repetitions), the lowest total performance has a value of 6560 for CoMoRe versus 2950 for the CCMM, which is a critical value for the change process. In the next time step, the performance starts to increase. At $t=12$ (for 100.000 repetitions), the total performance for the proposed CoMoRe method is 10070 and has exceeded the initial total performance (9900), while the total performance for the CCMM is 5850, significantly less than the initial total performance. Thus, the new desired state, which improves performance over the initial state, has been reached in a shorter time ($t=12$), representing a 20% time reduction.

The results of the Total Performance Improvement (defined in Equation (10)) with the CoMoRe and CCMM methods are compared in

Table 9. Comparison of Total Performance Improvement for 100, 1.000, 10.000, and 100.000 repetitions between the CoMoRe and CCMM methods for 100 workers and tasks ($n=100$).

	Total Performance Improvement (%)
	Repetitions	100	1.000	10.000	100.000
	0	0.00%	0.00%	0.00%	0.00%
	1	9.22%	9.14%	9.12%	9.13%
	2	35.81%	35.35%	35.22%	35.26%
	3	58.91%	58.31%	58.03%	58.09%
	4	75.26%	74.51%	74.26%	74.29%
	5	91.47%	90.54%	90.27%	90.30%
	6	109.51%	108.55%	108.18%	108.18%
Time$\left(t\right)$	7	124.17%	122.85%	122.36%	122.39%
	8	124.17%	122.85%	122.36%	122.39%
	9	112.31%	110.96%	110.59%	110.62%
	10	98.53%	97.36%	97.10%	97.09%
	11	83.73%	82.87%	82.62%	82.61%
	12	72.93%	72.29%	72.16%	72.15%
	13	64.34%	63.62%	63.64%	63.64%
	14	57.87%	57.46%	57.38%	57.41%
	15	53.09%	52.82%	52.72%	52.74%

below.

As demonstrated in Table 9, the CoMoRe method provides a significant improvement compared to the CCMM method in all cases. At the critical time periods of $t=7$ and $t=8$, where a lower total performance is observed, the CoMoRe method achieves a significantly better result, approximately 122% improved compared to the CCMM method.

It is also important to emphasize that in the second experiment with the larger allocation problem ($n=100$), the improvement rates were higher than in the first experiment ($n=10$). This can be attributed to the larger set of workers and tasks, which provided more opportunities for optimal allocation, consequently leading to a substantial enhancement in overall performance, as evidenced in Table 8 and Table 9.

The CoMoRe algorithm is a computational approach that involves solving the HRAP through the utilization of the Hungarian algorithm. According to the literature, the Hungarian algorithm is known to exhibit a complexity of $O\left(n^3\right)$. In its remaining parts, the CoMoRe algorithm does not present a computational complexity of a higher order. More specifically,

Table 10. Execution time and percentage change for different algorithm parts and matrix sizes.

	Execution Time (s, %)
Algorithm Part	Matrix Size 10 × 10		Matrix Size 100 × 100		Time Change (%)
Hungarian	28.25 s	3.6%	826.98 s	46.0%	2827.4%
Remainder	752.79 s	96.4%	969.13 s	54.0%	28.7%
Total	781.04 s	100.0%	1796.11 s	100%	130.0%

presents the execution time of the Hungarian part of the algorithm, the time that corresponds to the remaining part, and the total execution time of the CoMoRe algorithm. It is evident from the data presented in Table 10 that the Hungarian part of the algorithm for a $10\times 10$ matrix needs only 28.25 s, which is 3.6% of the total execution time, but for a $100\times 100$ matrix, it needs 826.98 s, which is 46% of the total execution time. Therefore, the execution time of the Hungarian part increases by over 2800% as the matrix size increases from $10\times 10$ to $100\times 100$. The remaining part has a small increase of approximately 28.7%. The total time shows a modest increase of approximately 130%. In conclusion, while the Hungarian algorithm constitutes the primary computational issue, the overall complexity of the method remains manageable for moderate matrix sizes. The reported runtimes were measured when running the algorithm on a computer with the following characteristics: Intel® Core™ i7-8700 CPU @ 3.20 GHz, RAM 32.0 GB.

5. Conclusions and Limitations

In order to address and manage RtC, this study presented and evaluated a novel approach called CoMoRe. This concept is based on the ongoing observation and redistribution of human resources to tasks throughout the change period. It involves the early reallocation of human resources and the regular evaluation of employee performance. This approach enhances overall performance significantly. Classical Change Management Models have low efficiency in managing RtC. As a result, in many change implementation processes, the total performance suffers critical decreases, which leads to the abandonment or failure of the change process.

In order to verify the efficiency of the proposed CoMoRe method, suitable experiments were designed and executed. According to the experimental results, the total performance of the CoMoRe method is better in all change period intervals compared to the Classical Change Management Model (CCMM). The CoMoRe method aids decision making in this complex situation. In addition, the critical value of the maximum drop in total performance is much smaller when using the CoMoRe method. The experimental results show that this critical performance value is up to 122% higher when using the CoMoRe method compared to the CCMM, and in many cases, this is the critical time for the manager to decide on whether to abandon or continue the change implementation. In addition, the experimental results show that CoMoRe effectively improves overall performance relatively quickly and that the time to reach the new desired state is reduced by up to 20%.

However, it is important to consider some of the risks and limitations of the CoMoRe approach. Continuous monitoring and resource reallocation require a high level of real-time data monitoring, which can be resource-intensive and requires advanced data management systems. In addition, the success of the approach depends on the ability to accurately evaluate employee performance at different stages of the change process, which may be subject to variability, depending on the context of the organization. Furthermore, it is important to acknowledge the fundamental limitation that all employees can perform all tasks, and tasks can be performed by one employee. In addition, the resistance of employees to frequent job changes has not been given adequate consideration.

The proposed idea of continuous monitoring and reallocation used in the CoMoRe method could be applied to all change management problems. In future work, the possibility of using this model in other, more complex human resource allocation problems will be investigated.