A Mathematical Method for Optimized Decision-Making and Performance Improvement Through Training and Employee Reallocation Under Resistance to Change

Abstract

The decrease in employee performance that occurs during organizational change is one of the main problems that this study attempts to address. This phenomenon, which is known as resistance to change, has been directly linked to the failure or abandonment of change initiatives when performance drops to critical levels. This study proposes an innovative approach to organizational change management based on a model that integrates real-time performance monitoring and employee reassignment to tasks. This approach contributes to improving overall system performance and stabilizing costs by achieving a reduction in resistance to change through staff training and dynamic reallocation of human resources. The method utilizes Evolutionary Dynamic Multi-Objective Optimization with the aim of both maximizing performance and minimizing costs. It incorporates the performance of employees in each task and the associated costs, enabling continuous adjustment of task assignments in accordance with temporal variability in the factors that affect the success of organizational change. Experimental simulations show that the proposed method leads to a considerable enhancement in overall system performance, cost stabilization, and a significant reduction in the risk of change abandonment. More specifically, the proposed method demonstrates an improvement in total performance from 55% to over 200% in comparison to three reference methods. Furthermore, it achieves faster recovery and a lower performance drop, especially in critical stages, providing optimized decision-making during the change process and leading to the new desired and improved state being achieved in a time that is up to 27% shorter, consequently reducing the risk of abandonment. The proposed method operates as both an optimization tool and a real-time decision support system. The continuous analysis of employee performance and cost provides actionable indications of the current state of change, allowing for timely detection and intervention.

1. Introduction

In the corporate and organizational context, change is frequently initiated as a strategy to address challenges and optimize operational efficiency and effectiveness [1,2]. Despite their commendable intentions, a significant proportion of these attempts ultimately prove unsuccessful. Specifically, approximately 70% of changes are either not completed within the designated time frame or are entirely abandoned [2,3,4]. A wide range of models and methodologies have been established for the efficient management of change, most of which are based on a predefined sequence of stages [5,6,7,8]. Nevertheless, the attitude of employees, particularly the resistance they exhibit during the implementation process, plays a pivotal role in the success or failure of a change. Employees who are to be affected by a change often experience emotional distress and uncertainty [9,10,11,12]. This emotional turbulence has been identified as a significant contributing factor to the failure of numerous change initiatives, as staff behavior can impede the implementation process [13,14,15]. Individuals’ reactions to changing situations vary; some welcome them positively, while others exhibit strong resistance [16]. Many organizational change initiatives fail due to insufficient training of the individuals involved, particularly in relation to the specific nature and demands of the change process [17]. Training processes have been recognized as critical mechanisms that play a strategic role in enhancing the effectiveness and readiness of employees in the face of organizational change. Despite their importance, the existing literature and current practices mainly focus on training before the change process starts, resulting in the systematic neglect of the impact of training during the change process. This omission limits the ability of organizations to timely and adaptively support their human resources in critical phases of transition.

Research indicates that factors such as the nature of an employee’s occupation appear to exert an influence on both their job performance and the extent of their resistance to change (RtC) [18,19]. In this context, it becomes evident that human behavior constitutes a pivotal element in the effective transition of organizations to new operating models. Human resources play a crucial role in the success of an organization, especially in times of organizational change. In this context, appropriate staff training becomes necessary, as it enhances the adaptability and self-efficacy of employees in the face of change. It is essential that managers seek not only to optimize the use and allocation of available human resources in different departments or systems, but also to strategically invest in skills development through targeted training programs. Integrating training into personnel allocation processes can significantly contribute to improving critical functions related to performance and productivity. The importance of the proper utilization and training of human resources has been recognized in many business sectors [17]. In order to effectively manage complex and evolving transformations involving the coexistence of multiple objectives, organizations can benefit from computational approaches such as Dynamic Multi-Objective Optimization (DMOO). Specifically, Evolutionary Dynamic Multi-Objective Optimization (EDMO) offers an adaptive method for modeling and solving change management challenges over time. Dynamic Multi-Objective Optimization Problems (DMOPs) are problems involving multiple optimization objectives that are subject to some constraints, where the objectives and/or constraints change over time. Evolutionary Dynamic Multi-Objective Optimization (EDMO) is a relatively new but rapidly growing area of research. EDMO uses evolutionary approaches to address multi-objective optimization problems that involve time-varying changes in their objective functions, constraints, and/or environmental parameters [20].

The evolution of organizational change management has included the development of a variety of approaches, at both the theoretical and practical levels [8,21]. The collection of information through questionnaires and interviews, that is, through quantitative and qualitative research, is a key tool in the decision-making phase. Through this process, the necessary steps for the implementation of a specific change can be determined, as well as the strategy for the change’s overall management. In addition, readiness for change can be enhanced through appropriate staff training, while timely selection of the bodies or leaders who will provide guidance for the upcoming change also plays an important role [6,22,23]. Recent research has proposed that RtC can be managed by focusing on continuously monitoring employees and dynamically reallocating them during the change process [24,25].

Traditional multi-objective change management methods are often time-consuming and fail to respond promptly to RtC and the need for targeted training. This results in an inability to intervene effectively at the right time, which often leads to the abandonment or incomplete implementation of organizational change. Significant research gaps exist in the relevant literature:

• Existing models do not incorporate real-time, dynamic adaptation to employee resistance and training needs during organizational change.
• Current approaches use traditional communication tools, such as interviews, seminars, and information sessions. These tools are time-consuming and inflexible, making them unable to respond immediately to RtC and training requirements.
• Additionally, most models treat human resource allocation as a static process, overlooking the dynamic nature of employees’ behavior and their evolving resistance throughout the change process.

The main innovation of the method proposed in this paper lies in its adoption of a dynamic, time-dependent human resource allocation strategy, which is based on continuous monitoring of four critical parameters: performance, cost, resistance to change, and training. Personnel allocation is adjusted at regular intervals during the change process, taking into account these factors. In this way, appropriate decisions can be made that help the change process to succeed.

The method applies the principles of Evolutionary Dynamic Multi-Objective Optimization (EDMO), allowing for the continuous adjustment of task assignments based on temporal variability in the factors that affect the success of organizational change.

Task assignments are adjusted dynamically based on fluctuations in employee performance, task-related costs, levels of resistance, and individual training needs. Thus, the main objectives of this study are as follows:

• The development of a dynamic EDMO model, which simultaneously monitors and optimizes multiple and often conflicting objectives (performance versus cost).
• Evaluation of the model’s effectiveness in real-time training and monitoring in terms of improving performance and cost stabilization.
• Comparison of the dynamic model with traditional static and dynamic models in terms of their ability to respond to complex and evolving conditions of organizational change.

The originality of the proposed Performance Improvement Through Training and Employee Reallocation (PITTER) method lies in its integration of dynamic, real-time task allocation with multi-objective optimization in the context of organizational change. Unlike traditional models that treat human resource allocation as a static or one-time process, PITTER continuously monitors and adapts task assignments based on two primary, conflicting objectives: maximizing performance and minimizing cost. What distinguishes this model is its incorporation of behavioral and training-related factors such as RtC and individual training needs, which dynamically influence the core objectives. These factors are modeled as time-dependent variables that primarily affect performance and, secondarily, cost, thereby enhancing the realism and adaptability of the optimization process. From a theoretical point of view, PITTER bridges the gap between change management concepts (e.g., resistance, adaptation, and training) and computational optimization methods. Computationally, the model adopts an Evolutionary Dynamic Multi-Objective Optimization (EDMO) approach that is specifically adapted to human-centered organizational environments. This enables adaptive decision-making in response to continuously evolving employee states and task-related requirements. Therefore, the PITTER model contributes to the field of organizational change by extending the EDMO methodology and by offering a practical tool for dynamic personnel allocation under uncertainty and behavioral variability.

The rest of this paper is organized as follows. A review of the literature on change management models and Dynamic Multi-Objective Optimization Problems is presented in Section 2. Section 3 introduces the proposed method, providing an in-depth description of the problem and the applied methodology. The designed experiments and their results, along with a detailed discussion, are given in Section 4. Finally, Section 5 gathers and comments on the conclusions of the study and highlights its limitations.

2. Literature Review

2.1. Change Management Models

The literature presents both practical and theoretical models for managing change in organizations. Kurt Lewin, who founded the first classical model, described organizational change as a three-stage process: “Unfreeze”, “Change”, and “Freeze” [26,27]. This theory was also the basis for subsequently proposed classical change models, such as Beer’s model [28], Kotter’s 8-Step Model [11], and Hiatt’s model [29,30]. Several studies also present methodologies that focus on the readiness of the organization before the upcoming change. According to these studies, training, communication skills, and the selection of change agents play a decisive role [6,9,17,21]. Organizational change is described as a linear sequence of steps, from an initial stage to a desired future point.

The three-stage process of organizational change is also used as a basis for the continuous monitoring and reallocation method proposed in [25], which is illustrated as in Figure 1. This method adopts a more adaptive strategy that is capable of dynamically responding to changing conditions and human resource reactions, enhancing the stability and effectiveness of the change process.

Several contemporary studies offer alternative approaches to managing organizational change. Arazmjoo and Rahmanseresht [31] propose a dynamic meta-heuristic model that adapts to the specificities of each case, while Maes and Hootegem [32] understand change as a multidimensional and nonlinear process. McDermott et al. [33] present a practical framework for assessing the readiness and maturity of an organization for continuous improvement, identifying both strong foundations and areas that require strengthening. However, most of these proposed methods are very time-consuming, which means that RtC is not addressed in a timely manner, resulting in the abandonment or incomplete implementation of changes. Therefore, the existing literature presents significant research gaps that require further investigation.

Recent research has introduced a time-sensitive approach to managing RtC, focusing on continuously monitoring and dynamically reallocating human resources during the change process [24,25]. These methods are based on the Hungarian algorithm for assignment optimization, and allow for regular adjustment of the change strategy based on the actual response of employees. Experimental results show that these approaches can significantly increase overall performance and reduce the required change implementation time. However, these specific methods are not multi-objective and do not take into account the staff training process.

2.2. Dynamic Multi-Objective Optimization Problems

Dynamic Multi-Objective Optimization Problems (DMOPs) are an important and rapidly growing field of research, as they represent problems involving multiple and conflicting objectives that must be optimized in an environment that changes over time [20]. Optimization in such dynamic environments is important for real-world applications, such as resource management in crisis situations or human resource allocation in changing organizational situations. A DMOP can be described mathematically as a problem of minimizing (or maximizing) a vector of objective functions $F(x,t)$, which depend on the decision variable x and time t. The problem is also subject to constraints that may change over time.

Without loss of generality, the mathematical representation of DMOPs is given by [20]:

$$\begin{array}{c}\hfill \mathrm{Minimize}F(x,t)={(f_1(x,t),\dots ,f_{M_t}(x,t))}^T,\end{array}$$

(1)

$$\mathrm{subject}\mathrm{to}\left\{\begin{array}{cc}{h}_i(x,t)=0,\hfill & i=1,\dots ,n_h\left(t\right),\hfill \\ g_i(x,t)\ge 0,\hfill & i=1,\dots ,n_g\left(t\right),\hfill \\ x\in {\Omega }_x,t\in {\Omega }_t\hfill \end{array}\right.$$

(2)

where $M_t$ is the number of conflicting objectives, and $n_h\left(t\right)$ and $n_g\left(t\right)$ are the number of equality and inequality constraints at time t, respectively. ${\Omega }_x\subseteq R^n$ is the decision space, and ${\Omega }_t\subseteq R$ is the time space. $F(x,t):{\Omega }_x\times {\Omega }_t\to R^{M_t}$ is the objective vector function that evaluates solution x at time t.

The solution space forms a Pareto front, where the solutions are optimal, but in the sense that none performs better than the others on all objectives simultaneously. DMOPs are frequently encountered in real-world problems, as they reflect situations in which objectives and constraints change over time, with organizations trying to minimize or maximize multiple objectives simultaneously.

The Evolutionary Dynamic Multi-Objective Optimization (EDMO) method uses evolutionary algorithms, which dynamically adapt to changes and are able to track the evolution of the Pareto front in such problems, thus allowing them to be successfully solved. Non-dominated Sorting Genetic Algorithm II (NSGA-II) is one of the most popular evolutionary algorithms for multi-objective optimization. It is based on non-dominated sorting of solutions, with the aim of maintaining a good distribution of solutions along the Pareto front.

In the previous decade, studies such as that conducted by Hutzschenreuter et al. [34] were already approaching dynamic resource allocation in stochastic environments through applying multi-objective optimization strategies. Although this is an early example, it highlights the importance of interpretable and adaptive solutions for decision-makers, an aspect that is further reinforced in modern EDMO-based applications.

The use of DMOPs (and advanced EDMO techniques) in organizational change management treats change as a complex, time-dependent problem with multiple evolving parameters. It represents an innovative, computationally supported approach that offers adaptability, decision-making support, and the integration of both human and operational goals. An illustrative application of such an approach was presented in a recent study concerning the allocation of multi-skilled workers in a brake production line, where time-dependent variations in efficiency due to fatigue, learning, and recovery were taken into account. Furthermore, the use of an enhanced NSGA-II algorithm in combination with Variable Neighborhood Search techniques achieved high efficiency in identifying Pareto-optimal solutions in dynamic, multi-criteria environments [35].

Similar multi-objective optimization approaches have also been applied to order coordination and task allocation problems, such as joint order batching and picking. The use of multi-objective evolutionary algorithms in combination with multiple criteria decision-making techniques has yielded operational benefits in terms of cost reduction and improved efficiency. These applications underline the potential of adopting similar strategies for human resource allocation during organizational change [36]. The literature also reports applications of DMOPs in diverse fields, such as planning and scheduling, system control and design, industrial production, data science, and unmanned aerial vehicle system recognition [20,37,38,39,40,41].

3. The Performance Improvement Through Training and Employee Reallocation (PITTER) Method

3.1. Problem Description

This article focuses on addressing employees’ RtC. Proper management plays a critical role in the successful completion of changes. In many cases, change plans are abandoned due to unsuccessful management of intense resistance. This human behavior during the change process is presented in the literature [5] as the “change curve.” The depth of the fall and the time required for recovery are often such critical factors in the change process that they can even lead to the abandonment of plans. The NuRe method [24] and the CoMoRe method [25] constitute the first attempts to extend the classical HRAP concept. The CoMoRe method extends the NuRe approach by incorporating continuous monitoring and readjustment of staffing allocation throughout the change process, at regular intervals. In this way, the RtC of each employee is regularly considered, allowing for timely adjustment of staff assignment in the early stages of the change.

The proposed Performance Improvement Through Training and Employee Reallocation (PITTER) model advances the CoMoRe approach by incorporating the dynamics of both training and RtC, in a way that captures their effects on actual performance. The PITTER method considers not only the performance of each job, but also the associated operating costs. Furthermore, in addition to continuously monitoring RtC, it also incorporates the need for continuous staff training. In this way, it implements a multi-criteria optimization process, through which staff assignment is carried out based on a combination of factors, such as employee performance, cost per job, RtC, and the need for training.

Let us assume that a company is planning to implement an organizational change. The company consists of n employees, who are required to perform n corresponding tasks. The company’s goal is to achieve maximum productivity by utilizing human resources effectively, while minimizing operating costs. This can be achieved by optimizing personnel allocation, taking into account both the performance of each employee and the cost of each job. When the change process begins, the individual performance of each employee is negatively affected due to RtC. This resistance reduces the employee’s ability to perform their job effectively, thus reducing overall performance. However, during the change process, employee performance can be gradually improved through targeted training. Training helps reduce resistance, leading to the recovery and enhancement of employee performance over time.

The problem described above is based on the following assumptions:

(i)

The number of employees remains constant throughout the change process.

(ii)

The initial performance of each employee is known.

(iii)

The initial cost for each employee is known.

(iv)

Each employee can perform all tasks.

(v)

During the change period, each employee presents a resistance that follows the change curve model [5].

(vi)

This resistance is reduced when training is provided.

(vii)

Training is cumulative for each employee (i.e., its effect adds up over time) and is discontinued when the employee no longer exhibits resistance that affects their performance.

The above assumptions may limit realism and generalizability. In particular, the assumption that all workers have the same abilities and that the cost of each task remains constant over time does not fully capture the complexity of real organizational conditions, such as skill heterogeneity, training curves, and dynamic changes in resources and costs. However, these assumptions are considered reasonable within the context of this study, as the organizational change is designed to be implemented in a relatively short time frame, within which such changes are unlikely to have a substantial impact. In addition, the model assumes the existence of integrated information systems, through which data is available in real time, allowing for continuous monitoring and immediate adjustment in case of deviation from the initial conditions.

The proposed mathematical model and the objective functions are as follows:

$$\mathrm{Maximize}\mathrm{total}\mathrm{performance}:f_1(x,t)=\sum _{i=1}^n\sum _{j=1}^n{P}_{ij}\left(t\right)x_{ij}\left(t\right)$$

(3)

$$\mathrm{Minimize}\mathrm{total}\mathrm{cost}:f_2(x,t)=\sum _{i=1}^n\sum _{j=1}^n{C}_{ij}\left(t\right)x_{ij}\left(t\right)$$

(4)

where $P_{ij}$ is the performance when worker i is assigned to task j, and $C_{ij}$ represents the cost associated with assigning worker i to task j, subject to the following constraints:

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

(5)

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

(6)

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

(7)

Equation (8) calculates the level of training $T_{ij}\left(t\right)$ received by worker i assigned to task j at time t:

$$T_{ij}\left(t\right)=k·max\left(R_{ij}\left(t\right),0\right))$$

(8)

where k is a training factor and $R_{ij}$(t) is the RtC of worker i when assigned to task j at time t. The training factor k is modeled as a random variable with a triangular distribution in the interval [0, 0.10], expressing the degree to which training is effective for the employee.

Equation (9) calculates the cumulative training of worker i up to time $t+1$:

$$C{T}_i(t+1)=C{T}_i\left(t\right)+T_{ij}\left(t\right)$$

(9)

where $C{T}_i$(t) is the cumulative training of worker i up to time t, and $T_{ij}\left(t\right)$ is given by Equation (8).

By using these variables, the performance $P_{ij}$ of worker i when assigned to task j at time $t+1$ can be defined as follows:

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

(10)

where $P_{ij}\left(t\right)$ is the worker’s performance at time t, $R_{ij}\left(t\right)$ is their RtC at time $\left(t\right)$, $C{T}_i\left(t\right)$ is the cumulative training of worker i up to time t.

3.2. Description of the PITTER Application

At the start of the change process, employees are randomly assigned to specific jobs. At this stage, the employees do not yet exhibit RtC. After this point, the decline in employee efficiency that results from employee reactions begins to appear. The innovative aspect of the proposed method is that it dynamically monitors these changes in efficiency at regular intervals and adjusts the allocation of personnel, along with controlling the cost per job. It also monitors and adjusts the training provided, depending on the magnitude of each employee’s resistance, in order to reduce costs. Thus, by taking all of the above into account during the change process, the overall performance of employees can be improved. The following steps must be carried out in order to implement the proposed method. The process is also visually presented using a flowchart in Figure 2.

Step 1:

Initialization of the System. The number n of workers and jobs, which is assumed to be equal, is determined. Then, the initial cost matrix $C_{ij}(t=0)$ is formulated, which includes the cost of each worker i in each job j. At the same time, the initial performance matrix ($P_{ij},t=0$) is initialized, which has the same dimensions $n\times n$ as the cost matrix.

Step 2:

Random Assignment of Workers to Tasks. An initial random assignment of workers to available tasks is performed. The use of randomness at this stage serves to create a neutral initial state for the system. At this point, no resistance to their change of position has yet developed on the part of the workers, so no training process is needed. Immediately afterwards, the total performance and the total cost of the assignment are calculated, based on the corresponding Equations (3) and (4).

Step 3:

Creation of Resistance and Training Matrices. At each time step t, the resistance matrix $R_{ij}\left(t\right)$ is constructed for each pair of worker i and task position j through a process that is described in detail in the Experiments Section. Based on the resistance matrix values, the corresponding training matrix $T_{ij}\left(t\right)$ is obtained using Equation (8), which determines the level of training that must be provided to each employee i in order to reduce their resistance during the change process. The matrices have the same dimensions $n\times n$.

Step 4:

Calculation of New Performance Values. The performance $P_{ij}(t+1)$ of each employee is recalculated using Equation (10), which takes into account the effects of both training and resistance.

Step 5:

Application of the NSGA-II Algorithm. The NSGA-II algorithm is applied to solve the multi-objective problem comprising two objectives: maximizing the total performance and minimizing the total assignment cost, as described in Equations (3) and (4). Based on the Pareto front, one of the non-dominated solutions is selected through a process that is described in detail in the Experiments Section.

Step 6:

Updating Cumulative Employee Training. The level of training of each employee is added to their cumulative training level, affecting their performance in the future steps of the process, using Equations (8) and (9).

Step 7:

Repeating the Process. Steps 3–6 are repeated for each time step $t=1,2,\dots ,T$, simulating the full duration of the organizational change process. At each time step, both the total performance and the total assignment cost are recalculated. The total performance is calculated as the sum of the performance values in the selected assignment pairs, and the total cost is calculated as the sum of the assignment costs for the same pairs. Furthermore, the current generation of NSGA-II algorithm solutions is used as the initial conditions in the next time step.

4. Experiments and Results

In order to verify the effectiveness of the proposed PITTER method, appropriate experiments were designed and implemented. The results of the experimental tests, both graphical and numerical, are presented in this section. The applicability of the proposed method is investigated and the benefits that can be drawn from the experimental findings are examined. In order to fulfill the needs of the tests, a simulation program was developed, using the Python 3.12 programming language, that made use of the pymoo library for multi-objective optimization and the implementation of evolutionary algorithms [42]. Models of organizational change show that human behavior gradually changes over time. The initial stages of the change process are dominated by reactions toward and denial of change, which develops RtC. As time progresses, this attitude transforms into gradual acceptance, ultimately leading to increased performance, as described in detail in Section 3.

Two simulation scenarios were carried out with the aim of studying the efficiency of the PITTER method in solving problems of different sizes. A hypothetical company was chosen as a basis for implementing an organizational change process. In both experiments, the company had an equal number n of employees and corresponding tasks. In the first experiment, $n=10$, and in the second experiment, the number of employees and tasks was increased to $n=100$, in order to evaluate the computational efficiency of the method in a larger-scale environment. In both cases, a period of organizational change was simulated, during which the influence of human behavior on the task assignment process was examined. The duration of this period was divided into 15 consecutive time intervals ($T=15$), over which the evolution of the main variables of the model was monitored: performance, assignment costs, resistance to change, and the level of training of employees.

As a basis for modeling human behavior in our experiments during the change phase, the characteristic curve presented in Panagiotopoulos and Chatzis [25] was used. This curve illustrates the progression of employee performance at discrete time intervals during the transition from the initial stage to the final stage of organizational change. More specifically, performance starts near the maximum level (100%) and gradually decreases to about 70% in the early stages of change, reflecting the uncertainty and resistance of employees. Then, a gradual trend of recovery follows. A symmetric triangular distribution was applied to the values of the curve to incorporate stochastic variability. The use of this distribution allows for the expression of natural variation without altering the basic dynamics of the proposed curve.

The choice of a triangular distribution to model randomness in the resistance and training effects reflects the lack of precise empirical data, as well as the need for a flexible, bounded distribution with finite lower and upper limits that can be easily interpreted. Commonly used in business simulations, the triangular distribution allows expert estimations of the minimum, maximum, and most likely values to be incorporated, while avoiding unrealistic tails approaching zero or infinity. This could happen if heavy-tailed, unbounded, or infinite-support distributions, such as the exponential or log-normal distribution, were used.

In this work, we adopt the basic features of the Classical Change Management Model (CCMM) and use them as a reference curve (ground truth) for the new experiments. More specifically, the values of employees’ RtC for each time interval, from t = 0 to t = 15, are obtained in the same way as in

Table 1. The lower and upper values of the symmetric triangular distributions used to generate the RtC values (the red color indicates a positive resistance effect; green indicates a negative resistance effect [25]).

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]	[-]

[25], except that in our experiments, resistance begins to appear at time t = 1. This determines the minimum and maximum resistance values. In the table, positive resistance values are presented in red, and represent a negative attitude of employees towards the change (increased resistance). On the contrary, negative resistance values are presented in green, and indicate a positive attitude and intention to accept the change.

The proposed PITTER method will be compared with the CCMM method and two other main benchmark methods: NSGA-II and CoMoRe. The first is a classical implementation of the well-known evolutionary algorithm NSGA-II, which operates directly on the actual optimization problem without adaptive training mechanisms. This allows for a direct comparison of PITTER’s performance against a purely evolutionary baseline. Moreover, CoMoRe is a more recent optimization method that incorporates job reassignment mechanisms to enhance performance. These two approaches serve as benchmarks for assessing the efficiency and solution quality of PITTER in multi-objective optimization scenarios.

4.1. First Experiment: Algorithm Implementation

The execution of the algorithm starts at time t = 0, simultaneously with the start of the change period. According to the flowchart presented in Figure 2, the first step involves the creation of a 10×10 performance matrix $P_{ij}$, which contains the initial performance values of the workers for each job. These values are randomly determined to fall within the interval of 90% to 100%, based on the assumption from Section 3, according to which each worker is able to perform any of the available jobs. Therefore, at this initial stage, the performance of each worker for each job corresponds to a random value between 90 and 100. In parallel with the performance matrix, a 10 × 10 cost matrix is created, in which each element expresses the cost of assigning a worker to a specific job. The cost values are generated according to the triangular distribution in the normalized interval [0.8, 1.2]. These values can then be adjusted to a random value between 80 and 120 to correspond to cost units. The cost remains constant at each step of the algorithm for each combination of worker and job. The results are displayed in

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

Performance (${\mathit{P}}_{\mathit{ij}}$(t = 0))
	Jobs ($\mathit{j}$)
Workers ($\mathit{i}$)	1	2	3	4	5	6	7	8	9	10
1	95	90	93	93	97	99	93	95	92	94
2	97	96	98	98	100	91	96	97	97	98
3	91	95	99	98	99	94	93	90	93	95
4	90	92	93	98	91	93	93	93	97	90
5	91	99	99	90	100	94	97	93	92	97
6	92	90	90	94	95	95	96	98	94	91
7	94	99	100	100	98	91	91	97	99	99
8	93	96	97	92	90	93	95	99	100	94
9	94	96	94	94	93	94	94	98	94	93
10	100	97	95	95	90	91	95	99	93	90

and

Table 3. Initial cost matrix $C_{ij}(t=0)$ for each worker and job.

Cost (${\mathit{C}}_{\mathit{ij}}$(t = 0))
	Jobs ($\mathit{j}$)
Workers ($\mathit{i}$)	1	2	3	4	5	6	7	8	9	10
1	95	87	89	96	106	116	112	88	114	92
2	86	102	99	103	102	94	116	101	100	106
3	115	94	88	94	107	89	95	94	91	115
4	93	106	84	82	101	108	106	102	96	105
5	97	100	93	99	89	93	94	106	91	114
6	91	84	107	98	105	102	101	98	106	91
7	112	112	105	99	108	98	101	104	99	108
8	90	113	111	92	102	88	114	99	101	86
9	107	83	85	96	95	93	108	92	102	106
10	99	117	101	112	91	113	99	98	95	103

.

In step 2, an initial, random assignment of workers to available jobs is performed. The use of randomness at this stage serves to create a neutral initial state for the system. At this point, no resistance to their change of position has yet developed on the part of the workers, so no training process is needed. Immediately afterwards, the total performance and the total cost of the assignment are calculated, based on the corresponding Equations (3) and (4).

Table 4. Random allocation at $t=0$.

Workers (i)	Jobs (j)	Performance (${\mathit{P}}_{\mathit{ij}}$(t = 0))	Cost ${\mathit{C}}_{\mathit{ij}}$
1	10	94	92
2	1	97	86
3	3	99	88
4	4	98	82
5	5	100	89
6	7	96	101
7	9	99	99
8	6	93	88
9	2	96	83
10	8	99	98
Total	–	971	906

simplifies Table 2 and Table 3. It shows the couples of allocated workers and tasks, and the corresponding worker performance and cost values. In the last line of the table, the summed values of performances and costs are also presented. Notice that the maximum total performance can reach the value of 1000 (100 × 10). However, in this example, the random allocation gave a total performance value of 971 and a total cost value of 906.

At this initial stage, RtC has not yet arisen. The total calculated performance represents the initial state of the system. The specific random allocation of workers to available jobs, and the total performance resulting from this, are adopted as a reference point for comparing the proposed method with the other methods. The initial conditions were kept the same for all methods to ensure fairness in the comparison.

In step 3, RtC arises, causing a decrease in worker performance. To represent this, a 10 × 10 resistance matrix $R_{ij}$ is created, which assigns each worker–job combination a random value in the range [0, 20], as shown in Table 1. An indicative example of the generated values is listed in

Table 5. Initial resistance matrix $R_{ij}(t=0)$ for each worker and job.

Resistance (${\mathit{R}}_{\mathit{ij}}$(t = 0))
	Jobs ($\mathit{j}$)
Workers ($\mathit{i}$)	1	2	3	4	5	6	7	8	9	10
1	12	6	5	10	17	16	2	6	1	12
2	7	17	2	1	8	6	11	0	7	19
3	6	8	11	2	3	9	12	17	6	9
4	19	1	14	16	3	3	12	7	15	18
5	13	15	11	7	11	9	19	4	3	8
6	15	15	15	19	18	8	4	3	0	5
7	17	13	19	14	1	14	14	2	13	0
8	5	3	0	7	10	3	20	6	4	13
9	20	13	13	6	0	12	2	2	0	3
10	6	20	0	10	20	1	7	15	2	12

.

After this, a training matrix $T_{ij}$ of the same dimensions is also generated, which reflects the level of training received by each worker per position. This matrix is calculated using Equation (8). In this way, the system incorporates the positive effect of training on managing RtC, with the direct aim of gradually recovering employee performance. The resulting training values for this step are presented in

Table 6. Initial training matrix $T_{ij}(t=0)$ for each worker and job.

Training (${\mathit{T}}_{\mathit{ij}}$(t = 0))
	Jobs ($\mathit{j}$)
Workers ($\mathit{i}$)	1	2	3	4	5	6	7	8	9	10
1	0.32	0.35	0.32	0.76	0.89	1.03	0.15	0.28	0.07	0.64
2	0.55	0.45	0.08	0.05	0.46	0.10	0.62	0.00	0.49	0.90
3	0.35	0.64	0.82	0.12	0.22	0.58	0.62	0.90	0.30	0.61
4	1.26	0.05	1.27	1.22	0.09	0.12	0.87	0.18	0.62	1.02
5	0.97	0.68	0.74	0.31	0.53	0.41	1.28	0.33	0.19	0.65
6	0.95	0.40	1.02	1.02	1.36	0.41	0.29	0.10	0.00	0.28
7	1.49	0.83	0.53	0.47	0.09	1.27	0.26	0.09	0.61	0.00
8	0.30	0.15	0.00	0.38	0.32	0.11	0.86	0.36	0.13	0.68
9	1.29	0.60	0.49	0.39	0.00	0.48	0.17	0.13	0.00	0.10
10	0.37	1.06	0.00	0.35	1.50	0.02	0.29	0.48	0.15	0.70

.

Subsequently, in step 4, the new performance values ($P_{ij}(t=1)$) are recalculated using Equation (10), which incorporates both the effect of resistance and the contribution of training.

Then, in step 5, the NSGA-II algorithm is applied to solve a multi-objective optimization problem with two objectives: maximizing the total performance and minimizing the total assignment cost. The algorithm’s specific parameters are set with typical values, as presented in

Table 7. Parameters of NSGA-II algorithm.

Population Size	Generations	Crossover Probability	Mutation Probability
100	200	0.7	1/n

.

The Pareto front is calculated for each time step, and one of the non-dominated solutions is selected for the next time step based on the following process. An “ideal” reference point is selected from the Pareto front, which is supposed to have the maximum performance ($P_{\max }$) and the minimum cost ($C_{\min }$). The Euclidean distance between each Pareto-optimal solution i and the ideal point ($P_{\max },C_{\min }$) is then calculated as shown in Equation (11):

$$d_i=\sqrt{{(P_i-P_{\max })}^2+{(C_i-C_{\min })}^2}$$

(11)

where

• $d_i$ is the distance of solution i from the ideal point;
• $P_i$ is the total performance of solution i;
• $C_i$ is the total assignment cost of solution i;
• $P_{\max }$ is the highest performance across all solutions;
• $C_{\min }$ is the lowest cost across all solutions.

The solution i with the smallest distance $d_i$ is considered the most balanced with respect to both objectives, and is selected as the final allocation of the current time step. Based on this solution, a new assignment table is created which specifies the new position of each worker. The performance and cost matrices are updated and their sums are calculated. These calculations are made exclusively based on the initial performance and cost values of the workers.

Additionally, in step 6, the cumulative training matrix for each employee is updated using Equation (9), reflecting the accumulated training received and influencing employee performance in future time steps.

Steps 3 to 6 are repeated for all time steps $t=1,2,\dots T$, simulating the entire duration of the organizational change process. At each time step, both the total efficiency and the total cost are computed. The total efficiency is calculated as the sum of the performance values corresponding to the selected assignment pairs, while the total cost is computed as the sum of the fixed assignment costs for those same pairs. Furthermore, the current generation of solutions is used as the initial conditions for the next time step, enabling NSGA-II to develop new solutions based on prior optimization outcomes. Throughout all the iterations, the NSGA-II algorithm is consistently applied to solve the multi-objective optimization problem comprising two goals: maximizing the total efficiency and minimizing the total assignment cost.

To better understand the management of conflicting objectives (Step 5), the algorithm was applied iteratively at all time steps $t=1,2,\dots ,T$. Figure 3 presents the Pareto fronts of total performance versus cost generated at each time step (t = 0 to 15) using the NSGA-II optimization process. Each point represents a potential NSGA-II solution, with the horizontal axis denoting performance and the vertical axis indicating cost. The color of each point reflects the time step t at which the solution was generated. Specific markers are used to highlight characteristic solutions: green upward triangles (▲) represent the maximum performance at each time step, orange crosses (×) mark solutions with the minimum performance, blue downward triangles (▼) indicate solutions with the minimum cost, and violet squares (■) denote those with the maximum cost. Red stars (★) highlight the selected point, calculated using Equation (11), which balances both objective functions. Solutions with an asterisk occupy the lower part of the graph, indicating high performance combined with relatively low cost, a result that supports the effectiveness of PITTER in finding balanced solutions. The dashed red line connects the selected points across time, revealing the trajectory of the model’s decision-making process. Notably, the selected solutions shift progressively towards higher performance with relatively stable cost, reflecting PITTER’s ability to adapt to the two objective functions.

4.2. First Experiment: Results and Analysis

To evaluate the performance of the proposed method, we ran the algorithm iteratively, taking into account randomness in the initial state of the performance and resistance matrices. The existence of random variables in the problem necessitated repeated execution of the model to ensure statistical reliability. Specifically, experiments were conducted using 100, 1000, and 2000 independent iterations. In each case, the average total performance and the average total cost were recorded. It was observed that the results obtained with the 2000 iterations converged to those obtained with 1000 iterations; therefore, it was judged that a further increase was not necessary.

The proposed method (PITTER) was compared with three other state-of-the-art methods: (a) the Classical Change Management Model (CCMM), which is based on the classical change curve and assumes fixed assignments, no training, and no positional changes over time; (b) the NSGA-II method, which applies evolutionary multi-objective optimization without adaptive training mechanisms; and (c) the CoMoRe method, which involves continuous monitoring and readjustment of the staffing allocation throughout the change process, at regular intervals. Figure 4 illustrates a comparison between the proposed method and the other methods in terms of the average performance and cost over time.

Table 8. Comparison of average total performance and coefficient of variation (CV) for compared methods (100 repetitions).

Total Performance
Time	PITTER	CV	CCMM	CV	NSGA-II	CV	CoMoRe	CV
0	969	0.27%	969	0.27%	969	0.27%	969	0.27%
1	971	0.41%	868	2.35%	972	0.40%	935	1.01%
2	914	1.17%	645	6.23%	910	1.37%	819	2.63%
3	810	2.66%	497	9.82%	783	3.08%	703	4.05%
4	732	3.76%	408	12.71%	666	4.48%	625	4.71%
5	705	4.43%	339	16.04%	588	5.43%	564	5.39%
6	695	4.84%	277	19.67%	527	6.27%	509	5.95%
7	696	5.21%	238	23.59%	470	7.38%	473	6.45%
8	725	5.10%	233	24.01%	433	7.83%	468	6.51%
9	782	5.25%	273	20.44%	427	7.71%	510	6.17%
10	887	5.08%	335	16.85%	472	7.37%	575	6.05%
11	1017	4.62%	436	13.82%	535	6.98%	687	5.56%
12	1188	4.87%	546	11.58%	646	5.72%	809	4.67%
13	1378	4.62%	697	9.57%	770	5.10%	979	4.23%
14	1611	4.79%	867	8.62%	941	4.45%	1181	3.66%
15	1875	4.54%	1035	8.63%	1144	4.43%	1376	3.40%

and

Table 9. Comparison of average total performance and coefficient of variation (CV) for compared methods (1000 repetitions).

Total Performance
Time	PITTER	CV	CCMM	CV	NSGA-II	CV	CoMoRe	CV
0	971	0.02%	971	0.02%	971	0.02%	971	0.02%
1	970	0.23%	871	2.19%	970	0.18%	935	0.92%
2	913	1.19%	652	6.92%	908	1.25%	817	2.50%
3	809	2.78%	504	10.90%	784	2.87%	701	3.69%
4	731	3.88%	415	13.86%	665	4.23%	623	4.58%
5	702	4.44%	345	17.13%	586	5.05%	561	5.24%
6	693	4.76%	285	21.35%	523	5.87%	506	6.07%
7	697	5.24%	245	25.10%	468	6.70%	468	6.62%
8	721	5.38%	240	25.63%	431	7.45%	463	6.69%
9	779	5.52%	279	22.16%	426	7.50%	505	6.23%
10	883	5.30%	339	18.55%	467	7.16%	570	5.71%
11	1010	5.29%	440	14.80%	532	6.41%	682	5.02%
12	1184	5.03%	549	12.46%	644	5.63%	804	4.41%
13	1368	4.87%	699	10.24%	768	4.99%	977	3.97%
14	1603	4.62%	868	9.05%	941	4.25%	1177	3.65%
15	1865	4.45%	1039	8.13%	1138	3.91%	1373	3.44%

summarize the corresponding arithmetic values used to create the curves in Figure 4. It is evident from Figure 4, as well as from Table 8 and Table 9, that the PITTER method achieves significantly higher overall performance compared to all the other methods. Furthermore, it can be observed that at the initial critical points, where there is a drop in overall performance, PITTER exhibits a much smaller decrease. Another important observation from both the graphical and numerical results is that the overall performance is significantly better than that achieved by the other methods. The improvement in performance achieved by the proposed model strengthens commitment to change and reduces the likelihood of abandoning the process, which is often observed in organizations when performance falls to critically low levels.

Table 8 shows that in the experiments with 100 repetitions, the average total performance starts ($t=0$) at a value of 969 for all methods, while Table 9 shows that in the experiments with 1000 repetitions, the average total performance starts ($t=0$) at a value of 971 for all methods. From $t=1$ to $t=7$, the overall performance of the proposed PITTER method begins to show a significant improvement compared to the other methods’ performance. At $t=6$ for 100 repetitions, the lowest total performance is achieved by PITTER, with a value of 695, compared to 277 for the CCMM, 527 for NSGA-II, and 509 for CoMoRe. The CCMM method at $t=8$ for 100 repetitions exhibits the lowest total performance, with a value of 233. This is the most critical point in the change process. The NSGA-II method exhibits the lowest total performance at $t=9$ for 1000 repetitions, with a value of 426. Also, the CoMoRe method exhibits the lowest total performance, with a value of 463, at $t=8$ for 1000 repetitions.

From $t=7$ the performance of PITTER, starts to increase. At $t=11$ for 100 repetitions, the total performance of the PITTER method is 1017, exceeding its initial total performance (969), while the total performance of the CCMM is less than its initial total performance, at a value of 436. Also at $t=11$, NSGA-II and CoMoRe exhibit performance values that are lower than their initial total performance, at 535 and 687, respectively. Thus, the new desired state that improves performance compared to the initial state is reached in a shorter time, reaching up to 4 time periods out of a total of 15 (representing a 27% improvement).

When comparing the coefficient of variation (CV) across 100 and 1000 repetitions, a clearer picture of algorithm stability emerges regarding performance values. PITTER shows less variation even with increased iterations (e.g., CV = 0.02% at $t=0$ and max CV = 5.52%). This consistency confirms its robustness and reliability. In contrast, CCMM exhibits high variation, with its CV values peaking at 25.63% at $t=8$. This highlights potential internal volatility in its optimization process. NSGA-II displays moderate variance (max CV = 7.5%), while CoMoRe continues to demonstrate solid and consistent behavior, with CVs between 3.44% and 6.69%. Moreover, comparing the results for 100 and 1000 repetitions indicates that the values of variation for all methods are not significantly influenced by the number of repetitions.

To facilitate a more direct comparison of the results, the Total Performance Improvement $\left(TPI\right)$ was calculated as follows:

$$TPI={\displaystyle \frac{T{P}_{PITTER}-T{P}_{ComparedMethod}}{T{P}_{ComparedMethod}}}\times 100$$

(12)

where $T{P}_{PITTER}$ and $T{P}_{ComparedMethod}$ denote the total performance achieved by PITTER and by the compared methods (i.e., CCMM, NSGA-II, and CoMoRe), respectively.

Table 10. Comparison of Total Performance Improvement for 100 and 1000 repetitions between PITTER and compared methods.

Total Performance Improvement (%)
Repetitions	100			1000
Time ($\mathit{t}$)	PITTER vs. CCMM	PITTER vs. NSGA-II	PITTER vs. CoMoRe	PITTER vs. CCMM	PITTER vs. NSGA-II	PITTER vs. CoMoRe
0	0.00	0.00	0.00	0.00	0.00	0.00
1	11.87	-0.10	3.85	11.37	0.00	3.74
2	41.71	0.44	11.60	40.03	0.55	11.75
3	62.98	3.45	15.22	60.52	3.19	15.41
4	79.41	9.91	17.12	76.14	9.92	17.34
5	107.96	19.90	25.00	103.48	19.80	25.13
6	150.90	31.88	36.54	143.16	32.50	36.96
7	192.44	48.09	47.15	184.49	48.93	48.93
8	211.16	67.44	54.91	200.42	67.29	55.72
9	186.45	83.14	53.33	179.21	82.86	54.26
10	164.78	87.92	54.26	160.47	89.08	54.91
11	133.26	90.09	48.03	129.55	89.85	48.09
12	117.58	83.90	46.85	115.66	83.85	47.26
13	97.70	78.96	40.76	95.71	78.13	40.02
14	85.81	71.20	36.41	84.68	70.35	36.19
15	81.16	63.90	36.26	79.50	63.88	35.83

presents the Total Performance Improvement (TPI) results for the two different experimental settings: 100 and 1000 repetitions. At $t=0$, all methods start with the same initial conditions, having the same performance values and corresponding $TPI$ values equaling 0. In the 100-repetitions scenario, the improvement in PITTER’s performance in comparison to that of CCMM peaks at 211% at $t=8$, highlighting the significant performance drop of CCMM during critical phases of change. PITTER consistently outperforms all the other methods across all time intervals. Specifically, its performance improvement compared to NSGA-II reaches a maximum of approximately 90% at $t=11$, while its performance improvement compared to the CoMoRe method peaks at about 55% at $t=8$. These results indicate that PITTER enables faster and more stable convergence to an improved system state. This consistent advantage in both experimental settings confirms the effectiveness of the proposed method.

Table 11. The total cost results for 100 and 1000 repetitions for the proposed PITTER method and the compared methods.

Total Cost
Repetitions	100				1000
Time ($\mathit{t}$)	PITTER	CCMM	NSGA-II	CoMoRe	PITTER	CCMM	NSGA-II	CoMoRe
0	904	904	904	904	929	929	929	929
1	908	904	907	995	928	929	927	1013
2	921	904	920	998	936	929	935	1015
3	938	904	936	1003	952	929	951	1015
4	941	904	939	1003	956	929	955	1015
5	943	904	942	1003	957	929	957	1015
6	944	904	943	1005	958	929	957	1015
7	944	904	942	1007	959	929	957	1015
8	945	904	942	1006	958	929	958	1015
9	945	904	941	1006	959	929	958	1015
10	945	904	943	1004	959	929	958	1015
11	946	904	944	1008	960	929	959	1015
12	946	904	946	1003	960	929	960	1015
13	949	904	947	1004	961	929	962	1015
14	951	904	949	1006	963	929	964	1014
15	954	904	952	1005	965	929	966	1016

presents the total cost values for the PITTER method and the compared methods over time for 100 and 1000 repetitions. At $t=0$, all methods start with the same cost value, acting as a neutral starting point. As the process progresses, the total cost of the PITTER method increases slightly due to dynamic reallocations and the calculation of the ideal point. In the 1000-repetitions scenario, the cost of PITTER remains only slightly higher than that of the CCMM (typically below 4%), demonstrating that the additional cost is controllable. Similar behavior is observed in the 100-repetitions scenario, where the cost value gradually increases from 904 to 954, while the value for CCMM is maintained at 904. However, it is worth noting that, even when the cost for PITTER is slightly increased, this method offers clearly better performance compared to the CCMM. This fact confirms that targeted training and reallocation of workers offer significant benefits without significantly increasing the total cost. Overall, the proposed method achieves a balanced approach between improving performance and stabilizing the cost at acceptable levels, which makes it particularly suitable for application in dynamic and changing environments.

The PITTER method shows costs similar to those for the NSGA-II method at almost all time points. The CoMoRe method consistently exhibits higher costs at all time points and for all simulation scenarios. Specifically, its cost exceeds that of PITTER by approximately 6–7% on average, indicating higher resource requirements. Although CoMoRe can maintain satisfactory performance levels, its high cost makes this method less efficient in environments where cost optimization is a critical factor.

Figure 5 illustrates the dynamic evolution of employee resistance and training over time achieved with the PITTER method, using two heat maps. The first map shows the level of resistance for each employee at each time point. Warm colors indicate high resistance (adaptation difficulty), and cool colors indicate negative resistance (acceptance). Initially, resistance is high for several employees, but it gradually decreases and even becomes negative in some cases, which highlights the important role of training. The second map shows the training provided to each employee. Training is more intense at the beginning, when resistance is higher. It significantly diminishes after the midpoint of the timeline as employees become familiar with the new conditions. Overall, the figure shows a system that adapts training interventions based on actual needs, resulting in a gradual reduction in resistance and in the need for additional training. Analysis of these heat maps depicting the evolution of resistance and training interventions throughout the implementation of the PITTER model clearly demonstrates the model’s effectiveness. In the early time steps (t = 1 to t = 4), several employees exhibit high resistance levels, most notably Employees 3, 6, 9, and 10. The model, employing multi-objective optimization with respect to performance and cost, allocates intensive training specifically to these individuals during the same periods. For instance, Employee 6 receives 2.27 units of training at t = 3, which directly correlates with a sharp drop in resistance from 28.2 at t = 3 to 6.9 at t = 4, with it eventually reaching −29.4 at t = 15. Notably, from t = 6 onward, the training intensity is reduced to nearly zero for all employees. Moreover, the continued reduction in resistance should be interpreted in light of the cumulative training that each employee receives up to a given time point. While the intensity of interventions declines significantly after $t=6$, the effects of earlier training sessions are not lost, but rather accumulate, enhancing employees’ adaptability.

Table 12. Examples of reallocations of employees to tasks during the change period.

Time (t)	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Employee ($\mathit{i}$)	Tasks ($\mathit{j}$)
1	10	10	2	7	7	7	7	7	7	7	7	7	7	7	7	7
2	1	1	1	1	1	1	1	1	1	1	1	1	6	1	1	2
3	3	3	6	3	3	3	3	3	3	3	3	3	3	3	3	3
4	4	4	8	6	6	6	6	6	6	6	4	6	4	6	6	6
5	5	5	5	4	4	4	4	4	4	4	8	4	1	4	8	8
6	7	7	7	5	5	5	5	5	5	5	5	5	5	5	5	5
7	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9
8	6	6	3	2	2	2	2	2	2	2	6	2	2	2	2	1
9	2	2	10	10	10	10	10	10	10	10	2	10	10	10	4	4
10	8	8	4	8	8	8	8	8	8	8	10	8	8	8	10	10

provides an example of the decisions made regarding the reallocation of employees to tasks during the implementation of PITTER. Employee 6 begins with task 7, then is reallocated to task 5 at time $t=3$ and maintains this position until the end of the change period. Employee 7 remains assigned to the same task (task 9) for the whole duration of the change period. In general, employees are expected to face approximately two reallocations during the change period.

4.3. Second Experiment: Algorithm Implementation

Following the first experiment, a second one was conducted in which the size of the hypothetical company was expanded to 100 workers and 100 corresponding jobs ($n=100$). The change period in which human behavior was simulated was kept at 15 time steps $(T=15)$. The algorithm was implemented with 100 repetitions, aiming to evaluate the effectiveness and efficiency of the proposed PITTER method.

Table 13. Comparison of the total performance and coefficient of variation (CV) results between the proposed PITTER method and the compared methods for 100 repetitions and 100 workers and jobs ($n=100$).

Total Performance
Time	PITTER	CV	CCMM	CV	NSGA-II	CV	CoMoRe	CV
0	9694	0.24%	9694	0.24%	9694	0.24%	9694	0.24%
1	9701	0.23%	8706	0.70%	9703	0.24%	9852	0.11%
2	8888	0.69%	6498	2.30%	8862	0.66%	9255	0.31%
3	7369	1.73%	5006	3.30%	7178	1.93%	8480	0.43%
4	6560	2.11%	4105	4.32%	5987	2.35%	7831	0.62%
5	6304	2.21%	3403	5.42%	5278	2.49%	7280	0.81%
6	6254	2.27%	2802	6.57%	4695	2.86%	6782	0.83%
7	6315	2.34%	2406	7.62%	4203	3.25%	6434	0.92%
8	6614	2.49%	2356	7.76%	3888	3.55%	6386	0.93%
9	7235	2.22%	2757	6.62%	3879	3.35%	6832	0.91%
10	8292	2.16%	3354	5.53%	4318	3.00%	7528	0.76%
11	9532	2.10%	4359	4.24%	4970	2.69%	8765	0.74%
12	11,204	1.90%	5456	3.56%	6041	2.47%	10,125	0.68%
13	12,986	1.93%	6954	3.07%	7229	2.31%	12,051	0.61%
14	15,203	1.90%	8652	2.63%	8842	2.14%	14,261	0.52%
15	17,676	1.77%	10,354	2.51%	10,721	1.80%	16,419	0.60%

presents and compares the aggregated results for the PITTER method and the compared methods.

Table 13 compares the overall performance results between PITTER and the other methods, for a problem with 100 workers and 100 tasks and with 100 repetitions. As can be seen, the compared methods start with the same performance level (9694) at t = 0. From t = 1 onwards, PITTER consistently outperforms the CCMM, with the difference peaking at t = 8, at which point PITTER’s average total performance has a value of 6614, in comparison to 2356 for the CCMM. At the same time step (t = 8), at which point all the methods exhibit their lowest performance, the values for NSGA-II and CoMoRe are 3888 and 6386 respectively, both of which are lower than PITTER’s value (6614). At t = 12, the total performance value of the proposed PITTER method reaches 11,204, exceeding the initial total performance (9694), while the total performance for the CCMM is lower than its initial total performance, with a value of 5456. In addition, NSGA-II at t = 12 has a performance value of 6041, significantly lower than its initial total performance. CoMoRe has a performance value of 10125, which exceeds its initial total performance, but is lower than PITTER’s performance (11,204). Thus, PITTER reaches the new desired state in a shorter time and exhibits better total performance.

A clear trend in the coefficient of variation (CV) can be observed as the sample size increases from n = 10 to n = 100. In particular, all methods benefit from reduced variation. This reduction in the CV with increasing n suggests improved statistical stability and reliability of the results. PITTER, in comparison to the CCMM and NSGA-II, shows less variation (e.g., CV = 0.24% at t = 0 and max CV = 2.49%). The CCMM exhibits higher variation values, peaking at 7.76% at t = 8, and NSGA-II also displays generally higher variance values (max CV = 3.55%). The CoMoRe method presents low CV values, with a maximum value of 0.93%.

Table 14. Comparison of Total Performance Improvement for 100 repetitions between PITTER and compared methods.

Total Performance Improvement (%)
Time ($\mathit{t}$)	PITTER vs. CCMM	PITTER vs. NSGA-II	PITTER vs. CoMoRe
0	0.00	0.00	0.00
1	11.43	−0.02	−1.53
2	36.78	0.30	−3.97
3	47.20	2.66	−13.10
4	59.80	9.58	−16.22
5	85.24	19.45	−13.40
6	123.23	33.20	−7.79
7	162.51	50.24	−1.86
8	180.70	70.13	3.58
9	162.48	86.52	5.91
10	147.20	92.02	10.15
11	118.67	91.78	8.75
12	105.35	85.45	10.65
13	86.75	79.65	7.76
14	75.72	71.93	6.60
15	70.72	64.87	7.66

presents the Total Performance Improvement (TPI) results for 100 repetitions. PITTER’s improvement in performance compared to the CCMM peaks at about 180% at $t=8$, highlighting the significant performance drop of CCMM during critical phases of change. Furthermore, its improvement in comparison to NSGA-II reaches a maximum of approximately 92% at $t=10$. In contrast, CoMoRe outperforms PITTER in the early stages ($t=0,\dots 7$), but PITTER outperforms CoMoRe from t = 8 onwards, with a performance improvement that stabilizes at around 7–10%. These results indicate that PITTER enables faster and more stable convergence to an improved system state. In summary, the results clearly demonstrate that PITTER not only achieves substantial and early performance improvements compared to existing methods such as CCMM and NSGA-II, but also exhibits strong adaptability, ultimately outperforming CoMoRe.

Table 15. Comparison of average total cost between PITTER and compared methods.

Average Total Cost
Time ($\mathit{t}$)	PITTER	CCMM	NSGA-II	CoMoRe
0	9245	9245	9245	9245
1	9224	9245	9220	9985
2	9292	9245	9262	9988
3	9420	9245	9394	9986
4	9454	9245	9424	9990
5	9433	9245	9422	10,000
6	9431	9245	9419	9996
7	9426	9245	9413	10,008
8	9415	9245	9400	10,007
9	9406	9245	9394	10,003
10	9396	9245	9386	9996
11	9385	9245	9378	9998
12	9384	9245	9384	9998
13	9382	9245	9385	10,000
14	9390	9245	9396	9988
15	9405	9245	9405	9990

presents the average total cost for PITTER and the compared methods. The evolution of the average total cost over time highlights PITTER’s dynamic adaptation capabilities. While the CCMM’s cost remains static throughout, PITTER exhibits slight fluctuations in cost before it stabilizes within a range that is consistently lower compared to CoMoRe’s cost and comparable to that of NSGA-II. Notably, CoMoRe maintains the highest cost across all time steps, indicating that it has a lower balance capability. PITTER, despite small oscillations, sustains low cost levels that are close to the theoretical lower bound (set by the CCMM), demonstrating its ability to balance optimization between objective functions with adaptability over time.

5. Conclusions and Limitations

In today’s era, organizational change initiatives are essential for increasing the competitiveness of businesses and organizations, and are usually implemented by utilizing modern information systems. However, these initiatives are often abandoned or only partially implemented due to employees’ resistance to change, which leads to a gradual decrease in performance during the critical initial stages of implementation.

This paper presents the innovative PITTER method, which aims to facilitate better decision-making with regard to change management problems through multi-objective optimization. Technological innovations allow us to monitor and extract data continuously through information systems. The method applies the principles of Evolutionary Dynamic Multi-Objective Optimization, allowing for continuous adjustment of task assignments based on fluctuations in employee performance, costs, resistance to change levels, and individual training needs.

Through simulations, it was demonstrated that the method can adapt intelligently over time, proposing solutions that achieve high performance and relatively stable costs while minimizing RtC. While initial assignments show increased resistance, this is reduced over time through the implementation of targeted reallocation and training. Extensive experiments were carried out with different problem sizes: 10 workers for 10 job positions, and 100 workers for 100 job positions. In all cases, the proposed method consistently showed higher overall performance compared to three state-of-the-art methods. At the most critical point of change, when the drop in performance reaches its maximum, PITTER exhibits a much smaller decrease in performance. For the problem involving 10 workers and 10 jobs, the performance of the PITTER method was reduced from 971 to 693 (−28.6%), while the CCMM showed a drop from 971 to 240 (−75.3%), the NSGA-II method showed a decrease from 971 to 426 (−56.1%), and the CoMoRe method showed a reduction from 971 to 463 (−52.3%). Moreover, the PITTER method achieved the new desired state, characterized by improved performance compared to the initial state, in less time than all the other methods in all the experiments. Analysis of the coefficient of variation confirmed the robustness of the PITTER method.

Visualization of the results through heat maps of resistance and training highlighted the behavior of the system over time. Training should be mainly provided in the first time steps, when resistance is high, and should be progressively reduced as employees gain experience and adapt to the new situation. The reduction in resistance observed over time seems to be related to both the continuous reallocation and the increase in cumulative training, confirming the dynamic nature and intelligent adaptability of the proposed approach.

The results consistently demonstrate that, particularly during the critical period when organizations typically experience the steepest decline in output due to RtC, PITTER maintained significantly higher performance levels compared to the other models. This substantial reduction in the performance drop showcases PITTER’s robustness under stress and its effectiveness in minimizing disruption during change. Furthermore, PITTER recovered employee performance faster than the compared methods across all the tested scenarios, reinforcing its efficiency and timeliness. Notably, the PITTER model operates as both an optimization method and a real-time decision support system. By continuously analyzing employee performance and costs, it provides actionable insights into the ongoing state of change, enabling timely detection and intervention.

Despite the positive results and high efficiency of the proposed PITTER model, its application is accompanied by certain limitations and risks that must be taken into account. First, its methodology is based on the existence of real-time performance, cost, training, and resistance data for each employee. From an implementation perspective, deploying such a system would require robust information infrastructure that is capable of collecting, processing, and acting on employee-level data in real time, an element that may pose challenges in resource-constrained environments.

Furthermore, the model assumes that all employees can perform all tasks, which, in practice, is not always the case. Also, the constant redistribution of tasks may cause psychological fatigue or dissatisfaction. The use of dynamic, algorithm-driven training reassignment raises ethical considerations regarding transparency, fairness, and autonomy, especially if employees are not made aware of the decision logic or if the model’s recommendations are used to enforce compliance.

Organizations must therefore balance efficiency gains with responsible data use, privacy safeguards, and mechanisms that account for human oversight. More broadly, the results suggest that adaptive, data-informed change management can yield long-term benefits with limited intervention, but its successful deployment requires technical readiness, organizational trust, and ethical foresight.

However, these assumptions are considered reasonable within the context of this study, as the organizational change is designed to be implemented in a relatively short time frame, within which such changes are unlikely to have a substantial impact. In addition, the model assumes the existence of integrated information systems, through which data is available in real time, allowing for continuous monitoring and immediate adjustment in the case of deviation from the initial conditions.

Future extensions of the model can incorporate worker–job compatibility matrices, time-varying cost functions, and productivity-based adjustment mechanisms to further enhance its realism and practical value. The present approach ultimately achieves a balance between modeling simplicity and practical flexibility, keeping the decision-making process operational, trackable, and adaptive.