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Enabling Knowledge Discovery in Multi-Objective Optimizations of Worker Well-Being and Productivity

April 2022
Sustainability 14(9):4894

DOI:10.3390/su14094894

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Authors:

Aitor Iriondo

University of Skövde

Henrik Smedberg

University of Skövde

Dan Högberg

University of Skövde

Anna Syberfeldt

University of Skövde

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Usually, optimizing productivity and optimizing worker well-being are separate tasks performed by engineers with different roles and goals using different tools. This results in a silo effect which can lead to a slow development process and suboptimal solutions, with one of the objectives, either productivity or worker well-being, being given precedence. Moreover, studies often focus on finding the best solutions for a particular use case, and once solutions have been identified and one has been implemented, the engineers move on to analyzing the next use case. However, the knowledge obtained from previous use cases could be used to find rules of thumb for similar use cases without needing to perform new optimizations. In this study, we employed the use of data mining methods to obtain knowledge from a real-world optimization dataset of multi-objective optimizations of worker well-being and productivity with the aim to identify actionable insights for the current and future optimization cases. Using different analysis and data mining methods on the database revealed rules, as well as the relative importance of the design variables of a workstation. The generated rules have been used to identify measures to improve the welding gun workstation design.

Flow diagram of the knowledge discovery process.

…

Solution space of cycle time and average RULA score í µí°¸í µí± of all manikins.

…

Anthropometric measures of manikins.

…

Indices, parameters, variables, and objectives of the optimization model.

…

Optimization algorithm configuration.

…

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Citation: Iriondo Pascual, A.;

Smedberg, H.; Högberg, D.;

Syberfeldt, A.; Lämkull, D. Enabling

Knowledge Discovery in

Multi-Objective Optimizations of

Worker Well-Being and Productivity.

Sustainability 2022,14, 4894. https://

doi.org/10.3390/su14094894

Academic Editor: Lucian-Ionel Cioca

Received: 24 March 2022

Accepted: 11 April 2022

Published: 19 April 2022

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sustainability

Article

Enabling Knowledge Discovery in Multi-Objective

Optimizations of Worker Well-Being and Productivity

Aitor Iriondo Pascual 1, * , Henrik Smedberg 1, Dan Högberg 1, Anna Syberfeldt 1and Dan Lämkull 2

1Virtual Engineering Research Environment, School of Engineering Science, University of Skövde,

541 28 Skövde, Sweden; henrik.smedberg@his.se (H.S.); dan.hogberg@his.se (D.H.);

anna.syberfeldt@his.se (A.S.)

2Advanced Manufacturing Engineering, Volvo Car Corporation, 405 31 Göteborg, Sweden;

dan.lamkull@volvocars.com

*Correspondence: aitor.iriondo.pascual@his.se

Abstract:

Usually, optimizing productivity and optimizing worker well-being are separate tasks

performed by engineers with different roles and goals using different tools. This results in a silo effect

which can lead to a slow development process and suboptimal solutions, with one of the objectives,

either productivity or worker well-being, being given precedence. Moreover, studies often focus

on ﬁnding the best solutions for a particular use case, and once solutions have been identiﬁed and

one has been implemented, the engineers move on to analyzing the next use case. However, the

knowledge obtained from previous use cases could be used to ﬁnd rules of thumb for similar use cases

without needing to perform new optimizations. In this study, we employed the use of data mining

methods to obtain knowledge from a real-world optimization dataset of multi-objective optimizations

of worker well-being and productivity with the aim to identify actionable insights for the current and

future optimization cases. Using different analysis and data mining methods on the database revealed

rules, as well as the relative importance of the design variables of a workstation. The generated rules

have been used to identify measures to improve the welding gun workstation design.

Keywords:

ergonomics; digital human modeling; productivity; simulation; optimization; knowledge

discovery

1. Introduction

Simulation is widely used in industries such as the automotive industry because it

can efﬁciently create, test, and optimize the design of products and production systems

in the virtual world without any need to create, test, and optimize prototypes in the

physical world [

–

]. Using simulation saves time and money and allows a more thorough

investigation of the solution space. These improvements in productivity have led to

simulation being used in the design of workstations [

]. Simulation tools using digital

human modeling (DHM) are also used in designing workstations to assess workers’ well-

being [6].

However, simulations for optimizing productivity and simulations for assessing

worker well-being are usually performed by people with different roles (production en-

gineers solve productivity problems, while ergonomics specialists consider worker well-

being). They have different focuses or objectives and use different tools. This can create

silo effects, leading to slow development processes and suboptimal solutions.

Productivity and worker well-being often go hand in hand, because improving work-

ing conditions usually increases productivity [

–

]. However, sometimes the goals of

productivity and well-being are at odds. Companies need to ﬁnd and implement solutions

in their production facilities to maintain proﬁtability, output, and quality, as well as the

well-being of workers. Previous research has identiﬁed the core elements of DHM tools

and suggested a structured process for applying DHM tools in the design and development

Sustainability 2022,14, 4894. https://doi.org/10.3390/su14094894 https://www.mdpi.com/journal/sustainability

Sustainability 2022,14, 4894 2 of 14

process [

–

] at the design level of a workstation [

]. There are also applied optimization

techniques to ﬁnd design solutions that improve well-being and productivity [

–

]. But

while there are tools available to optimize worker well-being or productivity, there are no

tools available to consider both productivity and well-being while also considering the

anthropometric diversity of workers.

In addition, studies often focus on ﬁnding the best solutions for a speciﬁc use case, and

once solutions have been obtained and one of them has been implemented, the engineers

move on to analyze the next use case. But setting up a use case and ﬁnding optimal

solutions is time-consuming and requires skills and tools. Therefore, it would be beneﬁcial

to extract knowledge from existing use cases to ﬁnd rules of thumb that apply to upcoming

similar use cases, thereby reducing the need to perform new optimizations.

The aim of this paper is to employ the use of data mining methods to ﬁnd knowledge

about the solutions to a multi-objective optimization problem (MOOP) for optimizing both

productivity and worker well-being, that both describes the properties of the current use

case, and that potentially can be used in future use cases of similar MOOPs. Knowledge

discovery has successfully been used in real-world cases for decision making in the litera-

ture, recently in [

] where the authors used clustering and association rule analysis for

cantilever design problems with three and four objectives. In [

] the authors used machine

learning to ﬁnd relationships between the variables and objectives in a multi-objective

problem of ﬁnding sweet spots in shale-gas reservoirs.

We have used data mining to ﬁnd decision rules that can extract such knowledge

from optimization datasets of multi-objective optimizations of worker well-being and

productivity. The database generated in a previous multi-objective optimization application

study [

] was mined to ﬁnd rules that can be applied to similar workstations. The rules

were created with the intention of balancing worker well-being and productivity, taking

into account the anthropometric diversity of workers, so as to ﬁnd critical solutions that

can distinguish speciﬁc populations. The analysis of the multi-objective optimization

application study database is meant to demonstrate that data mining approaches and

knowledge discovery, in general, can generate rules that can be applied in the design of

future workstations with a consequent reduction of the effort of engineers.

2. Method

We used the database of a multi-objective optimization of worker well-being and

productivity application study of a welding gun workstation [

] to apply knowledge

discovery methods to obtain knowledge for future workstation designs.

2.1. Application Study

The case study represents a manual welding task within manufacturing at Volvo Cars.

This task involves the use of one or more of the three welding guns available for seven

welding spots. The welding gun can be grasped in different positions, and workers need to

adopt different postures when welding the seven spots. Since the gun is supported by a

lifting device, workers are not affected by the weight of the gun. Inertia effects from moving

the guns are not considered. The welding guns are not ﬁxed in a single position; therefore,

each spot can be welded by using the guns from different sides of the workstation. In

addition, the task is performed by different workers, so the welding posture can change

due to the anthropometric measurements of each worker. The task is repetitive, and the

workers need to perform it over a full workday. Therefore, there is a risk of work-related

musculoskeletal disorders (WMSD), especially in the upper limbs. The optimization was

run for both worker well-being and productivity objectives.

2.1.1. Model Deﬁnition

The virtual model was modeled in the DHM tool IPS IMMA [

] by representing the

welding gun workstation by imported CAD geometries. A family of 14 manikins (7 female,

7 male) was created by using an anthropometric module [

] in the DHM tool used in

Sustainability 2022,14, 4894 3 of 14

the study, based on key anthropometric variables aimed to represent the anthropometric

diversity of the workers at the factory, i.e., stature and elbow height (Figure 1).

Sustainability 2022, 14, x FOR PEER REVIEW 3 of 15

2.1.1. Model Definition

The virtual model was modeled in the DHM tool IPS IMMA [21] by representing the

welding gun workstation by imported CAD geometries. A family of 14 manikins (7 fe-

male, 7 male) was created by using an anthropometric module [22] in the DHM tool used

in the study, based on key anthropometric variables aimed to represent the anthropomet-

ric diversity of the workers at the factory, i.e., stature and elbow height (Figure 1).

Figure 1. Virtual model of the welding gun workstation in IPS IMMA.

The welding process for each welding gun at each welding spot was simulated for

the entire manikin family. Table 1 shows the values for the stature and elbow height of

the manikins simulated for the use case.

Table 1. Anthropometric measures of manikins.

Manikin Number Stature (mm) Elbow Height (mm) Sex

1 1629 984 Female

2 1755 1091 Male

3 1656 1020 Female

4 1780 1134 Male

5 1668 963 Female

6 1794 1068 Male

7 1800 1094 Female

8 1936 1221 Male

9 1602 949 Female

10 1731 1047 Male

11 1590 1006 Female

12 1717 1114 Male

13 1457 875 Female

14 1574 961 Male

2.1.2. Well-Being and Productivity Evaluation

We evaluated the productivity of the welding workstation by measuring the cycle

time of the welding sequence from the simulation. The cycle time was calculated by con-

sidering the actions of the workers performing the sequence. These actions included both

value-adding operations (e.g., the time to weld a welding spot) and non-value-adding

Figure 1. Virtual model of the welding gun workstation in IPS IMMA.

The welding process for each welding gun at each welding spot was simulated for

the entire manikin family. Table 1shows the values for the stature and elbow height of the

manikins simulated for the use case.

Table 1. Anthropometric measures of manikins.

Manikin Number Stature (mm) Elbow Height (mm) Sex

1 1629 984 Female

2 1755 1091 Male

3 1656 1020 Female

4 1780 1134 Male

5 1668 963 Female

6 1794 1068 Male

7 1800 1094 Female

8 1936 1221 Male

9 1602 949 Female

10 1731 1047 Male

11 1590 1006 Female

12 1717 1114 Male

13 1457 875 Female

14 1574 961 Male

2.1.2. Well-Being and Productivity Evaluation

We evaluated the productivity of the welding workstation by measuring the cycle time of

the welding sequence from the simulation. The cycle time was calculated by considering the

actions of the workers performing the sequence. These actions included both value-adding op-

erations (e.g., the time to weld a welding spot) and non-value-adding operations (

e.g., changing

the welding gun, changing the welding side, and moving between welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [

] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve

Sustainability 2022,14, 4894 4 of 14

postural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes are

required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objectives,

that is, it is a multi-objective optimization model. The indices, parameters, variables, and

objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

w=1 . . . WWelding spots TW Welding time (s)

g=1 . . . GWelding guns TG Time to change welding gun (s)

s=1 . . . SWelding sides TS Time to change welding side (s)

m=1 . . . MManikins TF Time to move to a far position (s)

sq =1 . . . SQ Welding sequence TN Time to move to a near position (s)

Variables PGsq Previous gun: 1 if different, 0 if same

XwWelding spot sequence PSsq Previous side: 1 if different, 0 if same

YwWelding gun used at each welding spot PFsq 1 if previous spot is far, 0 if near

ZwWelding side at each welding spot PNsq 1 if previous spot is near, 0 if far

Objectives ERmsgw

RULA score for a manikin on a side with a

welding gun at a welding spot

CT Cycle time of welding process (s)

ERmAverage RULA score per manikin in the

welding process

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

Average RULA score of all manikins in the

welding process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calculated

as a mean value for all the manikins using all welding spots. The risk of WMSDs is therefore

calculated by a single objective:

MIN

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

=∑M

m=1

∑SQ

sq=1ERmsgw

M(1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

MIN CT =

∑

sq=1

TW +

∑

sq=2

PGsq ·TG +

∑

sq=2

PSsq ·TS +

∑

sq=2

PFsq·T F +

∑

sq=2

PNsq ·TN (2)

2.1.4. Optimization Method

Many real-world optimization problems involve multiple conﬂicting objectives and

therefore lead to multiple Pareto-optimal solutions, that is, the optimal solution for one

optimization objective may not be optimal for another objective [

]. Therefore, solving

a MOOP is about balancing the trade-offs among conﬂicting objectives. This complexity

also affects the process of obtaining optimal solutions while performing optimization.

Due to their population-based nature, multi-objective evolutionary algorithms are often

used for solving MOOPs. The evolutionary algorithm NSGA-II was used to optimize

Sustainability 2022,14, 4894 5 of 14

this application study because of its efﬁciency in multi-objective optimizations [

]. The

parameters used for the optimization are presented in Table 3.

Table 3. Optimization algorithm conﬁguration.

Optimization Algorithm NSGA-II

Population size 150

Child population size 150

Tournament size 2

Mutation operator Polynomial

Mutation probability 0.2

Crossover probability 0.9

Crossover operator SBX

Maximum iterations 25,000

2.2. Knowledge Discovery

We sought to extract general knowledge from the solutions to the MOOP. A MOOP

solution can be seen as inhabiting two different spaces: the decision space, where the

decision variables exist, and the objective space where the objective values exist. While

optimization algorithms drive the search to ﬁnd higher performing solutions in the objective

space, data mining methods can be used to ﬁnd knowledge about preferred solutions

in terms of the decision space. To generate knowledge, we deﬁned the preference by

analyzing the solutions, and then applied a data mining method to generate decision rules

to describe those preferences. The process of knowledge discovery is done in several

steps: (1) data ﬁltering, (2) data clustering, (3) data visualization, (4) rule extraction, and

(5) knowledge interpretation.

The ﬁrst step, data ﬁltering, was done by removing the duplicates in the database to

remove any bias in the resulting knowledge (Figure 2). In the second step, data clustering,

we identiﬁed four principal objectives: lowest cycle time, lowest average RULA score for all

manikins, balance between average RULA score for all manikins and cycle time, and worker

diversity inclusion rules. In the next step, data visualization, we analyzed the database

by using parallel coordinates, boxplots, and 2D and 3D scatter plots. Later, knowledge

discovery was performed using inﬂuence score by rank (InfS-R) and ﬂexible pattern mining

(FPM) methods [

]. In the ﬁnal step, knowledge interpretation, we analyzed the generated

rules and related them to the speciﬁc implications in the application study to generate

reproducible knowledge for future workstation designs.

Sustainability 2022, 14, x FOR PEER REVIEW 6 of 15

Figure 2. Flow diagram of the knowledge discovery process.

2.2.1. FPM

FPM [27] is a recently developed method for obtaining decision rules in the decision

space, based on selections made by the decision maker in the objective space. FPM is an

extension of sequential pattern mining [28] and can find rules of the forms 𝑥𝑐

, 𝑥

𝑐, and 𝑥=𝑐

 for a decision variable 𝑥 and constant values 𝑐, 𝑐, and 𝑐. The FPM

procedure finds decision rules about the decision space that describes selections made in

the objective space. To run the process, the decision maker must supply a set of selected

solutions and a set of unselected solutions. The resulting FPM rules can be seen as a tuple

containing the following elements: label, referring to the name of the decision variable;

sign, referring to one of the signs <, >, or = ; value, referring to the constant value of the

rule; sig., referring to the significance of the rule, that is, the percentage of the solutions in

the selected set that the rule covers; and unsig., referring to the unselected significance

(unsignificance), that is, the percentage of solutions in the unselected set that the rule co-

vers. Note that since the significance and unsignificance can be found simply by counting

the solutions covered by a single rule, the same can be done for interactions of two or

more rules. In Section 3 we show three levels of FPM rule interactions. An interesting and

descriptive FPM rule would have high significance and low unselected significance. The

ratio of significance over unselected significance serves as a general metric for a good rule.

2.2.2. InfS-R

Factor screening to find which variable has the most influence in a model can be a

useful tool for understanding the model and how the variables interact [29]. Recently, an

approach for finding influential variables in the resulting solution set from a multi-objec-

tive optimization problem was presented in [26]. The approach defines two methods. One

finds an influence score for the decision variables in terms of how they affect the solutions

on the Pareto-optimal front; this method is called influence score by Pareto front (InfS-P).

The other method finds an influence score for decision variables in terms of how they

affect the convergence on the Pareto front by considering the rank of the solutions after

non-dominated sorting, called InfS-R. Both methods divide the solutions into different

selections and find FPM rules to describe the differences between them. The frequency of

and significance of the different variables is then used to determine how influential they

Figure 2. Flow diagram of the knowledge discovery process.

Sustainability 2022,14, 4894 6 of 14

2.2.1. FPM

FPM [

] is a recently developed method for obtaining decision rules in the decision

space, based on selections made by the decision maker in the objective space. FPM is

an extension of sequential pattern mining [

] and can ﬁnd rules of the forms

{xi<c1}

{xi>c2}

, and

{xi=c3}

for a decision variable

and constant values

, and

. The

FPM procedure ﬁnds decision rules about the decision space that describes selections made

in the objective space. To run the process, the decision maker must supply a set of selected

solutions and a set of unselected solutions. The resulting FPM rules can be seen as a tuple

containing the following elements: label, referring to the name of the decision variable; sign,

referring to one of the signs <, >, or = ; value, referring to the constant value of the rule; sig.,

referring to the signiﬁcance of the rule, that is, the percentage of the solutions in the selected

set that the rule covers; and unsig., referring to the unselected signiﬁcance (unsigniﬁcance),

that is, the percentage of solutions in the unselected set that the rule covers. Note that since

the signiﬁcance and unsigniﬁcance can be found simply by counting the solutions covered

by a single rule, the same can be done for interactions of two or more rules. In Section 3

we show three levels of FPM rule interactions. An interesting and descriptive FPM rule

would have high signiﬁcance and low unselected signiﬁcance. The ratio of signiﬁcance

over unselected signiﬁcance serves as a general metric for a good rule.

2.2.2. InfS-R

Factor screening to ﬁnd which variable has the most inﬂuence in a model can be a

useful tool for understanding the model and how the variables interact [

]. Recently, an

approach for ﬁnding inﬂuential variables in the resulting solution set from a multi-objective

optimization problem was presented in [

]. The approach deﬁnes two methods. One

ﬁnds an inﬂuence score for the decision variables in terms of how they affect the solutions

on the Pareto-optimal front; this method is called inﬂuence score by Pareto front (InfS-P).

The other method ﬁnds an inﬂuence score for decision variables in terms of how they

affect the convergence on the Pareto front by considering the rank of the solutions after

non-dominated sorting, called InfS-R. Both methods divide the solutions into different

selections and ﬁnd FPM rules to describe the differences between them. The frequency of

and signiﬁcance of the different variables is then used to determine how inﬂuential they

are. We use InfS-R to ﬁnd the relative inﬂuence of the contribution of certain variables to

generating Pareto-optimal solutions.

3. Results

The solution space from the optimization is presented in a 2D scatter plot (Figure 3) of

the colliding objectives of average RULA for all manikins and cycle time.

Sustainability 2022, 14, x FOR PEER REVIEW 7 of 15

are. We use InfS-R to find the relative influence of the contribution of certain variables to

generating Pareto-optimal solutions.

3. Results

The solution space from the optimization is presented in a 2D scatter plot (Figure 3)

of the colliding objectives of average RULA for all manikins and cycle time.

Figure 3. Solution space of cycle time and average RULA score 𝐸𝑅



of all manikins.

The solutions that correspond to the non-dominated solutions represent the Pareto

front for this optimization (marked by “+” in Figure 3) and are the best solutions of the

optimization. These solutions are shown in Table 4.

Table 4. Results from optimization.

Result Selected 𝑪𝑻 (s) 𝑬𝑹



Sequence

Lowest 𝐶𝑇 47 3.09

Spot sequence: 7-1-3-2-5-4-6

Gun sequence: 3-3-3-3-3-3-3

Side sequence: 1-1-1-1-2-2-2

Compromise be-

tween 𝐶𝑇 and 𝐸𝑅



63 2.89

Spot sequence: 4-5-6-7-1-2-3

Gun sequence: 3-3-3-3-2-2-2

Side sequence: 2-2-2-1-1-1-1

Lowest 𝐸𝑅



85 2.86

Spot sequence: 4-5-6-7-1-2-3

Gun sequence: 4-5-6-7-1-2-3

Side sequence: 2-2-2-1-1-1-1

3.1. Data Filtering

The database of the application study was filtered by removing duplicates. Also, in

order to help the data mining process, related variables were merged. In this case, the

welding guns and the welding sides were converted into a single variable “gun and side”

before proceeding with the data mining. To convert gun and side to the same variable, the

variables were converted into a single integer per spot, 𝐺𝑆. Due to the availability of the

guns and sides in different welding spots, the range was different for every welding spot

(Table 5).

Figure 3. Solution space of cycle time and average RULA score

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

of all manikins.

Sustainability 2022,14, 4894 7 of 14

The solutions that correspond to the non-dominated solutions represent the Pareto

front for this optimization (marked by “+” in Figure 3) and are the best solutions of the

optimization. These solutions are shown in Table 4.

Table 4. Results from optimization.

Result Selected CT (s)

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

Sequence

Lowest CT 47 3.09

Spot sequence: 7-1-3-2-5-4-6

Gun sequence: 3-3-3-3-3-3-3

Side sequence: 1-1-1-1-2-2-2

Compromise between CT and

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

63 2.89

Spot sequence: 4-5-6-7-1-2-3

Gun sequence: 3-3-3-3-2-2-2

Side sequence: 2-2-2-1-1-1-1

Lowest

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

85 2.86

Spot sequence: 4-5-6-7-1-2-3

Gun sequence: 4-5-6-7-1-2-3

Side sequence: 2-2-2-1-1-1-1

3.1. Data Filtering

The database of the application study was ﬁltered by removing duplicates. Also, in

order to help the data mining process, related variables were merged. In this case, the

welding guns and the welding sides were converted into a single variable “gun and side”

before proceeding with the data mining. To convert gun and side to the same variable, the

variables were converted into a single integer per spot,

GSw

. Due to the availability of the

guns and sides in different welding spots, the range was different for every welding spot

(Table 5).

Table 5.

Corresponding value for every

GSw

depending on the gun and side availability at each spot.

g= 1 g= 2 g= 3

s= 1 s= 2 s= 1 s= 2 s= 1 s= 2

w=1GS1=1 X GS1=2 X GS1=3GS1=4

w=2GS2=1 X GS2=2 X GS2=3GS2=4

w=3GS3=1 X GS3=2 X GS3=3GS3=4

w=4 X X X X GS4=1GS4=2

w=5 X X X X GS5=1GS5=2

w=6 X X X X GS6=1GS6=2

w=7GS7=1 X GS7=2 X GS7=3 X

Note: X is unavailable.

3.2. Data Clustering

The selected clusters that need to be analyzed represent the (1) lowest cycle time

(

) (marked by “+”), (2) lowest average RULA score for all manikins (

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

)

(marked

by “-”),

(3) the

balance between average RULA score for all manikins and cycle time

(marked by “x”), and (4) worker diversity inclusion rules. The clusters of (1) lowest

and

(2) lowest

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

were deﬁned by selecting the solutions with the lowest scores. The cluster

(3) (balance

between

and

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

) was deﬁned as all solutions that had a lower

than

cluster (2), and lower

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

than cluster (1) (Figure 4).

Sustainability 2022,14, 4894 8 of 14

Sustainability 2022, 14, x FOR PEER REVIEW 8 of 15

Table 5. Corresponding value for every 𝐺𝑆



depending on the gun and side availability at each

spot.

𝒈=𝟏 𝒈=𝟐 𝒈=𝟑

𝒔=𝟏 𝒔=𝟐 𝒔=𝟏 𝒔=𝟐 𝒔=𝟏 𝒔=𝟐

𝑤=1 𝐺𝑆=1 X 𝐺𝑆=2 X 𝐺𝑆=3 𝐺𝑆=4

𝑤=2 𝐺𝑆=1 X 𝐺𝑆=2 X 𝐺𝑆=3 𝐺𝑆=4

𝑤=3 𝐺𝑆=1 X 𝐺𝑆=2 X 𝐺𝑆=3 𝐺𝑆=4

𝑤=4 X X X X

𝐺𝑆=1 𝐺𝑆=2

𝑤=5 X X X X

𝐺𝑆=1 𝐺𝑆=2

𝑤=6 X X X X

𝐺𝑆=1 𝐺𝑆=2

𝑤=7 𝐺𝑆=1 X 𝐺𝑆=2 X 𝐺𝑆=3 X

Note: X is unavailable.

3.2. Data Clustering

The selected clusters that need to be analyzed represent the (1) lowest cycle time (𝐶𝑇)

(marked by “+”), (2) lowest average RULA score for all manikins (𝐸𝑅



) (marked by “-”),

(3) the balance between average RULA score for all manikins and cycle time (marked by

“x”), and (4) worker diversity inclusion rules. The clusters of (1) lowest 𝐶𝑇 and (2) lowest

𝐸𝑅



were defined by selecting the solutions with the lowest scores. The cluster of (3) (bal-

ance between 𝐶𝑇 and 𝐸𝑅



) was defined as all solutions that had a lower 𝐶𝑇 than cluster

(2), and lower 𝐸𝑅



than cluster (1) (Figure 4).

Figure 4. Selected clusters for lowest 𝐶𝑇 (marked by “+”), compromise between 𝐶𝑇 and 𝐸𝑅



(marked by “x”), and lowest 𝐸𝑅



(marked by “-”).

An initial analysis of the manikins was necessary to select the cluster for (4) (diversity

inclusion rules) since the critical manikins were still not identified.

3.3. Data Visualization

A boxplot analysis of the average RULA score of each manikin (𝐸𝑅



) was made to

evaluate the critical manikins and consider worker anthropometric diversity (Figure 5).

Figure 4.

Selected clusters for lowest

(marked by “+”), compromise between

and

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

(marked

by “x”), and lowest

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

(marked by “-”).

An initial analysis of the manikins was necessary to select the cluster for (4) (diversity

inclusion rules) since the critical manikins were still not identiﬁed.

3.3. Data Visualization

A boxplot analysis of the average RULA score of each manikin (

ERm

) was made to

evaluate the critical manikins and consider worker anthropometric diversity (Figure 5).

Sustainability 2022, 14, x FOR PEER REVIEW 9 of 15

Figure 5. Boxplot analysis of the average RULA score of each manikin (𝐸𝑅





Manikins 13 and 14 have higher average RULA scores than other manikins for all

solutions (Figure 5). These are the manikins with the lowest stature in the population con-

sidered (Table 1). The cluster for (4) (diversity inclusion rules) was therefore formed by

the best solutions for the 𝐸𝑅



 of manikins 13 and 14, 𝐸𝑅



 and 𝐸𝑅



 (marked by “x” in

Figure 6).

Figure 6. Selection of results for cluster 4, diversity inclusion rules.

3.4. Knowledge Discovery

To obtain rules from the results of the application study, InfS-R [26] was used to de-

termine the relative importance of the variables in the optimization. The first InfS-R

ranked the non-dominated sorting for the objectives 𝐶𝑇 and 𝐸𝑅



. The variables studied

were the selection of welding gun and side for every welding spot (𝐺𝑆 or SpotW G/S in

figures) and the welding sequence (𝑋) (Figure 7).

Figure 5. Boxplot analysis of the average RULA score of each manikin (ERm).

Manikins 13 and 14 have higher average RULA scores than other manikins for all

solutions (Figure 5). These are the manikins with the lowest stature in the population

considered (Table 1). The cluster for (4) (diversity inclusion rules) was therefore formed

by the best solutions for the

ERm

of manikins 13 and 14,

ER13

and

ER14

(marked by “x” in

Figure 6).

Sustainability 2022,14, 4894 9 of 14

Sustainability 2022, 14, x FOR PEER REVIEW 9 of 15

Figure 5. Boxplot analysis of the average RULA score of each manikin (𝐸𝑅





Manikins 13 and 14 have higher average RULA scores than other manikins for all

solutions (Figure 5). These are the manikins with the lowest stature in the population con-

sidered (Table 1). The cluster for (4) (diversity inclusion rules) was therefore formed by

the best solutions for the 𝐸𝑅



 of manikins 13 and 14, 𝐸𝑅



 and 𝐸𝑅



 (marked by “x” in

Figure 6).

Figure 6. Selection of results for cluster 4, diversity inclusion rules.

3.4. Knowledge Discovery

To obtain rules from the results of the application study, InfS-R [26] was used to de-

termine the relative importance of the variables in the optimization. The first InfS-R

ranked the non-dominated sorting for the objectives 𝐶𝑇 and 𝐸𝑅



. The variables studied

were the selection of welding gun and side for every welding spot (𝐺𝑆 or SpotW G/S in

figures) and the welding sequence (𝑋) (Figure 7).

Figure 6. Selection of results for cluster 4, diversity inclusion rules.

3.4. Knowledge Discovery

To obtain rules from the results of the application study, InfS-R [

] was used to

determine the relative importance of the variables in the optimization. The ﬁrst InfS-R

ranked the non-dominated sorting for the objectives

and

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 15

operations (e.g., changing the welding gun, changing the welding side, and moving be-

tween welding spots).

We used the Rapid Upper Limb Assessment (RULA) method [23] to evaluate the risk

of WMSDs. We considered RULA appropriate since the work stresses mainly involve pos-

tural stresses on the upper limbs, as the weight of the welding guns is supported by a

lifting device. For each posture assessed, RULA gives a risk score from 1 to 7, which results

in four action levels. A score of 1 to 2 is acceptable, a score of 3 to 4 suggests changes may

be required, 5 to 6 indicates changes will soon be required, and 7 indicates that changes

are required immediately.

2.1.3. Mathematical Modeling of Optimization

The optimization model considers both worker well-being and productivity objec-

tives, that is, it is a multi-objective optimization model. The indices, parameters, variables,

and objectives of the optimization model are shown in Table 2.

Table 2. Indices, parameters, variables, and objectives of the optimization model.

Indices Parameters

𝑤=1…𝑊 Welding spots 𝑇𝑊 Welding time (s)

𝑔=1…𝐺 Welding guns 𝑇𝐺 Time to change welding gun (s)

𝑠=1…𝑆 Welding sides 𝑇𝑆 Time to change welding side (s)

𝑚=1…𝑀 Manikins 𝑇𝐹 Time to move to a far position (s)

𝑠𝑞 = 1…𝑆𝑄 Welding sequence 𝑇𝑁 Time to move to a near position (s)

Variables 𝑃𝐺 Previous gun: 1 if different, 0 if same

𝑋 Welding spot sequence 𝑃𝑆 Previous side: 1 if different, 0 if same

𝑌 Welding gun used at each

welding spot 𝑃𝐹 1 if previous spot is far, 0 if near

𝑍 Welding side at each weld-

ing spot 𝑃𝑁 1 if previous spot is near, 0 if far

Objectives 𝐸𝑅 RULA score for a manikin on a side

with a welding gun at a welding spot

𝐶𝑇 Cycle time of welding pro-

cess (s)

𝐸𝑅





Average RULA score per

manikin in the welding

process

𝐸𝑅



Average RULA score of all

manikins in the welding

process

A multi-objective optimization of the average of the RULA scores for all the manikins

and the cycle time was performed. The mean RULA score of the 14 manikins was calcu-

lated as a mean value for all the manikins using all welding spots. The risk of WMSDs is

therefore calculated by a single objective:

𝑀𝐼𝑁 𝐸𝑅



= ∑∑𝐸𝑅



𝑆𝑄



 𝑀 (1)

The cycle time was calculated as the sum of the welding time at each welding spot

and the time to change welding gun, welding spot, and welding side:

. The variables studied

were the selection of welding gun and side for every welding spot (GSwor SpotW G/S in

ﬁgures) and the welding sequence (Xw) (Figure 7).

Sustainability 2022, 14, x FOR PEER REVIEW 10 of 15

Figure 7. And 𝐸𝑅



 to analyze the diversity inclusion (Figure 8).

Figure 8. InfS-R of 𝐸𝑅



 and 𝐸𝑅



 for 𝐺𝑆 and 𝑋 variables.

After the InfS-R analysis, an FPM analysis was run for the four clusters (1) lowest

cycle time (marked by “+” in Figure 4), (2) lowest average RULA score for all manikins

(marked by “-” in Figure 4), (3) balance between average RULA score for all manikins and

cycle time (marked by “x” in Figure 4), and (4) worker diversity inclusion rules (marked

by “x” in Figure 6). The FPM analysis was run for three levels of rule-interactions and 0.5

minimum significance and minimum support. After that, the rules were filtered to the

higher ratio of significance/unsignificance to obtain the most relevant rules for the four

clusters. The significance, unsignificance, and ratio of the obtained rules in the four clus-

ters are presented in Table 6.

Table 6. Rules obtained for the four cases by FPM.

FPM

Case Filtered Rules Sig. (%) Unsig. (%) Ratio

Lowest 𝐶𝑇

𝐺𝑆 == 4 91.53 27.07 3.38

𝐺𝑆 > 2 100 40.85 2.45

𝐺𝑆 == 3 79.1 28.86 2.74

𝐺𝑆 == 4 && 𝐺𝑆 > 2 && 𝐺𝑆 == 3 75.14 7.58 9.91

Figure 7. And ER14 to analyze the diversity inclusion (Figure 8).

Sustainability 2022,14, 4894 10 of 14