# Optimization of Human-Aware Manufacturing and Logistics Systems: A Comprehensive Review of Modeling Approaches and Applications

Thibault Prunet, Nabil Absi, Valeria Borodin, Diego Cattaruzza

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Thibault Prunet, Nabil Absi, Valeria Borodin, Diego Cattaruzza. Optimization of Human-Aware Manufacturing and Logistics Systems: A Comprehensive Review of Modeling Approaches and Applications. EURO Journal on Transportation and Logistics, 2024, pp.100136. 10.1016/j.ejtl.2024.100136. hal-04616576

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# Optimization of human-aware logistics and manufacturing systems: A comprehensive review of modeling approaches and applications

Thibault Prunet<sup>a,b,*</sup>, Nabil Absi<sup>a</sup>, Valeria Borodin<sup>a,c</sup>, Diego Cattaruzza<sup>d</sup>

## ARTICLE INFO

### Keywords:

- Optimization
- Human factors
- Industry 5.0
- Manufacturing
- Logistics
- Ergonomics

## ABSTRACT

Historically, Operations Research (OR) discipline has mainly been focusing on economic concerns. Since the early 2000s, human considerations are gaining increasing attention, pushed by the growing societal concerns of sustainable development on the same terms as the economic and ecological ones. This paper is the first part of a work that aims at reviewing the efforts dedicated by the OR community to the integration of human factors into logistics and manufacturing systems. A focus is put on the modeling and solution approaches used to consider human characteristics, their practical relevance, and the complexity induced by their integration within optimization models. The material presented in this work has been retrieved through a semi-systematic search of the literature. Then, a comprehensive analysis of the retrieved corpus is carried out to map the related literature by class of problems encountered in logistics and manufacturing. These include warehousing, vehicle routing, scheduling, production planning, and workforce scheduling and management. We investigate the mathematical programming techniques used to integrate human factors into optimization models. Finally, a number of gaps in the literature are identified, and new suggestions on how to suitably integrate human factors in OR problems encountered in logistics and manufacturing systems are discussed.

## Contents

<table><tr><td>1.</td><td>Introduction</td><td>2</td></tr><tr><td>2.</td><td>Terminology, related background, scope, and motivations</td><td>4</td></tr><tr><td>2.1.</td><td>Definitions of human-related key concepts</td><td>4</td></tr><tr><td>2.2.</td><td>Previous reviews</td><td>5</td></tr><tr><td>2.3.</td><td>Scope</td><td>5</td></tr><tr><td>2.4.</td><td>Motivations</td><td>6</td></tr><tr><td>3.</td><td>Methodology</td><td>6</td></tr><tr><td>3.1.</td><td>Material collection methodology</td><td>6</td></tr><tr><td>3.2.</td><td>Summary tables: Format and convention</td><td>7</td></tr><tr><td>4.</td><td>Logistics systems</td><td>8</td></tr><tr><td>4.1.</td><td>Warehousing</td><td>8</td></tr><tr><td>4.2.</td><td>Vehicle routing</td><td>8</td></tr><tr><td>5.</td><td>Manufacturing systems</td><td>9</td></tr><tr><td>5.1.</td><td>Production scheduling</td><td>9</td></tr><tr><td>5.2.</td><td>Assembly line balancing</td><td>11</td></tr><tr><td>5.3.</td><td>Production planning and inventory management</td><td>11</td></tr><tr><td>5.4.</td><td>Design of systems</td><td>12</td></tr><tr><td>6.</td><td>Workforce-related problems</td><td>14</td></tr><tr><td>6.1.</td><td>Workforce scheduling</td><td>14</td></tr><tr><td>6.1.1.</td><td>Job rotation</td><td>14</td></tr></table>

<footnote><sup>a</sup> Mines Saint-Etienne, Univ. Clermont Auvergne, CNRS, UMR 6158 LIMOS, Center CMP, Departement SFL, F-13541 Gardanne, France</footnote>

<footnote><sup>b</sup> CERMICS, Ecole des Ponts, Marne la Vallée, France</footnote>

<footnote><sup>c</sup> IMT Atlantique, LS2N-CNRS, La Chantrerie, 4, rue Alfred Kastler, Nantes cedex 3, F-44307, France</footnote>

<footnote><sup>d</sup> Univ. Lille, CNRS, Centrale Lille, Inria, UMR 9189 - CRISAL - Centre de Recherche en Informatique de Lille, F-59000 Lille, France</footnote>

<footnote>* Corresponding author at: Mines Saint-Etienne, Univ. Clermont Auvergne, CNRS, UMR 6158 LIMOS, Center CMP, Departement SFL, F-13541 Gardanne, France. E-mail address: thibault.prunet@enpc.fr (T. Prunet).</footnote>
<figure><img src="image_2.png" /></figure>

# Optimization of human-aware logistics and manufacturing systems: A comprehensive review of modeling approaches and applications

Thibault Prunet<sup>a,b,*</sup>, Nabil Absi<sup>a</sup>, Valeria Borodin<sup>a,c</sup>, Diego Cattaruzza<sup>d</sup>

## ARTICLE INFO

### Keywords:

- Optimization
- Human factors
- Industry 5.0
- Manufacturing
- Logistics
- Ergonomics

## ABSTRACT

Historically, Operations Research (OR) discipline has mainly been focusing on economic concerns. Since the early 2000s, human considerations are gaining increasing attention, pushed by the growing societal concerns of sustainable development on the same terms as the economic and ecological ones. This paper is the first part of a work that aims at reviewing the efforts dedicated by the OR community to the integration of human factors into logistics and manufacturing systems. A focus is put on the modeling and solution approaches used to consider human characteristics, their practical relevance, and the complexity induced by their integration within optimization models. The material presented in this work has been retrieved through a semi-systematic search of the literature. Then, a comprehensive analysis of the retrieved corpus is carried out to map the related literature by class of problems encountered in logistics and manufacturing. These include warehousing, vehicle routing, scheduling, production planning, and workforce scheduling and management. We investigate the mathematical programming techniques used to integrate human factors into optimization models. Finally, a number of gaps in the literature are identified, and new suggestions on how to suitably integrate human factors in OR problems encountered in logistics and manufacturing systems are discussed.

## Contents

<table><tr><td>1.</td><td>Introduction</td><td>2</td></tr><tr><td>2.</td><td>Terminology, related background, scope, and motivations</td><td>4</td></tr><tr><td>2.1.</td><td>Definitions of human-related key concepts</td><td>4</td></tr><tr><td>2.2.</td><td>Previous reviews</td><td>5</td></tr><tr><td>2.3.</td><td>Scope</td><td>5</td></tr><tr><td>2.4.</td><td>Motivations</td><td>6</td></tr><tr><td>3.</td><td>Methodology</td><td>6</td></tr><tr><td>3.1.</td><td>Material collection methodology</td><td>6</td></tr><tr><td>3.2.</td><td>Summary tables: Format and convention</td><td>7</td></tr><tr><td>4.</td><td>Logistics systems</td><td>8</td></tr><tr><td>4.1.</td><td>Warehousing</td><td>8</td></tr><tr><td>4.2.</td><td>Vehicle routing</td><td>8</td></tr><tr><td>5.</td><td>Manufacturing systems</td><td>9</td></tr><tr><td>5.1.</td><td>Production scheduling</td><td>9</td></tr><tr><td>5.2.</td><td>Assembly line balancing</td><td>11</td></tr><tr><td>5.3.</td><td>Production planning and inventory management</td><td>11</td></tr><tr><td>5.4.</td><td>Design of systems</td><td>12</td></tr><tr><td>6.</td><td>Workforce-related problems</td><td>14</td></tr><tr><td>6.1.</td><td>Workforce scheduling</td><td>14</td></tr><tr><td>6.1.1.</td><td>Job rotation</td><td>14</td></tr></table>

<footnote><sup>a</sup> Mines Saint-Etienne, Univ. Clermont Auvergne, CNRS, UMR 6158 LIMOS, Center CMP, Departement SFL, F-13541 Gardanne, France</footnote>

<footnote><sup>b</sup> CERMICS, Ecole des Ponts, Marne la Vallée, France</footnote>

<footnote><sup>c</sup> IMT Atlantique, LS2N-CNRS, La Chantrerie, 4, rue Alfred Kastler, Nantes cedex 3, F-44307, France</footnote>

<footnote><sup>d</sup> Univ. Lille, CNRS, Centrale Lille, Inria, UMR 9189 - CRISTAL - Centre de Recherche en Informatique de Lille, F-59000 Lille, France</footnote>

<footnote>* Corresponding author at: Mines Saint-Etienne, Univ. Clermont Auvergne, CNRS, UMR 6158 LIMOS, Center CMP, Departement SFL, F-13541 Gardanne, France. E-mail address: thibault.prunet@enpc.fr (T. Prunet).</footnote>
<table><tbody><tr><td>6.1.2. Work-rest scheduling</td><td>15</td></tr><tr><td>6.1.3. Shift scheduling</td><td>16</td></tr><tr><td>6.2. Workforce management</td><td>16</td></tr><tr><td>6.2.1. Workforce planning</td><td>16</td></tr><tr><td>6.2.2. Workforce assignment</td><td>17</td></tr><tr><td>7. Mathematical programming considerations</td><td>17</td></tr><tr><td>7.1. Objective function</td><td>18</td></tr><tr><td>7.1.1. Single objective optimization</td><td>18</td></tr><tr><td>7.1.2. Multi-objective optimization</td><td>19</td></tr><tr><td>7.2. Constraints</td><td>20</td></tr><tr><td>7.3. Parameters</td><td>21</td></tr><tr><td>7.3.1. Varying task time</td><td>21</td></tr><tr><td>7.3.2. Varying quality</td><td>22</td></tr><tr><td>7.3.3. Heterogeneous workforce</td><td>22</td></tr><tr><td>8. Discussion and future research</td><td>23</td></tr><tr><td>8.1. Discussion on the relationship between HFs and fields of application</td><td>23</td></tr><tr><td>8.2. Under-represented decision problems</td><td>23</td></tr><tr><td>8.3. Modeling of modern industrial practices</td><td>25</td></tr><tr><td>9. Conclusions</td><td>25</td></tr><tr><td>CRediT authorship contribution statement</td><td>26</td></tr><tr><td>Declaration of competing interest</td><td>26</td></tr><tr><td>Acknowledgments</td><td>26</td></tr><tr><td>References</td><td>26</td></tr></tbody></table>

## Preamble

Given the large volume of material reviewed, which does not enable the authors to present a substantive analysis in a single paper, the current literature review has been split into two separate papers (parts), that are highly connected. We refer to the present paper as the first part, and to its twin paper (Prunet et al., 2024) as the second part. Although an introduction is present in both parts, the scope definition, the positioning within the landscape of the related literature, and the methodology applied to collect the relevant material are only discussed in detail in the first part. Then, the retrieved corpus is studied and discussed by adopting three different points of view:

* Application area, where we discuss how human factors are treated in each class of problem within the logistics and manufacturing communities. This work is presented in the first part, Sections 4–6. The results of the material collection are provided with tables in these sections.

* Human factors, where we discuss which human factors are investigated. For each factor, we study the Human-Aware Models used to model and quantify it, and the advantages and limitations of such models. This is done in the second part, Sections 3–8.

* Mathematical optimization, where we discuss the integration of human-aware considerations within optimization models. The study focuses on the impact on the models, in terms of objective function, constraints, parameters, and the associated complexity burden. This is done in the first part, Section 7.

As an illustration, let us consider a paper studying an assembly line balancing problem that accounts for the ergonomic risk related to awkward posture by imposing a maximal exposure at each workstation. The paper is discussed in terms of application as an assembly line in Section 5.2, in terms of human factors regarding awkward postures in Prunet et al. (2024) Section 5.3, and in terms of mathematical optimization for using threshold constraints in Section 7.2. Then, future research directions are discussed in both parts of the work. Note that, in the current paper (first part), we often refer to human-aware models without a proper explanation of the related concepts. The interested reader is referred to the second part (Prunet et al., 2024) to get this information.

## 1. Introduction

Operations Research (OR) has been historically focused on economic considerations, reflecting the concerns present in the industry. With the globalization of the economy, the increasing level of competition and demand customization have led to growing economic pressure on decision-makers. This pressure has been particularly high in the logistics and manufacturing fields to reduce costs and improve the efficiency of operations, quality of services, and system agility. The concomitant development of data-driven optimization of operations, applied to a large variety of complex industrial problems, has shaped the current landscape of OR. The advance in the accessibility to computing power allows us to consider and successfully treat more complex problems that do not limit their scope to economic considerations. In this sense, additional topical considerations have begun to appear in decision models after the early 2000s, following a more global societal shift, where ecological and social responsibility is more and more accounted for by decision-makers, as growing pressure from stakeholders. This trend is illustrated by the rise of two related paradigms namely, sustainable development, and Industry 5.0, presented in the following paragraphs.

**Sustainable development.** This concept is increasingly becoming a major paradigm that reframes the global strategy of companies and organizations. The concept is defined as “the development that meets the need of the present without compromising the ability of future generations to meet their own needs” (Keeble, 1988). The main idea of this paradigm is to consider social and environmental indicators together with economic ones when considering business decisions and performance assessments. The three pillars of sustainable development, namely economic, environmental, and social, are considered on the same level of importance, explaining the increasing concerns toward the social responsibility of companies. Decent working conditions is actually one of the 17 sustainable development goals, that constitute the 2030 Agenda of sustainable development ratified by the United Nations in 2015.<fnref n="1" /> According to the International Labour Organization

<footnote n="1">¹ The resolution A/RES/70/1 of the seventieth general assembly of the United Nations of 21 October 2015 on the 2030 Agenda of sustainable development. https://sdgs.un.org/2030agenda Access: September 20, 2022.</footnote>
<table><tbody><tr><td>6.1.2. Work-rest scheduling</td><td>15</td></tr><tr><td>6.1.3. Shift scheduling</td><td>16</td></tr><tr><td>6.2. Workforce management</td><td>16</td></tr><tr><td>6.2.1. Workforce planning</td><td>16</td></tr><tr><td>6.2.2. Workforce assignment</td><td>17</td></tr><tr><td>7. Mathematical programming considerations</td><td>17</td></tr><tr><td>7.1. Objective function</td><td>18</td></tr><tr><td>7.1.1. Single objective optimization</td><td>18</td></tr><tr><td>7.1.2. Multi-objective optimization</td><td>19</td></tr><tr><td>7.2. Constraints</td><td>20</td></tr><tr><td>7.3. Parameters</td><td>21</td></tr><tr><td>7.3.1. Varying task time</td><td>21</td></tr><tr><td>7.3.2. Varying quality</td><td>22</td></tr><tr><td>7.3.3. Heterogeneous workforce</td><td>22</td></tr><tr><td>8. Discussion and future research</td><td>23</td></tr><tr><td>8.1. Discussion on the relationship between HFs and fields of application</td><td>23</td></tr><tr><td>8.2. Under-represented decision problems</td><td>23</td></tr><tr><td>8.3. Modeling of modern industrial practices</td><td>25</td></tr><tr><td>9. Conclusions</td><td>25</td></tr><tr><td>CRediT authorship contribution statement</td><td>26</td></tr><tr><td>Declaration of competing interest</td><td>26</td></tr><tr><td>Acknowledgments</td><td>26</td></tr><tr><td>References</td><td>26</td></tr></tbody></table>

## Preamble

Given the large volume of material reviewed, which does not enable the authors to present a substantive analysis in a single paper, the current literature review has been split into two separate papers (parts), that are highly connected. We refer to the present paper as the first part, and to its twin paper (Prunet et al., 2024) as the second part. Although an introduction is present in both parts, the scope definition, the positioning within the landscape of the related literature, and the methodology applied to collect the relevant material are only discussed in detail in the first part. Then, the retrieved corpus is studied and discussed by adopting three different points of view:

* Application area, where we discuss how human factors are treated in each class of problem within the logistics and manufacturing communities. This work is presented in the first part, Sections 4–6. The results of the material collection are provided with tables in these sections.

* Human factors, where we discuss which human factors are investigated. For each factor, we study the Human-Aware Models used to model and quantify it, and the advantages and limitations of such models. This is done in the second part, Sections 3–8.

* Mathematical optimization, where we discuss the integration of human-aware considerations within optimization models. The study focuses on the impact on the models, in terms of objective function, constraints, parameters, and the associated complexity burden. This is done in the first part, Section 7.

As an illustration, let us consider a paper studying an assembly line balancing problem that accounts for the ergonomic risk related to awkward posture by imposing a maximal exposure at each workstation. The paper is discussed in terms of application as an assembly line in Section 5.2, in terms of human factors regarding awkward postures in Prunet et al. (2024) Section 5.3, and in terms of mathematical optimization for using threshold constraints in Section 7.2. Then, future research directions are discussed in both parts of the work. Note that, in the current paper (first part), we often refer to human-aware models without a proper explanation of the related concepts. The interested reader is referred to the second part (Prunet et al., 2024) to get this information.

## 1. Introduction

Operations Research (OR) has been historically focused on economic considerations, reflecting the concerns present in the industry. With the globalization of the economy, the increasing level of competition and demand customization have led to growing economic pressure on decision-makers. This pressure has been particularly high in the logistics and manufacturing fields to reduce costs and improve the efficiency of operations, quality of services, and system agility. The concomitant development of data-driven optimization of operations, applied to a large variety of complex industrial problems, has shaped the current landscape of OR. The advance in the accessibility to computing power allows us to consider and successfully treat more complex problems that do not limit their scope to economic considerations. In this sense, additional topical considerations have begun to appear in decision models after the early 2000s, following a more global societal shift, where ecological and social responsibility is more and more accounted for by decision-makers, as growing pressure from stakeholders. This trend is illustrated by the rise of two related paradigms namely, sustainable development, and Industry 5.0, presented in the following paragraphs.

**Sustainable development.** This concept is increasingly becoming a major paradigm that reframes the global strategy of companies and organizations. The concept is defined as “the development that meets the need of the present without compromising the ability of future generations to meet their own needs” (Keeble, 1988). The main idea of this paradigm is to consider social and environmental indicators together with economic ones when considering business decisions and performance assessments. The three pillars of sustainable development, namely economic, environmental, and social, are considered on the same level of importance, explaining the increasing concerns toward the social responsibility of companies. Decent working conditions is actually one of the 17 sustainable development goals, that constitute the 2030 Agenda of sustainable development ratified by the United Nations in 2015.<fnref n="1" /> According to the International Labour Organization

<footnote n="1">¹ The resolution A/RES/70/1 of the seventieth general assembly of the United Nations of 21 October 2015 on the 2030 Agenda of sustainable development. https://sdgs.un.org/2030agenda Access: September 20, 2022.</footnote>
(ILO)<fnref n="2" /> and the World Health Organization (WHO),<fnref n="3" /> over 2.3 million people die yearly from work-related causes (Takala et al., 2014). Studies show that, at any given time, 20% of employed adults suffer from Work-related Musculoskeletal Disorders (WMSD) (Vézina et al., 2011). Furthermore, from an economic perspective, the direct and indirect costs of work-related injuries are estimated at 4% of the world GDP (Takala et al., 2014). Therefore, the improvement of working conditions and the reduction of work-related health problems are still an important challenge worldwide.

**Industry 5.0.** This is an emerging concept referring to a change of paradigm in the organization of logistics and manufacturing systems, which are the focus of the present work. Industry 5.0 proposes a shift from a system-centric vision to a human-centric vision of industrial systems, by placing the role and well-being of operators at the center of the process design (Lu et al., 2022). Sustainability and resilience are the two other pillars of Industry 5.0. The consideration of human factors, at physical, cognitive, perceptual, and psychosocial levels, is especially relevant in logistics and manufacturing fields, especially considering the development of human-machine interactions (Wang et al., 2017), or the aging of the working population (Calzavara et al., 2020).

The need to account for human factors in decision support models for logistics and manufacturing systems will continue to gain importance in the near future. Two arguments support this claim:

* **Regulatory aspect:** Companies in the logistics and manufacturing sectors still rely heavily on manual labor, especially for tasks requiring a high degree of precision and flexibility. This is, for example, the case for truck drivers in logistics, order pickers in warehousing (Grosse et al., 2015b), or assembly line operators (Battini et al., 2016a). Furthermore, these jobs can account for a high level of physical and cognitive stress, repetitive movements, lifting tasks, and awkward positions. The increasing demand for social accountability of companies has led to a growing number of laws regulating the working conditions in the industry. In logistics, the European regulation EC 561/2006⁴ and the American Hours of Service of Drivers regulation<fnref n="5" /> both propose a framework to regulate the driving and working times of truck drivers. The manufacturing sector has also been subject to numerous regulations aimed at reducing ergonomic risks in workplaces. Among others, one can cite the Directive No. 2006/42/EC of the European Parliament on machinery usage,<fnref n="6" /> the Directive No. 89/391/EEC on general measures to encourage improvements in safety and health of workers,<fnref n="7" /> or the Occupational Safety and Health Act of 1970.<fnref n="8" /> Furthermore, several ergonomics standards have been developed by the International

Organization for Standardization and the European Committee on Standardization to design production systems. Dul et al. (2004) listed up to 174 international ergonomic standards for production systems, going from general recommendations on the design of processes to specific requirements for manual handling, human-computer interactions, mental load, noise, heat, etc. Therefore, planning models increasingly need to account for human factors in order to produce industrially coherent solutions.

* **Integration aspect:** The second driver of the relevance of human considerations in logistics and manufacturing refers to the modeling of human characteristics and behaviors. Several empirical studies have identified a clear link between the ergonomic burden and individual performance in the industry (see e.g., Shikdar and Sawaqed (2003), Erdinç and Yeow (2011) and Ivarsson and Eek (2016)). In addition to poor ergonomic conditions, numerous other factors can impact the productivity of employees. These include fatigue (Yung et al., 2020), noise exposure (Szalma and Hancock, 2011), individual learning (Grosse et al., 2015a), stress and psychosocial factors (Halkos and Bousinakis, 2010), etc. Overall, the study of human factors is essential to understand and model the productivity of employees accurately. Logistics and manufacturing are heavily relying on the optimization of their operations, it is, therefore, crucial to model as accurately as possible the duration of the operations. This will gain even more importance with the spread of the Industry 5.0 paradigm. Oriented toward process automation, human-robot collaboration is becoming more common in production systems, where human operators and robots work on the same workstations. A thorough comprehension of the modeling of human characteristics is crucial for the success of such systems (Wang et al., 2017).

From an academic perspective, the issue of improving working conditions has been mainly tackled by Human Factors and Ergonomics (HF/E), as a human-centered scientific discipline aiming at a better understanding of the interactions between human operators and production or service systems (see Section 2). HF/E lies at the interface between psychology, anthropometry, physiology, mechanics, design, and engineering (Bridger, 2018). This inter-disciplinarity results in a variety of methods used to evaluate work situations, from observational methods to statistics, passing by biomechanics, system theory, epidemiology, and occupational medicine. A number of these methods are presented in the second part (Prunet et al., 2024) of this review. However, OR and mathematical programming have not been part of the ergonomist toolbox until the beginning of the 21st century. To our best knowledge, the pioneering work of Carnahan et al. (2000) was the first to use OR as a tool for ergonomic purposes to optimize a job rotation schedule (see Section 6.1.1).

In the OR literature, economic considerations have historically been largely dominant (Dekker et al., 2012). However, other trends have emerged recently. Ecological considerations have made their way into the optimization literature, e.g., with green logistics (Dekker et al., 2012; Sbihi and Eglese, 2010), sustainable manufacturing operations scheduling (Giret et al., 2015) or circular economy in production planning (Suzanne et al., 2020). Human-aware considerations have also been considered for a couple of decades, from different perspectives, with different degrees of modeling accuracy. It is, however, still a maturing topic that can be difficult to get a grasp of for a newcomer, addressed by different research communities within OR via various approaches. Human factors are hence quite challenging to integrate into existing optimization models for several reasons:

* **At the problem statement level:** Given an industrial situation, identifying the most relevant human factors to consider is challenging without sufficient field experience.

* **At the modeling level:** Once the relevant factors are identified, it is neither easy nor obvious to propose appropriate quantitative modeling.

<footnote n="2">² Database on labour statistics of The International Labour Organization. https://ilostat.ilo.org/ Access: September 20, 2022.</footnote>

<footnote n="3">³ World Health Organization Mortality Database. https://www.who.int/data/data-collection-tools/who-mortality-database Access: September 20, 2022.</footnote>

<footnote n="4">⁴ The European Community (EC) regulation No 561/2006 of 15 March 2006 on machine work. https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX%3A32006R0561 Access: September 20, 2022.</footnote>

<footnote n="5">⁵ The Federal Motor Carrier Safety Administration regulation No. 49 CFR Parts 385, 386, 390 and 395 about Hours of Service of Drivers. https://www.govinfo.gov/content/pkg/FR-2011-12-27/pdf/2011-32696.pdf Access: September 20, 2022.</footnote>

<footnote n="6">⁶ The Directive No. 2006/42/EC of the European Parliament and of the Council of 17 May 2006 on machinery usage. https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX%3A32006L0042 Access: September 20, 2022.</footnote>

<footnote n="7">⁷ The European Council Directive No. 89/391/EEC of 12 June 1989 on the introduction of measures to encourage improvements in the safety and health of workers at work. https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX%3A31989L0391 Access: September 20, 2022.</footnote>

<footnote n="8">⁸ The Occupational Safety and Health Act of 1970 https://www.osha.gov/laws-regs/oshact/completeoshact Access: September 20, 2022.</footnote>
(ILO)<fnref n="2" /> and the World Health Organization (WHO),<fnref n="3" /> over 2.3 million people die yearly from work-related causes (Takala et al., 2014). Studies show that, at any given time, 20% of employed adults suffer from Work-related Musculoskeletal Disorders (WMSD) (Vézina et al., 2011). Furthermore, from an economic perspective, the direct and indirect costs of work-related injuries are estimated at 4% of the world GDP (Takala et al., 2014). Therefore, the improvement of working conditions and the reduction of work-related health problems are still an important challenge worldwide.

**Industry 5.0.** This is an emerging concept referring to a change of paradigm in the organization of logistics and manufacturing systems, which are the focus of the present work. Industry 5.0 proposes a shift from a system-centric vision to a human-centric vision of industrial systems, by placing the role and well-being of operators at the center of the process design (Lu et al., 2022). Sustainability and resilience are the two other pillars of Industry 5.0. The consideration of human factors, at physical, cognitive, perceptual, and psychosocial levels, is especially relevant in logistics and manufacturing fields, especially considering the development of human-machine interactions (Wang et al., 2017), or the aging of the working population (Calzavara et al., 2020).

The need to account for human factors in decision support models for logistics and manufacturing systems will continue to gain importance in the near future. Two arguments support this claim:

* **Regulatory aspect:** Companies in the logistics and manufacturing sectors still rely heavily on manual labor, especially for tasks requiring a high degree of precision and flexibility. This is, for example, the case for truck drivers in logistics, order pickers in warehousing (Grosse et al., 2015b), or assembly line operators (Battini et al., 2016a). Furthermore, these jobs can account for a high level of physical and cognitive stress, repetitive movements, lifting tasks, and awkward positions. The increasing demand for social accountability of companies has led to a growing number of laws regulating the working conditions in the industry. In logistics, the European regulation EC 561/2006⁴ and the American Hours of Service of Drivers regulation<fnref n="5" /> both propose a framework to regulate the driving and working times of truck drivers. The manufacturing sector has also been subject to numerous regulations aimed at reducing ergonomic risks in workplaces. Among others, one can cite the Directive No. 2006/42/EC of the European Parliament on machinery usage,<fnref n="6" /> the Directive No. 89/391/EEC on general measures to encourage improvements in safety and health of workers,<fnref n="7" /> or the Occupational Safety and Health Act of 1970.<fnref n="8" /> Furthermore, several ergonomics standards have been developed by the International

Organization for Standardization and the European Committee on Standardization to design production systems. Dul et al. (2004) listed up to 174 international ergonomic standards for production systems, going from general recommendations on the design of processes to specific requirements for manual handling, human-computer interactions, mental load, noise, heat, etc. Therefore, planning models increasingly need to account for human factors in order to produce industrially coherent solutions.

* **Integration aspect:** The second driver of the relevance of human considerations in logistics and manufacturing refers to the modeling of human characteristics and behaviors. Several empirical studies have identified a clear link between the ergonomic burden and individual performance in the industry (see e.g., Shikdar and Sawaqed (2003), Erdinç and Yeow (2011) and Ivarsson and Eek (2016)). In addition to poor ergonomic conditions, numerous other factors can impact the productivity of employees. These include fatigue (Yung et al., 2020), noise exposure (Szalma and Hancock, 2011), individual learning (Grosse et al., 2015a), stress and psychosocial factors (Halkos and Bousinakis, 2010), etc. Overall, the study of human factors is essential to understand and model the productivity of employees accurately. Logistics and manufacturing are heavily relying on the optimization of their operations, it is, therefore, crucial to model as accurately as possible the duration of the operations. This will gain even more importance with the spread of the Industry 5.0 paradigm. Oriented toward process automation, human-robot collaboration is becoming more common in production systems, where human operators and robots work on the same workstations. A thorough comprehension of the modeling of human characteristics is crucial for the success of such systems (Wang et al., 2017).

From an academic perspective, the issue of improving working conditions has been mainly tackled by Human Factors and Ergonomics (HF/E), as a human-centered scientific discipline aiming at a better understanding of the interactions between human operators and production or service systems (see Section 2). HF/E lies at the interface between psychology, anthropometry, physiology, mechanics, design, and engineering (Bridger, 2018). This inter-disciplinarity results in a variety of methods used to evaluate work situations, from observational methods to statistics, passing by biomechanics, system theory, epidemiology, and occupational medicine. A number of these methods are presented in the second part (Prunet et al., 2024) of this review. However, OR and mathematical programming have not been part of the ergonomist toolbox until the beginning of the 21st century. To our best knowledge, the pioneering work of Carnahan et al. (2000) was the first to use OR as a tool for ergonomic purposes to optimize a job rotation schedule (see Section 6.1.1).

In the OR literature, economic considerations have historically been largely dominant (Dekker et al., 2012). However, other trends have emerged recently. Ecological considerations have made their way into the optimization literature, e.g., with green logistics (Dekker et al., 2012; Sbihi and Eglese, 2010), sustainable manufacturing operations scheduling (Giret et al., 2015) or circular economy in production planning (Suzanne et al., 2020). Human-aware considerations have also been considered for a couple of decades, from different perspectives, with different degrees of modeling accuracy. It is, however, still a maturing topic that can be difficult to get a grasp of for a newcomer, addressed by different research communities within OR via various approaches. Human factors are hence quite challenging to integrate into existing optimization models for several reasons:

* **At the problem statement level:** Given an industrial situation, identifying the most relevant human factors to consider is challenging without sufficient field experience.

* **At the modeling level:** Once the relevant factors are identified, it is neither easy nor obvious to propose appropriate quantitative modeling.

<footnote n="2">² Database on labour statistics of The International Labour Organization. https://ilostat.ilo.org/ Access: September 20, 2022.</footnote>

<footnote n="3">³ World Health Organization Mortality Database. https://www.who.int/data/data-collection-tools/who-mortality-database Access: September 20, 2022.</footnote>

<footnote n="4">⁴ The European Community (EC) regulation No 561/2006 of 15 March 2006 on machine work. https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX%3A32006R0561 Access: September 20, 2022.</footnote>

<footnote n="5">⁵ The Federal Motor Carrier Safety Administration regulation No. 49 CFR Parts 385, 386, 390 and 395 about Hours of Service of Drivers. https://www.govinfo.gov/content/pkg/FR-2011-12-27/pdf/2011-32696.pdf Access: September 20, 2022.</footnote>

<footnote n="6">⁶ The Directive No. 2006/42/EC of the European Parliament and of the Council of 17 May 2006 on machinery usage. https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX%3A32006L0042 Access: September 20, 2022.</footnote>

<footnote n="7">⁷ The European Council Directive No. 89/391/EEC of 12 June 1989 on the introduction of measures to encourage improvements in the safety and health of workers at work. https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX%3A31989L0391 Access: September 20, 2022.</footnote>

<footnote n="8">⁸ The Occupational Safety and Health Act of 1970 https://www.osha.gov/laws-regs/oshact/completeoshact Access: September 20, 2022.</footnote>
* *At the instance level:* The data collection on this part often requires extensive field observations and measurements, or dedicated lab studies.

* *At the solution level:* The integration of human considerations often has a significant impact on problem complexity. Tools and frameworks commonly used in the HF/E community do not usually have convenient mathematical properties such as linearity or convexity.

This review aims at bridging the understanding gap of OR academics and practitioners about HF/E methods, and at providing them with a broad understanding of the related problems, by presenting the models, methods, and tools used in the literature to design human-aware optimization methods for logistics and manufacturing systems.

Due to the length of the manuscript, the present work is divided into two separate papers. After the scope delineation, the first part of this review (the current paper) conducts a quantitative and thematic analysis of the retrieved corpus according to a semi-systematic methodology. Section 2 provides the related background of the present work with respect to the existing literature and defines clearly the scope of the review. Section 3 presents the search methodology used for the material collection. Sections 4 to 6 give an overview of the retrieved literature corpus structured by class of problems encountered in logistics and manufacturing systems, namely: logistics (warehousing and vehicle routing), production systems (production scheduling, assembly line balancing, production planning, and system design), and workforce-related problems (workforce scheduling and management). Section 7 is specially dedicated to investigating the impact of human-aware considerations on mathematical models. Particular attention is put on the features added to an optimization model (e.g., new constraints, modification of the objective function) to account for the human factors, and the impact on solution methods. Section 8 discusses the main finding of this first part, and proposes research directions. Finally, Section 9 concludes this first part of the review. In the second part of this work (Prunet et al., 2024), the focus is set on the modeling of human characteristics. The different modeling constructs found in the related literature are presented and contextualized. Prunet et al. (2024) has been written with the idea of being used as a survey of the different modeling of human factors for interested academics and practitioners.

## 2. Terminology, related background, scope, and motivations

In this section, the present review is put in context and motivated with respect to the literature. First, we propose comprehensive definitions of the human-related key concepts used throughout this work. Then we survey and synthesize our findings from the existing related reviews. From this analysis, we propose a clear delineation of the scope of this review.

### 2.1. Definitions of human-related key concepts

In the OR literature, the key terms related to human-aware optimization are found with various definitions and interpretations, the most prominent one being the term *human factors*. A naive interpretation from an OR practitioner would define it as any characteristic or behavior related to the human nature of employees. However, *Human Factors and Ergonomics* also refers to a scientific discipline, defined as follows by the International Ergonomics Association<fnref n="9" />:

Ergonomics (or human factors) is the scientific discipline concerned with the understanding of interactions among humans and other elements of a system, and the profession that applies theory, principles, data, and methods to design in order to optimize human well-being and overall system performance. The terms ergonomics and human factors are often used interchangeably or as a unit (e.g., human factors/ergonomics – HF/E or E/HF), a practice that is adopted by the IEA.

As the topic of this review is prone to cross-disciplinary work, we stress the importance of avoiding the confusion between human factors and HF/E to facilitate mutual comprehension between researchers with different backgrounds. Interested readers can find a more thorough definition and explanations on HF/E in Wogalter et al. (1998). Starting from this clarification, let us adopt the following convention for the remainder of this paper:

* **Human Factors and Ergonomics (HF/E):** as a scientific discipline that studies the interactions between a human operator and his/her work system, emphasizing the improvement of working conditions. HF/E research frameworks usually identify four critical elements in human-system interactions: *physical* related to the human body, *mental* related to the task cognitive complexity, *perceptual* related to the human perceptions (e.g., hearing, sight, etc.) and *psychosocial* related to the interactions with colleagues and management (Salvendy and St, 2022).

* **Operations Research (OR):** as a scientific discipline that aims at providing better decisions by the analysis and modeling of complex systems, and the development of efficient decision-support algorithms based on advanced mathematical methods. A typical OR work involves optimizing the performances of a work system through the following steps: 1. the observation and analysis of a work environment, 2. the development of a simplified mathematical model for this environment, 3. the design of an efficient algorithm to solve the problem, and 4. the industrial evaluation of the returned solution.

* **Work-related Musculoskeletal Disorder (WMSD):** as an injury or a disease that affects the body's structural systems (i.e., the bones, tissues, nervous or circulatory systems), caused by a work situation. Examples of WMSDs include (but are not limited to) low back pain, carpal tunnel syndrome, tendinitis, or trigger finger. WMSDs encompass a large portion of work-related injuries, but some do not affect the musculoskeletal system (e.g., hearing loss, excessive heat exposure).

* **Ergonomic Risk (ER):** referring to the additional risk factor of developing WMSD, or any other occupational accident, disease, or injury, for an employee due to a specific work situation. This concept is found under different names in the literature, without a clear difference: ergonomic load, ergonomic workload, ergonomic burden, ergonomic strain, etc.

* **Risk Factors:** as workplace situations that cause wear and tear for the body, and increase the ergonomic risk for employees. These include repetition, awkward posture, lifting, noise, work stress, etc.

* **A Human Factor (HF):** as a characteristic or behavior typically human. This can be a factor affecting the individual performance of workers and the ability to perform tasks (e.g., fatigue, learning, forgetting), the safety of workers (e.g., work-related injuries, awkward postures), the interests of workers (e.g., satisfaction, motivation), or any other real-life human characteristic interacting with the optimization of a production or service system.

* **A Human-Aware Model (HAM):** as a quantitative model that explicitly translates a HF into a mathematical expression, which can, in turn, be used in an optimization problem (e.g., in a constraint or as an objective function). In other terms, the concept of HAM is the transposition of HF/E methods into an OR

<footnote n="9">⁹ The International Ergonomics Association (IEA). https://iea.cc/what-is-ergonomics/ Access: September 20, 2022.</footnote>
* *At the instance level:* The data collection on this part often requires extensive field observations and measurements, or dedicated lab studies.

* *At the solution level:* The integration of human considerations often has a significant impact on problem complexity. Tools and frameworks commonly used in the HF/E community do not usually have convenient mathematical properties such as linearity or convexity.

This review aims at bridging the understanding gap of OR academics and practitioners about HF/E methods, and at providing them with a broad understanding of the related problems, by presenting the models, methods, and tools used in the literature to design human-aware optimization methods for logistics and manufacturing systems.

Due to the length of the manuscript, the present work is divided into two separate papers. After the scope delineation, the first part of this review (the current paper) conducts a quantitative and thematic analysis of the retrieved corpus according to a semi-systematic methodology. Section 2 provides the related background of the present work with respect to the existing literature and defines clearly the scope of the review. Section 3 presents the search methodology used for the material collection. Sections 4 to 6 give an overview of the retrieved literature corpus structured by class of problems encountered in logistics and manufacturing systems, namely: logistics (warehousing and vehicle routing), production systems (production scheduling, assembly line balancing, production planning, and system design), and workforce-related problems (workforce scheduling and management). Section 7 is specially dedicated to investigating the impact of human-aware considerations on mathematical models. Particular attention is put on the features added to an optimization model (e.g., new constraints, modification of the objective function) to account for the human factors, and the impact on solution methods. Section 8 discusses the main finding of this first part, and proposes research directions. Finally, Section 9 concludes this first part of the review. In the second part of this work (Prunet et al., 2024), the focus is set on the modeling of human characteristics. The different modeling constructs found in the related literature are presented and contextualized. Prunet et al. (2024) has been written with the idea of being used as a survey of the different modeling of human factors for interested academics and practitioners.

## 2. Terminology, related background, scope, and motivations

In this section, the present review is put in context and motivated with respect to the literature. First, we propose comprehensive definitions of the human-related key concepts used throughout this work. Then we survey and synthesize our findings from the existing related reviews. From this analysis, we propose a clear delineation of the scope of this review.

### 2.1. Definitions of human-related key concepts

In the OR literature, the key terms related to human-aware optimization are found with various definitions and interpretations, the most prominent one being the term *human factors*. A naive interpretation from an OR practitioner would define it as any characteristic or behavior related to the human nature of employees. However, *Human Factors and Ergonomics* also refers to a scientific discipline, defined as follows by the International Ergonomics Association<fnref n="9" />:

Ergonomics (or human factors) is the scientific discipline concerned with the understanding of interactions among humans and other elements of a system, and the profession that applies theory, principles, data, and methods to design in order to optimize human well-being and overall system performance. The terms ergonomics and human factors are often used interchangeably or as a unit (e.g., human factors/ergonomics – HF/E or E/HF), a practice that is adopted by the IEA.

As the topic of this review is prone to cross-disciplinary work, we stress the importance of avoiding the confusion between human factors and HF/E to facilitate mutual comprehension between researchers with different backgrounds. Interested readers can find a more thorough definition and explanations on HF/E in Wogalter et al. (1998). Starting from this clarification, let us adopt the following convention for the remainder of this paper:

* **Human Factors and Ergonomics (HF/E):** as a scientific discipline that studies the interactions between a human operator and his/her work system, emphasizing the improvement of working conditions. HF/E research frameworks usually identify four critical elements in human-system interactions: *physical* related to the human body, *mental* related to the task cognitive complexity, *perceptual* related to the human perceptions (e.g., hearing, sight, etc.) and *psychosocial* related to the interactions with colleagues and management (Salvendy and St, 2022).

* **Operations Research (OR):** as a scientific discipline that aims at providing better decisions by the analysis and modeling of complex systems, and the development of efficient decision-support algorithms based on advanced mathematical methods. A typical OR work involves optimizing the performances of a work system through the following steps: 1. the observation and analysis of a work environment, 2. the development of a simplified mathematical model for this environment, 3. the design of an efficient algorithm to solve the problem, and 4. the industrial evaluation of the returned solution.

* **Work-related Musculoskeletal Disorder (WMSD):** as an injury or a disease that affects the body's structural systems (i.e., the bones, tissues, nervous or circulatory systems), caused by a work situation. Examples of WMSDs include (but are not limited to) low back pain, carpal tunnel syndrome, tendinitis, or trigger finger. WMSDs encompass a large portion of work-related injuries, but some do not affect the musculoskeletal system (e.g., hearing loss, excessive heat exposure).

* **Ergonomic Risk (ER):** referring to the additional risk factor of developing WMSD, or any other occupational accident, disease, or injury, for an employee due to a specific work situation. This concept is found under different names in the literature, without a clear difference: ergonomic load, ergonomic workload, ergonomic burden, ergonomic strain, etc.

* **Risk Factors:** as workplace situations that cause wear and tear for the body, and increase the ergonomic risk for employees. These include repetition, awkward posture, lifting, noise, work stress, etc.

* **A Human Factor (HF):** as a characteristic or behavior typically human. This can be a factor affecting the individual performance of workers and the ability to perform tasks (e.g., fatigue, learning, forgetting), the safety of workers (e.g., work-related injuries, awkward postures), the interests of workers (e.g., satisfaction, motivation), or any other real-life human characteristic interacting with the optimization of a production or service system.

* **A Human-Aware Model (HAM):** as a quantitative model that explicitly translates a HF into a mathematical expression, which can, in turn, be used in an optimization problem (e.g., in a constraint or as an objective function). In other terms, the concept of HAM is the transposition of HF/E methods into an OR

<footnote n="9">⁹ The International Ergonomics Association (IEA). https://iea.cc/what-is-ergonomics/ Access: September 20, 2022.</footnote>
context. A typical HAM can be expressed as a function mapping the different states of a human-system to a set of real numbers, which can be interpreted as the “ergonomic score” of the states. For instance, the NIOSH equation is a HAM that evaluates the ergonomic risk related to manual handling. Based on a set of criteria (e.g., weight, handling posture, duration), a score can be computed for each handling task that needs to be scheduled in a shift and used as input for a related optimization problem.

## 2.2. Previous reviews

The integration of a HF in optimization problems is a broad subject. As such, several reviews/surveys have been published on the topic. However, these works often focus on a single topic of logistics and manufacturing, yet with a scope broader than pure optimization problems, i.e., including material from other disciplines, such as industrial engineering or HF/E. In this section, a brief overview of the most relevant reviews is provided.

* **Warehousing:** (Grosse et al., 2015b, 2017b) study the integration of HFs in order picking (i.e., the action of retrieving, or “picking”, items from the storage area to prepare orders) models. Grosse et al. (2017b) perform a content analysis of the retrieved literature, and thus give a broad overview of the topics of interest and related trends. With a tighter scope, Grosse et al. (2015b) place the emphasis on planning models in order picking, by presenting a systematic methodology and introducing a new conceptual framework and taxonomy to classify and analyze this research stream. De Lombaert et al. (2022) study human aspects in the scope of order picking planning models, with a focus on the integration into mathematical models and insights from semi-structured interviews of practitioners.

* **Vehicle routing problem:** Vega-Mejía et al. (2019) review the VRP with triple bottom line sustainable objectives, one of those being social. However, the paper focuses more on economic and ecological aspects, as they are more representative of their review corpus, the social aspect only being briefly discussed. Matl et al. (2018) propose a review on workload equity in the VRP and provide an in-depth analysis on the topic.

* **Production scheduling:** As reflected by the reviews on the topic, the scheduling community has been quite prolific in the consideration of HFs into their mathematical models. The reader is referred to Lodree et al. (2009) for a general narrative review about Human-Aware Modeling in the scheduling domain. Lodree et al. (2009) deal with works on the topic published prior to 2007, including both OR-related and empirical HF/E studies, and provide an insightful analysis and a modeling framework on the sequencing of human tasks. The introduction of learning aspects has also been extensively studied by the scheduling community, from the early works on learning in management science to the most recent development of this stream. Biskup (2008) provides a review on scheduling integrating learning jointly with a relevant analysis of the practical aspects of learning, as well as a discussion on the mathematical implications of the different ways to model such effects. Azzouz et al. (2018) present an update of the review of Biskup (2008), and propose a taxonomy and a classification framework to map the related areas of the prolific stream of scheduling with learning effects. From an OR perspective, Cheng et al. (2004) present a short survey on the mathematical implications of time-dependent processing times on scheduling models.

* **Assembly lines:** Assembly lines are also a well-established research topic for human-aware optimization, due to the inherent balance of the workload between workers, which can be seen as a balance of the ER. Otto and Battaia (2017) propose a systematic review on line balancing and job rotation to reduce the physical

ER in assembly. The authors provide an analysis of both the HAMs available for assembly line practitioners, and the mathematical perspective of integrating such considerations in existing models. Albeit not a review paper, Peltokorpi et al. (2014) provides a network analysis of the different performance factors for assembly lines.

* **Lot sizing:** Jaber et al. (2022) review the integration of learning curves in lot sizing models. The focus is put on the different learning curve models and how they are integrated into the models. The results are presented chronologically to highlight the development of the field.

* **Workforce planning:** This class of problems has also been studied, especially with skill considerations. De Bruecker et al. (2015) present a state-of-the-art review on workforce planning with skills, focusing on both mathematical modeling and managerial implications. The authors also propose a new taxonomy for this research stream, based on what skills are exactly modeling, and how they are integrated into decision models. Their taxonomy constitutes the basis of our analysis of skills in (Prunet et al. (2024), Skills). Xu and Hall (2021) study fatigue in workforce scheduling in a broad sense. They focus on the work-rest scheduling and shift scheduling problems accounting for human fatigue and derive insights from empirical studies and opportunities for OR applications.

* **Reviews focusing on specific HFs:** Several works review the literature focusing on a given HF instead of an area of logistics and manufacturing. Karsu and Morton (2015) survey the issue of equity in OR models with an emphasis on the modeling implications. Anzanello and Fogliatto (2011) provide a narrative review on learning curves, with a focus on mathematical models. Glock et al. (2019b) propose a systematic review on the applications of learning curves in operations management, and Grosse et al. (2015a) performed a meta-analysis of empirical studies on the use of learning curves in a production context. Katiraee et al. (2021) review the literature modeling heterogeneously the workforce in production systems. Finally, several reviews study the integration of HFs in logistics and manufacturing systems with an HF/E point of view, without considering mathematical models: Padula et al. (2017) on job rotation to prevent WMSD, Kolus et al. (2018) on human errors and their implications, Jahanmahin et al. (2022a) on human-robot collaboration, and Muhs et al. (2018) on the temporal variability of tasks performed by a human operator.

To conclude, one can see that the integration of HFs in the optimization of logistics and manufacturing systems are extensively studied and reviewed. However, most of these reviews focus either on a single topic, or they conduct the study only through an OR or HF/E perspective, thus giving a restricted view of this interdisciplinary topic. In the present paper, we aim at broadening the scope to give a general picture and a more holistic analysis of the subject, that has not been done previously in the literature. In that sense, the present work can be seen as an extension of previous works on HF an operations management (Larco Martinelli, 2010; Neumann and Dul, 2010), but with a clear focus on optimization. Grosse et al. (2017a) provide a first attempt at such a work, yet the restricted length of the paper does not allow the authors to provide an in-depth analysis.

## 2.3. Scope

The present work aims at surveying the research stream dedicated to the integration of HF in the optimization of logistics and manufacturing systems. As a consequence, to be relevant for this work, a paper must deal with:

**I. Optimization.** Despite being at the interface between several disciplines, we chose to review only the papers presenting an optimization model, either explicitly or implicitly, but clearly defined.
context. A typical HAM can be expressed as a function mapping the different states of a human-system to a set of real numbers, which can be interpreted as the “ergonomic score” of the states. For instance, the NIOSH equation is a HAM that evaluates the ergonomic risk related to manual handling. Based on a set of criteria (e.g., weight, handling posture, duration), a score can be computed for each handling task that needs to be scheduled in a shift and used as input for a related optimization problem.

## 2.2. Previous reviews

The integration of a HF in optimization problems is a broad subject. As such, several reviews/surveys have been published on the topic. However, these works often focus on a single topic of logistics and manufacturing, yet with a scope broader than pure optimization problems, i.e., including material from other disciplines, such as industrial engineering or HF/E. In this section, a brief overview of the most relevant reviews is provided.

* **Warehousing:** (Grosse et al., 2015b, 2017b) study the integration of HFs in order picking (i.e., the action of retrieving, or “picking”, items from the storage area to prepare orders) models. Grosse et al. (2017b) perform a content analysis of the retrieved literature, and thus give a broad overview of the topics of interest and related trends. With a tighter scope, Grosse et al. (2015b) place the emphasis on planning models in order picking, by presenting a systematic methodology and introducing a new conceptual framework and taxonomy to classify and analyze this research stream. De Lombaert et al. (2022) study human aspects in the scope of order picking planning models, with a focus on the integration into mathematical models and insights from semi-structured interviews of practitioners.

* **Vehicle routing problem:** Vega-Mejía et al. (2019) review the VRP with triple bottom line sustainable objectives, one of those being social. However, the paper focuses more on economic and ecological aspects, as they are more representative of their review corpus, the social aspect only being briefly discussed. Matl et al. (2018) propose a review on workload equity in the VRP and provide an in-depth analysis on the topic.

* **Production scheduling:** As reflected by the reviews on the topic, the scheduling community has been quite prolific in the consideration of HFs into their mathematical models. The reader is referred to Lodree et al. (2009) for a general narrative review about Human-Aware Modeling in the scheduling domain. Lodree et al. (2009) deal with works on the topic published prior to 2007, including both OR-related and empirical HF/E studies, and provide an insightful analysis and a modeling framework on the sequencing of human tasks. The introduction of learning aspects has also been extensively studied by the scheduling community, from the early works on learning in management science to the most recent development of this stream. Biskup (2008) provides a review on scheduling integrating learning jointly with a relevant analysis of the practical aspects of learning, as well as a discussion on the mathematical implications of the different ways to model such effects. Azzouz et al. (2018) present an update of the review of Biskup (2008), and propose a taxonomy and a classification framework to map the related areas of the prolific stream of scheduling with learning effects. From an OR perspective, Cheng et al. (2004) present a short survey on the mathematical implications of time-dependent processing times on scheduling models.

* **Assembly lines:** Assembly lines are also a well-established research topic for human-aware optimization, due to the inherent balance of the workload between workers, which can be seen as a balance of the ER. Otto and Battaia (2017) propose a systematic review on line balancing and job rotation to reduce the physical

ER in assembly. The authors provide an analysis of both the HAMs available for assembly line practitioners, and the mathematical perspective of integrating such considerations in existing models. Albeit not a review paper, Peltokorpi et al. (2014) provides a network analysis of the different performance factors for assembly lines.

* **Lot sizing:** Jaber et al. (2022) review the integration of learning curves in lot sizing models. The focus is put on the different learning curve models and how they are integrated into the models. The results are presented chronologically to highlight the development of the field.

* **Workforce planning:** This class of problems has also been studied, especially with skill considerations. De Bruecker et al. (2015) present a state-of-the-art review on workforce planning with skills, focusing on both mathematical modeling and managerial implications. The authors also propose a new taxonomy for this research stream, based on what skills are exactly modeling, and how they are integrated into decision models. Their taxonomy constitutes the basis of our analysis of skills in (Prunet et al. (2024), Skills). Xu and Hall (2021) study fatigue in workforce scheduling in a broad sense. They focus on the work-rest scheduling and shift scheduling problems accounting for human fatigue and derive insights from empirical studies and opportunities for OR applications.

* **Reviews focusing on specific HFs:** Several works review the literature focusing on a given HF instead of an area of logistics and manufacturing. Karsu and Morton (2015) survey the issue of equity in OR models with an emphasis on the modeling implications. Anzanello and Fogliatto (2011) provide a narrative review on learning curves, with a focus on mathematical models. Glock et al. (2019b) propose a systematic review on the applications of learning curves in operations management, and Grosse et al. (2015a) performed a meta-analysis of empirical studies on the use of learning curves in a production context. Katiraee et al. (2021) review the literature modeling heterogeneously the workforce in production systems. Finally, several reviews study the integration of HFs in logistics and manufacturing systems with an HF/E point of view, without considering mathematical models: Padula et al. (2017) on job rotation to prevent WMSD, Kolus et al. (2018) on human errors and their implications, Jahanmahin et al. (2022a) on human-robot collaboration, and Muhs et al. (2018) on the temporal variability of tasks performed by a human operator.

To conclude, one can see that the integration of HFs in the optimization of logistics and manufacturing systems are extensively studied and reviewed. However, most of these reviews focus either on a single topic, or they conduct the study only through an OR or HF/E perspective, thus giving a restricted view of this interdisciplinary topic. In the present paper, we aim at broadening the scope to give a general picture and a more holistic analysis of the subject, that has not been done previously in the literature. In that sense, the present work can be seen as an extension of previous works on HF an operations management (Larco Martinelli, 2010; Neumann and Dul, 2010), but with a clear focus on optimization. Grosse et al. (2017a) provide a first attempt at such a work, yet the restricted length of the paper does not allow the authors to provide an in-depth analysis.

## 2.3. Scope

The present work aims at surveying the research stream dedicated to the integration of HF in the optimization of logistics and manufacturing systems. As a consequence, to be relevant for this work, a paper must deal with:

**I. Optimization.** Despite being at the interface between several disciplines, we chose to review only the papers presenting an optimization model, either explicitly or implicitly, but clearly defined.
II. logistics or manufacturing. According to the Cambridge Business English Dictionary (Press, 2011), logistics and manufacturing are defined as follows:

**Logistics:** The process of planning and organizing to make sure that resources are in the places where they are needed so that an activity or process happens effectively.

**Manufacturing:** The business of producing goods in large numbers, especially in factories.

These definitions cover the classical topics of OR, including planning and scheduling, when applied to a production process. However, other side activities enabling manufacturing to be processed, effectively and efficiently, are also covered by these definitions, namely: inventory management, warehousing, vehicle routing, and lot sizing operations.

III. Human factors. We consider that a paper fits in the scope if it considers the modeling of a HF or deals with the improvement of the employees' welfare.

## 2.4. Motivations

The research stream on human-aware optimization in logistics and manufacturing systems is consistently growing. However, the related topics are studied through the lens of a specific field of application, or a specific human factor. The main goal of this paper is to fill this gap by providing a holistic picture of this broad topic, and a coherent analysis of the research stream. The second objective is to propose to interested practitioners a comprehensive overview of the available models to represent and quantify human characteristics, both from the HF/E and OR perspectives. These goals are expressed through the following research questions addressed throughout both the current paper and the second part of the work (Prunet et al., 2024):

* Which HFs are studied in the related literature, and in which logistics and manufacturing areas are they present?

* How are HFs modeled in the related literature, and which HAMs are available to take them into account?

* How are HAMs integrated into optimization models, and how does their integration impact the models from a mathematical programming perspective?

The two parts of the work are intended as a “guidance-type” presentation of human-aware optimization, to help researchers at identifying relevant human factors for their problems, appropriate quantitative models for these factors, and references to further theoretical and applied works on the topic.

# 3. Methodology

## 3.1. Material collection methodology

This section presents the methodology followed to collect the material for this review. The most common types of methodological approaches used to perform a literature review are: systematic, semi-systematic, narrative, integrative, and meta-analysis (Snyder, 2019). Motivated by the large number of papers fitting the scope defined in Section 2.3, we opt for a semi-systematic methodology. In short, the search methodology is systematic, to ensure that all relevant topics are covered by the review. However, the amount of material does not realistically allow a systematic analysis of every in-scope work, and thus the analysis and writing are narrative. This means that for some topics (specifically, papers dealing with skills and/or learning), the decision to include them in scope is made at the discretion of the authors. The reader interested in systematic reviews on specific topics is referred to Section 2.2. Nevertheless, one should note that, even though

<table><caption>**Table 1**
List of keywords in the search string.</caption><thead><tr><th>Logistics and manufacturing</th><th>Human-aware modeling</th></tr></thead><tbody><tr><td>warehous*, storage, pick*, batch*, assembly, production, "lot sizing", manufactur*, planning, routing, logistic*, schedul*, maritime</td><td>AND musculoskeletal, welfare, postur*, lift*, "human factor*", ergonomic*, "human error*", "learning curve", "learning effect", "forgetting", "human learning", pain, noise, bored*, fatigue, break, rest, cognitive, equity, safe, discomfort, turnover, absenteeism, vibration, repetit*, injury, "social benefit*", skill*, psychosocial, "workload smoothing"</td></tr></tbody></table>

a number of papers are excluded, the systematic search methodology ensures that all relevant topics and modeling approaches are covered in this paper. With the same philosophy, we highlight that the length of a given section does not necessarily reflect the bibliometric importance of the covered topic.

The material is collected using Scopus and Web of Science databases, by applying the following set of rules and selection criteria (SC):

* According to the scope of this review, two sets of keywords are created, one for logistics and manufacturing, and one for human-aware modeling. A search query is created for the databases with one word from each of the two sets, presented in Table 1. Following a preparatory scan of the literature, the list of keywords has been created at the discretion of the authors with the objective of covering as many scientific works as possible dealing with Human-Aware Logistics and Manufacturing Systems.

* Only papers published in English are considered.

* All publication dates are considered up to 2022.

* (SC1) A category filter is applied on both databases to target the relevant papers. On Scopus, the search is limited to Computer Science and Decision Science categories. On Web of Science, the following categories are considered: Computer Science (Theory methods, artificial intelligence & interdisciplinary applications), Operations research and management science, Engineering Industrial, Management, Transportation, Transportation science technology & Mathematics interdisciplinary applications.

* (SC2) Only articles published in journals and book chapters are considered. Conference proceedings are excluded from this study in order to keep the size of the studied corpus manageable.

* (SC3) From the collected list of papers, duplicates are removed, and we only retain the works that satisfy the following three conditions based on their title, keywords, and abstract, in accordance with what is presented in Section 2.3:

1. The paper provides an optimization mathematical model, or an optimization solution method.

2. The paper explicitly considers Human-Aware Modeling in its title, abstract, or keywords. The mention of HF or social welfare is explicit. Moreover, these aspects are explicitly modeled.

3. The paper deals with logistics or manufacturing.

As a result, a total of 844 papers are retrieved after the application of (SC3).

* (SC4) After a thorough reading, only relevant papers are included. Studies dealing with skills and learning include a lot of papers, and we decided to exclude some of them. Even if the exclusion process is not reproducible, the following guidelines are applied for the paper selection:

1. Papers falling in the scope of the review and focusing their contribution on Human-Aware Modeling are systematically included. This ensures that every relevant assessment or
## II. logistics or manufacturing.
According to the Cambridge Business English Dictionary (Press, 2011), logistics and manufacturing are defined as follows:

**Logistics:** The process of planning and organizing to make sure that resources are in the places where they are needed so that an activity or process happens effectively.

**Manufacturing:** The business of producing goods in large numbers, especially in factories.

These definitions cover the classical topics of OR, including planning and scheduling, when applied to a production process. However, other side activities enabling manufacturing to be processed, effectively and efficiently, are also covered by these definitions, namely: inventory management, warehousing, vehicle routing, and lot sizing operations.

### III. Human factors.
We consider that a paper fits in the scope if it considers the modeling of a HF or deals with the improvement of the employees' welfare.

## 2.4. Motivations

The research stream on human-aware optimization in logistics and manufacturing systems is consistently growing. However, the related topics are studied through the lens of a specific field of application, or a specific human factor. The main goal of this paper is to fill this gap by providing a holistic picture of this broad topic, and a coherent analysis of the research stream. The second objective is to propose to interested practitioners a comprehensive overview of the available models to represent and quantify human characteristics, both from the HF/E and OR perspectives. These goals are expressed through the following research questions addressed throughout both the current paper and the second part of the work (Prunet et al., 2024):

* Which HFs are studied in the related literature, and in which logistics and manufacturing areas are they present?

* How are HFs modeled in the related literature, and which HAMs are available to take them into account?

* How are HAMs integrated into optimization models, and how does their integration impact the models from a mathematical programming perspective?

The two parts of the work are intended as a “guidance-type” presentation of human-aware optimization, to help researchers at identifying relevant human factors for their problems, appropriate quantitative models for these factors, and references to further theoretical and applied works on the topic.

# 3. Methodology

## 3.1. Material collection methodology

This section presents the methodology followed to collect the material for this review. The most common types of methodological approaches used to perform a literature review are: systematic, semi-systematic, narrative, integrative, and meta-analysis (Snyder, 2019). Motivated by the large number of papers fitting the scope defined in Section 2.3, we opt for a semi-systematic methodology. In short, the search methodology is systematic, to ensure that all relevant topics are covered by the review. However, the amount of material does not realistically allow a systematic analysis of every in-scope work, and thus the analysis and writing are narrative. This means that for some topics (specifically, papers dealing with skills and/or learning), the decision to include them in scope is made at the discretion of the authors. The reader interested in systematic reviews on specific topics is referred to Section 2.2. Nevertheless, one should note that, even though

<table><caption>**Table 1**
List of keywords in the search string.</caption><thead><tr><th>Logistics and manufacturing</th><th>Human-aware modeling</th></tr></thead><tbody><tr><td>warehous*, storage, pick*, batch*, assembly, production, "lot sizing", manufactur*, planning, routing, logistic*, schedul*, maritime</td><td>AND musculoskeletal, welfare, postur*, lift*, "human factor*", ergonomic*, "human error*", "learning curve", "learning effect", "forgetting", "human learning", pain, noise, bored*, fatigue, break, rest, cognitive, equity, safe, discomfort, turnover, absenteeism, vibration, repetit*, injury, "social benefit*", skill*, psychosocial, "workload smoothing"</td></tr></tbody></table>

a number of papers are excluded, the systematic search methodology ensures that all relevant topics and modeling approaches are covered in this paper. With the same philosophy, we highlight that the length of a given section does not necessarily reflect the bibliometric importance of the covered topic.

The material is collected using Scopus and Web of Science databases, by applying the following set of rules and selection criteria (SC):

* According to the scope of this review, two sets of keywords are created, one for logistics and manufacturing, and one for human-aware modeling. A search query is created for the databases with one word from each of the two sets, presented in Table 1. Following a preparatory scan of the literature, the list of keywords has been created at the discretion of the authors with the objective of covering as many scientific works as possible dealing with Human-Aware Logistics and Manufacturing Systems.

* Only papers published in English are considered.

* All publication dates are considered up to 2022.

* (SC1) A category filter is applied on both databases to target the relevant papers. On Scopus, the search is limited to Computer Science and Decision Science categories. On Web of Science, the following categories are considered: Computer Science (Theory methods, artificial intelligence & interdisciplinary applications), Operations research and management science, Engineering Industrial, Management, Transportation, Transportation science technology & Mathematics interdisciplinary applications.

* (SC2) Only articles published in journals and book chapters are considered. Conference proceedings are excluded from this study in order to keep the size of the studied corpus manageable.

* (SC3) From the collected list of papers, duplicates are removed, and we only retain the works that satisfy the following three conditions based on their title, keywords, and abstract, in accordance with what is presented in Section 2.3:

1. The paper provides an optimization mathematical model, or an optimization solution method.

2. The paper explicitly considers Human-Aware Modeling in its title, abstract, or keywords. The mention of HF or social welfare is explicit. Moreover, these aspects are explicitly modeled.

3. The paper deals with logistics or manufacturing.

As a result, a total of 844 papers are retrieved after the application of (SC3).

* (SC4) After a thorough reading, only relevant papers are included. Studies dealing with skills and learning include a lot of papers, and we decided to exclude some of them. Even if the exclusion process is not reproducible, the following guidelines are applied for the paper selection:

1. Papers falling in the scope of the review and focusing their contribution on Human-Aware Modeling are systematically included. This ensures that every relevant assessment or
<figure><img src="image_2.png" /><figcaption>Fig. 1. Prisma flow diagram of the literature search and inclusion process.</figcaption></figure>

modeling approach found in the literature is addressed by
the present review.

2. Papers focusing their research contributions on the algorithmic side, and using a basic *ad hoc* HAM are more likely to be excluded. For example, when tackling the topic related to *skills*, the majority of papers use a simple constraint to impose the compatibility between tasks to schedule and workers that are allowed to perform them. Despite its vast use, this simple HAM presents a limited interest in the scope of this review, thus most of the papers proposing it are not included.

After applying (SC4), 504 papers are excluded. The final corpus thus includes 340 papers, which are studied and discussed in the current work.

Fig. 1 displays the flow of the selection process. The value of *n* represents the number of papers resulting from the corresponding search.

*Structure of the paper.* Sections 4–6 provide a presentation of the collected material, decomposed by field of application within logistics and manufacturing. Three main areas of application are identified: *logistics systems*, *manufacturing systems*, and *workforce-related problems* that could be applied in various contexts. Each section is then decomposed into specific subsections. Note that this structure aims at easing the reading, by decomposing the presentation of the collected material into sections of similar length. Note that we do not aim at introducing a consistent classification of the field. An inductive approach has been used for the classification: studies are clustered based on the similarity of the problem studied in terms of field of application, time horizon, main decision variables, and problem structure. Therefore an overlap is present among some sections, and some works could be classified into several categories. However, we decided to include each paper in a single section, where it seemed the most relevant. The taxonomy applied in different sections relies on previous literature studies when available, for example, the work of Lodree et al. (2009) for workforce scheduling problems.

3.2. *Summary tables: Format and convention*

The collected material is presented through summary tables in the next sections. To facilitate navigation, the tables' entries refer to the sections of both this paper and the second part (Prunet et al., 2024). The tables contain the following columns:

• *Reference:* The reference of the paper in the bibliography.

* Case study: This column indicates if the work is applied to a real-life case study.

* **Modeling:** This column specifies how the HAM used in the paper is integrated into the optimization model. The different options correspond to the subsections of Section 7, and include MO for true multi-objective, MO-He for a heterogeneous aggregation of several objective functions, MO-Ho for a homogeneous aggregation of several objectives, and SO for a single objective function. Concerning the constraints, CC is used for compatibility constraints, TC for threshold constraints, TWC for time window constraints, FSC for forbidden sequence constraints, and FBC for forward-backward constraints. Concerning the data, VTT designates a variable task time, and VQ a variable quality.

* **Heterogeneous workforce (HW):** This column is dedicated to the modeling of the workforce. More precisely, we check if the workforce is modeled heterogeneously or not, i.e., if different employees are modeled with different characteristics, or if they are all interchangeable. If the modeling is heterogeneous, this column specifies which parameter is a defining characteristic of an employee. The range of options includes the skills *S*, the learning rate *LR*, physical properties *PP*, cognitive and psychosocial properties *CPP*, and preferences *P*.

* **HAM:** This column indicates the quantitative model used in the paper to represent the considered human factor. The identified options correspond to the sections of the second part of this review (Prunet et al., 2024).
<figure><img src="image_3.png" /><figcaption>Fig. 1. Prisma flow diagram of the literature search and inclusion process.</figcaption></figure>

modeling approach found in the literature is addressed by
the present review.

2. Papers focusing their research contributions on the algorithmic side, and using a basic *ad hoc* HAM are more likely to be excluded. For example, when tackling the topic related to *skills*, the majority of papers use a simple constraint to impose the compatibility between tasks to schedule and workers that are allowed to perform them. Despite its vast use, this simple HAM presents a limited interest in the scope of this review, thus most of the papers proposing it are not included.

After applying (SC4), 504 papers are excluded. The final corpus thus includes 340 papers, which are studied and discussed in the current work.

Fig. 1 displays the flow of the selection process. The value of *n* represents the number of papers resulting from the corresponding search.

*Structure of the paper.* Sections 4–6 provide a presentation of the collected material, decomposed by field of application within logistics and manufacturing. Three main areas of application are identified: *logistics systems*, *manufacturing systems*, and *workforce-related problems* that could be applied in various contexts. Each section is then decomposed into specific subsections. Note that this structure aims at easing the reading, by decomposing the presentation of the collected material into sections of similar length. Note that we do not aim at introducing a consistent classification of the field. An inductive approach has been used for the classification: studies are clustered based on the similarity of the problem studied in terms of field of application, time horizon, main decision variables, and problem structure. Therefore an overlap is present among some sections, and some works could be classified into several categories. However, we decided to include each paper in a single section, where it seemed the most relevant. The taxonomy applied in different sections relies on previous literature studies when available, for example, the work of Lodree et al. (2009) for workforce scheduling problems.

3.2. *Summary tables: Format and convention*

The collected material is presented through summary tables in the next sections. To facilitate navigation, the tables' entries refer to the sections of both this paper and the second part (Prunet et al., 2024). The tables contain the following columns:

• *Reference:* The reference of the paper in the bibliography.

* Case study: This column indicates if the work is applied to a real-life case study.

* **Modeling:** This column specifies how the HAM used in the paper is integrated into the optimization model. The different options correspond to the subsections of Section 7, and include MO for true multi-objective, MO-He for a heterogeneous aggregation of several objective functions, MO-Ho for a homogeneous aggregation of several objectives, and SO for a single objective function. Concerning the constraints, CC is used for compatibility constraints, TC for threshold constraints, TWC for time window constraints, FSC for forbidden sequence constraints, and FBC for forward-backward constraints. Concerning the data, VTT designates a variable task time, and VQ a variable quality.

* **Heterogeneous workforce (HW):** This column is dedicated to the modeling of the workforce. More precisely, we check if the workforce is modeled heterogeneously or not, i.e., if different employees are modeled with different characteristics, or if they are all interchangeable. If the modeling is heterogeneous, this column specifies which parameter is a defining characteristic of an employee. The range of options includes the skills *S*, the learning rate *LR*, physical properties *PP*, cognitive and psychosocial properties *CPP*, and preferences *P*.

* **HAM:** This column indicates the quantitative model used in the paper to represent the considered human factor. The identified options correspond to the sections of the second part of this review (Prunet et al., 2024).
<table><caption>**Table 2**
Warehousing references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="3">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Marvel et al. (2001)</td><td>✓</td><td></td><td>CC</td><td></td><td></td><td>Handling</td></tr><tr><td>Hwang et al. (2003)</td><td></td><td>SO</td><td></td><td></td><td></td><td>Biomechanical</td></tr><tr><td>Grosse et al. (2013)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Grosse and Glock (2015)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Battini et al. (2016b)</td><td></td><td>MO</td><td></td><td></td><td></td><td>EE, RA</td></tr><tr><td>Calzavara et al. (2017)</td><td></td><td>MO</td><td></td><td></td><td></td><td>EE</td></tr><tr><td>Otto et al. (2017)</td><td></td><td>SO</td><td></td><td></td><td></td><td>Handling</td></tr><tr><td>Battini et al. (2017b)</td><td>✓</td><td></td><td></td><td></td><td>S</td><td>Posture, RA</td></tr><tr><td>Al-Araidah et al. (2017)</td><td></td><td></td><td></td><td></td><td></td><td>Visual, anthropometric</td></tr><tr><td>Larco et al. (2017)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Expert collaboration</td></tr><tr><td>Matusiak et al. (2017)</td><td>✓</td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Hong (2018)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Diefenbach and Glock (2019)</td><td></td><td>MO</td><td></td><td></td><td></td><td>EE</td></tr><tr><td>Glock et al. (2019a)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Biomechanical</td></tr><tr><td>Calzavara et al. (2019a)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>EE, posture</td></tr><tr><td>Zhang et al. (2019a)</td><td>✓</td><td></td><td></td><td>VTT</td><td>PP, LR</td><td>Skills, learning</td></tr><tr><td>Kudelska and Pawłowski (2020)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Implicit</td></tr><tr><td>Gajsek et al. (2021)</td><td>✓</td><td>MO-He</td><td></td><td></td><td></td><td>EE, posture</td></tr><tr><td>Feng and Hu (2021)</td><td>✓</td><td></td><td></td><td>VTT</td><td>S</td><td>Skills, fatigue effect</td></tr><tr><td>Gajšek et al. (2021)</td><td></td><td>MO</td><td></td><td></td><td></td><td>EE, posture</td></tr><tr><td>Kapou et al. (2022)</td><td>✓</td><td>MO-He</td><td>CC</td><td></td><td></td><td>Handling</td></tr><tr><td>Mou (2022)</td><td></td><td>MO</td><td></td><td>VTT</td><td>S</td><td>Skills, learning, equity</td></tr></tbody></table>

# 4. Logistics systems

## 4.1. Warehousing

Warehousing activities, and especially order picking, still heavily rely on manual labor (de Koster et al., 2007), and the work can be physically demanding. The integration of HFs into mathematical models has therefore gained attention from OR researchers on this topic, as presented in Table 2. In this context the most common HFs are the risk of WMSDs, employees learning, and fatigue. An interested reader is referred to Grosse et al. (2015b) and De Lombaert et al. (2022) for dedicated reviews on the topic.

**WMSD risk assessment.** An order picker is subject to various risk factors for WMSDs linked to the material handling activity, especially the frequent lifting of products (Otto et al., 2017; Kapou et al., 2022), and the awkward postures required to perform the picks, both for the hand/wrist and the entire body (Al-Araidah et al., 2017; Glock et al., 2019a; Calzavara et al., 2019a). Studies aim at mitigating this risk at different levels of decisions. First, regarding the design of the picking area layout, there is the possibility of rotating the pallets to enable easier access to the stored items (Glock et al., 2019a; Calzavara et al., 2019a) use the OWAS method to evaluate different situations. The optimization of the storage decisions also plays an important role in ER of the operators. Otto et al. (2017) integrate storage and zoning decisions to balance the ER among employees, and Kudelska and Pawłowski (2020) study the impact of storage decisions using simulation. The picker routing decisions are studied, for example, by Al-Araidah et al. (2017) with the goal of clustering the items so that the picker (on a vehicle) can safely pick several products.

**Learning.** Grosse et al. (2013) and Grosse and Glock (2015) study the impact of employee learning and forgetting on storage assignment and reassignment decisions in the warehouse. The topic has been applied to omni-channel supermarkets, where the order picking is integrated with batching or delivery decisions (Zhang et al., 2019a; Mou, 2022).

**Fatigue with energy expenditure.** Due to the variety of elementary tasks performed by a picker (e.g., walking, picking, pushing a trolley), a holistic HAM such as energy expenditure is suited to the context. Calzavara et al. (2017) and Calzavara et al. (2019a) use the energy expenditure in their models to integrate the choice of picking from a full pallet, or from half pallets on the floor and upper shelves, balancing efficiency and ER. This HAM is often considered when optimizing

the storage decisions, where an ergonomic objective is used on top of the classical picking efficiency optimization (Battini et al., 2016b; Diefenbach and Glock, 2019; Gajšek et al., 2021; Gajšek et al., 2021).

**Other HFs.** Larco et al. (2017) use a regression from a worker opinion survey on the discomfort of the picking operations in different situations as an input to their model, and Matusiak et al. (2017) conduct a regression analysis from historical data to determine the different skills and skill levels of the employees. Workload equity among pickers is also considered (Mou, 2022).

## 4.2. Vehicle routing

The Vehicle Routing Problem (VRP) and its extensions represent an important class of problems studied in the OR literature, where the aim is to assign a set of customer visits to vehicles while optimizing the total traveled distance. Table 3 presents the works on the VRP in the scope of this review. Two main HFs are studied in VRP: the fatigue of drivers, and the equity between them. The topic of drivers' fatigue is tackled either from a regulation perspective, with the *Hours of Service (HOS) regulations*, or with an approach focused on rest breaks.

**Fatigue with HOS regulations.** Recent regulations enforce the explicit scheduling of rest breaks in routing plans for logistics providers (see Prunet et al. (2024), Regulatory breaks). These HOS regulations lead to the development of VRP works on the topic. These works aim at optimizing a routing plan that is valid for classical VRP constraints (e.g., capacity, time windows), while respecting the HOS regulations on drivers working and driving times. The starting time and duration of the rest breaks are introduced as new decisions to be scheduled in the model. This makes the problem more challenging (see Section 7.2 on forward-backward constraints). HOS regulations have been rigorously introduced for the VRP by the seminal work of Goel (2009), although some earlier works deal with the breaks scheduling aspect via less sophisticated methods (Brandao and Mercer, 1997). Recent works on this problem may include additional considerations, such as driver well-being (Rancourt and Paquette, 2014; Khaitan et al., 2022), green objectives (Zarouk et al., 2022; Dukkanci et al., 2022) or real-life side constraints (Goel et al., 2021).

**Fatigue with rest breaks.** The scheduling of driver breaks has also been considered in the VRP without relying on actual regulation frameworks. A common consideration is the scheduling of a *meal break* in the routing plan, to enable drivers to get a full break during their shift. This HAM
<table><caption>**Table 2**
Warehousing references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="3">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Marvel et al. (2001)</td><td>✓</td><td></td><td>CC</td><td></td><td></td><td>Handling</td></tr><tr><td>Hwang et al. (2003)</td><td></td><td>SO</td><td></td><td></td><td></td><td>Biomechanical</td></tr><tr><td>Grosse et al. (2013)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Grosse and Glock (2015)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Battini et al. (2016b)</td><td></td><td>MO</td><td></td><td></td><td></td><td>EE, RA</td></tr><tr><td>Calzavara et al. (2017)</td><td></td><td>MO</td><td></td><td></td><td></td><td>EE</td></tr><tr><td>Otto et al. (2017)</td><td></td><td>SO</td><td></td><td></td><td></td><td>Handling</td></tr><tr><td>Battini et al. (2017b)</td><td>✓</td><td></td><td></td><td></td><td>S</td><td>Posture, RA</td></tr><tr><td>Al-Araidah et al. (2017)</td><td></td><td></td><td></td><td></td><td></td><td>Visual, anthropometric</td></tr><tr><td>Larco et al. (2017)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Expert collaboration</td></tr><tr><td>Matusiak et al. (2017)</td><td>✓</td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Hong (2018)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Diefenbach and Glock (2019)</td><td></td><td>MO</td><td></td><td></td><td></td><td>EE</td></tr><tr><td>Glock et al. (2019a)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Biomechanical</td></tr><tr><td>Calzavara et al. (2019a)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>EE, posture</td></tr><tr><td>Zhang et al. (2019a)</td><td>✓</td><td></td><td></td><td>VTT</td><td>PP, LR</td><td>Skills, learning</td></tr><tr><td>Kudelska and Pawłowski (2020)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Implicit</td></tr><tr><td>Gajsek et al. (2021)</td><td>✓</td><td>MO-He</td><td></td><td></td><td></td><td>EE, posture</td></tr><tr><td>Feng and Hu (2021)</td><td>✓</td><td></td><td></td><td>VTT</td><td>S</td><td>Skills, fatigue effect</td></tr><tr><td>Gajšek et al. (2021)</td><td></td><td>MO</td><td></td><td></td><td></td><td>EE, posture</td></tr><tr><td>Kapou et al. (2022)</td><td>✓</td><td>MO-He</td><td>CC</td><td></td><td></td><td>Handling</td></tr><tr><td>Mou (2022)</td><td></td><td>MO</td><td></td><td>VTT</td><td>S</td><td>Skills, learning, equity</td></tr></tbody></table>

# 4. Logistics systems

## 4.1. Warehousing

Warehousing activities, and especially order picking, still heavily rely on manual labor (de Koster et al., 2007), and the work can be physically demanding. The integration of HFs into mathematical models has therefore gained attention from OR researchers on this topic, as presented in Table 2. In this context the most common HFs are the risk of WMSDs, employees learning, and fatigue. An interested reader is referred to Grosse et al. (2015b) and De Lombaert et al. (2022) for dedicated reviews on the topic.

**WMSD risk assessment.** An order picker is subject to various risk factors for WMSDs linked to the material handling activity, especially the frequent lifting of products (Otto et al., 2017; Kapou et al., 2022), and the awkward postures required to perform the picks, both for the hand/wrist and the entire body (Al-Araidah et al., 2017; Glock et al., 2019a; Calzavara et al., 2019a). Studies aim at mitigating this risk at different levels of decisions. First, regarding the design of the picking area layout, there is the possibility of rotating the pallets to enable easier access to the stored items (Glock et al., 2019a; Calzavara et al., 2019a) use the OWAS method to evaluate different situations. The optimization of the storage decisions also plays an important role in ER of the operators. Otto et al. (2017) integrate storage and zoning decisions to balance the ER among employees, and Kudelska and Pawłowski (2020) study the impact of storage decisions using simulation. The picker routing decisions are studied, for example, by Al-Araidah et al. (2017) with the goal of clustering the items so that the picker (on a vehicle) can safely pick several products.

**Learning.** Grosse et al. (2013) and Grosse and Glock (2015) study the impact of employee learning and forgetting on storage assignment and reassignment decisions in the warehouse. The topic has been applied to omni-channel supermarkets, where the order picking is integrated with batching or delivery decisions (Zhang et al., 2019a; Mou, 2022).

**Fatigue with energy expenditure.** Due to the variety of elementary tasks performed by a picker (e.g., walking, picking, pushing a trolley), a holistic HAM such as energy expenditure is suited to the context. Calzavara et al. (2017) and Calzavara et al. (2019a) use the energy expenditure in their models to integrate the choice of picking from a full pallet, or from half pallets on the floor and upper shelves, balancing efficiency and ER. This HAM is often considered when optimizing

the storage decisions, where an ergonomic objective is used on top of the classical picking efficiency optimization (Battini et al., 2016b; Diefenbach and Glock, 2019; Gajšek et al., 2021; Gajšek et al., 2021).

**Other HFs.** Larco et al. (2017) use a regression from a worker opinion survey on the discomfort of the picking operations in different situations as an input to their model, and Matusiak et al. (2017) conduct a regression analysis from historical data to determine the different skills and skill levels of the employees. Workload equity among pickers is also considered (Mou, 2022).

## 4.2. Vehicle routing

The Vehicle Routing Problem (VRP) and its extensions represent an important class of problems studied in the OR literature, where the aim is to assign a set of customer visits to vehicles while optimizing the total traveled distance. Table 3 presents the works on the VRP in the scope of this review. Two main HFs are studied in VRP: the fatigue of drivers, and the equity between them. The topic of drivers' fatigue is tackled either from a regulation perspective, with the *Hours of Service (HOS) regulations*, or with an approach focused on rest breaks.

**Fatigue with HOS regulations.** Recent regulations enforce the explicit scheduling of rest breaks in routing plans for logistics providers (see Prunet et al. (2024), Regulatory breaks). These HOS regulations lead to the development of VRP works on the topic. These works aim at optimizing a routing plan that is valid for classical VRP constraints (e.g., capacity, time windows), while respecting the HOS regulations on drivers working and driving times. The starting time and duration of the rest breaks are introduced as new decisions to be scheduled in the model. This makes the problem more challenging (see Section 7.2 on forward-backward constraints). HOS regulations have been rigorously introduced for the VRP by the seminal work of Goel (2009), although some earlier works deal with the breaks scheduling aspect via less sophisticated methods (Brandao and Mercer, 1997). Recent works on this problem may include additional considerations, such as driver well-being (Rancourt and Paquette, 2014; Khaitan et al., 2022), green objectives (Zarouk et al., 2022; Dukkanci et al., 2022) or real-life side constraints (Goel et al., 2021).

**Fatigue with rest breaks.** The scheduling of driver breaks has also been considered in the VRP without relying on actual regulation frameworks. A common consideration is the scheduling of a *meal break* in the routing plan, to enable drivers to get a full break during their shift. This HAM
<table><caption>**Table 3**
Vehicle routing references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="2">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Brandao and Mercer (1997)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Kim et al. (2006)</td><td>✓</td><td>MO-He</td><td>TWC</td><td></td><td>Meal breaks, equity</td></tr><tr><td>Erera et al. (2008)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Goel (2009)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Ceselli et al. (2009)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Benjamin and Beasley (2010)</td><td></td><td></td><td>TC, TWC</td><td></td><td>Meal breaks</td></tr><tr><td>Kok et al. (2010b)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Kok et al. (2010a)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Prescott-Gagnon et al. (2010)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Wen et al. (2011)</td><td>✓</td><td></td><td>FBC</td><td>S</td><td>HOS regulations</td></tr><tr><td>Goel (2012)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Melton and Ingalls (2012)</td><td></td><td>MO-He</td><td></td><td></td><td>Psychosocial</td></tr><tr><td>Hollis and Green (2012)</td><td>✓</td><td>MO-He</td><td>TWC</td><td></td><td>Visual, meal breaks</td></tr><tr><td>Rancourt et al. (2013)</td><td></td><td></td><td>FBC</td><td></td><td>Regulation breaks, psychosocial</td></tr><tr><td>Rancourt and Paquette (2014)</td><td>✓</td><td>MO</td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Goel and Vidal (2014)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Rattanamanee et al. (2015)</td><td></td><td>SO</td><td>TC</td><td>PP</td><td>EE</td></tr><tr><td>El Hachemi et al. (2015)</td><td>✓</td><td></td><td>TWC</td><td></td><td>Meal breaks</td></tr><tr><td>Battini et al. (2015)</td><td>✓</td><td></td><td></td><td>LR</td><td>Learning</td></tr><tr><td>Min and Melachrinoudis (2016)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Coelho et al. (2016)</td><td></td><td></td><td>TWC</td><td></td><td>Meal breaks</td></tr><tr><td>Liu (2016)</td><td></td><td>MO-He</td><td></td><td></td><td>Equity</td></tr><tr><td>Bowden and Ragsdale (2018)</td><td></td><td></td><td>TC</td><td></td><td>HOS regulations</td></tr><tr><td>Mathlouthi et al. (2018)</td><td></td><td></td><td>CC, TWC</td><td>S</td><td>Skills, meal breaks</td></tr><tr><td>von Elmbach et al. (2019)</td><td></td><td>SO</td><td></td><td></td><td>Handling</td></tr><tr><td>Yan et al. (2019)</td><td></td><td></td><td></td><td>VTT</td><td>Skills, fatigue effect</td></tr><tr><td>Matl et al. (2019)</td><td></td><td>MO</td><td></td><td></td><td>Equity</td></tr><tr><td>Lehuédé et al. (2020)</td><td></td><td>MO</td><td></td><td></td><td>Equity</td></tr><tr><td>Kandakoglu et al. (2020)</td><td>✓</td><td>MO-He</td><td>CC, TWC</td><td>S</td><td>Meal break, equity, skills</td></tr><tr><td>Rabbani et al. (2020)</td><td></td><td>MO</td><td></td><td></td><td>Equity</td></tr><tr><td>Mayerle et al. (2020)</td><td></td><td></td><td>TWC, FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Anoshkina and Meisel (2020)</td><td></td><td>MO-He</td><td>CC</td><td>S</td><td>Skills, psychosocial</td></tr><tr><td>Ulmer et al. (2020)</td><td></td><td>MO</td><td></td><td>VTT</td><td>Learning</td></tr><tr><td>Vital and Hsieh (2021)</td><td></td><td></td><td>FBC</td><td>S, CPP</td><td>HOS regulations</td></tr><tr><td>Bakker et al. (2021)</td><td>✓</td><td></td><td></td><td></td><td>Learning</td></tr><tr><td>Haitam et al. (2021)</td><td></td><td></td><td>TWC</td><td></td><td>Meal breaks</td></tr><tr><td>Goel et al. (2021)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Zarouk et al. (2022)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Sartori et al. (2022)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>De Genaro Chiroli et al. (2022)</td><td></td><td></td><td>TWC, FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Fu and Ma (2022)</td><td>✓</td><td></td><td>TC</td><td></td><td>EE</td></tr><tr><td>Dukkanci et al. (2022)</td><td></td><td>MO</td><td></td><td></td><td>Equity</td></tr><tr><td>Eskandarzadeh and Fahimnia (2022)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Xu et al. (2022)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Khaitan et al. (2022)</td><td></td><td>MO</td><td>FBC</td><td></td><td>HOS regulations, satisfaction</td></tr><tr><td>Li et al. (2022)</td><td></td><td>MO</td><td></td><td></td><td>Equity</td></tr></tbody></table>

is often modeled with time window constraints, in which the break must be scheduled (Kim et al., 2006; Benjamin and Beasley, 2010; Coelho et al., 2016; Kandakoglu et al., 2020). Driver fatigue and rest breaks have also been considered with other HAMs that are worth mentioning. In Bowden and Ragsdale (2018) and Fu and Ma (2022), fatigue is modeled based on biomathematical approaches as a lack of alertness and increased sleepiness. Service times at customer locations are modeled as dependent on the fatigue level of the employee in Yan et al. (2019).

**Equity.** Workload equity has been a growing trend in VRP in the last years, focusing on the drivers' workload as it is reviewed in the present work, as well as a general balance of the available resources (Matl et al., 2018). In the corpus, an equity objective is often included in studies focusing on real-life applications, such as nurse visit routing and scheduling (Kandakoglu et al., 2020) or waste collection problems (Kim et al., 2006; Rabbani et al., 2020). From a more general perspective, Matl et al. (2019) compare different equity functions for the VRP, and assess the impact on the solution depending on which resource is balanced among drivers: number of visited customers, traveled distance, load handled, etc.

**Other HFs.** Additional topics of interest found in the VRP literature include the familiarity of drivers with the routes they are assigned

to, where the driving/processing times decrease if one driver is familiar with the itinerary and/or customer locations. This is modeled using either an exogenous parameter for each driver (Ulmer et al., 2020), or more dynamically with learning curves (Battini et al., 2015; Bakker et al., 2021). Anoshkina and Meisel (2020) study the intra-day and interday technician routing, accounting for skills and team consistency. Khaitan et al. (2022) account for the driver well-being, modeled by fuzzy reasoning based on natural language processing of the corresponding studies.

# 5. Manufacturing systems

## 5.1. Production scheduling

The general definition of production and machine scheduling is very broad (Chen et al., 1998), and can fit a large class of problems. In this section, we consider scheduling problems where the main decisions are the assignment and sequencing of a set of jobs on a set of machines. This differs from the other sections dealing with scheduling problems, where the main decision is the scheduling of human operators' activities. In this case, the HFs are indirectly accounted for in optimization models, since they are not intrinsically represented by the decision variables. Existing studies, presented in Table 4, mainly
<table><caption>**Table 3**
Vehicle routing references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="2">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Brandao and Mercer (1997)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Kim et al. (2006)</td><td>✓</td><td>MO-He</td><td>TWC</td><td></td><td>Meal breaks, equity</td></tr><tr><td>Erera et al. (2008)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Goel (2009)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Ceselli et al. (2009)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Benjamin and Beasley (2010)</td><td></td><td></td><td>TC, TWC</td><td></td><td>Meal breaks</td></tr><tr><td>Kok et al. (2010b)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Kok et al. (2010a)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Prescott-Gagnon et al. (2010)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Wen et al. (2011)</td><td>✓</td><td></td><td>FBC</td><td>S</td><td>HOS regulations</td></tr><tr><td>Goel (2012)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Melton and Ingalls (2012)</td><td></td><td>MO-He</td><td></td><td></td><td>Psychosocial</td></tr><tr><td>Hollis and Green (2012)</td><td>✓</td><td>MO-He</td><td>TWC</td><td></td><td>Visual, meal breaks</td></tr><tr><td>Rancourt et al. (2013)</td><td></td><td></td><td>FBC</td><td></td><td>Regulation breaks, psychosocial</td></tr><tr><td>Rancourt and Paquette (2014)</td><td>✓</td><td>MO</td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Goel and Vidal (2014)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Rattanamanee et al. (2015)</td><td></td><td>SO</td><td>TC</td><td>PP</td><td>EE</td></tr><tr><td>El Hachemi et al. (2015)</td><td>✓</td><td></td><td>TWC</td><td></td><td>Meal breaks</td></tr><tr><td>Battini et al. (2015)</td><td>✓</td><td></td><td></td><td>LR</td><td>Learning</td></tr><tr><td>Min and Melachrinoudis (2016)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Coelho et al. (2016)</td><td></td><td></td><td>TWC</td><td></td><td>Meal breaks</td></tr><tr><td>Liu (2016)</td><td></td><td>MO-He</td><td></td><td></td><td>Equity</td></tr><tr><td>Bowden and Ragsdale (2018)</td><td></td><td></td><td>TC</td><td></td><td>HOS regulations</td></tr><tr><td>Mathlouthi et al. (2018)</td><td></td><td></td><td>CC, TWC</td><td>S</td><td>Skills, meal breaks</td></tr><tr><td>von Elmbach et al. (2019)</td><td></td><td>SO</td><td></td><td></td><td>Handling</td></tr><tr><td>Yan et al. (2019)</td><td></td><td></td><td></td><td>VTT</td><td>Skills, fatigue effect</td></tr><tr><td>Matl et al. (2019)</td><td></td><td>MO</td><td></td><td></td><td>Equity</td></tr><tr><td>Lehuédé et al. (2020)</td><td></td><td>MO</td><td></td><td></td><td>Equity</td></tr><tr><td>Kandakoglu et al. (2020)</td><td>✓</td><td>MO-He</td><td>CC, TWC</td><td>S</td><td>Meal break, equity, skills</td></tr><tr><td>Rabbani et al. (2020)</td><td></td><td>MO</td><td></td><td></td><td>Equity</td></tr><tr><td>Mayerle et al. (2020)</td><td></td><td></td><td>TWC, FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Anoshkina and Meisel (2020)</td><td></td><td>MO-He</td><td>CC</td><td>S</td><td>Skills, psychosocial</td></tr><tr><td>Ulmer et al. (2020)</td><td></td><td>MO</td><td></td><td>VTT</td><td>Learning</td></tr><tr><td>Vital and Hsieh (2021)</td><td></td><td></td><td>FBC</td><td>S, CPP</td><td>HOS regulations</td></tr><tr><td>Bakker et al. (2021)</td><td>✓</td><td></td><td></td><td></td><td>Learning</td></tr><tr><td>Haitam et al. (2021)</td><td></td><td></td><td>TWC</td><td></td><td>Meal breaks</td></tr><tr><td>Goel et al. (2021)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Zarouk et al. (2022)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Sartori et al. (2022)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>De Genaro Chiroli et al. (2022)</td><td></td><td></td><td>TWC, FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Fu and Ma (2022)</td><td>✓</td><td></td><td>TC</td><td></td><td>EE</td></tr><tr><td>Dukkanci et al. (2022)</td><td></td><td>MO</td><td></td><td></td><td>Equity</td></tr><tr><td>Eskandarzadeh and Fahimnia (2022)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Xu et al. (2022)</td><td></td><td></td><td>FBC</td><td></td><td>HOS regulations</td></tr><tr><td>Khaitan et al. (2022)</td><td></td><td>MO</td><td>FBC</td><td></td><td>HOS regulations, satisfaction</td></tr><tr><td>Li et al. (2022)</td><td></td><td>MO</td><td></td><td></td><td>Equity</td></tr></tbody></table>

is often modeled with time window constraints, in which the break must be scheduled (Kim et al., 2006; Benjamin and Beasley, 2010; Coelho et al., 2016; Kandakoglu et al., 2020). Driver fatigue and rest breaks have also been considered with other HAMs that are worth mentioning. In Bowden and Ragsdale (2018) and Fu and Ma (2022), fatigue is modeled based on biomathematical approaches as a lack of alertness and increased sleepiness. Service times at customer locations are modeled as dependent on the fatigue level of the employee in Yan et al. (2019).

**Equity.** Workload equity has been a growing trend in VRP in the last years, focusing on the drivers' workload as it is reviewed in the present work, as well as a general balance of the available resources (Matl et al., 2018). In the corpus, an equity objective is often included in studies focusing on real-life applications, such as nurse visit routing and scheduling (Kandakoglu et al., 2020) or waste collection problems (Kim et al., 2006; Rabbani et al., 2020). From a more general perspective, Matl et al. (2019) compare different equity functions for the VRP, and assess the impact on the solution depending on which resource is balanced among drivers: number of visited customers, traveled distance, load handled, etc.

**Other HFs.** Additional topics of interest found in the VRP literature include the familiarity of drivers with the routes they are assigned

to, where the driving/processing times decrease if one driver is familiar with the itinerary and/or customer locations. This is modeled using either an exogenous parameter for each driver (Ulmer et al., 2020), or more dynamically with learning curves (Battini et al., 2015; Bakker et al., 2021). Anoshkina and Meisel (2020) study the intra-day and interday technician routing, accounting for skills and team consistency. Khaitan et al. (2022) account for the driver well-being, modeled by fuzzy reasoning based on natural language processing of the corresponding studies.

# 5. Manufacturing systems

## 5.1. Production scheduling

The general definition of production and machine scheduling is very broad (Chen et al., 1998), and can fit a large class of problems. In this section, we consider scheduling problems where the main decisions are the assignment and sequencing of a set of jobs on a set of machines. This differs from the other sections dealing with scheduling problems, where the main decision is the scheduling of human operators' activities. In this case, the HFs are indirectly accounted for in optimization models, since they are not intrinsically represented by the decision variables. Existing studies, presented in Table 4, mainly
<table><caption>**Table 4**
Production scheduling references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="2">Modeling</th><th rowspan="2">Param.</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th></tr></thead><tbody><tr><td>Biskup (1999)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Cheng and Wang (2000)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Mosheiov (2001)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Mosheiov and Sidney (2003)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Wang and Xia (2005)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Tang et al. (2006)</td><td>✓</td><td></td><td></td><td>VTT, VQ</td><td>S</td><td>Skills</td></tr><tr><td>Wang (2007)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Wu and Lee (2008)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Aravindkrishna et al. (2009)</td><td></td><td></td><td>FSC</td><td></td><td></td><td>Implicit</td></tr><tr><td>Lee and Wu (2009)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Eren (2009)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Lodree and Geiger (2010)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Anzanello and Fogliatto (2010)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Janiak and Rudek (2010)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Skills, learning</td></tr><tr><td>Pargar and Zandieh (2012)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Lee et al. (2012)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Nembhard and Bentefouet (2012)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Learning</td></tr><tr><td>Wang et al. (2013)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Skills</td></tr><tr><td>Zhang et al. (2013)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Costa et al. (2014)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Anzanello et al. (2014)</td><td>✓</td><td></td><td>TC</td><td>VTT</td><td></td><td>Learning, repetitive movements</td></tr><tr><td>Bautista et al. (2015)</td><td>✓</td><td></td><td></td><td>VTT</td><td></td><td>Learning, fatigue effect</td></tr><tr><td>Ji et al. (2015)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Ruiz-Torres et al. (2015)</td><td></td><td>MO</td><td>TC</td><td></td><td>P</td><td>Satisfaction</td></tr><tr><td>Amirian and Sahraeian (2015)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>He (2016)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Zhu et al. (2017)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Pei et al. (2017)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Gong et al. (2018)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Przybylski (2018)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Li et al. (2018b)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Lu et al. (2019)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Noise</td></tr><tr><td>Petronijevic et al. (2019)</td><td></td><td></td><td></td><td></td><td></td><td>Learning, LFFRM</td></tr><tr><td>Sanchez-Herrera et al. (2019)</td><td></td><td></td><td></td><td></td><td>S</td><td>Fatigue effect</td></tr><tr><td>Jamili (2019)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Sun et al. (2019)</td><td>✓</td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Wang et al. (2019)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Sheikhalishahi et al. (2019)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Human error</td></tr><tr><td>Ruiz-Torres et al. (2019)</td><td></td><td>MO-He</td><td></td><td></td><td>P</td><td>Satisfaction</td></tr><tr><td>Gong et al. (2020a)</td><td></td><td></td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Savino et al. (2020)</td><td></td><td></td><td>TC</td><td></td><td></td><td>Posture</td></tr><tr><td>Kaya et al. (2020)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Noise, vibration, posture</td></tr><tr><td>Şenyiğit et al. (2020)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning, repetitive movements</td></tr><tr><td>Fu et al. (2020)</td><td></td><td></td><td>MO</td><td></td><td></td><td>Noise</td></tr><tr><td>Gong et al. (2020b)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Marichelvam et al. (2020)</td><td>✓</td><td></td><td></td><td>VTT</td><td>S, LR, PP</td><td>Skills, learning</td></tr><tr><td>Wang et al. (2020)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect, motivation</td></tr><tr><td>Zhang et al. (2021)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills, learning</td></tr><tr><td>Berti et al. (2021)</td><td></td><td></td><td></td><td>VTT</td><td>S, PP</td><td>Skills, EE, RA</td></tr><tr><td>Chen et al. (2021)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Hongyu and Xiuli (2021)</td><td></td><td>MO</td><td>CC</td><td>VTT</td><td>S</td><td>Skills, whole body</td></tr><tr><td>Tan et al. (2021)</td><td>✓</td><td>MO</td><td>CC, TC</td><td></td><td>S, PP</td><td>Skills, EE</td></tr><tr><td>Snauwaert and Vanhoucke (2021)</td><td></td><td></td><td>CC</td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Rinaldi et al. (2022)</td><td>✓</td><td></td><td>TC</td><td>VTT</td><td>S</td><td>Skills, handling, posture</td></tr><tr><td>Zhang et al. (2022)</td><td>✓</td><td></td><td>TC</td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Peng et al. (2022)</td><td></td><td>MO</td><td></td><td>VTT</td><td></td><td>Learning, noise</td></tr><tr><td>Lou et al. (2022)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr></tbody></table>

focus on modeling learning, fatigue, or integrating perceptual HFs. An interested reader is referred to Biskup (2008) and Azzouz et al. (2018) for reviews dedicated to learning in machine scheduling.

**Learning.** The most common HAM found in the production scheduling literature is the organizational learning. The underlying idea is that the more similar tasks are repeated, the more *know-how* is acquired and the execution time decreases accordingly. One could argue that learning might not be determinant for production scheduling, given its short-term planning horizon. However, this effect has been widely accepted (Biskup, 2008). This topic has been extensively studied in the context of single machine scheduling (Biskup, 1999), parallel machine scheduling (Eren, 2009), or flow-shop scheduling (Wang and

Xia, 2005). In this context, processing times and/or setup times are sequence-dependent (Amirian and Sahraeian, 2015), or dependent on the sum of processing times of similar tasks already processed (Cheng and Wang, 2000). It is also common to suppose that the processing times depend on both the position and the sum of processing times for similar tasks already processed (Wu and Lee, 2008; Wang et al., 2019).

**Fatigue.** With a modeling technique similar to that of the organizational learning, the processing times of the tasks are affected by the fatigue level of the operators. In the scope of production scheduling, fatigue is often not modeled at the individual level of the operator, but as a general factor. The modeling approach uses the fatigue effect and rate-modifying activities (see Prunet et al. (2024)). In short, the
<table><caption>**Table 4**
Production scheduling references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="2">Modeling</th><th rowspan="2">Param.</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th></tr></thead><tbody><tr><td>Biskup (1999)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Cheng and Wang (2000)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Mosheiov (2001)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Mosheiov and Sidney (2003)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Wang and Xia (2005)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Tang et al. (2006)</td><td>✓</td><td></td><td></td><td>VTT, VQ</td><td>S</td><td>Skills</td></tr><tr><td>Wang (2007)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Wu and Lee (2008)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Aravindkrishna et al. (2009)</td><td></td><td></td><td>FSC</td><td></td><td></td><td>Implicit</td></tr><tr><td>Lee and Wu (2009)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Eren (2009)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Lodree and Geiger (2010)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Anzanello and Fogliatto (2010)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Janiak and Rudek (2010)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Skills, learning</td></tr><tr><td>Pargar and Zandieh (2012)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Lee et al. (2012)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Nembhard and Bentefouet (2012)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Learning</td></tr><tr><td>Wang et al. (2013)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Skills</td></tr><tr><td>Zhang et al. (2013)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Costa et al. (2014)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Anzanello et al. (2014)</td><td>✓</td><td></td><td>TC</td><td>VTT</td><td></td><td>Learning, repetitive movements</td></tr><tr><td>Bautista et al. (2015)</td><td>✓</td><td></td><td></td><td>VTT</td><td></td><td>Learning, fatigue effect</td></tr><tr><td>Ji et al. (2015)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Ruiz-Torres et al. (2015)</td><td></td><td>MO</td><td>TC</td><td></td><td>P</td><td>Satisfaction</td></tr><tr><td>Amirian and Sahraeian (2015)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>He (2016)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Zhu et al. (2017)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Pei et al. (2017)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Gong et al. (2018)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Przybylski (2018)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Li et al. (2018b)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Lu et al. (2019)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Noise</td></tr><tr><td>Petronijevic et al. (2019)</td><td></td><td></td><td></td><td></td><td></td><td>Learning, LFFRM</td></tr><tr><td>Sanchez-Herrera et al. (2019)</td><td></td><td></td><td></td><td></td><td>S</td><td>Fatigue effect</td></tr><tr><td>Jamili (2019)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Sun et al. (2019)</td><td>✓</td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Wang et al. (2019)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Sheikhalishahi et al. (2019)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Human error</td></tr><tr><td>Ruiz-Torres et al. (2019)</td><td></td><td>MO-He</td><td></td><td></td><td>P</td><td>Satisfaction</td></tr><tr><td>Gong et al. (2020a)</td><td></td><td></td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Savino et al. (2020)</td><td></td><td></td><td>TC</td><td></td><td></td><td>Posture</td></tr><tr><td>Kaya et al. (2020)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Noise, vibration, posture</td></tr><tr><td>Şenyiğit et al. (2020)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning, repetitive movements</td></tr><tr><td>Fu et al. (2020)</td><td></td><td></td><td>MO</td><td></td><td></td><td>Noise</td></tr><tr><td>Gong et al. (2020b)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Marichelvam et al. (2020)</td><td>✓</td><td></td><td></td><td>VTT</td><td>S, LR, PP</td><td>Skills, learning</td></tr><tr><td>Wang et al. (2020)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect, motivation</td></tr><tr><td>Zhang et al. (2021)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills, learning</td></tr><tr><td>Berti et al. (2021)</td><td></td><td></td><td></td><td>VTT</td><td>S, PP</td><td>Skills, EE, RA</td></tr><tr><td>Chen et al. (2021)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Hongyu and Xiuli (2021)</td><td></td><td>MO</td><td>CC</td><td></td><td>S</td><td>Skills, whole body</td></tr><tr><td>Tan et al. (2021)</td><td>✓</td><td>MO</td><td>CC, TC</td><td></td><td>S, PP</td><td>Skills, EE</td></tr><tr><td>Snauwaert and Vanhoucke (2021)</td><td></td><td></td><td>CC</td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Rinaldi et al. (2022)</td><td>✓</td><td></td><td>TC</td><td>VTT</td><td>S</td><td>Skills, handling, posture</td></tr><tr><td>Zhang et al. (2022)</td><td>✓</td><td></td><td>TC</td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Peng et al. (2022)</td><td></td><td>MO</td><td></td><td>VTT</td><td></td><td>Learning, noise</td></tr><tr><td>Lou et al. (2022)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr></tbody></table>

focus on modeling learning, fatigue, or integrating perceptual HFs. An interested reader is referred to Biskup (2008) and Azzouz et al. (2018) for reviews dedicated to learning in machine scheduling.

**Learning.** The most common HAM found in the production scheduling literature is the organizational learning. The underlying idea is that the more similar tasks are repeated, the more *know-how* is acquired and the execution time decreases accordingly. One could argue that learning might not be determinant for production scheduling, given its short-term planning horizon. However, this effect has been widely accepted (Biskup, 2008). This topic has been extensively studied in the context of single machine scheduling (Biskup, 1999), parallel machine scheduling (Eren, 2009), or flow-shop scheduling (Wang and

Xia, 2005). In this context, processing times and/or setup times are sequence-dependent (Amirian and Sahraeian, 2015), or dependent on the sum of processing times of similar tasks already processed (Cheng and Wang, 2000). It is also common to suppose that the processing times depend on both the position and the sum of processing times for similar tasks already processed (Wu and Lee, 2008; Wang et al., 2019).

**Fatigue.** With a modeling technique similar to that of the organizational learning, the processing times of the tasks are affected by the fatigue level of the operators. In the scope of production scheduling, fatigue is often not modeled at the individual level of the operator, but as a general factor. The modeling approach uses the fatigue effect and rate-modifying activities (see Prunet et al. (2024)). In short, the
integration of the fatigue effect into a model means that productivity decreases as time passes. This is often modeled with a linear decay function (Lodree and Geiger, 2010). When scheduled, rate-modifying activities (i.e., rest breaks) enable the recovery of the operators and restore the productivity to its maximum level (see, e.g., Zhu et al. (2017)). Analytical results on the scheduling problem with fatigue are provided by Lodree and Geiger (2010). In some studies, the deteriorating effect is modeled by a more sophisticated function, where adaptation improves productivity at the beginning of the work shift, and fatigue reduces it at the end (see, e.g., Bautista et al. (2015)).

**Perceptual factors.** In some studies, a perceptual risk factor is integrated into models via the addition of a dedicated objective function, for example, related to noise pollution (Lu et al., 2019), or dust pollution (Fu et al., 2020). Kaya et al. (2020) consider noise pollution, alongside with vibration exposure and posture.

**Other HFs.** The machine productivity may be affected by other factors than learning or fatigue, for example, skills (Wang et al., 2013; Costa et al., 2014), boredom (Wang et al., 2020), or rest breaks (Berti et al., 2021). Finally, Sheikhalishahi et al. (2019) study a production scheduling problem with human errors, and incorporate them into an optimization model.

## 5.2. Assembly line balancing

Assembly Line Balancing (ALB) represents a particular class of scheduling problems, which are of great importance in manufacturing systems. The goal of these problems is to assign a set of tasks to a set of workstations and to schedule them over a finite time horizon. Each task is defined by a (constant) processing time, and subject to precedence relations with other tasks. It is asked to minimize a given function related to the balance of the workload among all stations or to minimize the number of stations for a given cycle time. HFs have been extensively addressed while studying ALB. This is not surprising considering its nature. In fact, the usual objective function of these problems is already to balance the workload among workstations. In the classical literature, the workload is often expressed as a function of operation processing times, but it is not far-fetched to think of workload as a physical workload for human operators. Furthermore, assembly line balancing problems are highly combinatorial, and their instances often admit a large number of optimal solutions. In this case, it is natural to discriminate between these solutions using a second objective function. Table 5 presents the works on this research stream, which focuses on skills, WMSDs, and fatigue. An interested reader is referred to Otto and Battaia (2017) for a review dedicated to the balancing of the physical ER via ALB, and to Peltokorpi et al. (2014) for an integrated analysis on the relevant HFs for assembly lines.

**Skills.** The skill level of an operator may be modeled through compatibility constraints (see Section 7.2), where some assignments task/workstation are infeasible because the task at hand requires a specific skill set, that the employee operating this workstation does not possess (Koltai and Tatay, 2013; Manavizadeh et al., 2013). Another option is to consider employee skills in terms of their impact on the task duration (see Section 7.3.1). In this case, all assignments task/workstation are feasible, but the processing time is affected by the skill level of the operator (Samouei and Ashayeri, 2019; Polat et al., 2016; Zhang and Gen, 2011). In some works, the processing time depends on the physical properties of the operators (e.g., age, gender) instead of actual skills. For instance, Efe et al. (2018) use this HAM, where the numerical values are derived from a statistical regression from an empirical dataset.

**WMSD risk assessment.** The workload to be balanced in ALB is often considered in terms of ER, which may be modeled via WMSD risk assessment methods. The repetitiveness of the assembly work is, for instance, linked to the apparition of WMSDs (Occhipinti, 1998). The OCRA index is the most common HAM for this kind of risk, and is used in several studies that aim at balancing the ER, either alone (Zhang et al., 2020; Akyol and Baykasoglu, 2019; Tiacci and Mimmi, 2018), or jointly with other methods (Bautista et al., 2016b). An awkward posture is another major risk factor in assembly work and is commonly considered in the ALB literature. Different HAMs may be used to model the postural load in ALB, for instance, the OWAS (Cheshmehgaz et al., 2012), the RULA (Bautista et al., 2016b) or the REBA index (Bortolini et al., 2017). Manual handling is also a risk factor considered in ALB (Bautista et al., 2016b).

**Fatigue.** Energy expenditure, as a fatigue HAM, is often use to compute the ER in the ALB literature. Battini et al. (2016a) propose a method called the *predetermined motion energy system* to easily compute the energy expenditure in assembly work. This HAM may then be integrated into optimization models in various ways. For instance, Battini et al. (2016a) and Bautista et al. (2016a) use it as an objective function to balance. In Finco et al. (2020b) and Ostermeier (2020), the energy expenditure of an operator affects the task duration at the corresponding workstation. This might also be done indirectly with the integration of rest allowance (Finco et al., 2021). A maximal value on the accumulated energy expenditure may also be used to prevent an important workload imbalance (Battini et al., 2017a).

**Other HFs.** Similar to other scheduling problems, a learning effect may occur when processing similar tasks at a given workstation, for instance in Otto and Otto (2014) and Ostermeier (2020). Another interesting research stream focuses on human-robot collaboration in assembly line balancing, where the high-ER tasks are primarily assigned to robots, or operators equipped with exoskeletons (Dalle Mura and Dini, 2022; Weckenborg et al., 2022).

## 5.3. Production planning and inventory management

This section covers the optimization problems related to the planning of manufacturing activities at the tactical level. Production planning and inventory management are crucial leverage of performance in any manufacturing system (Jans and Degraeve, 2008). Table 6 presents the retrieved corpus on the topic, which mostly focuses on learning, human errors, and fatigue. An interested reader is referred to Jaber et al. (2022) for a review on the integration of learning curves in lot sizing models.

**Learning and forgetting.** This topic is by far the most studied in production planning. In the context of batch manufacturing, there can be a long time between the production of two similar batches, and a significant forgetting effect can occur during this period. It is seen as an increased setup cost, and in that case, it is natural to study the impact of learning and forgetting effects on the optimal batch size. The topic has received some attention in the early literature (Muth and Spremann, 1983; Smunt, 1987). Different forgetting functions have been studied to model this HF (Teyarachakul et al., 2011). In more recent studies, it is common to use more sophisticated learning models. For example, the learning and forgetting processes affect both the productivity and the quality of the production in Jeang and Rahim (2019) and Jaber and Bonney (2003). Kazemi et al. (2016a) account for both motor and cognitive learning. In Jaber and Peltokorpi (2020), the number of employees working in a team affects the learning process. From the perspective of inventory management, Kazemi et al. (2015) and Kazemi et al. (2016b) study learning in the Economic Order Quantity (EOQ) with empirical studies. They realized semi-structured interviews with industry experts to gain practical insights to design a more accurate learning curve for the EOQ model they develop. Zanoni et al. (2012) study the vendor-managed inventory problem with learning and forgetting curves.
integration of the fatigue effect into a model means that productivity decreases as time passes. This is often modeled with a linear decay function (Lodree and Geiger, 2010). When scheduled, rate-modifying activities (i.e., rest breaks) enable the recovery of the operators and restore the productivity to its maximum level (see, e.g., Zhu et al. (2017)). Analytical results on the scheduling problem with fatigue are provided by Lodree and Geiger (2010). In some studies, the deteriorating effect is modeled by a more sophisticated function, where adaptation improves productivity at the beginning of the work shift, and fatigue reduces it at the end (see, e.g., Bautista et al. (2015)).

**Perceptual factors.** In some studies, a perceptual risk factor is integrated into models via the addition of a dedicated objective function, for example, related to noise pollution (Lu et al., 2019), or dust pollution (Fu et al., 2020). Kaya et al. (2020) consider noise pollution, alongside with vibration exposure and posture.

**Other HFs.** The machine productivity may be affected by other factors than learning or fatigue, for example, skills (Wang et al., 2013; Costa et al., 2014), boredom (Wang et al., 2020), or rest breaks (Berti et al., 2021). Finally, Sheikhalishahi et al. (2019) study a production scheduling problem with human errors, and incorporate them into an optimization model.

## 5.2. Assembly line balancing

Assembly Line Balancing (ALB) represents a particular class of scheduling problems, which are of great importance in manufacturing systems. The goal of these problems is to assign a set of tasks to a set of workstations and to schedule them over a finite time horizon. Each task is defined by a (constant) processing time, and subject to precedence relations with other tasks. It is asked to minimize a given function related to the balance of the workload among all stations or to minimize the number of stations for a given cycle time. HFs have been extensively addressed while studying ALB. This is not surprising considering its nature. In fact, the usual objective function of these problems is already to balance the workload among workstations. In the classical literature, the workload is often expressed as a function of operation processing times, but it is not far-fetched to think of workload as a physical workload for human operators. Furthermore, assembly line balancing problems are highly combinatorial, and their instances often admit a large number of optimal solutions. In this case, it is natural to discriminate between these solutions using a second objective function. Table 5 presents the works on this research stream, which focuses on skills, WMSDs, and fatigue. An interested reader is referred to Otto and Battaia (2017) for a review dedicated to the balancing of the physical ER via ALB, and to Peltokorpi et al. (2014) for an integrated analysis on the relevant HFs for assembly lines.

**Skills.** The skill level of an operator may be modeled through compatibility constraints (see Section 7.2), where some assignments task/workstation are infeasible because the task at hand requires a specific skill set, that the employee operating this workstation does not possess (Koltai and Tatay, 2013; Manavizadeh et al., 2013). Another option is to consider employee skills in terms of their impact on the task duration (see Section 7.3.1). In this case, all assignments task/workstation are feasible, but the processing time is affected by the skill level of the operator (Samouei and Ashayeri, 2019; Polat et al., 2016; Zhang and Gen, 2011). In some works, the processing time depends on the physical properties of the operators (e.g., age, gender) instead of actual skills. For instance, Efe et al. (2018) use this HAM, where the numerical values are derived from a statistical regression from an empirical dataset.

**WMSD risk assessment.** The workload to be balanced in ALB is often considered in terms of ER, which may be modeled via WMSD risk assessment methods. The repetitiveness of the assembly work is, for instance, linked to the apparition of WMSDs (Occhipinti, 1998). The OCRA index is the most common HAM for this kind of risk, and is used in several studies that aim at balancing the ER, either alone (Zhang et al., 2020; Akyol and Baykasoglu, 2019; Tiacci and Mimmi, 2018), or jointly with other methods (Bautista et al., 2016b). An awkward posture is another major risk factor in assembly work and is commonly considered in the ALB literature. Different HAMs may be used to model the postural load in ALB, for instance, the OWAS (Cheshmehgaz et al., 2012), the RULA (Bautista et al., 2016b) or the REBA index (Bortolini et al., 2017). Manual handling is also a risk factor considered in ALB (Bautista et al., 2016b).

**Fatigue.** Energy expenditure, as a fatigue HAM, is often used to compute the ER in the ALB literature. Battini et al. (2016a) propose a method called the *predetermined motion energy system* to easily compute the energy expenditure in assembly work. This HAM may then be integrated into optimization models in various ways. For instance, Battini et al. (2016a) and Bautista et al. (2016a) use it as an objective function to balance. In Finco et al. (2020b) and Ostermeier (2020), the energy expenditure of an operator affects the task duration at the corresponding workstation. This might also be done indirectly with the integration of rest allowance (Finco et al., 2021). A maximal value on the accumulated energy expenditure may also be used to prevent an important workload imbalance (Battini et al., 2017a).

**Other HFs.** Similar to other scheduling problems, a learning effect may occur when processing similar tasks at a given workstation, for instance in Otto and Otto (2014) and Ostermeier (2020). Another interesting research stream focuses on human-robot collaboration in assembly line balancing, where the high-ER tasks are primarily assigned to robots, or operators equipped with exoskeletons (Dalle Mura and Dini, 2022; Weckenborg et al., 2022).

## 5.3. Production planning and inventory management

This section covers the optimization problems related to the planning of manufacturing activities at the tactical level. Production planning and inventory management are crucial leverage of performance in any manufacturing system (Jans and Degraeve, 2008). Table 6 presents the retrieved corpus on the topic, which mostly focuses on learning, human errors, and fatigue. An interested reader is referred to Jaber et al. (2022) for a review on the integration of learning curves in lot sizing models.

**Learning and forgetting.** This topic is by far the most studied in production planning. In the context of batch manufacturing, there can be a long time between the production of two similar batches, and a significant forgetting effect can occur during this period. It is seen as an increased setup cost, and in that case, it is natural to study the impact of learning and forgetting effects on the optimal batch size. The topic has received some attention in the early literature (Muth and Spremann, 1983; Smunt, 1987). Different forgetting functions have been studied to model this HF (Teyarachakul et al., 2011). In more recent studies, it is common to use more sophisticated learning models. For example, the learning and forgetting processes affect both the productivity and the quality of the production in Jeang and Rahim (2019) and Jaber and Bonney (2003). Kazemi et al. (2016a) account for both motor and cognitive learning. In Jaber and Peltokorpi (2020), the number of employees working in a team affects the learning process. From the perspective of inventory management, Kazemi et al. (2015) and Kazemi et al. (2016b) study learning in the Economic Order Quantity (EOQ) with empirical studies. They realized semi-structured interviews with industry experts to gain practical insights to design a more accurate learning curve for the EOQ model they develop. Zanoni et al. (2012) study the vendor-managed inventory problem with learning and forgetting curves.
<table><caption>**Table 5**
Assembly line balancing references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="3">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Doerr et al. (2000)</td><td></td><td></td><td>TC</td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Carnahan et al. (2001)</td><td></td><td>MO-He</td><td></td><td>VTT</td><td></td><td>Biomechanical</td></tr><tr><td>Chiang and Urban (2006)</td><td></td><td></td><td></td><td></td><td></td><td>Skills</td></tr><tr><td>Choi (2009)</td><td></td><td>MO-He</td><td></td><td></td><td></td><td>Implicit</td></tr><tr><td>Moon et al. (2009)</td><td></td><td>MO-Ho</td><td>CC</td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Corominas et al. (2010)</td><td></td><td></td><td></td><td></td><td>S</td><td>Skills</td></tr><tr><td>Otto and Scholl (2011)</td><td></td><td>MO-He</td><td>TC</td><td>VTT</td><td>S</td><td>Whole body</td></tr><tr><td>Zhang and Gen (2011)</td><td></td><td></td><td></td><td></td><td>S</td><td>Skills</td></tr><tr><td>Mutlu and Özgörmüş (2012)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>Implicit</td></tr><tr><td>Cheshmehgaz et al. (2012)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Posture</td></tr><tr><td>Xu et al. (2012)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>Biomechanical</td></tr><tr><td>Koltai and Tatay (2013)</td><td></td><td></td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Manavizadeh et al. (2013)</td><td></td><td></td><td>CC</td><td></td><td></td><td>Skills</td></tr><tr><td>Kara et al. (2014)</td><td></td><td>MO-Ho</td><td>TC, CC</td><td></td><td>S, PP</td><td>EE, cognitive, skills</td></tr><tr><td>Koltai et al. (2014)</td><td>✓</td><td></td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Otto and Otto (2014)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Sotskov et al. (2015)</td><td></td><td></td><td></td><td>VTT</td><td></td><td></td></tr><tr><td>Battini et al. (2016a)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>EE</td></tr><tr><td>Bautista et al. (2016b)</td><td>✓</td><td>MO-He</td><td>TC</td><td></td><td></td><td>Handling, posture, repetitive movements</td></tr><tr><td>Polat et al. (2016)</td><td>✓</td><td></td><td>CC</td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Bautista et al. (2016a)</td><td>✓</td><td>SO</td><td></td><td></td><td></td><td>Handling, posture, repetitive movements</td></tr><tr><td>Ritt et al. (2016)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Battini et al. (2017a)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>EE</td></tr><tr><td>Bortolini et al. (2017)</td><td>✓</td><td>MO</td><td></td><td>VTT</td><td></td><td>Fatigue effect, posture</td></tr><tr><td>Aroui et al. (2017)</td><td>✓</td><td>SO</td><td></td><td></td><td>S</td><td>Implicit</td></tr><tr><td>Sadeghi et al. (2018)</td><td>✓</td><td>MO-He</td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Alghazi and Kurz (2018)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>Implicit</td></tr><tr><td>Efe et al. (2018)</td><td>✓</td><td></td><td></td><td>VTT</td><td>S, PP</td><td>Skills</td></tr><tr><td>Tiacci and Mimmi (2018)</td><td></td><td>MO-He</td><td></td><td></td><td></td><td>Repetitive movements</td></tr><tr><td>Salehi et al. (2018)</td><td>✓</td><td>MO-He</td><td>CC</td><td>VTT, VQ</td><td>S</td><td>Skills, human errors</td></tr><tr><td>Akyol and Baykasoğlu (2019)</td><td></td><td></td><td></td><td></td><td>S</td><td>Repetitive movements</td></tr><tr><td>Samouei and Ashayeri (2019)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Akyol and Baykasoğlu (2019)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Zhang et al. (2020)</td><td></td><td>MO</td><td></td><td>VTT</td><td>S</td><td>Repetitive movements</td></tr><tr><td>Finco et al. (2020b)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>EE, RA</td></tr><tr><td>Ostermeier (2020)</td><td>✓</td><td></td><td></td><td>VTT</td><td></td><td>Learning, LFFRM</td></tr><tr><td>Finco et al. (2021)</td><td>✓</td><td></td><td></td><td>VTT</td><td>PP</td><td>EE, RA</td></tr><tr><td>Ozdemir et al. (2021)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Handling, posture, biomechanical</td></tr><tr><td>Mokhtarzadeh et al. (2021)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Handling, posture, repetitive movements</td></tr><tr><td>Weckenborg et al. (2022)</td><td></td><td>MO</td><td>CC, TC</td><td></td><td></td><td>Skills, EE</td></tr><tr><td>Stecke and Mokhtarzadeh (2022)</td><td></td><td>MO-He</td><td>FBC</td><td></td><td></td><td>EE</td></tr><tr><td>Campana et al. (2022)</td><td></td><td>MO-Ho</td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Chutima and Khotsaenlee (2022)</td><td></td><td>MO</td><td>TC</td><td></td><td>PP</td><td>EE, equity</td></tr><tr><td>Katiraee et al. (2022)</td><td>✓</td><td></td><td>CC</td><td>VTT</td><td>S, PP</td><td>Skills, fatigue</td></tr><tr><td>Yilmaz (2022)</td><td></td><td>MO</td><td>CC</td><td></td><td>S</td><td>Skills, equity</td></tr></tbody></table>

**Human errors.** The topic of human errors is actually studied extensively in inventory and supply chain management, considering that it is not a prevalent topic in other decision problems. Gilotra et al. (2020) study a 2-echelon supply chain with considerations on carbon emissions and human errors. In Shin et al. (2018), the human errors are integrated as an additional cost in the objective function for a 2-echelon supply chain model. Khan et al. (2012) and Khan et al. (2014) study a vendor-buyer supply chain model with learning occurring on the production side, and human errors in the quality inspection for the customer side.

**Fatigue.** Employee fatigue is indirectly accounted for in production planning via the computation of a Rest Allowance (RA). The RA models the appropriate break duration to integrate in a given planning, in order to keep the ER at a reasonable level. The RA may be computed based on energy expenditure (Battini et al., 2017c; Condeixa et al., 2020) or based on the heat exposure of the employees (Korkulu and Bona, 2021). The RA can then be expressed as a monetary cost, based on wages paid during rest times, and integrated into the objective function. Fatigue may also be accounted for in terms of productivity: for example Givi et al. (2015b) propose a model where productivity and quality depend on the learning and forgetting effects as well as fatigue and recovery.

**Other HFs.** Another interesting work on the EOQ has been done by Ryan et al. (2011) in the framework of a collaboration between operation researchers and ergonomists. An ergonomic field study is conducted on a road maintenance site to identify the most relevant HFs, which are then integrated into an EOQ model. Sobhani et al. (2019) study the effect of the working environment on the vendor buyer inventory model, modeled as health-states via a Markov chain.

## 5.4. Design of systems

In this section, we present research works dealing with system design in a broad sense. Several classes of problems are represented, sharing the common point of using an optimization method to design the inherent aspects (e.g., layout, processes) of a manufacturing system. Table 7 presents the corresponding studies, which focus mostly on fatigue, perceptual factors and skills and learning.

**Fatigue.** Several studies use the energy expenditure to account for the ER when designing processes and layouts. Zhang et al. (2018) aim at balancing this ER and the handling distance, by optimizing the batch size and the sequencing of operations. Al-Zuheri et al. (2013, 2016) study an assembly process with workers walking from one station to another. In Diefenbach et al. (2020), the material handling is performed using an electric vehicle, and energy expenditure measures the ER of the loading and unloading operations.
<table><caption>**Table 5**
Assembly line balancing references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="3">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Doerr et al. (2000)</td><td></td><td></td><td>TC</td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Carnahan et al. (2001)</td><td></td><td>MO-He</td><td></td><td>VTT</td><td></td><td>Biomechanical</td></tr><tr><td>Chiang and Urban (2006)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Skills</td></tr><tr><td>Choi (2009)</td><td></td><td>MO-He</td><td></td><td></td><td></td><td>Implicit</td></tr><tr><td>Moon et al. (2009)</td><td></td><td>MO-Ho</td><td>CC</td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Corominas et al. (2010)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Otto and Scholl (2011)</td><td></td><td>MO-He</td><td>TC</td><td>VTT</td><td></td><td>Whole body</td></tr><tr><td>Zhang and Gen (2011)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Mutlu and Özgörmüş (2012)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>Implicit</td></tr><tr><td>Cheshmehgaz et al. (2012)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Posture</td></tr><tr><td>Xu et al. (2012)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>Biomechanical</td></tr><tr><td>Koltai and Tatay (2013)</td><td></td><td></td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Manavizadeh et al. (2013)</td><td></td><td></td><td>CC</td><td></td><td></td><td>Skills</td></tr><tr><td>Kara et al. (2014)</td><td></td><td>MO-Ho</td><td>TC, CC</td><td></td><td>S, PP</td><td>EE, cognitive, skills</td></tr><tr><td>Koltai et al. (2014)</td><td>✓</td><td></td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Otto and Otto (2014)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Sotskov et al. (2015)</td><td></td><td></td><td></td><td>VTT</td><td></td><td></td></tr><tr><td>Battini et al. (2016a)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>EE</td></tr><tr><td>Bautista et al. (2016b)</td><td>✓</td><td>MO-He</td><td>TC</td><td></td><td></td><td>Handling, posture, repetitive movements</td></tr><tr><td>Polat et al. (2016)</td><td>✓</td><td></td><td>CC</td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Bautista et al. (2016a)</td><td>✓</td><td>SO</td><td></td><td></td><td></td><td>Handling, posture, repetitive movements</td></tr><tr><td>Ritt et al. (2016)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Battini et al. (2017a)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>EE</td></tr><tr><td>Bortolini et al. (2017)</td><td>✓</td><td>MO</td><td></td><td>VTT</td><td></td><td>Fatigue effect, posture</td></tr><tr><td>Aroui et al. (2017)</td><td>✓</td><td>SO</td><td></td><td></td><td>S</td><td>Implicit</td></tr><tr><td>Sadeghi et al. (2018)</td><td>✓</td><td>MO-He</td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Alghazi and Kurz (2018)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>Implicit</td></tr><tr><td>Efe et al. (2018)</td><td>✓</td><td></td><td></td><td>VTT</td><td>S, PP</td><td>Skills</td></tr><tr><td>Tiacci and Mimmi (2018)</td><td></td><td>MO-He</td><td></td><td></td><td></td><td>Repetitive movements</td></tr><tr><td>Salehi et al. (2018)</td><td>✓</td><td>MO-He</td><td>CC</td><td>VTT, VQ</td><td>S</td><td>Skills, human errors</td></tr><tr><td>Akyol and Baykasoğlu (2019)</td><td></td><td></td><td></td><td></td><td>S</td><td>Repetitive movements</td></tr><tr><td>Samouei and Ashayeri (2019)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Akyol and Baykasoğlu (2019)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Zhang et al. (2020)</td><td></td><td>MO</td><td></td><td>VTT</td><td>S</td><td>Repetitive movements</td></tr><tr><td>Finco et al. (2020b)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>EE, RA</td></tr><tr><td>Ostermeier (2020)</td><td>✓</td><td></td><td></td><td>VTT</td><td></td><td>Learning, LFFRM</td></tr><tr><td>Finco et al. (2021)</td><td>✓</td><td></td><td></td><td>VTT</td><td>PP</td><td>EE, RA</td></tr><tr><td>Ozdemir et al. (2021)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Handling, posture, biomechanical</td></tr><tr><td>Mokhtarzadeh et al. (2021)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Handling, posture, repetitive movements</td></tr><tr><td>Weckenborg et al. (2022)</td><td></td><td>MO</td><td>CC, TC</td><td></td><td></td><td>Skills, EE</td></tr><tr><td>Stecke and Mokhtarzadeh (2022)</td><td></td><td>MO-He</td><td>FBC</td><td></td><td></td><td>EE</td></tr><tr><td>Campana et al. (2022)</td><td></td><td>MO-Ho</td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Chutima and Khotsaenlee (2022)</td><td></td><td>MO</td><td>TC</td><td></td><td>PP</td><td>EE, equity</td></tr><tr><td>Katiraee et al. (2022)</td><td>✓</td><td></td><td>CC</td><td>VTT</td><td>S, PP</td><td>Skills, fatigue</td></tr><tr><td>Yilmaz (2022)</td><td></td><td>MO</td><td>CC</td><td></td><td>S</td><td>Skills, equity</td></tr></tbody></table>

**Human errors.** The topic of human errors is actually studied extensively in inventory and supply chain management, considering that it is not a prevalent topic in other decision problems. Gilotra et al. (2020) study a 2-echelon supply chain with considerations on carbon emissions and human errors. In Shin et al. (2018), the human errors are integrated as an additional cost in the objective function for a 2-echelon supply chain model. Khan et al. (2012) and Khan et al. (2014) study a vendor-buyer supply chain model with learning occurring on the production side, and human errors in the quality inspection for the customer side.

**Fatigue.** Employee fatigue is indirectly accounted for in production planning via the computation of a Rest Allowance (RA). The RA models the appropriate break duration to integrate in a given planning, in order to keep the ER at a reasonable level. The RA may be computed based on energy expenditure (Battini et al., 2017c; Condeixa et al., 2020) or based on the heat exposure of the employees (Korkulu and Bona, 2021). The RA can then be expressed as a monetary cost, based on wages paid during rest times, and integrated into the objective function. Fatigue may also be accounted for in terms of productivity: for example Givi et al. (2015b) propose a model where productivity and quality depend on the learning and forgetting effects as well as fatigue and recovery.

**Other HFs.** Another interesting work on the EOQ has been done by Ryan et al. (2011) in the framework of a collaboration between operation researchers and ergonomists. An ergonomic field study is conducted on a road maintenance site to identify the most relevant HFs, which are then integrated into an EOQ model. Sobhani et al. (2019) study the effect of the working environment on the vendor buyer inventory model, modeled as health-states via a Markov chain.

## 5.4. Design of systems

In this section, we present research works dealing with system design in a broad sense. Several classes of problems are represented, sharing the common point of using an optimization method to design the inherent aspects (e.g., layout, processes) of a manufacturing system. Table 7 presents the corresponding studies, which focus mostly on fatigue, perceptual factors and skills and learning.

**Fatigue.** Several studies use the energy expenditure to account for the ER when designing processes and layouts. Zhang et al. (2018) aim at balancing this ER and the handling distance, by optimizing the batch size and the sequencing of operations. Al-Zuheri et al. (2013, 2016) study an assembly process with workers walking from one station to another. In Diefenbach et al. (2020), the material handling is performed using an electric vehicle, and energy expenditure measures the ER of the loading and unloading operations.
<table><caption>**Table 6**
Production planning references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="3">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Muth and Spremann (1983)</td><td></td><td></td><td></td><td></td><td></td><td>Learning</td></tr><tr><td>Smunt (1987)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Elmaghraby (1990)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Anderson and Parker (2002)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Jaber and Bonney (2003)</td><td></td><td></td><td></td><td>VTT, VQ</td><td></td><td>Learning, human errors</td></tr><tr><td>Ryan et al. (2011)</td><td>✓</td><td></td><td></td><td></td><td></td><td>Expert collaboration</td></tr><tr><td>Teyarachakul et al. (2011)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Khan et al. (2012)</td><td></td><td></td><td></td><td></td><td></td><td>Learning, human errors</td></tr><tr><td>Huang et al. (2012)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Learning</td></tr><tr><td>Zanoni et al. (2012)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Khan et al. (2014)</td><td></td><td></td><td></td><td></td><td></td><td>Learning, human errors</td></tr><tr><td>Givi et al. (2015b)</td><td></td><td>MO-Ho</td><td></td><td>VTT, VQ</td><td></td><td>Learning, LFFRM, human errors</td></tr><tr><td>Kazemi et al. (2015)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Andriolo et al. (2016)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Handling</td></tr><tr><td>Kazemi et al. (2016a)</td><td></td><td></td><td></td><td></td><td></td><td>Learning</td></tr><tr><td>Kazemi et al. (2016b)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning, expert collaboration</td></tr><tr><td>Khanna et al. (2017)</td><td></td><td></td><td></td><td>VQ</td><td></td><td>Human error</td></tr><tr><td>Battini et al. (2017c)</td><td></td><td>MO-Ho</td><td></td><td></td><td></td><td>EE, RA</td></tr><tr><td>Mokhtari and Hasani (2017)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Noise</td></tr><tr><td>Shin et al. (2018)</td><td></td><td>MO-Ho</td><td></td><td></td><td></td><td>Human error</td></tr><tr><td>Sobhani et al. (2019)</td><td>✓</td><td></td><td></td><td></td><td></td><td>Health state</td></tr><tr><td>Jeang and Rahim (2019)</td><td></td><td></td><td></td><td>VTT, VQ</td><td></td><td>Learning</td></tr><tr><td>Condeixa et al. (2020)</td><td></td><td>MO-Ho</td><td></td><td></td><td></td><td>EE, RA</td></tr><tr><td>Cui et al. (2020)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Total cost function</td></tr><tr><td>Gilotra et al. (2020)</td><td></td><td></td><td></td><td></td><td></td><td>Human errors</td></tr><tr><td>Jaber and Peltokorpi (2020)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Tiwari et al. (2020)</td><td></td><td></td><td></td><td>VQ</td><td></td><td>Errors</td></tr><tr><td>Cai et al. (2020)</td><td>✓</td><td></td><td>TC</td><td>VTT</td><td></td><td>EE, RA, handling</td></tr><tr><td>Korkulu and Bona (2021)</td><td></td><td>MO-Ho</td><td></td><td></td><td></td><td>EE, RA, heat</td></tr><tr><td>Fu et al. (2022)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Asadkhani et al. (2022)</td><td></td><td></td><td></td><td>VQ</td><td></td><td>Learning, errors</td></tr></tbody></table>

<table><caption>**Table 7**
System design references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="3">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Braun et al. (1996)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Biomechanical</td></tr><tr><td>Celano et al. (2004)</td><td></td><td></td><td></td><td></td><td></td><td>Psychosocial</td></tr><tr><td>Hopp et al. (2004)</td><td></td><td></td><td></td><td></td><td>S</td><td>Skills</td></tr><tr><td>Al-Zuheri et al. (2013)</td><td></td><td>MO</td><td></td><td></td><td>S, PP</td><td>EE, skills</td></tr><tr><td>Bukchin and Cohen (2013)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills, learning</td></tr><tr><td>Razavi et al. (2014)</td><td>✓</td><td>MO-Ho</td><td>TC</td><td></td><td></td><td>Noise</td></tr><tr><td>Al-Zuheri et al. (2016)</td><td>✓</td><td>MO</td><td>TC</td><td></td><td></td><td>EE</td></tr><tr><td>Botti et al. (2017)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>Repetitive movements</td></tr><tr><td>Antonio Diego-Mas et al. (2017)</td><td>✓</td><td>MO-He</td><td></td><td></td><td></td><td>Biomechanical</td></tr><tr><td>Hu and Chen (2017)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Olivella and Nembhard (2017)</td><td></td><td>SO</td><td></td><td></td><td>S</td><td>Skills</td></tr><tr><td>Li et al. (2018a)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Cognitive, biomechanical</td></tr><tr><td>Zhang et al. (2018)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>EE</td></tr><tr><td>Pistolesi and Lazzerini (2019)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Equity, visual</td></tr><tr><td>Glock et al. (2019c)</td><td>✓</td><td>MO-Ho</td><td>TC</td><td></td><td></td><td>LFFRM, biomechanical</td></tr><tr><td>Diefenbach et al. (2020)</td><td></td><td>SO</td><td></td><td></td><td></td><td>EE</td></tr><tr><td>Finco et al. (2020a)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Vibrations</td></tr><tr><td>Mateo et al. (2020)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>Handling, anthropometric</td></tr><tr><td>Bortolini et al. (2021)</td><td></td><td>MO</td><td>TC</td><td></td><td></td><td>Repetitive movements</td></tr><tr><td>Fu et al. (2022)</td><td>✓</td><td>MO-Ho</td><td></td><td></td><td></td><td>Fatigue, RA</td></tr><tr><td>Liau and Ryu (2022)</td><td></td><td>MO</td><td></td><td></td><td>S</td><td>Skills, posture</td></tr></tbody></table>

**Perceptual factors.** Finco et al. (2020a) and Razavi et al. (2014) study the design of an assembly line system, with the objective of minimizing the vibration (resp. noise) exposure of the operators. In both problems, several types of equipment are available to mitigate the exposure, either at the source or at the individual level. The cost of the system is balanced with the worker exposure. Considering visual factors, Pistolesi and Lazzerini (2019) study a disassembly line, where several operators work simultaneously on the product to disassemble. The main issue is to organize the operations so that workers are able to work simultaneously on different faces of the product.

**Skills and learning.** In several cases, it is the overall organization of the workforce that is designed. For example, the cross-training strategy is designed to improve the workforce flexibility in the works of Hopp et al. (2004) and Olivella and Nembhard (2017). A work-sharing strategy is designed by Bukchin and Cohen (2013), where new employees share a part of their workload during their training time.

**Other HFs.** In Botti et al. (2017) and Hu and Chen (2017), the problem is to determine if each process should be manual or automated, depending on its characteristics. Li et al. (2018a) study a facility layout problem, which integrates the physical and mental ER of employees.
<table><caption>**Table 6**
Production planning references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="3">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Muth and Spremann (1983)</td><td></td><td></td><td></td><td></td><td></td><td>Learning</td></tr><tr><td>Smunt (1987)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Elmaghraby (1990)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Anderson and Parker (2002)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Jaber and Bonney (2003)</td><td></td><td></td><td></td><td>VTT, VQ</td><td></td><td>Learning, human errors</td></tr><tr><td>Ryan et al. (2011)</td><td>✓</td><td></td><td></td><td></td><td></td><td>Expert collaboration</td></tr><tr><td>Teyarachakul et al. (2011)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Khan et al. (2012)</td><td></td><td></td><td></td><td></td><td></td><td>Learning, human errors</td></tr><tr><td>Huang et al. (2012)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Learning</td></tr><tr><td>Zanoni et al. (2012)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Khan et al. (2014)</td><td></td><td></td><td></td><td></td><td></td><td>Learning, human errors</td></tr><tr><td>Givi et al. (2015b)</td><td></td><td>MO-Ho</td><td></td><td>VTT, VQ</td><td></td><td>Learning, LFFRM, human errors</td></tr><tr><td>Kazemi et al. (2015)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Andriolo et al. (2016)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Handling</td></tr><tr><td>Kazemi et al. (2016a)</td><td></td><td></td><td></td><td></td><td></td><td>Learning</td></tr><tr><td>Kazemi et al. (2016b)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning, expert collaboration</td></tr><tr><td>Khanna et al. (2017)</td><td></td><td></td><td></td><td>VQ</td><td></td><td>Human error</td></tr><tr><td>Battini et al. (2017c)</td><td></td><td>MO-Ho</td><td></td><td></td><td></td><td>EE, RA</td></tr><tr><td>Mokhtari and Hasani (2017)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Noise</td></tr><tr><td>Shin et al. (2018)</td><td></td><td>MO-Ho</td><td></td><td></td><td></td><td>Human error</td></tr><tr><td>Sobhani et al. (2019)</td><td>✓</td><td></td><td></td><td></td><td></td><td>Health state</td></tr><tr><td>Jeang and Rahim (2019)</td><td></td><td></td><td></td><td>VTT, VQ</td><td></td><td>Learning</td></tr><tr><td>Condeixa et al. (2020)</td><td></td><td>MO-Ho</td><td></td><td></td><td></td><td>EE, RA</td></tr><tr><td>Cui et al. (2020)</td><td></td><td>MO</td><td></td><td></td><td></td><td>Total cost function</td></tr><tr><td>Gilotra et al. (2020)</td><td></td><td></td><td></td><td></td><td></td><td>Human errors</td></tr><tr><td>Jaber and Peltokorpi (2020)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Tiwari et al. (2020)</td><td></td><td></td><td></td><td>VQ</td><td></td><td>Errors</td></tr><tr><td>Cai et al. (2020)</td><td>✓</td><td></td><td>TC</td><td>VTT</td><td></td><td>EE, RA, handling</td></tr><tr><td>Korkulu and Bona (2021)</td><td></td><td>MO-Ho</td><td></td><td></td><td></td><td>EE, RA, heat</td></tr><tr><td>Fu et al. (2022)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Asadkhani et al. (2022)</td><td></td><td></td><td></td><td>VQ</td><td></td><td>Learning, errors</td></tr></tbody></table>

<table><caption>**Table 7**
System design references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="3">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Braun et al. (1996)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Biomechanical</td></tr><tr><td>Celano et al. (2004)</td><td></td><td></td><td></td><td></td><td></td><td>Psychosocial</td></tr><tr><td>Hopp et al. (2004)</td><td></td><td></td><td></td><td></td><td>S</td><td>Skills</td></tr><tr><td>Al-Zuheri et al. (2013)</td><td></td><td>MO</td><td></td><td></td><td>S, PP</td><td>EE, skills</td></tr><tr><td>Bukchin and Cohen (2013)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills, learning</td></tr><tr><td>Razavi et al. (2014)</td><td>✓</td><td>MO-Ho</td><td>TC</td><td></td><td></td><td>Noise</td></tr><tr><td>Al-Zuheri et al. (2016)</td><td>✓</td><td>MO</td><td>TC</td><td></td><td></td><td>EE</td></tr><tr><td>Botti et al. (2017)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>Repetitive movements</td></tr><tr><td>Antonio Diego-Mas et al. (2017)</td><td>✓</td><td>MO-He</td><td></td><td></td><td></td><td>Biomechanical</td></tr><tr><td>Hu and Chen (2017)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Olivella and Nembhard (2017)</td><td></td><td>SO</td><td></td><td></td><td>S</td><td>Skills</td></tr><tr><td>Li et al. (2018a)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Cognitive, biomechanical</td></tr><tr><td>Zhang et al. (2018)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>EE</td></tr><tr><td>Pistolesi and Lazzerini (2019)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Equity, visual</td></tr><tr><td>Glock et al. (2019c)</td><td>✓</td><td>MO-Ho</td><td>TC</td><td></td><td></td><td>LFFRM, biomechanical</td></tr><tr><td>Diefenbach et al. (2020)</td><td></td><td>SO</td><td></td><td></td><td></td><td>EE</td></tr><tr><td>Finco et al. (2020a)</td><td>✓</td><td>MO</td><td></td><td></td><td></td><td>Vibrations</td></tr><tr><td>Mateo et al. (2020)</td><td>✓</td><td></td><td>TC</td><td></td><td></td><td>Handling, anthropometric</td></tr><tr><td>Bortolini et al. (2021)</td><td></td><td>MO</td><td>TC</td><td></td><td></td><td>Repetitive movements</td></tr><tr><td>Fu et al. (2022)</td><td>✓</td><td>MO-Ho</td><td></td><td></td><td></td><td>Fatigue, RA</td></tr><tr><td>Liau and Ryu (2022)</td><td></td><td>MO</td><td></td><td></td><td>S</td><td>Skills, posture</td></tr></tbody></table>

**Perceptual factors.** Finco et al. (2020a) and Razavi et al. (2014) study the design of an assembly line system, with the objective of minimizing the vibration (resp. noise) exposure of the operators. In both problems, several types of equipment are available to mitigate the exposure, either at the source or at the individual level. The cost of the system is balanced with the worker exposure. Considering visual factors, Pistolesi and Lazzerini (2019) study a disassembly line, where several operators work simultaneously on the product to disassemble. The main issue is to organize the operations so that workers are able to work simultaneously on different faces of the product.

**Skills and learning.** In several cases, it is the overall organization of the workforce that is designed. For example, the cross-training strategy is designed to improve the workforce flexibility in the works of Hopp et al. (2004) and Olivella and Nembhard (2017). A work-sharing strategy is designed by Bukchin and Cohen (2013), where new employees share a part of their workload during their training time.

**Other HFs.** In Botti et al. (2017) and Hu and Chen (2017), the problem is to determine if each process should be manual or automated, depending on its characteristics. Li et al. (2018a) study a facility layout problem, which integrates the physical and mental ER of employees.
<table><caption>**Table 8**
Job rotation references (see Section 3.2 for the table legend).</caption><thead><tr><th rowspan="2">Reference</th><th rowspan="2">Case study</th><th colspan="2">Modeling</th><th rowspan="2">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Villeda and Dean (1990)</td><td></td><td></td><td>TC</td><td></td><td>Hazard exposure</td></tr><tr><td>Carnahan et al. (2000)</td><td></td><td>SO</td><td></td><td>PP</td><td>Handling</td></tr><tr><td>Tharmmaphornphilas and Norman (2004)</td><td>✓</td><td>SO</td><td></td><td>PP</td><td>Handling, noise</td></tr><tr><td>Bhadury and Radovilsky (2006)</td><td></td><td>MO</td><td></td><td></td><td>Motivation</td></tr><tr><td>Tharmmaphornphilas and Norman (2007)</td><td></td><td>SO</td><td></td><td>PP</td><td>Handling</td></tr><tr><td>Asawarungsaengkul and Nanthavanij (2008)</td><td></td><td></td><td>TC</td><td></td><td>Noise</td></tr><tr><td>Diego-Mas et al. (2009)</td><td></td><td>MO-He</td><td></td><td>PP, CPP</td><td>Biomechanical</td></tr><tr><td>Aryanezhad et al. (2009b)</td><td></td><td>MO-He</td><td>CC, TC</td><td>S, PP</td><td>Skills, noise</td></tr><tr><td>Nanthavanij et al. (2010)</td><td></td><td>SO</td><td>TC</td><td>VTT</td><td>Skills, hazard exposure</td></tr><tr><td>Azizi et al. (2010)</td><td></td><td>SO</td><td></td><td>VTT</td><td>Skills, motivation</td></tr><tr><td>Asensio-Cuesta et al. (2012b)</td><td>✓</td><td>MO-He</td><td></td><td></td><td>Repetitive movements</td></tr><tr><td>Asensio-Cuesta et al. (2012a)</td><td></td><td>MO-He</td><td>CC</td><td>S, PP, CPP</td><td>Skills, whole body</td></tr><tr><td>Otto and Scholl (2013)</td><td>✓</td><td>SO</td><td></td><td></td><td>Whole body</td></tr><tr><td>Huang and Pan (2014)</td><td>✓</td><td>SO</td><td></td><td></td><td>Anthropometric</td></tr><tr><td>Mossa et al. (2016)</td><td>✓</td><td></td><td>TC</td><td>VTT</td><td>Skills, repetitive movements</td></tr><tr><td>Yoon et al. (2016)</td><td>✓</td><td>SO</td><td>FSC</td><td>VTT</td><td>Posture</td></tr><tr><td>Wongwien and Nanthavanij (2017)</td><td></td><td></td><td>CC, TC</td><td>VTT</td><td>Skills, hazard exposure</td></tr><tr><td>Pata and Moura (2018)</td><td></td><td>SO</td><td>CC</td><td>PP, CPP</td><td>Implicit</td></tr><tr><td>Gebennini et al. (2018)</td><td>✓</td><td>MO</td><td>TC</td><td>PP</td><td>Handling, EE</td></tr><tr><td>Hochdörffer et al. (2018)</td><td>✓</td><td>MO-He</td><td>CC</td><td>S</td><td>Skills, whole body</td></tr><tr><td>Moussavi et al. (2019)</td><td>✓</td><td>SO</td><td>FSC</td><td></td><td>Biomechanical, equity</td></tr><tr><td>Sana et al. (2019)</td><td>✓</td><td>MO</td><td></td><td></td><td>Handling, repetitive movements, posture</td></tr><tr><td>Kovalev et al. (2019)</td><td></td><td>SO</td><td></td><td></td><td>Implicit</td></tr><tr><td>Botti et al. (2020)</td><td>✓</td><td>MO</td><td></td><td>PP, CPP</td><td>Repetitive movements</td></tr><tr><td>Mehdizadeh et al. (2020)</td><td></td><td>SO</td><td></td><td></td><td>Handling</td></tr><tr><td>Ayough et al. (2020)</td><td></td><td></td><td></td><td>VTT</td><td>Learning, motivation</td></tr><tr><td>Rerkjirattikal and Olapiriyakul (2021)</td><td></td><td></td><td>CC, TC</td><td>VTT</td><td>Skills, noise</td></tr><tr><td>Battini et al. (2022)</td><td>✓</td><td>MO</td><td></td><td>S, LR, CPP</td><td>Skills, noise, vibrations, RA, motivation</td></tr><tr><td>Dalle Mura and Dini (2022)</td><td>✓</td><td>MO</td><td>CC, TC, FSC</td><td>S, PP, CPP</td><td>Skills, EE</td></tr></tbody></table>

The mental strain is computed with the Subjective Workload Assessment Technique (SWAT) (Reid and Nygren, 1988), which evaluates job difficulty by giving a score between 1 and 3 to the three following different criteria: time load, psychological effort load, and psychological stress load.

# 6. Workforce-related problems

## 6.1. Workforce scheduling

### 6.1.1. Job rotation

Before being studied through the lens of OR researchers, job rotation first designates a managerial method that organizes worker shifts, such that an employee is assigned to different tasks/workstations throughout his/her shift. The purpose of this paradigm originates in HF/E with the objective of reducing occupational injuries and employee boredom. The frequent change of workstation indeed causes the physical exertion of the operator to be spread across different body regions, according to the proverb “a change is as good as a rest”. Assembly line balancing problems already aim at spreading the physical workload among workstations, yet it may not be able to eliminate completely workstations with high ER. In this case, job rotation ensures that several operators will share the burden of this workstation. Several field studies have highlighted the benefit of the implementation of job rotation: It reduces the exposure to awkward posture (Hinnen et al., 1992), cardiovascular load (Kuijer et al., 1999), or muscle fatigue (Hinnen et al., 1992). Furthermore, job rotation, as an organizational method, is also used by Human Resources to maintain a multi-skilled workforce, ensuring more flexibility to deal with variability (Otto and Battaia, 2017). Job rotation has been first formulated as a scheduling optimization problem by the pioneering work of Carnahan et al. (2000) that is, to the best of our knowledge, the first work that integrates methodologies from HF/E into OR and mathematical optimization. Table 8 presents the works on this stream, which study mostly WMSD risk, boredom, and skills. An interested reader is referred to Otto and Battaia (2017) for a review dedicated to the balancing of the physical ER via job rotation.

**WMSD risk assessment.** In job rotation scheduling, the objective is often to minimize the maximal ER accumulated by an operator over the planning horizon, computed via WMSD risk assessment methods. In these problems, it is often the case that economic-related quantities (e.g., size of the workforce, number of workstations) and operational ones (e.g., cycle time) have already been optimized and are used as input data. A common modeling method in job rotation is therefore to use a single objective function related to the maximum ER. It can be focused on the postural load, for example with the REBA index (Yoon et al., 2016), manual handling tasks with the JSI index (Tharmmaphornphilas and Norman, 2007), or whole body assessment methods like the EAWS (Otto and Scholl, 2013). It is also very frequent that several risk assessment methods are considered altogether in a single model with different objective functions. For example, Sana et al. (2019) use the NIOSH equation for lifting tasks, the OCRA index for repetitive tasks, and the RULA index for awkward postures. One of the main ideas behind job rotation is to ensure that one worker does not get assigned to a high ER task for a long period, thus avoiding increasing excessively the risk, especially on the same body region. A common modeling technique to avoid such situations is to use forbidden sequence constraints. In this case, the successive assignment of two high-workload tasks to the same operator is not allowed (Moussavi et al., 2019; Yoon et al., 2016).

**Boredom.** This factor, seen as a lack of motivation due to repetitive and monotonous work, may be accounted for with soft constraints, where one of the objectives is to minimize the maximal number of consecutive periods with the same task assigned to a given worker (Bhadury and Radovilsky, 2006). Another option to model boredom in job rotation scheduling consists in using a varying productivity rate for the employees, depending on how long they are affected to the same task (Azizi et al., 2010; Ayough et al., 2020; Battini et al., 2022).

**Skills.** As other classes of scheduling problems dealing with human operators, skill considerations are often present in the work on job rotation scheduling. This can be modeled with compatibility constraints, where certain workstations require specific skills that not all workers