1. Introduction
In any company, adequate attention to psychosocial risk (PSR) factors and the generation of efficient institutional policies regulating interpersonal relationships allow anticipating risks associated with a low productivity level. Looking to the future, algorithmic management, rapid changes in the structure of work and the workforce [
1,
2] pose an unknown situation, which possibly increased the risks of work stress. Problems such as high staff turnover, difficulties in communications, poor leadership, psycho-logical stressors, coping mechanisms, family work relationship, among other factors, constitute a barrier to the progress and evolution of organizations [
3,
4]. The benefits of attending to these psychosocial aspects include boosting productivity, wellbeing of their employees, moving towards a highly competitive company and improving market positioning [
5,
6].
In addition, in Industry 4.0, current digital tools (a new generation of sensors) and recent developments in information technologies (Big Data, Machine Learning, Artificial Intelligence, Internet-of-Things) play an essential role in the development of more competitive and globalizing companies. Furthermore, these new developments impact the workforce by obtaining advantages to improve worker motivation, implementing policies for organizational and human aspects and promoting health in the workplace [
7,
8,
9].
A large number of quality publications in the existing literature promote workers’ health. For example, the international ISO-45003 standard proposes implementing “good practices” to avoid PSRs and having a healthy work environment [
10,
11]. Likewise, the European Union Information Agency for Occupational Safety and Health (EU-OSHA) and the Spain National Institute for Safety and Health at Work (INSST) promoting the improvement of occupational safety and health conditions to decrease occupational hazards, work accidents, and occupational diseases [
12].
Furthermore, Cox et al. [
13] identify ten potentially dangerous work psychosocial characteristics, classifying them according to their relationship with the work context. In Kompier and Levi [
14], the checklists of the European Foundation for the Improvement of Living and Working Conditions (Eurofound) are discussed. In [
15], the Guide to the Actions of the Labor and Social Security Inspectorate on Psychosocial Risks points out the advantage of quickly, validly, and reliably information collecting using questionnaires complying with established requirements such as reliability and validity. In Sebastián et al. [
16], several treatment recommendations and ergonomic and psychosocial evaluations are given.
The attention of occupational PSR factors has led to the developing and compliance of regulations that consider that an unfavorable work environment can cause physical and mental illnesses [
10]. These regulations aim to improve work environments so that workers’ activities develop favorably.
Concerning the instruments identifying PSR factors, in Spain, both the Psychosocial Evaluation Procedure called Psychosocial Factors (FPSICO, for its acronym in Spanish) of the National Institute of Occupational Safety and Health (INSHT, for its acronym in Spanish) and the Copenhagen Psychosocial Questionnaire (CoPsoQ) of the Union Institute of Labor, Environment, and Health (ISTAS) contain questionnaires for diverse types of companies [
17,
18]. Furthermore, the European Working Conditions Surveys (EWCS) [
19] develop instruments to identify the employment situation, such as the Labor Day planning and duration, the work organization, training and learning, and physical and psychosocial risk factors. On the other hand, the Official Mexican Standard NOM-035 [
10] establishes the elements to identify, analyze and prevent PSR factors, and to promote a favorable organizational environment in the workplace.
In particular, in Leka et al. [
20], the policy context for managing work-related PSRs in the European Union (EU) is discussed. They highlight the importance of properly managing these risks, with the financial benefits for workers’ insurance premium payments. In Sureda [
21], PSR factors in one public hospital are evaluated with the FPSICO procedure, composed of 75 ten-level Likert items and seven factors: mental workload, temporal autonomy, job content, supervision-participation, role definition, worker’s interest, and personal relationships.
In light of these works, it can be seen that PSR assessment is becoming increasingly important for research on occupational safety and health. However, in [
22], it is pointed out that even though several sources guide the identification of PSRs, the probability and statistical evaluation of PSRs remain poorly studied. For example, in [
23], a significant correlation between work resources and work-related stress symptoms is shown.
As in other disciplines of knowledge, several propositions incorporate computational tools and artificial intelligence techniques to improve risk attention and occupational health. In Khakzad [
24], a heuristic is applied for using imprecise probabilities in a Bayesian network for system safety assessment under uncertainty. In Han et al. [
25], the Random Forest classification heuristic is implemented to select the optimal feature set work-related stress measured by physiological signals of electrocardiograms (ECG) and respiration (RSP). The detection of work stress was carried out with the support of a wearable device, concluding that excessive stress decreases work efficiency and leads to negative emotions and various diseases.
In one particular case, job rotation is a successful strategy used in manufacturing systems. Job rotation helps prevent musculoskeletal disorders, eliminates boredom, and increases job satisfaction and morale, providing benefits to both workers and the company. Asensio-Cuesta et al. [
26] developed a genetic algorithm for this problem, and Song et al. [
27] implemented a heuristic using factors related to workload ergonomic evaluation data generated in the workplace. On the other hand, Yan et al. [
28] developed data processing algorithms with real-time warning indicators for evaluating and signaling risk positions through a smartphone.
Concerning optimization processes, the Multi-dimensional Knapsack Problem (MKP) has been adapted to diverse problems requiring the selection of elements with capacity restrictions in containers. MKP has been applied to solve various practical problems in the industry, such as resource allocation, transportation [
29], and production planning [
30,
31]. In [
32], a survey of the multiple applications of 0–1 MKP is presented, emphasizing that the most popular approaches are based on metaheuristics, highlighting population-based strategies such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Ant Colony Optimization (ACO). Most of these procedures are evaluated using various benchmarks to demonstrate their effectiveness. Furthermore, Drake et al. [
33] propose a hyper-heuristic to select the arguments of crossover operators to solve a group of instances obtained from three well-known benchmark libraries (OR-Lib, SAC-94, and that presented by Glover and Kochenberger). In [
34], an approach was proposed in which a greedy algorithm is first used to reduce the search space, and then a linear programming algorithm is used to obtain the optimal values of some instances of the OR-Lib. In Dzalbs et al. [
35], a variant for population selection in a GA using several instances of two benchmark libraries (OR-Lib and Glover and Kochenberg) is presented. Finally, in [
36,
37], both ACO and PSO are used to solve several SAC-94 instances, achieving the optimal value in all of them.
From the existing occupational risk attention literature, and to the best of our knowledge: (1) There is no evidence that some methodology uses an optimization technique generating a subset of risk factors to be included in a plan for PSR factors’ attention. (2) There are no proposals considering a budget assigned to each area or department of the company for making decisions about the prioritization of occupational risk care.
This article proposes a new methodology to find the combination of PSR factors that maximizes the company’s attention level, considering the company’s budgets for each of its departments. The risk factors are first identified using the questionnaires recommended by the applicable regulations. Then, the problem of optimizing PSR is modeled as a Multiple Knapsack Problem (MKP). Finally, an optimal solution for this problem is found using an adaptation of the simulated annealing (SA) algorithm.
4. Discussion
This methodology is used to generate the first plan of attention to PSR factors. In the case study, the budget consumption matrix is obtained from the hp1 instance. Still, in a real case, its preparation requires great effort, since multiple meetings between the company departments are needed to agree on the amounts used to attend each risk factor and establish the budget ceiling. When solving the optimization model of this instance,
Table 7 shows the three solutions obtained using the budget consumed by each department. Again, it is essential to emphasize that companies must apply most of their assigned budget in order to achieve the most significant benefit, since an unconsumed budget would imply neglecting its purpose or mismanagement. In the instance of hp1, a competitive solution achieved a profit of 3405, consuming 99% of the budget of departments 1 and 3 and 98% of the budget of department 2. The benefits of using metaheuristics such as the SA-based approach presented in this work are evident. They can obtain several near-optimal solutions, and the decision-makers have several scenarios from which to select that which best aligns with the company’s objectives, such as the use of the greatest budget to obtain the greatest benefit in addressing psychosocial risks.
The cost matrix generation for each department, even without considering the risk levels presented in the company, provides the opportunity to incorporate future actions and move towards the continuous improvement of the organizational environment. In accordance with various methodologies described in the existing literature, the success of these projects type (continuous improvement) lies in communication. However, since this work involves psychosocial aspects, the application of diverse issues such as social support, the use of mechanisms of disagreement, and well-targeted training will make a difference. This methodology requires costs to attend to each PSR factor offering important support in decision making. This proposal reduces the tensions related to the creation of one intervention plan, since each department generally has its own prevention perspective according to its own goals and objectives. The generation of the cost matrix per department enriches the actions, activities and interventions that need to be followed in order to improve the organizational environment.
Regarding the metaheuristic used to solve the PSR optimization problem, it is clear that the smallest instances, the solution found by the SA algorithm, is the optimal value reported in the benchmark literature. For the other instances, the sampling error shown in
Figure 8 validates the two SA schemes’ quality and precision. The SA-fast scheme has a maximum RE no greater than 1.12%, representing competitive solutions found in a reasonable time. It is ideal for large PSR optimization problems. This behavior allows the SA algorithm to be incorporated into the technology platform with the enterprise security methodology [
60,
61,
62]. On the other hand, as shown for small instances, the SA-high scheme presents greater precision, where its implementation brings great benefits.
Regarding the statistical results, we observe that the proposed SA algorithm is competitive with those contrasted in the existing literature, demonstrating its independence.
Solving the PSR optimization problem has great relevance, due to the changes in the forms of work that are currently taking place [
1,
7,
8,
9,
63]. Algorithmic management [
2,
64,
65,
66], which assigns tasks and evaluates workers using data-driven systems, has proven to be efficient. However, at the same time, the present challenges of the psychosocial type should be considered. This presents a wide field of study for future works.
As future work, we intend to automate the identification of the level of attention that the PSR factor requires, incorporating, in addition to the questionnaire, information from interviews, minutes of discussion group meetings, and definitions of performance indicators aligned to the strategic objectives of the company, among other things.
5. Conclusions
Given the challenges that organizations face regarding digitization and process automation, technological tools play an essential role in supporting decision making. Changes in the workforce go hand in hand with job wellness and occupational health, hence the importance of using algorithms that optimize solutions to address psychosocial risks. In this work, a methodological scheme was presented that, on the basis of the detection of psychosocial risk factors in a company, the mapping to an MKP optimization model, and its solution using the SA algorithm, is able to obtain the subset of risk factors for a company with a maximum value at the level of care, that is, with a local-optimal solution that maximizes the benefit to the factors with the highest identified risk. This subset of selected factors can be incorporated into an optimal PSR treatment plan in the workplace. As shown by the evaluation of the method, the level of attention to risks is maximized under the limited budgets of a company’s departments. This methodology favors the organizational environment and promotes business competitiveness, complying with existing regulations for the identification, analysis and prevention of PSR factors.
By solving the benchmark instances for MKP, it was shown that the SA algorithm was able to solve the PSR optimization problem. The algorithm obtained values close to the optimum (and, in some cases, the global optimum) in the conducted tests.
The suggested metaheuristic was developed using two tuning schemes: SA-high and SA-fast. It can be observed that the second scheme had a better execution time (almost 80% faster than the first), sacrificing precision of results by a value within the range of 2–3%. These results are competitive, since the operation speed is one of the variables of interest under the new requirements given in the work scheme, such as algorithm management.
The results show that an SA-high scheme is a promising approach, since it achieves results below 1% for relative error. This implies that the results may be beneficial for a real PSR problem of a company.
As future work, it is intended to automate the identification of the level of attention that the PSR factor requires, incorporating, in addition to the questionnaire, information from interviews, minutes of discussion group meetings, and the definition of performance indicators aligned to the strategic objectives of the company, among other things.