Determining the Equilibrium Point between Efficiency and Well-Being in Enterprise Social Media Usage: A Hybrid Approach Using Response Surfaces and Optimization Methods

Abstract

With the progression of digital transformation in the workplace, the use of enterprise social media has become a daily routine in contemporary organizations. In the course of this transition, securing enterprise social media for both efficiency and individual well-being is pivotal as it steers digital transformation towards a sustainable future. Despite the huge benefits, the impact of enterprise social media on individuals is often seen as a double-edged sword, posing a managerial dilemma to organizations. To address this issue, our research developed a hybrid method aiming at maximizing efficiency and protecting employees’ psychological well-being with neither target being compromised. Polynomial regression with response surfaces was employed to visually elucidate the variations in work engagement and work exhaustion, thereby identifying the conditions for optimal values of work engagement. We then transformed the conflicting outcome variables into a single optimization goal. By calculating the equilibrium point and comparing various predictor limits, we determined an optimal condition to achieve both targets. Specifically, the equilibrium point is identified when employees’ psychological detachment slightly exceeds enterprise social media use. The optimal condition can be identified when two predictors are symmetrically aligned with each other. Our method demonstrates that a congruence framework of enterprise social media use is conducive to both efficiency and well-being, challenging the existing assertion that moderate usage is most favorable and questioning linear relationship assumptions. This study extends the innovative application of optimization techniques to broader managerial domains and provides practical solutions for reconciling the contradictory effects between well-being and efficiency, thereby promoting the sustainable success of enterprise social media.

1. Introduction

Orienting towards a sustainable future, organizations need not only to successfully implement digital transformation for improved productivity but also to prioritize protecting employees’ well-being during this transition. Compared to other innovative technologies, enterprise social media (ESM) is a more critical aspect of successful digital transformation, as its implementation costs are affordable regardless of the size of the organization and the improved work efficiency is immediately verified [1,2]. ESM refers to digital platforms designed to enhance communication, collaboration, and information sharing among employees within an organization [3]. Improving the utilization effects of the ESM at the individual level is significant and determines the prospect of digital transformation [4,5]. However, the adverse impacts such as work exhaustion and informative overload caused by ESM usage have become increasingly apparent [6,7]. In the process of steering digital transformation towards a sustainable future, answering the question of how efficiency and individuals’ well-being can be secured simultaneously is imperative, posing a complex challenge for organizations to navigate.

As a platform, ESM conveys considerable benefits to both organizational and individual productivity in areas such as video conferences, attendance management, geographical tracking, automatic replies, and e-document transfers, among others. The COVID-19 pandemic constrained physical connections among employees but, as a result, fostered virtual connections. Employees now rely heavily on these platforms for seamless communication and immediate responsiveness to various work requests, reshaping work routines. Influenced by the pandemic, many implementations of ESM de facto have been tailored for mobile devices like smartphones and tablets to further enhance workplace flexibility and job autonomy. Nevertheless, the pervasive application of mobile-based ESM has made its contradictory effects increasingly conspicuous, embodying as both negative and positive influences exerted on an individual’s efficiency. Similar to [8], who described the well-being paradox caused by human resource management systems, we contend that individuals encounter a comparable situation during ESM Usage (ESMU), in which the rise of both work engagement and work exhaustion is inevitable.

While the contradictory effects of ESMU have been documented in the existing literature, clear guidelines on addressing these effects remain scarce. Recommendations on how to balance the individual’s efficiency and well-being are inconsistent. Proponents from the positive perspective argue that increased usage of ESM leads to the ideal result of work engagement [9], while advocates from the negative perspective contend that excessive usage harms an employee’s well-being and should be restricted and managed [10]. Recent viewpoints suggest a neutral stance, synthesizing both perspectives by advocating for a moderate level of usage to yield optimal outcomes [11,12]. However, this latest view often prioritizes one side of the coin, thus failing to provide pragmatic solutions.

We suspect that this inconsistency likely arises because these perspectives rely on fragmented and isolated viewpoints to address the contradictory effects, raising the need for further investigation. Additionally, the existing findings show excessive reliance on conventional linear regression methods, rendering strategies for ESM utilization effects more arbitrary and less grounded in robust, mathematically validated evidence. Instead of proposing whether ESMU is more positively or negatively affecting individuals, or alternatively, holding linear assumptions about its impact, we aim to identify an equilibrium point within the fluctuating imbalance between efficiency and well-being. By identifying this equilibrium, it is possible to enable individuals to feel that using ESM for work activities is effectively beneficial while keeping negative feelings such as exhaustion below a critical threshold. This approach, in turn, would significantly facilitate ESM implementation towards a more sustainable future.

Specifically, this paper adopts a hybrid method consisting of two parts, Polynomial Regression with Response Surface Analysis (PRRSA) and Multi-objective Optimization with Genetic Algorithm (MOGA). PRRSA enhances our understanding of relationships between predictors and a response variable by graphing polynomial regression outcomes in three-dimensional space [13,14]. It is particularly effective in testing curvilinear effects, offering a nuanced view that common linear assumptions fail to capture. MOGA is a robust approach for addressing conflicting objectives [15]. It evaluates various conflicting goals, prioritizing them based on significance. Multi-objective problems can be tackled either by consolidating sub-objectives into a single function or by forming a Pareto front, representing a set of feasible optimal solutions [16]. The main novelties and worthy contributions of the proposed study can be outlined as follows:

• The use of nonlinear postulations in the analysis remedies the deficiencies noted in the previous literature, assisting in prudent and robust decision making within the scope of digital transformation.
• The implementation of a hybrid method considers the conflicting outcomes as an optimization target, thereby reconciling the contradictory effects and expanding the application sphere of the optimization method.
• Adopting a holistic view is able to provide managers with significant insights and guidance concerning the sustainable success of innovative technologies resembling ESM.

The remainder of this paper is structured as follows: Section 2 provides an overview of the related background. Section 3 delineates the step-by-step process in our methodology and highlights the methodological contributions. In Section 4, we present the experimental results in a sequence corresponding to the steps outlined in the methodology. Section 5 discusses the theoretical contributions and practical implications. Finally, Section 6 offers conclusions, highlights the limitations, and suggests directions for further research.

2. Related Background

2.1. The Contradictory Effects of ESMU on Individuals

Since the introduction of enterprise social media (ESM) in 2013 [17], research on its impacts on individuals has shown an evolutionary and spiral trajectory. Prior to the COVID-19 pandemic, scholars predominantly focused on the potential benefits of ESM (see [18] for more details). However, the widespread adoption of ESM platforms on mobile devices has led to a more comprehensive and balanced viewpoint, shifting from predominantly positive narratives to more conservative arguments that recognize both the beneficial and adverse effects of ESMU.

One typical criticized aspect lies in the extended availability facilitated by mobile ESM, bringing these conflicts to the forefront. Consequently, recent researchers favor a more neutral stance regarding its controversial impacts [19,20]. The Job Demands and Resources (JD-R) theory serves as a well-established framework that is frequently used to explain these contradictory effects. The JD-R model posits that job demands and job resources can trigger two independent processes: the health impairment process, characterized by the job demands–burnout pattern, and the motivational process, which describes the job resources–engagement pathway.

Substantial evidence supports this theory. From the job resources dimension, ESM enhances employees’ sense of job control by providing perceived job resources [21,22,23]. The improved connectivity and increased productivity resulting from ESM significantly boost employees’ productivity at work. Meanwhile, as the job demands, constant immersion in a digital environment saturated with work-related messages has blurred the boundaries between work and personal life, thereby undermining employees’ psychological well-being [24,25]. Mobile-based ESM has exacerbated occupational detriments such as stress, exhaustion, and burnout, ultimately impairing individuals’ long-term work performance [7,18].

In short, the extant literature suggests that using ESM for work offers several benefits, including enhanced work engagement, increased productivity in remote communications, swift responses, knowledge sharing, and knowledge archiving. These advantages highlight ESM’s potential for improving employee efficiency at work. However, its negative effects are also evident to employees, including sleep problems, sleep procrastination, work exhaustion, information fatigue, and boundary erosion. These adverse impacts primarily affect psychological well-being, leading to chronic impairments in health. The existence of both positive and negative results constitutes the contradictory effects between efficiency and well-being when using ESM for work.

2.2. WEG and WEH as Representations

Following the principles of JD-R theory, ESMU at work activates two distinct pathways of influence, in which the influenced outcomes are represented as work engagement and work exhaustion. Work engagement (WEG) refers to a positive, fulfilling, work-related state of mind characterized by vigor, dedication, and absorption [8]. As a valuable job resource, ESM enhances employees’ collaboration and productivity across various dimensions. In this sense, maximizing work efficiency via EMS platforms manifests as improved work engagement after usage [26]. Conversely, work exhaustion (WEH) is characterized by chronic physical and emotional depletion resulting from sustained and excessive work-related stress, leading to diminished effectiveness and a sense of helplessness and detachment from job responsibilities [27]. Excessive reliance on ESM signifies that an increasing number of work demands are being conveyed digitally, thereby depleting employees’ cognitive resources. Continuously fulfilling work responsibilities on ESM platforms irrespective of physical location further burdens work exhaustion feelings. As usage continues, the severity of work exhaustion escalates, adversely affecting well-being.

A synopsis of the previous findings is depicted in Figure 1. We distill these contradictory effects by portraying an imbalance fluctuation between WEG and WEH, which we term the work outcomes paradox. WEG and WEH are capable of embodying extreme cases, thereby accentuating the contradictory attributes. For other positive or negative impacts, the conflicting feelings experienced by employees may be less severe. Moreover, other impairments to mental well-being, such as procrastination or burnout (as indicated in Figure 1), are distal variables that may develop through complex and compounded linkages. Investigation of those variables deviates from our original purpose of addressing the duality between efficiency and well-being in the ESMU context.

Unlike prior studies constrained by traditional linear regression methods, we endeavor to propose a mathematical solution to reconcile these contradictory effects, as depicted in Figure 1. Let $f^{\prime }\left(x\right)$ represent the first objective and $f\left(x\right)$ represent the second objective. For simplicity, these two objectives are described by the single variable functions, allowing our proposed solution to be illustrated on a two-dimensional graph. We vaguely abstract the contradictory effects as one positive function and one negative function. Regardless of the specific situation and the fluctuation under different conditions, it is feasible to define a mathematical solution wherein both targets are acceptable. If we define x as belonging to the set of positive natural numbers, the point we highlight with a red solid circle on the X-axis is the favorable solution.

Furthermore, it is essential to integrate additional factors to orientate the contradictory effects towards a more positive and sustainable direction. Psychological detachment refers to an individual’s ability to mentally disengage from work during off-job time, which is considered a strong indicator of recovery experience [28]. In the Extended Stressor-Detachment Model, psychological detachment is proposed as a crucial mechanism linking stressors and strain reactions. Empirical evidence indicates that psychological detachment serves as a buffer against various stressors, including long work hours [29], prolonged mobile work exposure [30], and high work intensity [31]. Consequently, an (in)congruence framework between ESM use (ESMU) and psychological detachment (PSD) has been proposed, which may potentially optimize contradictory effects.

These prior findings contribute significantly to understanding how ESMU impacts individuals. However, they often fall into the dichotomy of viewing ESMU as either beneficial or detrimental, lacking a comprehensive perspective that addresses its contradictory effects. Seeking better solutions to simultaneously ensure efficiency and well-being is fundamentally about directing ESM towards a sustainable future.

2.3. The Case of the Chinese Workplace

Our research specifically focuses on the Chinese workplace, with a particular interest in public employees working in street-level bureaus. The rationale behind this focus is twofold. First, existing studies [32,33] have found that officials from public organizations in Eastern regions heavily utilize private social media for work-related discussions. This phenomenon can be attributed to the rapid development and widespread adoption of ESM platforms across various sectors. For instance, DingTalk has amassed 600 million users and more than 23 million enterprise organization accounts by the end of 2022 [34]. Additionally, the active user base of WeChat reached 1359 million by the first quarter of 2024 [35]. Although WeChat is not a typical ESM platform, its convenience and extensive user base blur the boundaries between work and non-work activities. Compared to ESM platforms commonly used in a Western context, the pervasiveness of these popular Chinese ESM platforms is remarkable, exacerbating the contradictory effects.

Second, the responsibilities and business operations of private sector organizations are heterogeneous, making it difficult to attribute employees’ efficiency strictly to ESM usage. Conversely, in Chinese public organizations, an increasing number of public services are provided digitally, and their digital transformation is well documented [36]. These institutions heavily rely on digital platforms to enhance the convenience of public service provision, requiring a high level of responsiveness from employees. The completion of responsibilities is majorly determined by a public employee’s efficiency when using ESM for work. The ethos of serving the public interest, regardless of whether employees are on or off duty, is highly valued. Consequently, it is more likely that public employees, either voluntarily or involuntarily, rely on ESM platforms to improve their work efficiency.

3. Methodology

To determine the equilibrium point, we developed a novel methodology based on PRRSA and MOGA, as illustrated in Figure 2. At the individual level, Enterprise Social Media Usage (ESMU) serves as the primary indicator contributing to the contradictory effects. Drawing on prior theoretical findings, psychological detachment (PSD) was incorporated to construct a holistic (in)congruence framework. If this equilibrium point exists (see the point on the seesaw in Figure 2), it could offer a pragmatic solution for the sustainable success of ESM and assist managerial decision making.

The devised methodology can be divided into six sequential steps:

• Conversion to Mathematical Formulation: We translated the contradictory effects into a mathematical model, incorporating variables ESMU, PSD, WEG, and WEH to address the research problem. Specifically, we sought to identify what conditions between ESMU and PSD would generate high WEG and low WEH simultaneously.
• Utilizing Survey-Based Data: We employed survey-based data as the data source due to its significant advantage in ease of operation and direct measurement of individual perceptions.
• Standard Statistical Examination: Following conventional schemes in behavioral science, we conducted a rigorous statistical examination of the data, thereby verifying the fit between the variables and the collected data.
• Assessment of Contradictory Effects: We examined whether the contradictory effects of ESMU applied to our sample, ensuring the adequacy and relevance of the final solution. This was achieved by assessing the path estimates across independent and dependent variables.
• The Curvilinear Patterns: We investigated the curvilinear patterns of WEG and WEH and further discussed the conditions that significantly increase WEG and decrease WEH. This step was executed using the PRRSA technique.
• Equilibrium Point Identification: We identified the equilibrium point and the conditions necessary to achieve two conflicting objectives concurrently. This step was executed using MOGA and Pareto front techniques.

The statistical examinations and data collection are standard procedures and, therefore, omitted in Figure 2. This comprehensive methodology encompasses several significant methodological contributions, which are listed as follows.

First, although we employed survey-based data, we assert that the collected data primarily served as input for PRRSA and MOGA analyses. This differentiates our method from conventional hypothesis-driven survey approaches. By doing so, we substantially broaden the application of survey-based data, breaking the traditional linkage between survey methods and linear regression. This approach empowers survey data to be effectively integrated with various advanced algorithms.

Second, concerning the optimization method, formulating the appropriate equations that accurately describe the research problem is crucial. We utilized the mathematical formulations derived from the response surface methodology to construct mathematical expressions for conflicting objectives, thereby extending the application scenarios of optimization methods in addressing traditional managerial challenges.

The details of each step are elaborated in the following sections. We commence this section by presenting PRRSA and MOGA, as these represent the core methodological contributions.

3.1. PRRSA

Polynomial regression is a type of multiple regression analysis in which the relationship between the independent variable X and the dependent variable Y is modeled as an nth-degree polynomial. The polynomial regression model is formulated as follows:

$$Y={\beta }_0+{\beta }_{1}X+{\beta }_2{X}^2+{\beta }_3{X}^3+\cdots +{\beta }_n{X}^n+ϵ$$

(1)

where ${\beta }_0,{\beta }_1,{\beta }_2,\dots ,{\beta }_n$ are the coefficients and $ϵ$ is the error term.

Response surface methods are a collection of mathematical and statistical techniques used for modeling and analysis of problems in which a response of interest is influenced by several variables. The main idea is to use a polynomial regression model to approximate the true relationship between the response and explanatory variables. In this regard, polynomial regression and response surfaces are usually combined as an integral tool in comprehending the curvilinear impacts between independent and dependent variables. The second-order model typically used in response surface methods is as follows:

$$Y={\beta }_0+\sum _{i=1}^k{\beta }_i{X}_i+\sum _{i=1}^k{\beta }_{ii}{X}_i^2+\sum _{i<j}{\beta }_{ij}{X}_i{X}_j+ϵ$$

(2)

where Y is the response, $X_i$ are the explanatory variables, ${\beta }_0,{\beta }_i,{\beta }_{ii},{\beta }_{ij}$ are the coefficients, and $ϵ$ is the error term.

A plethora of existing studies have utilized PRRSA to investigate nonlinear relationships across diverse contexts, corroborating its effectiveness and soundness in providing significant insights [37,38].

3.2. MOGA

The goal of multi-objective optimization is to identify all possible trade-offs among multiple conflicting functions. In the engineering industry, multi-objective optimization using genetic algorithms is widely used because manufacturing problems typically involve multiple targets, such as minimizing cost and maximizing performance. In practice, choosing a single optimal solution for multiple objectives is often very difficult. Therefore, a set of Pareto optimal solutions is provided to the decision maker. A multi-objective optimization problem can be mathematically formulated as follows:

$$\begin{array}{cc}\hfill min& \mathbf{y}=f\left(\mathbf{x}\right)={[f_1\left(\mathbf{x}\right),\dots ,f_m\left(\mathbf{x}\right)]}^T\hfill \\ \hfill \mathrm{s}.\mathrm{t}.& g_j\left(\mathbf{x}\right)\le 0(j=1,2,\dots ,p)\hfill \\ \hfill & h_k\left(\mathbf{x}\right)=0(k=1,2,\dots ,q)\hfill \\ \hfill & x_i^{min}\le x_i\le x_i^{max}(i=1,2,\dots ,n)\hfill \\ \hfill & \mathbf{x}={[x_1,x_2,\dots ,x_n]}^T\in \Theta \hfill \\ \hfill & \mathbf{y}={[y_1,y_2,\dots ,y_m]}^T\in \Psi \hfill \end{array}$$

(3)

where m is the number of optimized objective functions, $\Theta$ is the n-dimensional search space and is determined by the upper bound $x^{max}={[x_1^{max},\dots ,x_n^{max}]}^T$ and the lower bound $x^{min}={[x_1^{min},\dots ,x_n^{min}]}^T$, and $\Psi$ is the m-dimensional vector space of objective functions and is determined by $\Theta$ and $f\left(\mathbf{x}\right)$. Equations $g_i\left(x\right)\le 0(j=1,2,\dots ,p)$ and $h_k\left(x\right)=0(k=1,2,\dots ,q)$ denote p inequality constraints and q equality constraints.

Genetic algorithm (GA) is an adaptive heuristic search method based on population genetics. The GA transforms a set (population of individuals) each with an associated fitness value, into a new population (next generation). The key elements of GA are chromosome representation, selection, crossover, mutation, and fitness function computation. The goal of GA is to find the best or near-optimal solutions to complex problems. The pseudocode of a standard GA is shown in Algorithm A1 in Appendix B. The reader can refer to [39] for more details on GA. In managerial science, GA has been successfully applied to various resource-scheduling problems [40,41].

3.3. The Pareto Front

The definition of Pareto optimality can be expressed as follows: if the vector $\mathbf{x}=\{x_1^{*},x_2^{*},\dots ,x_n^{*}\}$ satisfies the condition $\nexists \mathbf{x}\in \Theta ,\mathbf{x}>{\mathbf{x}}^{*}$, then ${\mathbf{x}}^{*}$ is called a Pareto optimality solution, expressed as $P{S}^{*}$. The Pareto optimality solution set presented in the objective function space is called the Pareto front, which is mathematically expressed as follows:

$$P{F}^{*}=\{f\left({\mathbf{x}}^{*}\right)\mid {\mathbf{x}}^{*}\in P{S}^{*}\}$$

The Pareto front, as defined, is the set of all Pareto optimal solutions in the objective space, representing the best trade-offs among objectives. Each point on the Pareto front corresponds to a solution where improving one objective would lead to the deterioration of another. The importance of the Pareto front can be summarized in three key aspects: trade-off visualization, decision support, and solution diversity. First, it visualizes the trade-offs between conflicting objectives, helping decision makers understand the compromises involved [42]. Second, it provides a set of high-quality solutions, allowing decision makers to select the one that best aligns with their priorities [43]. Third, it presents a diverse range of solutions, beneficial for finding robust and adaptable options for various scenarios [44].

3.4. Measures and Data Collection

As shown in Figure 2, the input and output variables include ESMU, PSD, WEG, and WEH. We measured them with well-established questionnaires from prior literature. This approach allows us to directly address our research question without being obsessed with quantifying the magnitudes of efficiency and well-being. Additionally, given that the contradictory effects are more determined by employee’s perceptions, a questionnaire-based data collection method is suitable.

The four items used to measure ESMU were adapted from [45], which explored the reasons and behavior patterns of ESMU with a specific focus on employees, thus aligning well with our research problem.

PSD was measured using four indicators derived from [46]. This referenced study thoroughly discussed the linkage between smartphone use for work activities, decreased psychological detachment, and its impacts on mental well-being.

Work engagement was adapted from [47,48]. In their studies, they presented how mobile technology use helps individuals be more engaged in their work.

Work exhaustion was a measure of four items based on the articles [49,50]. They explored how work-related technology usage arouses the employee’s feeling of exhaustion, therefore causing detriments to individual efficiency.

These measurements were selected due to their high relevance and repeated examinations, demonstrating robust content validity. To ensure semantic equivalence across the two languages (Chinese and English), we employed a translation/back-translation procedure. All items were measured on a 5-point Likert scale, with anchors ranging from 1 (strongly disagree) to 5 (strongly agree).

Table A1. Variables and corresponding measurement.

Variables	Items
ESMU	1: I use ESM to obtain ideas and participate in work-related discussion.
	2: I use ESM to acquire solutions for work problems.
	3: I use ESM to manage and coordinate tasks with my colleagues.
	4: I use ESM to give and receive updates on events and issues in my work environment.
PSD	1: During after-work hours, I forgot my work.
	2: During after-work hours, I don’t think about my work at all.
	3: During after-work hours, I distance myself from my work.
	4: During after-work hours, I get a break from the demands of work, particularly those demands that come from ESM.
WEG	1: Using ESM for work makes me feel that I am bursting with energy.
	2: Using ESM for work makes me feel that I am enthusiastic about my work.
	3: When using ESM for work, I feel that I am immersed in my work.
	4: Using ESM for work makes me feel strong and vigorous towards my work.
	5: My work inspires me.
WEH	1: Using ESM for work makes me feel emotionally drained from my work.
	2: Using ESM for work makes me feel fatigued when I get up in the morning and have to face another day on the job.
	3: Using ESM for work makes me feel burned out from my work.
	4: Working all day is really a strain for me.

in Appendix A presents the details of each item.

From May to July 2023, questionnaires were distributed to 244 participants recruited through a series of training courses designed for public employees in an eastern city of China. All participants worked in street-level bureaus, where their responsibilities involve substantial communication and coordination tasks, thus exhibiting a strong reliance on ESM platforms during both work and non-work hours. Prior to participation, we distributed a plain paper asking about their use of ESM or general social media for work-related discussions in the previous two weeks and, if applicable, which platforms they used. The responses included WeChat, QQ, DingTalk, and internally developed ESMs. The behavioral patterns indicated that private social media platforms are primarily used for urgent tasks or communication with citizens and external partners, while internal ESM platforms are preferred for handling confidential files and adhering to standard work procedures. These respondents were deemed suitable for our research objectives and were consequently selected.

Upon confirming our target sample, we fully explained the purpose of our investigation to those willing to participate. Given that altruism and obedience are highly valued in public sectors, particularly within our cultural context, we emphasized the anonymity of the entire process. We assured participants that no sensitive information, such as specific positions or the institutions they currently serve, would be collected. This approach aimed to gather authentic responses by alleviating concerns about any potential negative impact on their careers.

Out of the 243 responses received, 43 were eliminated due to missing data or identical answers throughout the survey, resulting in 200 valid responses. While this dataset may not be large enough for making robust inferences using traditional linear regression methods, there is no clear answer in existing studies suggesting that small datasets are less reliable for response surface methodology and multi-objective optimization techniques. To the best of our knowledge, small datasets are commonly used in a variety of optimization technique applications [51,52,53], showing potent and robust performance. As our purpose is to determine the equilibrium point between efficiency and well-being, both large and small datasets have been deemed applicable and not peculiar. Accordingly, the remaining responses were retained for further analysis.

The socio-demographic characteristics of the participants are outlined as follows: 63.5% of the respondents are male and 36.5% are female. Age distributions are as follows: 11% are between 21 and 30 years old, 42.5% are between 31 and 40 years old, 31.5% are between 41 and 50 years old, and 15% are above 51 years old. Regarding work experience, 10.8% of the sample has less than 5 years of experience, 11.5% has between 5 and 10 years, and 78% has more than 10 years of work experience.

4. Results

In accordance with the proposed methodology, this section encompasses the results from standard statistical examination, assessment of contradictory effects, the curvilinear patterns, and equilibrium point identification. We begin with the standard statistical examination. Following this, PRRSA was utilized to identify the conditions that yield the optimal results for WEG and WEH separately. Finally, the MOGA technique was employed to quantify the optimal solution that simultaneously achieves the competing targets.

4.1. Standard Statistical Examination

As a survey-based data source, assessing the quality of the measurement model is necessary. Common Method Bias (CMB) was examined through Harman’s single-factor analysis [54]. This procedure was performed by utilizing the psych package in R programming software (version 4.3.1). The parameters of the fa() function were set to ensure that only one factor was extracted by specifying nfactors equal to one. The results indicate that the extracted factor accounted for only 28.04% of the variance, suggesting that CMB is not a significant contaminant in this context [55,56].

Other statistic examinations include Confirmatory Factor Analysis (CFA), as well as reliability and validity examinations. The CFA was conducted using the lavaan package with the cfa() function in R. The results showed that our model had a good fit with the data (${\displaystyle \frac{{\chi }^2}{df}}=1.58$; RMSEA = 0.054; CFI = 0.964; TLI = 0.957). Reliability, and convergent and discriminant validity were subsequently assessed using the combination of semTools, lavaan, and psych packages.

Table 1. Psychometric properties of the scale.

Reliability and Convergent Validity						Discriminant Validity
Construct	Items	Loading	Cronbach’s Alpha	CR	AVE	1	2	3	4
1. ESMU	ESMU1–ESMU4	0.755–0.919	0.862	0.906	0.708	0.841
2. PSD	PSD1–PSD4	0.737–0.862	0.811	0.873	0.634	−0.248	0.796
3. WEG	WEG1–WEG5	0.731–0.885	0.896	0.923	0.707	0.154	0.254	0.841
4. WEH	WEH1–WEH4	0.781–0.933	0.882	0.919	0.741	0.323	−0.246	−0.258	0.861

Note: Bold-faced elements are the square roots of AVEs.

shows that the Cronbach’s Alpha and Composite Reliability (CR) values are above 0.7, indicating satisfactory reliability [55]. The Average Variance Extracted (AVE) for each construct exceeds the recommended value of 0.5, confirming convergent validity [57]. Discriminant validity was verified using the method from [58], where the square root of AVE for each construct is greater than its correlations with other constructs. As shown in Table 1, the diagonal values exceed the corresponding row and column correlations, confirming discriminant validity. Further details on the recommended threshold values for psychometric properties can be found in numerous empirical studies [59,60]. Overall, the measurement model quality is satisfactory.

4.2. Assessment of Contradictory Effects

We examined whether the contradictory effects apply to our sample, as it is almost impossible to cover the entire population in the public sector. This assessment is a prerequisite for identifying feasible practices of equilibrium point and might play instrumental roles in enhancing generalizability. Following the conventional scheme, we used the bootstrapping method with 5000 subsamples to estimate the significance levels of the path coefficients. Our results show that ESMU is significantly related to work engagement ($\beta =0.231,p<0.05$) and work exhaustion ($\beta =0.279,p<0.001$). PSD has a significant positive effect on work engagement ($\beta =0.311,p<0.001$) but a significant negative effect on work exhaustion ($\beta =-0.177,p<0.05$). This result confirms that, within our sample, using ESM leads individuals to experience both increased work engagement and work exhaustion. The existence of contradictory effects may jeopardize the sustainable development of ESM during the digital transformation process. Therefore, finding an optimal balance is paramount.

4.3. The Curvilinear Patterns Using PRRSA

The polynomial regression involves two simple terms, two squared terms, and one interaction term, which are used to estimate the outcome variable. The equation is shown in Equation (2). According to this, we formulated the mathematical expression applying to our research question as follows:

$$f(x_1,x_2,w)=Z=w_0+w_1{x}_1+w_2{x}_2+w_3{x}_1^2+w_4{x}_1{x}_2+w_5{x}_2^2$$

(4)

where Z is the outcome variable (WEG or WEH), $x_1$ is ESMU, and $x_2$ presents PSD. Predictors were grand-mean centered to mitigate potential multicollinearity. Unlike scale centering, grand-mean centering reduces nonessential multicollinearity between linear terms and their quadratic counterparts, enhancing the result interpretability [61].

Table 2. Results of polynomial regressions.

Variables	Dependent: WEG		Dependent: WEH
	Model 1	Model 2	Model 3	Model 4
Intercept	3.646 (0.224) ***	3.321 (0.233) ***	4.379 (0.253) ***	4.409 (0.260) ***
Control variables
Gender (ref. male)	−0.274 (0.141)	−0.232 (0.135)	−0.074 (0.16)	−0.074 (0.151)
Working years (ref. below 5 years)
5–10 years	−0.246 (0.288)	−0.017 (0.281)	0.125 (0.325)	0.094 (0.314)
greater than 10 years	0.266 (0.224)	0.469 (0.217) *	−0.524 (0.253) *	−0.57 (0.243) *
Polynomial terms
$ESMU\left(b1\right)$		0.253 (0.096) **		0.280 (0.107) **
$PSD\left(b2\right)$		0.294 (0.074) ***		−0.242 (0.082) **
$ESMU\times ESMU\left(b3\right)$		0.061 (0.059)		−0.019 (0.066)
$ESMU\times PSD\left(b4\right)$		0.132 (0.065) *		−0.116 (0.073)
$PSD\times PSD\left(b5\right)$		0.096 (0.057)		0.016 (0.064)
$Adjusted{R}^2$	0.04	0.146	0.036	0.159
a1: slope along the LOC		0.55 (0.14) ***		0.04 (0.16)
a2: curvature on the LOC		0.29 (0.09) **		−0.12 (0.11)
a3: slope along the LOIC		−0.04 (0.10)		0.52 (0.11) ***
a4: curvature on the LOIC		0.03 (0.09)		0.11 (0.11)

Notes: Unstandardized coefficients are reported. The values in parentheses represent standard error. LOC denotes line of congruence. LOIC denotes line of incongruence. * p < 0.05, ** p < 0.01, *** p < 0.001.

displays the analysis results. In Model 1, the outcome variable was regressed on control variables. Model 2 extended this by including five predictors. The same steps were taken for work exhaustion in Models 3 and 4.

The five estimated regression coefficients in Table 2 were used to plot response surface graphs for result interpretation. Response surface analysis involves (1) identifying the first principal axis via the stationary point, and (2) computing the slope and curvature of the response surface along the congruence and incongruence lines. Drawing a perfect congruence line ($X=Y$), the slope of the congruence line (a1 in Table 2) represents how congruence between ESMU and PSD relates to work engagement, while the curvature (a2 in Table 2) indicates whether this relationship is linear or curvilinear. As can be seen in Figure 3, the response surface is convex, with the stationary point at $X_0=-1.628$, $Y_0=-0.4121$. The slope is positive and significant ($a_1=0.555,p<0.001$), suggesting that work engagement increases as both predictors increase. Moving along the congruence line (from the front of the graph to the back), the highest level of work engagement is found at the back corner of the graph where ESMU and PSD are both high. A significant and positive curvature ($a_2=0.29,p<0.01$) indicates that there is an inclined U-shaped curvilinear relationship. This diagram confirms that work engagement increases considerably when ESMU and PSD are congruent and high, compared to low and moderate levels.

We continue with the incongruence situation $X=-Y$. The stationary point was located at $X_0=-1.303,Y_0=2.481$. The slope of the incongruence line depicts how the direction of the discrepancy between predictors is related to the outcome variable. In Table 2, a significant and positive slope ($a_3=0.52,p<0.001$) indicates that work exhaustion would increase when the direction of the discrepancy is such that ESMU is higher than PSD rather than vice versa. As Figure 4 visualizes, work exhaustion is lower at the left corner where PSD exceeds ESMU than at the right corner where ESMU exceeds PSD. Following the incongruence line from left to right, the highest work exhaustion occurs at the upper right corner of the surface. Thus, the more ESMU exceeds PSD, the greater the work exhaustion. Therefore, to minimize work exhaustion, it is recommended to maintain PSD higher than ESMU.

The results based on PRRSA show that the high congruence framework generates the high WEG in a nonlinear manner, and the low WEH occurs when PSD is much greater than ESMU. In other words, when these two objectives are treated independently, no parameter configuration can achieve ideal results for both and, thus, no compromise solution can be identified. To address this issue, we converted the mathematical expressions derived from PRRSA into a problem definition suitable for MOGA. This approach is able to identify the equilibrium point between the two conflicting objectives.

4.4. Equilibrium Point Identification Using Pareto Front

In our case, the nature of contradictory effects shares similarities with the multi-objective problem. Therefore, a reasonable solution is to investigate the set of decision vectors, each of which satisfies the objective at an acceptable level without being dominated by any other solutions. WEG is the first objective ($f_1$) and WEH is the second objective ($f_2$). We use MATLAB programming software (version 2017b) to formulate the equations of ($f_1$) and ($f_2$), which are derived from the response surface analysis (see Table 2 and Equation (1)). The polynomial terms in the equation are set as 2. The optimization problem is converted into $Max{f}_1$ and $Min{f}_2$, and the equations for two objectives are formulated as follows:

$$\left\{\begin{array}{c}{f}_1(x,y)=Z=3.645+0.237x+0.284y+0.042x^2+0.149xy+0.067y^2\hfill \\ f_2(x,y)=Z=3.909+0.299x-0.234y-0.001x^2-0.112xy+0.042y^2\hfill \end{array}\right.$$

(5)

where x represents ESMU and y represents PSD. The problem is illustrated in Figure 5 for better understanding. The constraints could be equalities or inequalities, which define the search domain of functions. The curve along points AB is the Pareto-optimal frontier. Point A is a trade-off point at which $f_1$ is minimized and point B is a trade-off point where $f_2$ is minimized. Based on the PF graph, we can select appropriate solutions along the curve AB to satisfy various scenarios. In our specific problem, the circled region represents our target solutions where the problem can be solved ideally.

GA is particularly suited to finding a diverse set of Pareto optimal solutions. According to the pseudocode in Algorithm A1 (see Appendix B), the Pareto front is generated by the following steps.

• Initialization: Generate an initial population of potential solutions randomly.
• Evaluation: Evaluate the fitness of each individual based on the two objectives.
• Non-Dominated Sorting: Sort the population into different fronts based on Pareto dominance. The first front (Pareto front) consists of all non-dominated solutions. The second front consists of individuals dominated by those in the first front but not by each other, and so on.
• Crowding Distance Calculation: To maintain diversity within the Pareto front, calculate the crowding distance for each individual, which measures the density of solutions in the objective space around a particular solution.
• Selection, Crossover, and Mutation: Apply genetic operators to evolve the population across generations, ensuring that the diversity and quality of the Pareto front are maintained.
• Convergence: The algorithm converges when the population stabilizes, and further generations do not produce significantly better Pareto front solutions.

The whole process for Pareto front plotting was conducted via MATLAB programming software. Notably, we manually set numerical constraints for ESMU and PSD. Given that the survey data used for optimization is in the format of a Likert scale, the theoretical bounds for these two predictors range from 0 to 5. However, for ESMU, zero is meaningless because WEG and WEH are triggered by actual usage behavior (as discussed in the aforementioned sections). If the behavior does not exist (i.e., ESMU equals zero), there is no need to optimize the conflicting objectives. As such, the lower bound of ESMU was set to 1. A PF graph after the MOGA is plotted in Figure 6a. The circled region represents all optimal points that satisfy our specific target. Additionally, if the target is to maximize WEH, the solution remains accessible, as shown in Figure 6a.

Table 3. Selected PF points after MOGA.

	${\mathit{f}}_1$	${\mathit{f}}_2$	($\mathit{x},\mathit{y}$)
Candidate 1	12.027	2.594	(4.689, 4.854)
Candidate 2	9.964	2.981	(3.668, 4.353)
Candidate 3	10.276	2.924	(3.538, 4.682)
Candidate 4	10.663	2.856	(4.058, 4.506)
Candidate 5	12.684	2.462	(4.989, 5)

presents the values of the selected points (ideal solutions) depicted in Figure 6a. All five candidate solutions satisfy our target of producing values higher than 10 for $f_1$ and values lower than 3 for $f_2$, with the threshold values set at 3 and 10, respectively. It is evident that WEG is maximized and WEH is minimized only when both x and y are high, confirming the robustness of our prior results (see Candidates 1 and 5). In addition, these candidate PF solutions suggest that, when PSD is slightly higher than ESMU, the equilibrium point can be identified.

We continue to adjust the parameters of the two predictors and compare the PF graphs under different conditions. Each condition reflects a practical strategy by varying the configuration between ESMU and PSD.

• Scenario (a): This is the baseline case where ESMU varies between 1 and 5, and PSD ranges from 0 to 5. We expect that any alternative solution set is superior or at least equivalent to this baseline.
• Scenario (b): Here, the lower limits of ESMU and PSD are adjusted to 3, representing a situation where individuals encounter moderate to high levels of ESMU and PSD.
• Scenario (c): The upper bound of PSD is decreased to 3, reflecting a case where recovery experience is suppressed, yet flexible ESMU is applied.
• Scenario (d): Depicting an extreme situation where the individual experiences reduced PSD alongside asymmetrically raised ESMU.

Figure 6 illustrates all solutions on the Pareto front for scenarios (a), (b), (c), and (d).

Table 4. Comparison of the PF points across the scenarios.

	${\mathit{f}}_1$			${\mathit{f}}_2$
	Mean	Max	Min	Mean	Max	Min
Scenario (a)
All solutions on PF	7.996	12.684	3.926	3.305	4.208	2.462
Scenario (b)
All solutions on PF	10.101	12.700	7.350	2.962	3.465	2.459
$\Delta$PF	2.105	0.016	3.604	−0.343	−0.743	−0.003
Scenario (c)
All solutions on PF	6.303	9.568	3.933	3.732	4.521	3.376
$\Delta$PF	−1.693	−3.116	−0.007	0.427	0.313	0.914
Scenario (d)
All solutions on PF	6.574	9.485	4.734	4.002	4.797	3.379
$\Delta$PF	−1.422	−3.199	−0.808	0.697	0.589	0.917

compares the performance of optimal points on PF. We can first exclude scenarios (c) and (d) since their solution sets are inferior to the baseline case (see the degradation amount in Table 4). In scenario (b), nine candidate points based on two criteria generate a superior solution set compared to the baseline. For the first objective, the mean value in scenario (b) is much higher than the alternative points in other scenarios, and its minimum value is close to the mean value in scenario (a). For the second objective, the mean value in scenario (b) is lower than in the other scenarios, resulting in the desired balance.

In this study, we adopt point B as the equilibrium point to maximize the effects of WEG as illustrated in Figure 6. By configuring ESMU and PSD at high levels concurrently, we achieve an optimal outcome wherein WEG is maximized and WEH is minimized, yielding a ratio of 6:1 (see Table 4). Since the measurements of WEG and WEH are based on a Likert scale, this ratio primarily reflects the relative propensities of the two variables. Nevertheless, this ratio serves as a significant indicator, suggesting that, post-optimization, the balance between these two competing outcomes heavily favors the positive aspect. The maximization values obtained for work engagement should be interpreted as more figurative rather than absolute. Furthermore, in comparison to the baseline scenario, scenario (b) demonstrates the optimal condition, as evidenced by a significant increase in the number of favorable points, thereby expanding the range of ideal solutions.

5. Discussion and Contribution

First, our study advances the research on ESMU by emphasizing the equal importance of efficiency and well-being and elucidating their nonlinear patterns. The existing literature predominantly examines the relationship between a single predictor and one outcome variable via linear assumption, reaching inconsistent findings. We, instead, transcend this narrow focus by aiming to satisfy an overarching target: maximizing efficiency at the individual level during usage. Through a congruence framework between ESMU and PSD, our results reveal a curvilinear relationship between this congruence framework and work engagement. Notably, the response surface of work engagement remains nearly stable along the congruence line, with slight increases observed when both predictors are low. This allows us to challenge previous research, which has overemphasized the linearity methods, thereby neglecting potential nonlinear associations within the ESMU context. As stated by [62], future research examining the relationship between job performance and well-being must incorporate nonlinear speculations or cyclical investigations to advance methodological rigor. This finding, therefore, addresses the latest calls. Additionally, our work represents a critical departure from prior research, suggesting that using ESM does not inevitably lead to uniformly positive or negative outcomes.

Second, we demonstrated that the synergy between ESMU and PSD contributes to the enhancement of positive outcomes within conflicting objectives, indicating that adopting a holistic perspective can reconcile contradictory effects. This allows us to contribute to the existing body of research by illustrating that incorporating PSD is crucial for addressing the duality of ESMU at work. Unfortunately, the previous literature has not adequately and empirically delineated the potential influences of PSD on work engagement, particularly within a congruence framework. As argued by [63], the effect of technology use for work activities—whether beneficial or detrimental—likely varies according to contextual factors such as sufficient recovery experiences and organizational support. In our mathematical model, incorporating the mitigation factor positively affects the outcome, thereby supporting prior arguments. This finding also aligns with emerging narratives suggesting that organizations should respect after-hours time by limiting access to emails or mobile technologies to protect employee well-being [64]. We propose a reciprocal mechanism incorporating PSD that can sustainably promote the use of ESM from the user’s perspective.

Third, our study provides a specific quantification of the balance necessary to achieve optimal results. Utilizing the MOGA technique, we determined the equilibrium point where conflicting objectives can be reconciled. By simulating various configurations between the limits of PSD and ESMU, we observed that the optimal point (Point B) disappears when the PSD level is constrained to a low or moderate limit. Our findings further demonstrate that the equilibrium point is achievable when the PSD level is slightly higher than that of ESMU. By quantifying this balance level, we believe we significantly extend the understanding of the contradictory effects triggered by ESMU, distinguishing our work from prior studies that primarily focused on explanation and observation.

The main practical implication of our research is the recommendation for managers to adopt a holistic perspective to maximize the positive result of ESMU at the individual level. To illustrate, consider a hypothetical scenario during ESM implementation. Managers may observe that increased usage at the individual level leads to higher work exhaustion, adversely affecting long-term organizational efficiency and individual psychological well-being. While existing studies suggest constraining ESMU to protect employees from exhaustion, this strategy might harm productivity and responsiveness, making ESM implementation neither successful nor sustainable.

Managers, therefore, face the challenge of balancing conflicting targets to safeguard both employees’ efficiency and their mental well-being. We suggest that adopting a holistic view can positively influence outcomes. Managers must recognize that the level of fit between ESMU and PSD is crucial in identifying the equilibrium point. For employees who are heavily engaged in ESM-related activities, a slightly higher level of PSD may be necessary. Conversely, a lower level of PSD can be sufficient for those minimally involved in ESM-related tasks. The most detrimental scenario is one where the discrepancy in either direction is expanded, as this both impairs work engagement and increases work exhaustion.

6. Conclusions, Limitations, and Further Research

The equilibrium point provided heralds the prospects for sustainable success for ESM. The findings of our research can be concluded as follows. Our analyses demonstrated that ESMU is positively associated with both work engagement and work exhaustion, substantiating the existence of contradictory effects. We employed the PRRSA method to identify the conditions that promote high work engagement and low work exhaustion within a congruence framework. The results suggest that when ESMU aligns with PSD in a high-congruence situation it will produce the best result in work engagement. Conversely, when PSD exceeds ESMU, the greatest discrepancy in this direction will produce the lowest result of work exhaustion. Therefore, there seems no condition to achieve both targets simultaneously as they are competing with each other. This underscores the necessity of using an optimization method to address it. Finally, the MOGA technique revealed that the optimal solution, characterized by high work engagement and low work exhaustion, occurs when both ESMU and PSD are at high levels, with PSD slightly surpassing ESMU. Moreover, we found the congruence framework between ESMU and PSD predicts WEG in a nonlinear way, suggesting that the conventional linear regression method might be inappropriate for exploring the impacts of ESMU as the real influence might be more intricate.

In conclusion, by leveraging the PRRSA and MOGA methods, we provide a definitive answer regarding the degree of balance necessary to produce an optimal solution. We enrich the application of metaheuristic methods in addressing administrative dilemmas, a domain where such analyses remain sparse [65,66]. As the first study to mathematically illustrate the conditions and impacts of fit, this paper advances interdisciplinary research. During the process of digital transformation, organizations may encounter similar challenges while implementing innovative technologies, and our proposed method is poised to play a pivotal role in addressing these issues.

Limitations and Further Research

The primary limitation of the current research lies in its reliance on subjective measures as inputs for problem optimization. Unlike tangible variables such as cost, price, distance, or physical dimensions, the measurement of efficiency and well-being is challenging to quantify directly. While this approach is suitable in our research context—as we assess efficiency from a usage perspective rather than the system’s performance efficiency—it is nonetheless advisable to consider alternative measurements to enhance the accuracy of quantification. Developing stable and repeatable equations to mathematically describe contradictory effects would significantly contribute to the application of more optimization methods in managerial dilemmas.

We recognize that employing a larger dataset encompassing a diverse range of occupations and sectors would likely enhance the robustness of our results. This would not only validate the findings across different contexts but also help identify unique patterns and trends that may not be apparent in a more restricted sample. Thus, a heterogeneous sample that includes a more diverse population is recommended. Additionally, other relevant dimensions, such as organizational support and individual differences that may influence the equilibrium point, were not examined. Exploring these areas could yield further interesting insights.

By addressing these limitations and building upon the current findings, further research can substantially contribute to a more holistic and precise understanding of the contradictory effects of ESMU.

To close, while this study has significantly contributed to the methodological approaches, continual advancement in methodology is essential. The integration of machine learning methods with other optimization algorithms, such as the Harris Hawks optimization algorithm, could offer profound methodological improvements and enhance the comprehensive understanding of nonlinear influences within the ESMU impacts. We anticipate that this work will serve as a precursor, demonstrating that addressing managerial and behavioral issues does not necessarily depend on the conventional linear regression paradigm alone.