Particle Swarms Reformulated towards a Unified and Flexible Framework

The Particle Swarm Optimisation (PSO) algorithm has undergone countless modifications and adaptations since its original formulation in 1995. Some of these have become mainstream whereas many others have not been adopted and faded away. Thus, a myriad of alternative formulations have been proposed to the extent that the question arises as to what the basic features of an algorithm must be to belong in the PSO family. The aim of this paper is to establish what defines a PSO algorithm and to attempt to formulate it in such a way that it encompasses many existing variants. Therefore, different versions of the method may be posed as settings within the proposed unified framework. In addition, the proposed formulation generalises, decouples and incorporates features to the method providing more flexibility to the behaviour of each particle. The closed forms of the trajectory difference equation are obtained, different types of behaviour are identified, stochasticity is decoupled, and traditionally global features such as sociometries and constraint-handling are re-defined as particle's attributes.

Introduction
Inspired by earlier bird flock simulations, the Particle Swarm Optimisation (PSO) method was proposed in 1995 [34]. It is a global optimiser in the sense that it is able to escape poor suboptimal attractors by means of a swarm of particles performing a parallel collaborative search. In fact, it is a search rather than optimisation method, as no optimality criteria is checked or guaranteed.
The overall system behaviour emerges from a combination of each particle's individual and social behaviours [50]. The former is manifested by the trajectory of a particle pulled by its attractors, governed by a second order difference equation with three control coefficients. In the classical (and in most) versions of the algorithm, there is one individual attractor given by the particle's best experience, and one social attractor given by the best experience in its neighbourhood. The social behaviour is governed by the way the individually acquired information is shared among particles and therefore propagated throughout the swarm, which is controlled by the neighbourhood topology. The individual and social behaviours interact through the update of the social attractor. Thus, the two main features of the algorithm are the trajectory difference equation (and the setting of its coefficients) and the neighbourhood topology (a.k.a. sociometry).
In the early days, numerous empirical studies were carried out to investigate the influence of the coefficients in the trajectory difference equation on the overall performance of the method, and to provide guidelines for their settings [48,47,17,36]. Early theoretical work [41,42,2,13,52] provided insight into the inner workings of the method and some interesting findings of practical use such as Clerc et al.'s constriction factor(s) [13] to ensure convergence. These pioneering studies were a source of inspiration and set the foundations for an explosion of theoretical work. [54,35,10,31,29,46,37,44,3,11,45,18,51,12,24,26,7,19,8,21,9,6]). For recent reviews of the PSO method, refer to [5,20].

Trajectory Difference Equation
In classical PSO (CPSO), three forces govern a particle's trajectory: the inertia from its previous displacement, the attraction to its own best experience, and the attraction to the best experience in its neighbourhood. The importance awarded to each of them is controlled by three coefficients: the inertia (ω), the individuality (iw), and the sociality (sw) weights. Stochasticity is introduced to enhance exploration via random weights applied to iw and sw. The behaviour of a particle, and by extension of the PSO algorithm as a whole, is very sensitive to the settings of these control coefficients. The system of two 1 st -order difference equations for position and velocity updates in the CPSO algorithm proposed in [49] is rearranged in (1) as a single 2 nd -order Trajectory Difference Equation: ij is the coordinate j of the position of particle i at time-step t; xb (t) ij is the coordinate j of the best experience of particle i by time-step t; k is the index identifying the particle with the best experience in the neighbourhood of particle i at time-step t; ω, iw and sw are the inertia, individuality, and sociality weights, respectively (which may depend on i, j, t); and U (0,1) is a random number from a uniform distribution within [0,1] resampled anew every time it is referenced.
In the original formulation [34], ω = 1 and iw = sw = 2. This leads to an unstable system, as particles tend to diverge. The first strategy to prevent this was to bound the size of each component of a particle's displacement, which helps prevent the so-called explosion but does not ensure convergence or a fine-grain search. Instead, the coefficients in (1) can be set to ensure that.
Alternatively, Clerc et al. [13] analysed the trajectory of a deterministic particle in the original PSO (ω = 1) and developed so-called constriction factors (χ) that ensure convergence. Some authors include both ω and χ in their formulations [27,53].

Neighbourhood Topology
The original PSO algorithm [34] presented a global topology in which every particle has access to the memory of every other particle in the swarm. Local topologies were proposed soon thereafter [16]. Since then, a plethora of sociometries have been proposed [40,38,39,4]. Three classical ones are shown in Fig. 1.  The global topology tends to lead to a rapid loss of diversity, which may lead to premature convergence to a poor suboptimal solution. Whilst this can be controlled to some extent by the settings of the coefficients in the trajectory equation, numerous neighbourhood topologies have been proposed reducing connectivity to delay the propagation of information throughout the swarm.

Other Features
Other important features of the PSO algorithm are the initialisation of the particles [11,22,33,32], the synchrony of the memory updates [1], the size of the swarm [15,43], and the handling of constraints [24,30].
The PSO algorithm is an unconstrained search method, therefore requiring an external constraint-handling technique (CHT) to be integrated to handle these types of problems. A straightforward CHT is the Preserving Feasibility Method [23], in which infeasible experiences are banned from memory. Another one is the Penalty Method, in which infeasible solutions are penalised by augmenting the objective function and treating the problem as unconstrained. Some authors propose adaptive penalties by using adaptive coefficients in the penalty function [14] or by adapting the tolerance relaxation [28]. Innocente et al. [25] propose using a Preserving Feasibility with Priority Rules Method, in which the objective function values and the constraint violations are treated separately.
Since its original formulation in 1995, countless variants have been proposed. Some of them have become mainstream whereas many others have faded away. Thus, a myriad of alternative formulations have been proposed raising the question of what the basic features of an algorithm must be to belong in the PSO family. The aim of this paper is to establish what defines a PSO algorithm, and to attempt to formulate it in such a way that it encompasses many existing variants so that different versions may be posed as settings within the proposed unified framework. In addition, the proposed formulation generalises, decouples and incorporates new features providing more flexibility to the behaviour of each particle. The remainder of this paper is organised as follows: the overall proposed Reformulated PSO is introduced in Section 2, with the Global Features, the Individual Behaviour Features and the Social Behaviour Features discussed in more details in Sections 3, 4 and 5, respectively. Conclusions are provided in Section 6.

Reformulated Particle Swarm Optimisation
The proposed Reformulated Particle Swarm Optimisation (RePSO) method is structured in three sets of features: 1) Global Features (GFs), 2) Individual Behaviour Features (IBFs), and 3) Social Behaviour Features (SBFs). Fig. 2 shows a high-level description of RePSO, where IBFs and SBFs are both viewed as individual attributes of a particle (Particle Attributes).

Global Features
Despite being a swarm-intelligent method, some characteristics must still be defined at the swarm level. We define here three main subsets of global features: 1) Global Settings, 2) Initialisation, and 3) Termination Conditions. The first one consists of scalar settings like maximum search length (t max ) and swarm size (m), whereas the other two involve methods. Whilst the Neighbourhood Topology and the Constraint-Handling Technique are traditionally viewed as global features, it is porposed here that they be defined at the individual level.

Initialisation
It is important to differentiate two aspects of the initialisation in PSO: 1. The sampling method to be used to place m points over the search-space. 2. What variables associated with each particle are to be initialised.
Note that the particle's position update in RePSO -and in (1)-is a 2 nd order difference equation rather than the classical system of two 1 st order difference equations (position and velocity). Therefore, the variables which may be involved in the initialisation are the initial, the previous, and the memorised positions (x (1) , x (0) , xm (1) ) instead of two positions and one velocity (x (1) , xm (1) , v (1) ).
Sampling Method. Originally, initialisation was purely random from uniform distributions: x  Initial Conditions. This aspect of the PSO method seldom receives any attention from researchers or practitioners. Four types are proposed here: (1) This requires the sampling of each particle's position at the initial time-step (x (1) ). Stagnation implies that the previous position x (0) = x (1) , and that the particle has converged to its attractor: xm (1) = x (1) . Thus, movement starts purely due to cooperation (no inertia, no individual attractor).
3. One Position and One Memory: x (1) = x (0) = xm (1) Two positions per particle are sampled and compared, with the better one becoming xm (1) and the other x (1) = x (0) . Movement starts due to both cooperation and acceleration towards its individual attractor (no inertia).

Two Positions and
One Memory x (1) = x (0) = xm (1) = x (1) Three positions per particle are sampled and compared, with the best one becoming xm (1) . Thus, movement starts both due to all three sources: cooperation, inertia, and acceleration towards its individual attractor.
Initialised Variables Relation. For all initial conditions other than stagnation, more than one position is to be sampled per particle. The question is then whether these should be somehow related. Three alternatives are proposed here: 1. Perturbation: x (0) is generated from controlled perturbations on x (1) . If applicable, xm (1) is also generated from perturbations on x (1) .
2. Independent: Each population of positions is sampled independently.
3. Simultaneous: All populations of positions are sampled at once. For instance, if using the Latin Hypercube Sampling, there would be one single sampling with as many points as twice or three times the swarm size, as applicable.

Termination Conditions
The population-based nature of the method enables termination conditions different from the classical ones in numerical optimisation: 1) maximum number of iterations, and 2) convergence. Three types of conditions are identified here: 1) based on search length (or maximum number of iterations), 2) based on clustering measures (diversity loss), and 3) based on measures of convergence.

Individual Behaviour Features
These are the features of the algorithm which control the individual behaviour of a particle. Each particle has its own set of IBFs, which are viewed as particle attributes. The individual behaviour of a particle is materialised by its trajectory as it is pulled by its attractor. This is governed by a second order difference equation and the setting of its coefficients. The IBFs are grouped here in two main families, namely Deterministic Features and Stochastic Features.

Deterministic Features
Instead of viewing PSO as a guided random search method, it is viewed as a randomly-weighted deterministic search method. Thus, its desired deterministic behaviour is defined, adding only as much stochasticity as deemed beneficial. By formulating the position update as in (5), it is clear that any given particle at any given time is pulled by a single attractor which results from a randomly weighted average of the components of the individual and social attractors. Thus, the Trajectory Difference Equation in (1) may be expressed as in (5).
Since we are dealing with a single particle, sub-index i is dropped. For simplicity, let us assume (ω, φ) constant in every dimension and ∀t, dropping sub-index j and super-index (t). If stochasticity is removed, the deterministic coefficients (ω,φ) are referred to as Reference Trajectory Coefficients.
CPSO Recurrence Formulation. The CPSO Recurrence Formulation is as in (6), which is the deterministic version of (5). The generation of the overall attractor p (t) i is now decoupled, comprising a Social Behaviour Feature (SBF).
CPSO Closed-Form Formulation. This is obtained by solving the difference equation in (6). The roots of the characteristic polynomial are as in (7) and (8). The solution is per dimension and per particle (therefore dropping indices i and j), and the attractor p is stationary.
Case 1 (γ 2 > 0). The two roots of the characteristic polynomial are real-valued and different (r 1 = r 2 ). Therefore the closed-form for Case 1 is as in (9).
Case 2 (γ 2 = 0). The two roots of the characteristic polynomial are the same (r 1 = r 2 ), as shown in (10). Therefore the closed-form for Case 2 is as in (11).
Thus, the chosen trajectory equation in RePSO may be given by the Recurrence Formulation in (6) or by the Closed-Form Formulations in (9), (11) and (16). Other recurrence formulations as well as some considerantions to be taken into account for the closed-form formulation are beyond the scope of this paper.
Reference Trajectory Coefficients Settings. An analysis of the trajectory closed-forms shows that the magnitude of the dominant root r = max ( r 1 , r 2 ) controls convergence. Fastest convergence occurs for (φ,ω) = (1, 0), where r = 0 (see Fig. 3 (a)). The resulting convergence conditions are shown in (17), which define the area inside the convergence triangle (r < 1) shown in Fig. 3.
Whilst the magnitude of the dominant root controls the speed of convergence, the sign of the dominant root (if any) controls the Type of Behaviour : 1. Oscillatory: Roots are complex conjugates (no dominant root). 2. Monotonic: Dominant root is real-valued and positive. 3. Zigzagging: Dominant root is real-valued and negative.
These Types of Behaviour are bounded within specific Sectors in the (ω,φ) plane, each associated with one edge of triangular isolines (same r). These three Sectors are shown in Fig. 3 (b), where the white triangle separates the Convergence (inside) and Divergence regions. The settings of (ω,φ) can be chosen so as to achieve the desired behaviour and convergence speed.

Stochastic Features
The random weights in (1) affect the trajectory of a particle towards the overall attractor (p) whilst also affecting the generation of this attractor as a stochastic convex combination of the individual (xb i ) and the social (xb k ) attractors. Different from classical PSO formulations, these two features are decoupled here. The Stochastic Features within the IBFs are concerned only with the former.
Stochastic Scaling. This refers to whether the stochastic variables in (5) are sampled once per particle position update (vector scaling) or resampled anew per dimension as well (component scaling). The latter is sometimes used by mistake.
Stochastic Sampling. This refers to the probability distributions chosen for the control coefficients (ω, φ). In classical formulations, ω =ω (deterministic) whereas the probability distribution of φ is not directly chosen but resulting from the sum of two stochastic terms sampled from uniform distributions: φ = ι + σ as in (3). If they are sampled from the same interval (i.e. iw = sw), the resulting probability distribution of φ is triangular. Otherwise, it is trapezoidal. In the proposed RePSO, the user is allowed to choose any distribution for (ω, φ).
Trajectory Coefficients Sampling Settings. Once the distributions have been chosen, the parameters defining them must be set. For example, (φ min , φ max ) for a uniform distribution, or the standard deviation for a normal distribution.

Social Behaviour Features
These are the features of the algorithm which control the social behaviour of a particle. Despite being SBFs, they are defined as Particle Attributes in RePSO. A particle's social behaviour is governed by its access to other particles' memories (Local Sociometry) and by how it handles this information (social influence).

Local Sociometry
In classical formulations, the sociometry is a global feature. It can be defined as a regular graph, or irregulary by defining one connection at a time. In the latter case, the structure cannot be automatically generated nor is it scalable. In RePSO, automation and scalability are paramount. Therefore, a Local Sociometry is defined for each particle, with the Global Sociometry resulting from their assembly. This has the advantange that sociometry is a particle attribute, facilitating object-oriented implementation. Also that different social behaviours can be exhibited by different particles, and that irregular global sociometries are possible without renouncing automation or scalability. The Local Sociometry in RePSO is generated by defining the Neighbourhood Topology and potentially the Neighbourhood Extent. Examples of the former are the Global, Ring, Forward and Wheel topologies. The Neighbourhood Topology defines a methodology to generate unidirectional connections from the particle informed to its informers. The Neighbourhood Extent defines the neighbourhood size, if applicable (number of neighbours, distance of influence). An example of an unstructured global neighbourhood is shown in Fig. 4, where the Local Sociometry of particle 1 is the Global topology whilst that of particle 2 is the Ring topology. Other aspects may be considered, such as whether a particle's memory is part of its neighbourhood (X in the connectivity matrix in Fig. 4).

Current Information Update
Any particle holds two types of information: 1) current, and 2) memorised. The update of the former takes place by gathering information (e.g. memorised attractors), generating an overall attractor using the information gathered, and then applying the trajectory equation to update the current information. A particle may access the information currently held, the one memorised, or both from its neighbours (Information Gathering). This is an extension to classical formulations, where a particle can only access their memorised information.

Memorised Information Update
This controls the update of a particle's memory when it accesses new information. This is performed directly rather than through a trajectory equation. The question is what Type of Information is accessible to a particle's memory. Another feature affecting this update is the Synchrony, which defines whether a particle's memory is updated immediately after its currently held information is updated (asynchronous) or only after the currently held information of every particle is updated (synchronous). Typically, the update is synchronous.
RePSO also proposes to include the CHTs here. Thus, different particles may have different CHTs, and therefore may value a given location differently.

Conclusions
A general framework has been proposed aiming to encompass many variants of the PSO algorithm under one umbrella so that different versions may be posed as settings within the proposed unified framework. In addition, some extensions to the classical PSO method have been made such as the decoupling of the stochasticity that affects both the acceleration coefficient (φ) and the generation of the overall attractor, an extended treatment of the swarm initialisation, the particle trajectory closed forms, the identification of three types of deterministic behaviour to inform the setting of the control coefficients, and the global sociometry resulting from assembling local sociometries defined as particle attributes. Due to space constraints, most of these features are discussed only superficially.


Grading as a progressive technology for managing financial incentives of employees

One of the most efficient ways to financially motivate personnel is grading, which is conducted using a number of stages of grading system development and implementation. The grading mechanism is considered, the job evaluation is carried out according to the selected factors using the example of the specific company. Thesummary analysis of the research results is provided in the article. According to the conclusions, the use of grading contributes to theefficiency increase of staff motivation, which ultimately leads to the increased labor productivity.

Introduction
In the contemporary era of market economy ongoing development in Russia, the activities of any company should include continuous analysis and assessment of the efficiency of resource use, including personnel as a special and essential strategic factor in the country's transition to the innovative development [1,2].
Many approaches to determining the efficiency of personnel management can be found in the economic literature, however, the generally accepted methodology was not developed in domestic or world practice [3,4].
Personnel management system evaluation should be conducted for its functional subsystems using a number of indicators, which will allow to describe this systemin a comprehensive manner from the perspective of system approach [5].
As a rule, the key element of staff motivation is financial incentives, but such an important aspect as moral climate in a company, its social environment taking into account the specificity of human resources should not be forgotten. From this perspective, the staff also needs development, motivation to achieve the required results, adjustment to the working environment, etc. It is the staff motivation that is currently being disaggregated and, in comparison with the traditional Soviet-era principles, the set of motives for each local employee of the company has now considerably expanded, since the basic mix of employee needs has been changed, the very nature of work is being rebuilt, and the tactical and strategic purposes of an enterprise are being adjusted. The consequences of such changes mostly include new tools and techniques of personnel motivation (innovations) in business structures and in the social, political, economic life of thecountry as a whole.
As a result of the development of market relations, such events as the participation in the World Trade Organization, opening of representative offices of foreign organizations, labor migration led to the evolution of labor management. The effect of adjustment to the current situation includes the increased competition for highly skilled human capital, and, as a consequence, there are new tools for staff motivation. For instance, the system of grade levels can be considered one of such tools that has been developing in Russia since the beginning of the XX century. Let us present a brief characteristic of "grade" term for the detailed description of this system.
The study of current economic literature makes it possible to formulate the essence of the term "grade" as a fixed range of "weights", within which the posts have the identical status and the same tariff range of labor remuneration. With this, the set of grades is basically a system of grades, which is presented as a salary scale or a wage scale when using predetermined factors.
Currently, the grading system most effectively covers the totality of business processes, employee remuneration (its basic part) and is able to correspond with the staff motivation system [6].
The tasks shown in Figure 1 can be considered as the tasks that grading helps to solve in certain organizations. Grading is a set of procedures for determining and evaluating the ranking of posts, when they are divided into the corresponding grades in accordance with their importance to the organization. In other words, grading is the technology for grading system development. It is important to note further that the grading system turned out to be efficient and applicable almost worldwide, in all countries and is rightfully considered a worthy basis for the development of a transparent and adjustable personnel remuneration system. Grading came to Russia in the 1960s to replace the Soviet-era wage scale, which in practice turned out to be somewhat cumbersome for organizations in the conditions of rapidly evolving realities of the country's economy as a whole. The weak points of the previous tariff scale turned out to be the lack of transparency, the lack of economic logic and certain rigidity of the organizational structure. For example, it was necessary to formally indicate the post of the employee, for instance, "engineer of the i-th category", just to determine his salary [8].
Grading makes it possible to flexibly organize the post levels in the form of a scheme, taking into account not only qualification, but also other important factors according to their areas of responsibility, level of complexity of decisions made, etc. Under the grading rules, each post has its place in the ranking and receives a corresponding grade in the salary range [9,14].

Materials and methods
Particular attention should be paid to the issue of salary system development based on grades. Grading experts suggest a different number of stages for grading system development methodology in a company [13,15].
Based on the theoretical and empirical analysis carried out by the authors, the following main stages of grading system development and implementation in an organization are proposed (Table 1) Grading system development -identification of the number of grades; determinationoftheminimumandmaximumsalaryforea chgrade 5 Grading system implementation -holding a general meeting of employees in order to inform them about the implementation of the grading system in the enterprise; -preparation of information systems for grading system implementation; -carrying out organizational arrangements within structural units Let us describe each stage of grading system development in a company from the perspective of the integrated system approach.
Development and implementation of grades in a company is a complex and multifaceted process that requires great attention of a full group of specialists. Thus, it is important to form a working committee for job evaluation in the process of development and implementation of company's grading system. It should be noted that it is the expert commission, which should include professionals with relevant work experience, that rank and evaluate the importance of the factors.
The high adaptability of the grading system is explained by the fact that the set of assessed factors is formed according to the specifics of company's activities, based on economic, social, natural, and other conditions that arise both in the internal and external environment of any organization. Therefore, it is important to take into account both domestic and foreign experience of grading use when developing and implementing a grading system in a company. As a rule, the following factors can be used for grading system development: knowledge, experience, problem-solving skills, competence, responsibility, initiative, working conditions, labor intensity, communication skills, management skills, role in project performance, etc.
Let us consider the content of this and subsequent stages with regard to the grading system development for engineers of design and technological department of PAO "Shakhtinskiy zavod Gidroprivod" (Shakhty plant, PAO "SZG"). A brief description of this enterprise is as follows. PAO "SZG" was established in 1971 by several individuals with the authorized capital in the amount of 457990 rubles. The plant is engaged in the production of axial-piston hydraulic machines and radial-piston pumps. The consumers of PAO "SZG"products are enterprises located in different regions of Russia and abroad. The structure of the design andtechnological department of the enterprise is shown in Figure 2. The following factors were selected to develop the company's grading system: 1. personnel management; 2. responsibility; 3. independence of work; 4. experience; 5. level of expertise (qualification); 6. level of contact; 7. complexity of work; 8. cost of a mistake. According to the data in Figure 2, for each of the above eight evaluated factors, a scale of values is developed, which shows the nature of the work performed and reflects the increase in their level of complexity.
The scale of values for the evaluated factors with regard to D&T department of PAO "SZG" is shown in Figure 3, which presents the example of description of "Personnel management" factor levels.  Thus, the scale of values for the selected factors presented in Figure 3for PAO "SZG" company consists of six levels A, B, C, D, E, F. The distribution of points is conducted in ascending order from 1 to 6, where 1 point is assigned to level A and 6 points -to level E respectively.

Results
As a rule, the grading system implementation in a company involves compilation of a resulting table with job evaluation by selected factors, which, in turn, are divided into levels, and points are distributed on an incremental basis. Thus, according to the grading rules for PAO "SZG", the job evaluation for design engineer of the first category is conducted and the results are shown in Table 2. Table 2. Job evaluation of design engineer (of the first category) by factors inPAO "SZG"

Scale of values (in points)
Importance (5-point scale) Thus, the total score of the post evaluation of design engineer of the first category by factors amounts to 115 points. Scoring the posts analyzed is carried out according to the staffing table of D&T department. It should be noted that the selected factors are ambivalent, and distinction is required using importance weights, which determine the importance of a particular factor regarding other factors. In this case, the weight of all factors is taken as 100%. Figure 4 shows the horizontal and vertical calculation of points for company's posts.  Figure 4 points were obtained for the evaluated posts. These posts were arranged in a sequence according to the hierarchy, and then they were divided into groups, the so-called grades. The calculation of total scores for the posts of D&T departmentof PAO "SZG"made it possible to distribute the points as presented in Table 3. The detailed review of the organizational structure of PAO "SZG" leads to the conclusion that this company has the following departments: HR department, management, financial and economic planning departments, accounting department, production department, commercial and sales departments, legal department, department of information technology, etc. It is also necessary to categorize the posts of the company, for example, the categories may be as follows: management personnel, specialists, direct workers, auxiliary workers, service staff.

Personnel
The final and necessary stage of the grading systemdevelopment includes the establishment of official salaries and calculation of salary ranges. It should be noted that calculation of official salaries is conducted according to the results of scoring. It is necessary to select a number of posts in each grade, for which the relevant parameters of the specific post in the labor market should be taken into account and the need for compensatory financial incentives for a givenpost should be identified [17,18].
Before determining the official salaries for the company, it is necessary to analyze information about the market value of a given job. Moreover, it is essential to take into account the financial situation of the enterprise, corporate personnel policy and other factors that influence decision-making. Thus, to make a better management decision and coordinate it with the chief financial officer of the enterprise it is required to explore the labor market and estimate the average value (salary) of the identical post in other companies [19,20].
Accordingly, it is possible to establish a salary range for each grade, which is established not for a single post, but for the entire grade. For instance, the lower limit of the salary range corresponds to the minimum official salary, and, in fact, it should also correspond to the average value of the given post in the labor market. However, it should be kept in mind that a company that does not have large financial turnover, is not able to set a higher minimum official salary than the average minimum salary in the market.

Conclusions
Detailed study of the grading process leads to the conclusion that the established official salary is characterized by the importance and value of the post itself, but not by the employee's efficiency, therefore, it seems possible to establish the salary range for each grade. The salary range depends directly on the financial situation of the company, system of personnel motivation and development, which means that in most cases it has a constant value. That is, the employees will receive remuneration for the performance of their job duties at a "normal" rate in the amount of basic financial incentive.
If the value of the average market salary is set as the minimum official salary, then, accordingly, the post becomes especially attractive in the labor market, which in turn forms a competitive environment among job applicants. Therefore, this post, even with a low range of salary increment, entails the increase of its priority in the company relative to the competitors, which can certainly serve as a powerful motivating factor for increasing the efficiency of personnel. The result of the project for grading system development and implementation is basically a table with the description of all internal units including the titles of posts, their linear affiliation, subordination, grade number, integral indicators of the value of each post, belonging to the grade, salary range. Thus, the efficiency of the new remuneration system implementation in the company amounted to 6.5%. The use of grading contributed to the increase of staff motivation efficiency, which ultimately led to the increase of labor productivity. As a result of grading system implementation in PAO "SZG"the labor productivity increased by 2%.


Lean Manufacturing Tools Applied to Material Flow and Their Impact on Economic Sustainability

: This paper presents a second-order structural equation model that analyzes three lean manufacturing tools associated with material ﬂow, such as 5S, SMED, and continuous ﬂow related to economic sustainability. The variables relate to each other through six hypotheses, tested with 169 responses to a questionnaire applied to the Mexican maquiladora industry, using the partial least squares technique and 95% conﬁdence to estimate direct, the sum of indirect, and total effects. In addition, an analysis with conditional probabilities appears to determine how low and high implementation levels in independent variables affect the dependent variables’ occurrence. Findings indicate that 5S is a lean manufacturing tool with the most increased direct effects on SMED and continuous ﬂow. Additionally, values indicate that SMED is essential to maintain continuous ﬂow in production lines and is vital for economic sustainability due to the time reduction in setup.

Introduction
Market and supply chains (SC) are globalized, and sometimes the cost associated with SC represents 70% [1]. This is because a product may integrate components from different countries; some parts are assembled in another and sold in a different one, making them complex material flows [2]. In addition, some companies seek to be geographically close to their customers, so they establish subsidiaries in other countries to minimize the distance to the final market.
In the specific case of Mexico, given its proximity to the United States of America (USA) as one of the biggest world markets, some foreign companies establish assembly centers in the north. They also take advantage of low labor costs and high human resources training and tariff preferences due to trade agreements among those countries, including Canada [3].
Those companies are established in Mexico but have their headquarters in other countries, depending administratively on them, and traditionally, they are called maquiladoras [4]. There are currently 5171 companies of this type in Mexico, 493 in Chihuahua state,

LM and Sustainability
The LM implementation offers several benefits to companies, and Melton [9] was the first interested in associating it with companies' income. Recently, Islam [10] indicates that LM applies to the entire SC and reviews which partners gain better economic benefits. So, one important research area is the relationship that LM has with a company's financial sustainability.
The relationship between LM and sustainability is of academic interest; for example, Saetta and Caldarelli [11] relate LM for green production; Bai et al. [12] indicate that investing in LM tools applications generates environmental and operational benefits. However, LM and sustainability are not applied in isolation; for example, Cherrafi et al. [13] aggregate six sigma to that equation; Ghobadian et al. [14] integrate innovation, Varela et al. [15] recently combined industry 4.0, and finally, Burawat [16] added transformational leadership. In conclusion, LM is associated with sustainability together with other managerial or operative methodologies.
All prior research analyzes sustainability as a generic concept, and it has three main pillars: economic, environmental, and social. Additionally, in several recent studies, sustainability focuses only on environmental aspects, ignoring the social and economic ones. However, according to Kalyar et al. [17], the main goal in LM is to generate financial income for the company.
One of the initial studies associating LM with firm performance was reported by Shah and Ward [18] almost two decades ago. Other studies, such as Yang et al. [19], integrated other variables, such as environmental impact. However, it is not until Fullerton et al. [20] Sustainability 2021, 13, 10599 3 of 18 that a direct effect regarding the role of LM in the accounting and financial performance of the company is analyzed.

Specific LM Tools and Sustainability
Other studies refer to specific LM tools implementations, which are reductionist because LM is a set of managerial tools. For example, Aquilani et al. [21] and Green et al. [22] explore total quality management (TQM) impact on sustainability; Yazdi et al. [23] analyze overall equipment efficiency (OEE). In addition, Reis et al. [24] study total productive maintenance (TPM) and how it helps reduce the loss of raw materials due to deficiencies in machine calibration.
Additionally, Setiawan et al. [25] proposes a managerial model to associate 5S to sustainability in Indian manufacturing companies and Xu et al. [26] report the waste tool from LM to reduce the environmental impact in Chinese factories.

LM and Sustainability in the Maquiladora Industry
Research regarding LM tools in the MI is scarce in Mexico, even for the industrial, economic, and social importance, since several studies have focused on other research lines, such as SC. For example, Jun et al. [27] study TQM practices in MI as an antecedent of employee loyalty and satisfaction; García et al. [28] explore the JIT application and relate it to financial performance.
Likewise, Díaz-Reza et al. [29] analyze how MI applies SMED and how it has generated operational benefits and ignoring the economic income or cost reduction. Additionally, while García-Alcaraz et al. [30] report how MI applies information and communication technologies (ICT) to SC and associate their critical success factors to the benefits obtained. Finally, Morales-García et al. [31] report the effect of TPM and OEE in social sustainability, reducing accidents.
However, sustainability in MI has also been studied in an isolated way. For example, Velázquez et al. [32] report an overview of sustainability in the MI in Mexico, specifically in Sonora state; Munguía Vega et al. [33] report the integration of ergonomics and sustainability, focusing only on social sustainability.
However, Hadjimarcou et al. [34] indicate that sustainability and education in workers are the pillars in six strategies for a maquiladora's success. Cruthirds et al. [35] point out that Mexican maquiladoras have outstanding sustainability and responsive practices to gain financial income. In other words, LM practices are associated with the companies' sustainability since if they do not obtain an economic benefit, their implementation in the production lines is out of justification.
Currently, there are some studies relating LM to economic sustainability; for example, Chetthamrongchai and Jermsittiparsert [36] look for this relationship in the pharmaceutical industry in Thailand, while Fullerton and Wempe [37] do so in the United States of America. So, it is observed that research is required to relate the LM tools applied in the Mexican MI with economic benefits gained, since current studies are scarce or focus on analyzing only one LM tool with the overall performance.
This study aims to investigate a group of three LM tools associated with the material flow throughout the production system: 5S, SMED, and continuous flow, which are related to the economic sustainability they offer. Those LM tools are selected because SC in the MI is one of the most important, mainly due to the high importation and exportation rates in that industrial sector [38].
Additionally, tools such as SMED are associated with safety in workplaces because sometimes changeover occurs when machines are operating [39]. Additionally, Rodríguez-Méndez et al. [40] report that SMED is associated with other LM tools, such as JIT and facilitating on-time deliveries. Regarding 5S, Singh and Ahuja [41] indicate that this LM tool is associated directly with manufacturing performance, and it is a vital tool that generates discipline and high standards in the workplace. The novelty of this research is that it integrates three LM in only one model and relates them to economic sustainability using a statistical technique, quantifying their relationship. Additionally, sensitivity analysis indicates how high and low LM tool implementation levels affect the MI's economic income, facilitating supply chain managers' decision-making to focus resources on specific activities.
The article is structured as follows. After this introduction, section two presents a literature review about the four variables analyzed and justifies their relationships; the third section presents the methodology followed to meet the established objective; the fourth section presents the results. Finally, the fifth section presents the conclusions and industrial implications of the results found.

5S
The 5S methodology is a work philosophy that gives order and meaning to work dynamics, addressing workplace disorganization situations. The 5S are Seiri, Seiton, Seiso, Seiketsu, and Shitsuke (classification, organization, cleaning, standardization and improvement) [42]. In industrial practice, 5S focuses on improving conditions at workstations and employee habits. If the tools and equipment required to perform an activity are always classified, organized, clean, and ready to use, that becomes a custom or standard, the primary basis of 5S. As a consequence, the company obtains operational and productivity benefits [43].
However, reports indicate the extension of the lean 5S to 6S to ensure occupational safety and health [44], and some applications are reported by Misiurek and Misiurek [45] and Gnanaguru et al. [46]. However, recent studies report a new evolution, the 7S methodology, adding Spirit for employee engagement across all manufacturing levels [47,48].
In this research, the 5S implementation level in the MI is assessed by five items associated with employees' training for understanding the methodology: establishing cleaning procedures and standardizing the tools used, conducting audits to maintain those standards, giving recognition to employees for achievements, in addition to documenting the processes. In this research, it is assumed that if there are tools in place to carry out every activity, then the flow of the productive system is faster since it is easy to know where they are, and operations require low time.

Single-Minute Exchange of Die (SMED)
SMED is a response to the need to reduce production batches' size and looks to switch quickly from one product to another [49]. Traditionally, manufacturers prefer to assemble large quantities and prorate the setup cost over a high number of units. Otherwise, the entire fee associated with setup must be associated with few parts, increasing costs and reducing the market share [8].
SMED separates the time required to perform changeover, to prepare tools and machines, for internal preparation, and for external preparation. SMED divides all activities into internal and external. The internal activities are performed when the machines are working, while external activities need to stop them [50]. The central idea is to complete as many activities as possible when the machines are operating.
This research measures the SMED implementation level by seven items associated with the production system's flexibility for responding to demand adjustments. In addition, changeover with less than 10 min, if there are improvement groups, the ability to manufacture different products on a production line, and the percentage of orders delivered on time is investigated, among other things.
In this research, it is assumed that if the tools are tidy, clean, and in good condition in a workplace, then changeovers from one product to another should be fast because no time is wasted in locating them or preparing them to be used [51]. In addition, such clean workplaces avoid accidents that hinder the material flow along the production line, giving flexibility to the entire process [52]. Therefore, the following hypothesis is proposed: Hypothesis 1 (H1). The implementation of 5S in the maquiladora industry has a direct and positive effect on SMED.

Continuous Flow (COF)
In its ideal state, COF means that products are processed and transported directly from one stage of the production process to the next, one piece at a time, representing the optimal order size. Thus, each step of the production process works only on the part that the next one needs, just before the next one needs it. COF aims to eliminate massive inventories, delay deliveries, and ensure more market coverage since customized products can be manufactured.
To measure COF implementation in the MI, we observe whether production is organized as families, the supplier responsiveness, the tack time for activities and products, the amount of inventory in the process, and whether there are bottlenecks.
The MI must have clean, tidy work centers with tools in place to achieve the above, which facilitates quick changes that translate into a COF of parts [40]. Studies such as those by Piñeiro et al. [53] indicate that the 5S philosophy application in pharmaceutical production lines helps to decrease uncertainty in COF, so the following hypothesis is proposed: Hypothesis 2 (H2). The implementation of 5S in the maquiladora industry has a direct effect on continuous flow.
For the MI to be flexible and have a COF, it requires a great capacity to respond to customers and make changes quickly or in the shortest possible time [54], as this gives them the ability to adjust the production lines to generate different products, so the following hypothesis is proposed: Hypothesis 3 (H3). The implementation of SMED in the maquiladora industry has a direct effect on continuous flow.

Economic Sustainability (ES)
The LM application in MI is not fortuitous since managers expect to obtain benefits from their implementation, and the most important is ES. ES is a globalized term that includes financial and accounting aspects, which are undoubtedly essential, and integrates aspects associated with sustainability, where the optimization of available resources is sought [55]. In conclusion, ES means implementing profitable strategies and practices that improve the rational use of resources while maximizing the benefits provided by companies [56].
To measure ES in the MI, it is necessary to quantify the reduction in production costs [57], new product design, and energy consumption [58], inventory management, rejection of production orders, raw materials entering the production process, and waste generated from processing [59].
The ES may be due to various LM tools implemented in the production lines. Mohan, Sharma, and Lata [60] mention that workstations with installed programs such as 5S have increased efficiency, productivity, and financial performance. Additionally, Jugraj Singh and Inderpreet Singh [61] indicate that 5S, combined with quality programs, has supported a sustainable performance because these tools are the most important of LM. Therefore, the following hypothesis is proposed: Hypothesis 4 (H4). The implementation of 5S in the maquiladora industry has a direct effect on economic sustainability.
Another source of ES is SMED because it improves operating rates on production lines combined with other techniques. For example, Tekin, Arslandere, Etlioglu, Koyuncuoglu, and Tekin [8] indicate that SMED and Jidoka generate greater flexibility to production Sustainability 2021, 13, 10599 6 of 18 processes, reducing the idle time in machines due to product changes, and that means cost reduction. In turn, Díaz-Reza, García-Alcaraz, Martínez-Loya, Blanco-Fernández, Jiménez-Macías, and Avelar-Sosa [29] indicate that SMED has allowed MI to generate a greater diversity of products for final customers, representing the best market coverage and monetary income. Therefore, the following hypothesis is proposed: Hypothesis 5 (H5). The implementation of SMED in the maquiladora industry has a direct effect on economic sustainability.
Although mass production was efficient for a long time, it had the disadvantage of having little variety in products, but low production costs. These problems have been solved so that the ideal is to have a production order for a single product, as proposed by the COF, which gives more market coverage with customized products. The benefits of having a COF are that each product is produced only when required, minimizing inprocess inventories and storage [54]. Additionally, Vitayasak et al. [62] indicate that a machine's layout contributes to having a COF with a shorter waiting time for material, and an improved relationship with the customer strengthens the economic sustainability. Therefore, the following hypothesis is proposed: Hypothesis 6 (H6). The implementation of continuous flow in the maquiladora industry has a direct effect on economic sustainability. Figure 1 graphically presents the relationships between the analyzed variables that have been established as hypotheses. Observe the arrow direction to identify the independent variable where the arrow begins and the dependent variable where the arrow ends. In this proposed model, we assumed that all effects are positive. The following paragraphs describe the methodology for testing the proposed hypotheses.
Sustainability 2021, 13, x FOR PEER REVIEW 6 of 18 production processes, reducing the idle time in machines due to product changes, and that means cost reduction. In turn, Díaz-Reza, García-Alcaraz, Martínez-Loya, Blanco-Fernández, Jiménez-Macías, and Avelar-Sosa [29] indicate that SMED has allowed MI to generate a greater diversity of products for final customers, representing the best market coverage and monetary income. Therefore, the following hypothesis is proposed: The implementation of SMED in the maquiladora industry has a direct effect on economic sustainability.
Although mass production was efficient for a long time, it had the disadvantage of having little variety in products, but low production costs. These problems have been solved so that the ideal is to have a production order for a single product, as proposed by the COF, which gives more market coverage with customized products. The benefits of having a COF are that each product is produced only when required, minimizing in-process inventories and storage [54]. Additionally, Vitayasak et al. [62] indicate that a machine's layout contributes to having a COF with a shorter waiting time for material, and an improved relationship with the customer strengthens the economic sustainability. Therefore, the following hypothesis is proposed:

Questionnaire Design
To validate the hypotheses in Figure 1, information from the MI is required, so a questionnaire is designed based on a literature review conducted in databases such as Scopus, ScienceDirect, Springer, Ingenta, and others. The keywords in the search refer to the four variables analyzed: 5S, SMED, continuous flow, and economic sustainability. The literature review aims to identify activities indicating LM tool implementation levels and

Questionnaire Design
To validate the hypotheses in Figure 1, information from the MI is required, so a questionnaire is designed based on a literature review conducted in databases such as Scopus, ScienceDirect, Springer, Ingenta, and others. The keywords in the search refer to the four variables analyzed: 5S, SMED, continuous flow, and economic sustainability. The literature review aims to identify activities indicating LM tool implementation levels and parameters measuring economic sustainability [63]. This process represents a rational validation.
However, since the questionnaire is designed using a literature review process, obtaining items used by other authors in different countries and industrial sectors, a judge's validation is applied to adapt it to the Mexican MI [64]. The judges were three academic and ten industrial managers. Judges had to assess whether the items in the questionnaire had sufficiency, clarity, coherence, and relevance. After three rounds with judges, a final questionnaire was defined.
Based on the literature review and judges' validation, a first questionnaire draft is constructed, divided into three sections. The first section obtains demographic information from respondents, the industrial subsector, years of experience in current job positions, and gender. The second section contains items related to each of the three LM tools analyzed. In this case, the 5S are integrated by six items, SMED by seven items, and continuous flow by six items. Finally, the last section contains seven items associated with economic sustainability and how the MI measures the LM benefits.
Items must be answered on a 6-point Likert scale, where one indicates that the activity is not performed, or the benefit is not obtained. In contrast, six indicates that the activity is always performed, or the benefit is always obtained.

Questionnaire Administration
The questionnaire is applied to managers, engineers, and supervisors of production lines since they are the ones who know about the LM tools' implementation and the benefits obtained. The survey is applied to the MI established in Ciudad Juarez in Mexico. As previously stated, MI represents the primary industrial sector in that region, and it has a high social and economic impact [68].
Currently, there are 328 MIs in Ciudad Juárez, and that is the target population. The automotive sector accounts for 32%, electronics for 29%, medical for 7%, plastics and metals for 12%, call centers for 3%, packaging for 8%, and miscellaneous for 9% [69]. This MI is occupying 67% of the region's active direct labor force, followed by the business, personal, and home services sectors with only 9%, indicating indirectly associated enterprises [70].
The questionnaire is uploaded into a specialized webpage for online application since access to the MI is limited due to the COVID-19 pandemic. An email is sent to all potential respondents attaching the electronic link to the questionnaire. If after 15 days, no response to the questionnaire is obtained, a second invitation is sent, and if after three attempts, no reply is received, then that case is discarded.

Information Gathering and Debugging
The platform stays open to receive information from 1 October to 15 December 2020. After that date, a database in Excel format is downloaded and analyzed in SPSS v.25 software to perform a debugging process that includes the following tasks: • Standard deviation (SD) estimation. If SD values are less than 0.5, then that case is discarded as a non-committed respondent.

Latent Variable Validation
Before integrating latent variables in the model, all of them are validated according to the following indices: • R 2 and adjusted R 2 for parametric predictive validation, which must be greater than 0.02 [71]. • Cronbach's alpha and composite reliability index for internal consistency, which must be greater than 0.7 [72].

•
The average variance extracted (AVE) for discriminant validity, which must be greater than 0.5 [72].

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Variance inflation factor (VIF) for measuring collinearity between variables and common method bias (CMB), which must be less than 3.3 [73]. • Q 2 for nonparametric predictive validation, which should be similar to R 2 [71].
Here, it is essential to note that some indexes for latent variables are iteratively estimated, for example, the Cronbach's alpha and the VIF, until obtaining an acceptable value, and some items are discarded from the analysis to improve those validity indexes.

Descriptive Analysis of the Items
The items that remain in the latent variables after being validated are analyzed as follows to know the central and dispersion measures in univariate analysis [74]:

•
The median of the items is obtained as a measure of central tendency, given that the data are on an ordinal scale. High median values indicate that the item's activity is always executed, or the benefit is always obtained. Low values indicate that the activity is not achieved, or the benefit is not obtained.

•
The interquartile range of the items is obtained as a measure of dispersion, which is the difference between the third and first quartile. Low values indicate a high consensus among responders.

Structural Equation Model
The structural equation modeling (SEM) technique is selected to test the hypotheses proposed in Figure 1; specifically, the partial least squares (PLS) method, based on the linear regression technique, is used to estimate standardized dependence values between latent variables. PLS is integrated into the WarpPLS v.7 ® software [75], and it applies when there are no normally distributed data, obtained on an ordinal scale or with a small sample [71].
The analysis is performed with 95% confidence. Before the model is interpreted, specific efficiency and quality indexes of the model are validated, such as the following [71]:

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Average path coefficient (APC) to measure the global significance of the direct effect. The p-value associated must be less than 0.05. • Average R 2 (ARS) and average adjusted R 2 (AARS) to measure the variance explained by independent variables on dependent variables, and the associated p-value must be less than 0.05.

•
Average block VIF (AVIF) and average full collinearity VIF (AFVIF) to measure general collinearity, which should be less than 3.3. • Tenenhaus GoF index (GoF) measures the data to the model and should be greater than 0.36.
Three types of effects are measured. First, direct effects are used to test the hypothesis in Figure 1. A standardized β value is obtained using PLS for each relationship between variables and associated with a p-value that must be less than 0.05 [76]. The null hypothesis tested is β = 0, versus the alternative hypothesis that β = 0. If it is statistically proven that β = 0, then it is concluded that there is no relationship between the variables; otherwise, if it is proven that β = 0, there is a relationship.
The second one is called indirect effect and occurs through third variables named mediators and are of particular interest when the direct effects are not statistically significant. In this case, the total sum of indirect effects is reported with their associated p-value. Finally, the third one is the total effect, which represents the sum of direct and indirect effects.
Additionally, an R 2 value is reported with latent dependent variables in the model as a measure of variance explained by all independent variables, contributing an effect size (ES). So, for every direct, indirect, and total effect, an ES is reported.

Sensitivity Analysis
Since PLS performs its calculations based on standardized values, then probabilities can be calculated when the different variables occur at low P(Z < −1) and high P(Z > 1) scenarios [71]. Probabilities are calculated for the variables occurring in isolation in high and low scenarios, jointly in a combination of scenarios (represented by &) and the conditional probability of the dependent variable occurring, given that the dependent variable has occurred (represented by IF).
Specifically, this paper reports a probability of joint occurrence of two variables in different scenarios, such as P(Z i > 1) ∩ P(Z d > 1), P(Z i > 1) ∩ P(Z d < −1), P(Z i < −1) ∩ P(Z d > 1), and P(Z i < −1) ∩ P (Z d < −1), as well as the conditional probability for P(Z d > 1)/P(Z i > 1), P(Z d > 1)/P(Z i < 1), P(Z d < −1)/P(Z i > 1) and P(Z d < −1)/P(Z i < −1), where Z i represents a standardized value for an independent variable and Z d for a dependent variable; −1 represents a low scenario for a variable and 1 a high scenario.

Descriptive Analysis of the Sample and Items
One hundred and seventy-eight responses to the questionnaire were collected from 433 emails sent, giving a response rate of 41.10%; however, nine were discarded for not complying with the inclusion principles, so only 169 were analyzed (57 women and 112 men). Regarding experience in the position, 44 had 2 to 3 years, 26 had 3 to 5 years, 75 had 5 to 10 years, and 24 had more than ten years. The final dataset analyzed is available from Martínez Hernández and García Alcaraz [77]. Table 1 illustrates the respondents' industrial sectors and job positions, where it can be seen that the automotive and electrical sectors were the ones that participated the most, followed by medical and electronic. In this research, the machining, logistics, and electronic industrial sector have low participation. However, this sector participation is proportional to the current number of MI established in Ciudad Juarez, Mexico. Additionally, regarding the job position, it can be seen that supervisors and engineers were the most responsive, with 81 and 68, respectively, and representing 81.16%. This participation rate indicates that information analyzed in this research comes from persons in production lines every day, with experience in their job, and their opinions are reliable. Table 2 illustrates the descriptive analysis of the items, where the median as a measure of central tendency and the interquartile range as a measure of dispersion are shown. The items are ordered in descending way according to the median. According to those values, the most critical item for 5S is to have standards regarding how to carry out every piece of work, and the second most is to have documented methods and procedures. That indicates that Seiton and Seitketsu (order and standardization) are widely supervised when 5S is applied in MI. Table 2. Descriptive analysis of the items.

5S
Median IR There is a standard of how the work area should be maintained. The critical item for SMED is to follow a DMAIC procedure for its implementation because SMED aims to reduce the changeover times and to create awareness regarding the cost due to idle machinery. Regarding continuous flow, the most important is to have a production process organized on product families and identify the bottleneck as a barrier to material flow. Finally, the most important for economic sustainability is cost reduction due to raw material acquisition and increasing sales. Table 3 shows the validation indexes for latent variables. All variables meet the cut-off values established in the methodology, so they are integrated into the structural equation model. According to R 2 and adjusted R 2 , dependent variables have enough parametric predictive validity, composite reliability, and Cronbach's alpha indicates adequate internal and construct validity. Additionally, AVE indicates good convergent validity and VIF suggests the absence of CMB and collinearity problems. Finally, Q 2 demonstrates that there is acceptable nonparametric predictive validity in all dependent latent variables.

Structural Equation Model
Before interpreting the model, its efficiency indexes are calculated and listed below. According to those values, the model fulfills the cut-off value, so it is interpreted. APC indicates that the β values are adequated on average, and there are relationships among variables. ARS and AARS indicate adequated predictive validity in the model; AVIF and AFVIF indicate the absence of collinearity and the CMB problem. Finally, the GoF shows that the data have a good fit for the model. indicates that the β values are adequated on average, and there are relationships among variables. ARS and AARS indicate adequated predictive validity in the model; AVIF and AFVIF indicate the absence of collinearity and the CMB problem. Finally, the GoF shows that the data have a good fit for the model. Tenenhaus GoF (GoF) = 0.566, large ≥ 0.36 Figure 2 illustrates the model evaluated, where the β values and the associated pvalues are shown for every relationship. However, R 2 is illustrated for latent dependent variables. Figure 2 illustrates all the direct effects, and it is observed that all of them are statistically significant since the p-value associated with each β value is less than 0.05. Table 4 summarizes the relationships between variables, the hypothesis they represent, the β-values, their p-value, and the conclusion for them.

Direct effect
Interpreting the H1 as an example, findings indicate that there is enough statistical evidence to declare that 5S has a direct and positive effect on SMED because when the first variable increases its standard deviation in one unit, the second one goes up 0.571 units.   Figure 2 shows that the dependent variables have associated an R 2 value to measure the variance explained by the independent variables. However, it is unknown how much  Figure 2 illustrates all the direct effects, and it is observed that all of them are statistically significant since the p-value associated with each β value is less than 0.05. Table 4 summarizes the relationships between variables, the hypothesis they represent, the β-values, their p-value, and the conclusion for them. Interpreting the H 1 as an example, findings indicate that there is enough statistical evidence to declare that 5S has a direct and positive effect on SMED because when the first variable increases its standard deviation in one unit, the second one goes up 0.571 units. Figure 2 shows that the dependent variables have associated an R 2 value to measure the variance explained by the independent variables. However, it is unknown how much each independent variable contributes, called effect size (ES). For this reason, Table 5 illustrates the decomposition of this R 2 value into its components, or the ES of each independent variable. The sum of the ES in a dependent variable is equal to the R 2 value. According to the information contained in Table 5, we can conclude the following: • SMED is explained by 5S by 32.7%, and is the only variable that directly affects it. • COF is explained as 50.3%; however, 5S contributes 11.3%, and SMED contributes 39.0%. Given that the SEMD contribution to explaining COF is bigger, then those values allow concluding that maquiladoras that wish to have a COF in their production lines should focus on having high levels of SMED implementation because that means low idle time for machinery. • ES is explained as 46.3%; however, 5S contributes 9.8%, SMED contributes 12.4%, and COF contributes 24.1%. Those values conclude that COF is the most critical variable in explaining ES, so maquiladoras should be concerned about maintaining their production lines with a continuous flow to be economically profitable, increasing financial income. However, SMED favors COF and 5S favors SMED, so a critical route for LM techniques supporting ES is as follows: 5S→SMED→COF→ES. Table 6 illustrates the sum of indirect and total effects, the associated p-values, and the effect size (ES) for every relationship. Observe that all direct and total effects are statistically significant, as the associated p-values are less than 0.05 in all cases. There is a particular interest for the indirect effect between 5S→ES since the direct effect was only 0.190, but the indirect effect is 0.327; so, the indirect effect is 70% larger, indicating the importance of SMED and COF as mediating variables in that relationship.

Sum of Indirect and Total Effects
Something similar occurs with the indirect relationship between 5S→COF since the direct effect is only 0.210, but the indirect effect through SMED as a mediating variable is 0.327, 55% larger. Table 7 illustrates the sensitivity analysis. High scenarios are indicated by the symbol "+", and low scenarios are shown by "−". The joint probabilities in a combination of scenarios are represented by & and the conditional probabilities by If. For example, 5S+ has an occurrence probability of 0.219, but 5S− has 0.124. Additionally, the probability of finding 5S+ and SMED+ simultaneously in a production line is 0.083, a shallow value, because managers prefer to have high values; however, if 5S+ has occurred, then there is a conditional probability of 0.378 of finding SMED+, indicating the dependence importance. In addition, 5S− never is associated with SMED+ because the probabilities are zero. In conclusion, investment in 5S is a warranty for SMED in MI. All other relationships are described in the Conclusions section.

Regarding the Structural Equation Model
Regarding the hypotheses proposed in Figure 1, the following is concluded based on the β and p-value associated with the direct effects. H 1 . There is enough statistical evidence to state that 5S has a direct and positive effect on SMED implementation in MI, since when the first variable increases its standard deviation by one unit, the second goes up by 0.571 units. This result indicates that activities focused on maintaining a clean work area, with tools in place and high standards regarding all tasks, facilitate quick changeovers in maquiladora production lines to move from one product to another. With these achievements, maquiladoras will have greater flexibility with customers, and small lots deliver more customized batches, giving them a competitive advantage.
H 2 . There is enough statistical evidence to state that 5S has a direct and positive effect on implementing continuous flow in the MI, since when the first variable increases its standard deviation by one unit, the second goes up by 0.210 units. However, an indirect effect of 0.324 units through SMED as a mediating variable gives a total effect of 0.571 units. The above confirms that maintaining clean work areas, with tools in place and with high standards, allows generating a continuous flow in production lines of MI, reducing idle time in machinery. H 3 . There is enough statistical evidence to state that SMED has a direct and positive effect on implementing continuous flow in the MI since when the first variable increases its standard deviation by one unit, the second goes up by 0.567 units. This result indicates that rapid changeovers in production lines to move from one product to another in the MI facilitate the continuous flow of materials, since less time is lost with machines and equipment stopped for setups. H 4 . There is enough statistical evidence to state that the 5S implementation has a direct and positive effect on economic sustainability in the MI since when the first variable increases its standard deviation by one unit, the second one goes up by 0.190 units. However, 5S also has an indirect effect on ES, through COF and SMED, of 0.327 units, which gives a total effect of 0.518 units. The above findings indicate that the MI focused on maintaining clean work areas, having work tools in place, and maintaining high standards obtain economic benefits, indicating the monetary importance of 5S. Additionally, here it is essential to mention the role of the mediating variables of COF and SMED since the indirect effect through them is bigger than that generated directly.
H 5 . There is sufficient statistical evidence to state that the SMED implementation has a direct and positive effect on economic sustainability in MI, since when the first variable increases its standard deviation by one unit, the second goes up by 0.214 units. However, COF has an indirect effect of 0.218 units, giving a total effect of 0.432 units. These results indicate that the rapid changeovers in the production lines generate an economic benefit to the maquiladoras. This is because machines and tools have higher use and a reduced idle time, and the OEE increases. H 6 . There is enough statistical evidence to state that the COF implementation has a direct and positive effect on economic sustainability in MI, since when the first variable increases its standard deviation by one unit, the second increases it by 0.384 units. These results indicate that by having a COF in production lines, there are no inventories in the process. In addition, there is less waste, indicating that the machines and tools are in perfect condition, which translates into lower production costs.

Regarding the Sensitivity Analysis
Similarly, interpreting the sensitivity analysis, a manager can identify how low scenarios for variables are a risk or how favorable high scenarios obtain certain benefits. The following conclusions can be drawn:

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Managers should strive to achieve 5S+, which guarantees SMED+, COF+, and ES+ with a conditional probability of 0.378, 0.378, and 0.405. These findings indicate that investing and obtaining 5S+ will facilitate the implementation of SMED, COF, and ES. Additionally, 5S+ is weakly associated with SMED−, COF− and ES−, since the occurrence probabilities are 0.0054, 0.012, and 0.108, respectively. • However, 5S− is a significant risk for managers since the conditional probability of SMED−, COF− and ES− occurring is 0.524, 0.714, and 0.524, respectively. These findings indicate that 5S− is a barrier to proper SMED implementation or rapid changeovers in production lines, slowing down the process of adapting them to start the production process of another product. Additionally, they decrease the constant materials flow, affecting the production costs and competitiveness in the MI.

•
Managers should seek SMED+, since that facilitates obtaining COF+ and ES+ with a probability of 0.650 and 0.750, respectively. The above indicates that proper SMED implementation favors COF in the production lines and undoubtedly generates an economic benefit to MI since it reduces machine idle times due to changes in the production system. In addition, SMED+ has no association with COF− and ES−, as the conditional probabilities are low, only 0.050 and 0.100, respectively. • However, SMED− is a risk for the production lines since it can generate COF− and ES− with a probability of 0.800 and 0.600. These results indicate that low levels of SMED implementation can lead to a slow flow of materials in the production system and an increase in the production cost since there will be idle machines and some work in process. Similarly, SMED− is not associated with COF+ and ES+, as the conditional probabilities of occurrence are low, warranting the investment of resources by managers.
• Likewise, having a COF+ in the production lines should be ensured, as it favors ES+ with a probability of 0.636. However, managers should be careful not to have COF−, as that can generate ES− with a probability of 0.519.
As a general conclusion, it can be mentioned that LM tools associated with material flow, such as 5S, SMED, and continuous flow, are interrelated and have direct and total direct effects on economic sustainability in the MI. The findings indicate that implementing these LM tools is justified, as their implementation always offers benefits.

Limitations and Future Research
Lean manufacturing is a set of several tools; however, only three tools associated with materials flow in the production system have been analyzed in this study. Furthermore, the R 2 values for the dependent variables are less than one, indicating that other tools explain them and favor their implementation. In future work, the LM tools will be integrated according to the LM pillars and analyzed with second-order structural equation models, increasing the predictive capacity of the dependent variables, such as sustainability. Institutional Review Board Statement: Ethical review and approval were waived for this study, because Institutional Review Board Statement indicates that this research is based in an online survey and only requires to obtain an online consent from all responders and guarantee the anonymity for all of them.

Informed Consent Statement:
Online informed consent has been obtained from all responders to publish their information; however, the anonymity of all respondents has always been preserved throughout the questionnaire. The databases that have been created with all answers given are entirely anonymous.

Data Availability Statement:
The final dataset used for the structural equation model can be consulted at https://doi.org/10.17632/tht522mbph.1, accessed on 16 June 2021.


Effect of Diversification Strategy, Directors Compensation, Managerial Ownership and Company Sizes on Company Performance

Diversification strategy is chosen by managers of companies to develop their business that can improve the performance of a company. One way to evaluate the performance of company management is by give compensation. Ownership in the structure capital in company there are several kinds one sample of the managerial ownership is the ownership of shares owned by managers and employees. The size of the company can see the total assets owned by the company used to generate profits. Performance is a way to measure the level of success of a company from management activities whose information is obtained from the company's financial statements. The object of research is manufacturing sector companies listed on the Indonesia Stock Exchange (IDX) in 20152018, The results in the research in that the strategy of diversification, compensation of director’s and managerial ownership is not given affect to be able to the performance of the company, while the results of the size of the company influences the company's performance.

INTRODUCTION
The era of globalization now, the level of need for the use of technology is very high. The use of this technology is supported by a very adequate internet network so that communication in trade between countries is very easy and triggers the ASEAN Economic Community (AEC). One of the impacts of the AEC is that every company competes to become a excellect company. In addition to the impact caused by the AEC, company competition is also getting tougher due to the industrial revolution 4.0.
BBC.Com (2018), revolution 4.0 is a source of revolution where technology development is very fast and this technology can help companies expand market share easily. In the development and growth of companies in Indonesia, which is increasingly rapid, which causes each company to carry out operational activities will implement various strategies to survive and improve company performance.
Diversification strategy is a geographic expansion of the business as well as market share or making the products of a company into various types which are expected to improve company performance (Harto, 2005). Good or bad in company performance can be supported management in the company to choosed strategy for achieved purposed company, many strategies to choosed from management. Diversafication strategy is one of several corporate strategies. Reasearch on Lukman (2014) that the diversification strategy carried out by the company has a improve effect on company performance, and Azis, Hermawan, dan Rossieta. (2016) also that diversification strategies can reduce company performance.
can also solve conflict problems that often occur in companies The research Theeravanich (2013) which examines the compensation of directors, concludes that the compensation for directors has no positive effect on company performance. Meanwhile, research of the Azis, et all (2016) stated that compensation for directors be affected positive for company performance.
Managerial ownership is the one ownership structures in the company showing that the company is also owned by the company management and even by employees. Therefore, managerial ownership indicates that there is a share of share ownership from the management, but management remains an active party in various company operational activities (Wahyudi and Pawestri, 2006). With managerial ownership, it will have an indirect impact on the company in an effort to align the position of management and company employees with shareholders. The research at Short and Keasey (1999) who have examined the effect of managerial ownership on managerial performance, it is concluded that ownership has a positive impact on company performance.
Firm size as the last independent variable in this study is due to the inconsistency of research results in several studies that have been conducted. The Reasearch of Kurniasari (2014), to find out the size company can be seen of the total assets if value of the assets is getting bigger the more the company can be diversified to improve company performance, this is because large companies have large enough funding. The object of this study consists of manufacturing companies listed on the Indonesian stock exchange for the 2015-2018 period.

Agency Theory
This theory of a relationship involving two parties, the first party is called the principal party or also known as the owner, which consists of one or more people who make a relationship with two parties which are usually called agents or management, the principal party has an obligation. provide funds for operational activities while the agent manages the company to achieve company goals. Jensen and Meckling (1976), agency conflict has two relationships, the first is conflict caused by the manager and the shareholders, the manager acts in the interests of the manager by adding facilities with the aim of the manager's own interests that will be obtained from the company because the provision of such facilities will be at the expense of the shareholder or the principal.

Diversification Strategy
Strategy is a company way of achieved purpose vision and mission company, company objectives where the company can offer goods and services according to the needs of consumers (Rangkuti, 2014: 3).
There are two types of diversification strategies, related diversification strategies and unrelated diversification strategies. When the company switches to new business lines that are still related to the company's operational activities, while companies that implement a strategy in which the company's value chain is not in accordance with operational activities or what is usually called a diversified strategy activity is not related, the company will do things by acquiring other companies that have high opportunities for sustainability but with the problem of lack of funding sources in carrying out operational activities (David, 2015:133)

Compensation for The Board of Directors
If management in the company can be to worked together determining the strategies undertaken by the company in achieving company goals and solving various problems that occur such as agency conflicts in a company. In providing compensation is a reciprocal action on the performance of the board of directors during their function and is a sense of concern from the owner to the board of directors (Jensen and Meckling, 1976). In addition to being used to motivate management to improve company performance, board of directors compensation is used as a way to solve conflict problems that often occur in companies. Chen (2013), if the compensation for directors given is too large compared to the duties and responsibilities given to the directors, then the compensation will disturb the performance of a company.

Corporate Governance Mechanisms
Corporate governance is a system that directs and controls the relationship between investors, managers, creditors, government, employees in fulfilling the rights and obligations of these parties. In addition, the reason for one of the impacts of implementing corporate governance is that it can overcome the problem of agency conflicts in a company by overcoming monitoring and assessing the performance of a company and also controlling the behavior of managers who are concerned with the interests of managers. (Sutedi, 2012: 1) In implementing corporate governance, the objective is to be able to motivate managers to run according to the wishes of investors and to reduce agency problems that occur (Hamdani, 2016: 31). In this study, the corporate governance mechanism will use the managerial ownership factor, because managerial ownership is expected to affect the operational activities of the company which will affect the company's performance in achieving one of the company's many goals, namely to maximize the company's value.

Company Performance
Company performance is the level of success of management in managing the company to achieve success, company performance is measured using financial analysis tools so that can be measure whether management can manage the company well in achieving company goals (Rani, 2015).
In determining the company's performance, it is said to be good, it requires a complete and accurate company financial report, the income statement in the financial report can have an impact in the form of evaluating the performance of each component in the company's operational activities besides the performance also regarding the profitability carried out by the operational segment Brigham and Houston (2014: 133) company financial statements are used to evaluate company performance in terms of finance. In measuring the effectiveness of financial ratios, financial ratios include liquidity ratios, profitability ratios, and growth ratios. Brigham and Houston (2014: 134).
ROA is a measure of the success of the company in obtaining profits by utilizing assets owned by the company, ROA is the most important ratio among other profitability ratios for the company because of how managers solve problems and earn profits with available company assets, if the higher the ROA of a company it can be said that The company's performance has increased

The Effect of Diversification Strategy on Company Performance
Strategy is a company way of achieving goals, company objectives where the company can offer goods and services according to the needs of consumers (Rangkuti, 2014: 3). Along with the growing pace of the company in the process of making various types of products, it has an impact on consumers, where consumers will quickly feel bored with old products. The hypothesis that occurs in this study: H1: Diversification strategy be affected positive on Company performance

Effect of Compensation of Directors on Company Performance.
Compensation for directors is a reciprocal between the company and the manager, besides that it can also be used as a communication tool for evaluating the manager's performance in improving the company's performance and value. Apart from being used to motivate management to improve company performance, compensation for directors can also solve conflict problems that often occur in companies.
The conflict is about the different views and interests between the stakeholders and the company management. The results of research by Azis et al (2016) in the compensation for directors has a positive impact on company performance. This is because the effect of compensation can affect management control in company performance. Based on the elaboration, the hypothesis that occurs in this study.

Effect of Managerial Ownership on Company Performance
Tjeleni (2013) explains that managerial ownership is a condition in which management plays a role as a company manager and also as a share owner because management owns shares in the company. The function and role of management to manage the company is the responsibility of delegation of authority given by the owner of the company. The Reasearch Short and Keasey (1999) an Chen and Yu (2011) have examined the impact of managerial ownership on company performance, Them conclude that ownership managerial has a affected positive on company performance.

The Influence of Company Size on Company Performance
Reasearch of Kurniasari (2014), to find out the size company can be seen of the total assets if value of the assets is getting bigger the more the company can be diversified to improve company performance. This is because large companies have large enough funding. In calculating the size of the company, one method can be used, namely the logarithm of total assets owned by the company. Based on the elaboration, the hypothesis that occurs in this study.
H4: Company size be affected positive effect on company performance

RESEARCH METHOD
This research is a quantitative type of research in which this study to examine the effect of diversification strategies, director's compensation, ownership in managerial and size in the company performance. The object of this study will use manufacturing companies that have been listed on the IDX in the 2015-2018.
Company performance is the dependent variable in this study. Company performance is the level of success of management in managing the company to achieve success, company performance is measured using financial analysis tools so that it can be measured whether management can manage the company well in achieving company goals (Rani, 2015). ROA is a measure of the company's success in obtaining profits by utilizing assets owned by the company, according to Brigham and Houston (2014: 148), if the ROA value approaches 1, the more efficient the company's operations will be (Kurniasari, 2014).

ROA =
Diversification strategy is one of the strategies used by companies in expanding their business by carrying out a strategic business unit (SBU) or a subsidiary of Wisnuwardhana and Diyanti (2015). This research will use the measurement or level of company diversification by using the Herfindahl index which is derived from the sales of the company's business segments, the index is generated based on the square of sales of each operational segment which will be divided with company's total sales. If the results of the index are close to number 1, it can be said that the company is increasingly focused on one product line, whereas if the index results are close to number 0, the company is said to be diversifying its products. Villalonga (2004) In calculating the Herfindahl index it can be formulated as follows: Information: H: Herfindahl Index Si: The proportion of sales per segment of the company's total sales.
Compensation for directors is one of the management control mechanisms where the compensation for directors is expected to motivate management to improve company performance to achieve certain company goals. Apart from being used to motivate management to improve company performance, compensation for directors can also solve conflict problems that often occur in companies. The conflict is about the different views and interests between the stakeholders and the company management. Compensation for directors is a reciprocal between the company and the manager, besides that it can also be used as a communication tool for evaluating the manager's performance in improving the company's performance and value. In assessing the Managerial ownership in which the variable strengthens the independent variable in terms of affecting the dependent variable. Managerial ownership is part of the shareholder of management but is an active party in various company operational activities (Wahyudi and Pawestri, 2006). Sukrini (2012), managerial ownership is share ownership in a company where the ownership is owned by company management and even employees. To find out the percentage of active management, it can be measured by adding up the percentage of shares owned by active management. (Supriyadi, 2017)

KM = ℎ ℎ
Reasearch of Kurniasari (2014), to find out the size company can be seen of the total assets if value of the assets is getting bigger the more the company can be diversified to improve company performance. This is because large companies have large enough funding. In calculating the size of the company, one method can be used, namely the logarithm of total assets owned by the company (Wulandari and Septiani 2017) Firm Sizes = Ln (Total Asset)

RESULT AND DISCUSSION
In the descriptive statistics, this study explains that the dependent and independent variables used are: return on assets, diversification strategies, compensation for directors, managerial ownership and company size. The coefficient of the research diversification strategy (DU) independent variable has a negative value of -0.053, so it can be concluded that the diversification strategy will reduce ROA by 0.053 and also this strategy is positive with sig.t, namely 0.232 but 0.232> 0.05.
The coefficient of directors' compensation (KD) is 0.003, so it can be concluded that if the compensation for the directors increases, it will also increase the value of the company's ROA by 0.003 and the compensation for the directors is also positive with sig.t, namely 0.490 but 0.490> 0.05.
The coefficient of managerial ownership (KM) in this study shows a positive value of 0.06, so it can be concluded that if managerial ownership increases, it will also have an impact on ROA which increases by 0.06 and managerial ownership is also positive with sig.t, which is 0.076 however 0.076> 0.05 The coefficient of company size (SIZE) in this study also shows a positive value, which is equal to 0.014, so it can be concluded that if there is an increase in the value of the company size it will increase the ROA value by 0.014 and also have a positive sign with sig.t, which is 0.001 and 0.001 < 0,5.
Based on research analysis, it is concluded that the first hypothesis is not accepted, because diversification strategy do not have an impact on company performance, if the diversification strategy is not supported by the efficient and effective allocation of company resources.
That the second hypothesis in research of is no accepted, In the second hypothesis to provide evidence company performance can't be influenced by role of the directors' compensation. Due to the provision of compensation, both large and small, can only affect the motivation of the directors on a fairly small scale.
Based on the results of the research analysis, it is concluded that the third hypothesis is rejected, which proves that the role of managers in having share ownership in the company is proven to have no effect on company performance. This shows that managerial ownership in a company has not shown that managerial ownership can affect company performance. This is because the percentage of managerial ownership does not have a high enough level of materiality with other stock ownership.
The fourth hypothesis is accepted, that the size of the company will affect the performance of the company. This shows that company size can affect company performance because the size of the company will affect the company's performance.
The research limitedness, in the study there are four independent variables are diversification strategies, director's compensation, managerial ownership, and company size with these variables still unable to influence the dependent variable. The research sample only uses manufacturing companies with several criteria so that the manufacturing companies cannot be comprehensive. In the research sample only 4 years period so it cannot show the of diversification strategies in improving company performance.

CONCLUSIONS
The conclusions and limitations of the study, the researchers provided suggestions for further research. Expected to add measurements to the independent variables of diversification strategies such as cost leadership and differentiation (Azis, et al, 2016). Researchers are expected to add manufacturing companies with other companies in the research object. Researchers are expected to add the length of the period in the research sample so that they can see the trend of diversification strategies on company performance.