<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
<table><caption>**Table 9**
Work-rest 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="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>Bechtold (1979)</td><td></td><td></td><td></td><td></td><td></td><td>Fatigue effect</td></tr><tr><td>Bechtold et al. (1984)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Thompson (1990)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Bechtold (1991)</td><td></td><td></td><td></td><td>VTT</td><td>PP</td><td>Fatigue effect</td></tr><tr><td>Bechtold and Thompson (1993)</td><td></td><td></td><td></td><td>VTT</td><td>PP</td><td>Fatigue effect</td></tr><tr><td>Brusco and Jacobs (1993)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Aykin (1996)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Aykin (1998)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Mehrotra et al. (2000)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Brusco and Jacobs (2000)</td><td>✓</td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Gärtner et al. (2001)</td><td></td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Topaloglu and Ozkarahan (2003)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Topaloglu and Ozkarahan (2004)</td><td></td><td>MO-He</td><td>TWC</td><td></td><td>P</td><td>Work-stretch duration, hazard exposure</td></tr><tr><td>Janiak and Kovaliyov (2006)</td><td></td><td></td><td>FSC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Bard and Wan (2006)</td><td>✓</td><td></td><td>TWC, FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Thompson and Pullman (2007)</td><td></td><td></td><td></td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Janiak and Kovaliyov (2008)</td><td></td><td></td><td>FSC</td><td></td><td></td><td>Hazard exposure, work-stretch duration</td></tr><tr><td>Bard and Wan (2008)</td><td>✓</td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Rekik et al. (2008)</td><td></td><td></td><td>TWC, FBC</td><td></td><td></td><td>Meal breaks, work-stretch duration</td></tr><tr><td>Sawik (2010)</td><td></td><td></td><td>FSC</td><td></td><td>S</td><td>Hazard exposure, work-stretch duration</td></tr><tr><td>Rekik et al. (2010)</td><td>✓</td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Quimper and Rousseau (2010)</td><td></td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Restrepo et al. (2012)</td><td>✓</td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Chen et al. (2013)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Widl and Musliu (2014)</td><td></td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Jamshidi and Seyyed Esfahani (2014)</td><td></td><td>MO-Ho</td><td></td><td>VQ</td><td></td><td>Human errors, fatigue effects</td></tr><tr><td>Yi and Chan (2015)</td><td>✓</td><td></td><td></td><td></td><td>PP, CPP</td><td>Heat tolerance</td></tr><tr><td>Gérard et al. (2016)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Restrepo et al. (2016)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Yi and Wang (2017)</td><td></td><td></td><td>TC</td><td></td><td>PP</td><td>Heat tolerance</td></tr><tr><td>Bonutti et al. (2017)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Sungur et al. (2017)</td><td></td><td>MO</td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Zhao et al. (2019)</td><td></td><td>MO</td><td>TC</td><td>VTT</td><td></td><td>EE</td></tr><tr><td>Calzavara et al. (2019b)</td><td></td><td></td><td></td><td></td><td></td><td>EE, RA</td></tr><tr><td>Akkermans et al. (2019)</td><td></td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Li et al. (2020)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Álvarez et al. (2020)</td><td>✓</td><td></td><td></td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Fang et al. (2021)</td><td></td><td>MO-Ho</td><td>FBC</td><td>VTT</td><td>S</td><td>Skills, work-stretch duration</td></tr></tbody></table>

possess (Pata and Moura, 2018; Hochdörffer et al., 2018). Skills can also be modeled with different levels of proficiency, where the task duration will depend on the skill level of the employee it is assigned to Mossa et al. (2016) and Battini et al. (2022), or both the employee skill and boredom levels (Nanthavanij et al., 2010; Azizi et al., 2010).

**Other HFs.** On top of the classical WMSD risk assessment methods, perceptual risk factors are also considered to be mitigated by job rotation. These factors are, for example, the noise exposure of the operators (Tharmmaphornphilas and Norman, 2004; Aryanezhad et al., 2009b), or the vibration exposure (Battini et al., 2022). Ad hoc risk assessment methods based on biomechanical criteria are also commonly used (Moussavi et al., 2019).

### 6.1.2. Work-rest scheduling

In work-rest scheduling, the main decision is to determine when and how to place rest breaks in an employee's schedule. According to Lodree et al. (2009), the problem consists in "determining the number, placement, and duration of rest times during a work period". This problem is very relevant to industrial applications. Many empirical studies have shown the link between the fatigue level and: individual performances (Yung et al., 2020), diminished quality of work (Caruso, 2015), and increased safety problems (Lombardi et al., 2010). Unsurprisingly, the studies on work-rest scheduling, presented in Table 9, focus on break-related HAMs, i.e., meal breaks, work-stretch duration, fatigue, and the comparison between break scheduling methods. An interested reader is referred to Xu and Hall (2021) for a more detailed review of empirical work in work-rest scheduling.

**Fatigue via meal breaks.** One of the most basic approaches to integrating rest breaks into workforce scheduling is to consider meal breaks. This HAM is quite common, as it emerges from a very clear and straightforward operational constraint when establishing employees' schedules. In most jobs, a break is planned for the employees to get lunch. Hence, either the break is fixed in time, or a degree of flexibility is allowed for its scheduling. The easiest way to integrate flexibility to a given extent into scheduling models is to have a time window, in which the meal break should be scheduled. For these reasons, this approach has been used in the early literature on workforce scheduling (Thompson, 1990; Brusco and Jacobs, 2000), but also in more recent works on the topic (Chen et al., 2013; Brusco, 2008). The use of time windows is not restricted to meal breaks and can be used to add some flexibility when scheduling several breaks in a work shift (Mehrotra et al., 2000; Topaloglu and Ozkarahan, 2003; Bonutti et al., 2017).

**Fatigue via work-stretch duration.** Another common HAM for rest break scheduling is to use work-stretch duration modeled via forward-backward constraints (see Section 7.2). This approach is more sophisticated than using time windows, in the sense that it provides more possibilities. The schedules should abide by a set of "rules" about break placement. For example, a maximal work duration without a break, a minimal break time to be scheduled during a shift, a minimal duration for a break, a minimal duration between the shift beginning and the first break. Gärtner et al. (2001) is the first work, to our best knowledge, to propose this modeling framework, and other papers followed in this direction (Quimper and Rousseau, 2010; Restrepo et al., 2012; Rekik et al., 2010). An interested reader is referred to Widl and Musliu (2014) for a more theoretical analysis of the impact of work-stretch duration on scheduling models. In some cases, the rules determining
<table><caption>**Table 9**
Work-rest 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="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>Bechtold (1979)</td><td></td><td></td><td></td><td></td><td></td><td>Fatigue effect</td></tr><tr><td>Bechtold et al. (1984)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Thompson (1990)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Bechtold (1991)</td><td></td><td></td><td></td><td>VTT</td><td>PP</td><td>Fatigue effect</td></tr><tr><td>Bechtold and Thompson (1993)</td><td></td><td></td><td></td><td>VTT</td><td>PP</td><td>Fatigue effect</td></tr><tr><td>Brusco and Jacobs (1993)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Aykin (1996)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Aykin (1998)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Mehrotra et al. (2000)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Brusco and Jacobs (2000)</td><td>✓</td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Gärtner et al. (2001)</td><td></td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Topaloglu and Ozkarahan (2003)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Topaloglu and Ozkarahan (2004)</td><td></td><td>MO-He</td><td>TWC</td><td></td><td>P</td><td>Work-stretch duration, hazard exposure</td></tr><tr><td>Janiak and Kovaliyov (2006)</td><td></td><td></td><td>FSC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Bard and Wan (2006)</td><td>✓</td><td></td><td>TWC, FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Thompson and Pullman (2007)</td><td></td><td></td><td></td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Janiak and Kovaliyov (2008)</td><td></td><td></td><td>FSC</td><td></td><td></td><td>Hazard exposure, work-stretch duration</td></tr><tr><td>Bard and Wan (2008)</td><td>✓</td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Rekik et al. (2008)</td><td></td><td></td><td>TWC, FBC</td><td></td><td></td><td>Meal breaks, work-stretch duration</td></tr><tr><td>Sawik (2010)</td><td></td><td></td><td>FSC</td><td></td><td>S</td><td>Hazard exposure, work-stretch duration</td></tr><tr><td>Rekik et al. (2010)</td><td>✓</td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Quimper and Rousseau (2010)</td><td></td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Restrepo et al. (2012)</td><td>✓</td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Chen et al. (2013)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Widl and Musliu (2014)</td><td></td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Jamshidi and Seyyed Esfahani (2014)</td><td></td><td>MO-Ho</td><td></td><td>VQ</td><td></td><td>Human errors, fatigue effects</td></tr><tr><td>Yi and Chan (2015)</td><td>✓</td><td></td><td></td><td></td><td>PP, CPP</td><td>Heat tolerance</td></tr><tr><td>Gérard et al. (2016)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Restrepo et al. (2016)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Yi and Wang (2017)</td><td></td><td></td><td>TC</td><td></td><td>PP</td><td>Heat tolerance</td></tr><tr><td>Bonutti et al. (2017)</td><td></td><td></td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Sungur et al. (2017)</td><td></td><td>MO</td><td>TWC</td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Zhao et al. (2019)</td><td></td><td>MO</td><td>TC</td><td>VTT</td><td></td><td>EE</td></tr><tr><td>Calzavara et al. (2019b)</td><td></td><td></td><td></td><td></td><td></td><td>EE, RA</td></tr><tr><td>Akkermans et al. (2019)</td><td></td><td></td><td>FBC</td><td></td><td></td><td>Work-stretch duration</td></tr><tr><td>Li et al. (2020)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Fatigue effect</td></tr><tr><td>Álvarez et al. (2020)</td><td>✓</td><td></td><td></td><td></td><td></td><td>Meal breaks</td></tr><tr><td>Fang et al. (2021)</td><td></td><td>MO-Ho</td><td>FBC</td><td>VTT</td><td>S</td><td>Skills, work-stretch duration</td></tr></tbody></table>

possess (Pata and Moura, 2018; Hochdörffer et al., 2018). Skills can also be modeled with different levels of proficiency, where the task duration will depend on the skill level of the employee it is assigned to Mossa et al. (2016) and Battini et al. (2022), or both the employee skill and boredom levels (Nanthavanij et al., 2010; Azizi et al., 2010).

**Other HFs.** On top of the classical WMSD risk assessment methods, perceptual risk factors are also considered to be mitigated by job rotation. These factors are, for example, the noise exposure of the operators (Tharmmaphornphilas and Norman, 2004; Aryanezhad et al., 2009b), or the vibration exposure (Battini et al., 2022). Ad hoc risk assessment methods based on biomechanical criteria are also commonly used (Moussavi et al., 2019).

### 6.1.2. Work-rest scheduling

In work-rest scheduling, the main decision is to determine when and how to place rest breaks in an employee's schedule. According to Lodree et al. (2009), the problem consists in "determining the number, placement, and duration of rest times during a work period". This problem is very relevant to industrial applications. Many empirical studies have shown the link between the fatigue level and: individual performances (Yung et al., 2020), diminished quality of work (Caruso, 2015), and increased safety problems (Lombardi et al., 2010). Unsurprisingly, the studies on work-rest scheduling, presented in Table 9, focus on break-related HAMs, i.e., meal breaks, work-stretch duration, fatigue, and the comparison between break scheduling methods. An interested reader is referred to Xu and Hall (2021) for a more detailed review of empirical work in work-rest scheduling.

**Fatigue via meal breaks.** One of the most basic approaches to integrating rest breaks into workforce scheduling is to consider meal breaks. This HAM is quite common, as it emerges from a very clear and straightforward operational constraint when establishing employees' schedules. In most jobs, a break is planned for the employees to get lunch. Hence, either the break is fixed in time, or a degree of flexibility is allowed for its scheduling. The easiest way to integrate flexibility to a given extent into scheduling models is to have a time window, in which the meal break should be scheduled. For these reasons, this approach has been used in the early literature on workforce scheduling (Thompson, 1990; Brusco and Jacobs, 2000), but also in more recent works on the topic (Chen et al., 2013; Brusco, 2008). The use of time windows is not restricted to meal breaks and can be used to add some flexibility when scheduling several breaks in a work shift (Mehrotra et al., 2000; Topaloglu and Ozkarahan, 2003; Bonutti et al., 2017).

**Fatigue via work-stretch duration.** Another common HAM for rest break scheduling is to use work-stretch duration modeled via forward-backward constraints (see Section 7.2). This approach is more sophisticated than using time windows, in the sense that it provides more possibilities. The schedules should abide by a set of "rules" about break placement. For example, a maximal work duration without a break, a minimal break time to be scheduled during a shift, a minimal duration for a break, a minimal duration between the shift beginning and the first break. Gärtner et al. (2001) is the first work, to our best knowledge, to propose this modeling framework, and other papers followed in this direction (Quimper and Rousseau, 2010; Restrepo et al., 2012; Rekik et al., 2010). An interested reader is referred to Widl and Musliu (2014) for a more theoretical analysis of the impact of work-stretch duration on scheduling models. In some cases, the rules determining
<table><caption>**Table 10**
Shift 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">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Cai and Li (2000)</td><td></td><td></td><td>TC</td><td></td><td>Skills</td></tr><tr><td>Gans and Zhou (2002)</td><td></td><td>MO-Ho</td><td></td><td>S, LR</td><td>Skills, learning</td></tr><tr><td>Eitzen et al. (2004)</td><td>✓</td><td></td><td>TC</td><td>S</td><td>Skills, equity</td></tr><tr><td>Pan et al. (2010)</td><td></td><td>MO</td><td>CC, FSC</td><td>S, P</td><td>Skills, satisfaction</td></tr><tr><td>Knust and Schumacher (2011)</td><td></td><td></td><td>FBC</td><td></td><td>Satisfaction</td></tr><tr><td>Akbari et al. (2013)</td><td></td><td>SO</td><td>CC</td><td>VTT</td><td>Skills, fatigue effect, satisfaction</td></tr><tr><td>Lapegue et al. (2013)</td><td></td><td>MO</td><td>FBC</td><td></td><td>Equity</td></tr><tr><td>Nishi et al. (2014)</td><td></td><td>MO-He</td><td>FBC</td><td></td><td>Equity</td></tr><tr><td>Prot et al. (2015)</td><td>✓</td><td>MO</td><td>FBC</td><td></td><td>Equity</td></tr><tr><td>Dewi and Septiana (2015)</td><td>✓</td><td>MO-He</td><td></td><td></td><td>EE, cognitive</td></tr><tr><td>Cheng and Kuo (2016)</td><td></td><td>MO-He</td><td>FSC</td><td>S, P</td><td>Skills, satisfaction, equity</td></tr><tr><td>Shuib and Kamarudin (2019)</td><td>✓</td><td>SO</td><td>CC</td><td>S, P</td><td>Skills, satisfaction</td></tr><tr><td>Steenweg et al. (2020)</td><td></td><td>MO-He</td><td>CC</td><td>S</td><td>Skills, equity</td></tr><tr><td>Caballini and Paolucci (2020)</td><td>✓</td><td>MO-He</td><td>CC, TC, FSC</td><td>S</td><td>Skills, equity, handling, repetitive movements</td></tr><tr><td>Soriano et al. (2020)</td><td></td><td>MO-He</td><td></td><td>P</td><td>Satisfaction</td></tr></tbody></table>

the placement of breaks are modeled with sequence constraints. For example, Janiak and Kovaliyov (2006), Janiak and Kovaliyov (2008) and Sawik (2010) study the workforce scheduling problem in contaminated areas. In their modeling, inspired by the related work regulations, each work period must be followed by a rest period, whose length depends (exponentially) on the duration of the work period.

**Fatigue via other HAMs.** To reduce the fatigue level, the benefits of a rest break have also been studied. In the related works, the productivity of a given employee reduces over time, as his/her fatigue increases. Breaks are not necessarily included in a solution, but they enable full or partial recovery of the operator, resetting his/her productivity to its initial level. This approach is especially suited for applications focusing on the fatigue modeling aspect since the break placement and duration are linked to HF/E observational methods, instead of being an exogenous input data of the problem. This approach has been used in early works with the basic HAM developed by Bechtold (1979), then applied in early works on the topic (Bechtold et al., 1984; Bechtold, 1991), as well as more recent studies (Jamshidi and Seyyed Esfahani, 2014; Li et al., 2020).

**Comparison between break scheduling methods.** Finally, there are works that study different break placement methods, and analyze the impacts on the produced schedules. For example, Bechtold (1979) proposes several models of fatigue and rest periods in the context of workforce scheduling. Rekik et al. (2008) study the modeling of both time windows and work-stretch duration. Thompson and Pullman (2007) study the comparison between scheduling breaks in advance and doing so in real time.

**Other HFs.** The detailed modeling of the break scheduling rules may come from the factors related to the industrial application at hand, for example, heat exposure (Yi and Chan, 2015; Sadeghi-Dastaki and Afrazeh, 2018) or hazard exposure in contaminated areas (Janiak and Kovaliyov, 2006, 2008; Sawik, 2010).

### 6.1.3. Shift scheduling

In the Shift Scheduling Problem (SSP), the main decision is to allocate the employees of a given workforce to different work shifts over a certain time horizon, usually weeks or months (Lodree et al., 2009). Each shift is characterized by a staff requirement, given by a number of employees to be scheduled in the shift, often with the associated skill set required to perform the operations that are planned. The objective is often to minimize the cost of the plan with penalties, that can be applied to favor aspects desired in the solution: equity between employees, workers' preferences, overtime (Lodree et al., 2009). The corresponding studies are presented in Table 10, and focus on skills, working hours regulations and psychosocial factors.

**Skills.** Considering the nature of the SSP and the scope of the present review, it is not surprising that skills are one of the main HFs considered in SSP (Akbari et al., 2013; Cai and Li, 2000; Eitzen et al., 2004). Skills are seen as different qualifications for the employees: the manufacturing system cannot run during a shift if certain jobs are absent from the production site, or are not in a sufficient number. This is well illustrated in industrial case studies. For example, Shuib and Kamarudin (2019) study an SSP in a power station, and the skills correspond to the different positions: chief charge engineer, senior/junior block operators, first/second patrolmen, control operators, etc.

**Working hours regulations.** The manufacturing systems modeled with an SSP are often running on a 24 h schedule, thus including the shift scheduling aspect. And as such, working hours regulations are of foremost importance in the industrial context. In optimization models, this can be modeled with forward/backward constraints (Nishi et al., 2014; Knust and Schumacher, 2011; Prot et al., 2015) or forbidden sequence constraints (Cheng and Kuo, 2016; Pan et al., 2010).

**Psychosocial factors.** Another important class of HFs considered in SSP relates to the psychosocial risk factors, the most popular being employee preferences and equity. In the 24 h shift work, some shifts are more draining than others (i.e., night shifts). If applicable, some work periods are less preferred than others (i.e., weekends, public holidays). For a manager, it is crucial to account for these aspects to ensure fairness between employees and keep the workforce satisfied. In the mathematical models, several works integrate the shift preferences of the employees. In this case, each employee gives its preferred shifts, either with scores or via a ranking system (Cheng and Kuo, 2016; Knust and Schumacher, 2011; Pan et al., 2010). In some models, the maximization of preferences is the sole objective (Akbari et al., 2013; Shuib and Kamarudin, 2019). The equity concerns in the SSP literature are not limited to preferences, other measures are used to balance the workload between employees, like the total working time, or the assigned shifts on public holidays (Prot et al., 2015; Lapegue et al., 2013; Cheng and Kuo, 2016).

**Other HFs.** Fatigue may be considered in SSP (Akbari et al., 2013; Dewi and Septiana, 2015). It is indeed particularly relevant for industrial cases running on a 24 h schedule.

### 6.2. Workforce management

#### 6.2.1. Workforce planning

In this section, we focus on workforce planning problems. In this class of problems, the main decision is, for each period, to assign the employees to a set of tasks to be performed. The difference with
<table><caption>**Table 10**
Shift 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">HW</th><th rowspan="2">HAM</th></tr><tr><th>Obj.</th><th>Const.</th><th>Param.</th></tr></thead><tbody><tr><td>Cai and Li (2000)</td><td></td><td></td><td>TC</td><td></td><td>Skills</td></tr><tr><td>Gans and Zhou (2002)</td><td></td><td>MO-Ho</td><td></td><td>S, LR</td><td>Skills, learning</td></tr><tr><td>Eitzen et al. (2004)</td><td>✓</td><td></td><td>TC</td><td>S</td><td>Skills, equity</td></tr><tr><td>Pan et al. (2010)</td><td></td><td>MO</td><td>CC, FSC</td><td>S, P</td><td>Skills, satisfaction</td></tr><tr><td>Knust and Schumacher (2011)</td><td></td><td></td><td>FBC</td><td></td><td>Satisfaction</td></tr><tr><td>Akbari et al. (2013)</td><td></td><td>SO</td><td>CC</td><td>VTT</td><td>Skills, fatigue effect, satisfaction</td></tr><tr><td>Lapegue et al. (2013)</td><td></td><td>MO</td><td>FBC</td><td></td><td>Equity</td></tr><tr><td>Nishi et al. (2014)</td><td></td><td>MO-He</td><td>FBC</td><td></td><td>Equity</td></tr><tr><td>Prot et al. (2015)</td><td>✓</td><td>MO</td><td>FBC</td><td></td><td>Equity</td></tr><tr><td>Dewi and Septiana (2015)</td><td>✓</td><td>MO-He</td><td></td><td></td><td>EE, cognitive</td></tr><tr><td>Cheng and Kuo (2016)</td><td></td><td>MO-He</td><td>FSC</td><td>S, P</td><td>Skills, satisfaction, equity</td></tr><tr><td>Shuib and Kamarudin (2019)</td><td>✓</td><td>SO</td><td>CC</td><td>S, P</td><td>Skills, satisfaction</td></tr><tr><td>Steenweg et al. (2020)</td><td></td><td>MO-He</td><td>CC</td><td>S</td><td>Skills, equity</td></tr><tr><td>Caballini and Paolucci (2020)</td><td>✓</td><td>MO-He</td><td>CC, TC, FSC</td><td>S</td><td>Skills, equity, handling, repetitive movements</td></tr><tr><td>Soriano et al. (2020)</td><td></td><td>MO-He</td><td></td><td>P</td><td>Satisfaction</td></tr></tbody></table>

the placement of breaks are modeled with sequence constraints. For example, Janiak and Kovaliyov (2006), Janiak and Kovaliyov (2008) and Sawik (2010) study the workforce scheduling problem in contaminated areas. In their modeling, inspired by the related work regulations, each work period must be followed by a rest period, whose length depends (exponentially) on the duration of the work period.

**Fatigue via other HAMs.** To reduce the fatigue level, the benefits of a rest break have also been studied. In the related works, the productivity of a given employee reduces over time, as his/her fatigue increases. Breaks are not necessarily included in a solution, but they enable full or partial recovery of the operator, resetting his/her productivity to its initial level. This approach is especially suited for applications focusing on the fatigue modeling aspect since the break placement and duration are linked to HF/E observational methods, instead of being an exogenous input data of the problem. This approach has been used in early works with the basic HAM developed by Bechtold (1979), then applied in early works on the topic (Bechtold et al., 1984; Bechtold, 1991), as well as more recent studies (Jamshidi and Seyyed Esfahani, 2014; Li et al., 2020).

**Comparison between break scheduling methods.** Finally, there are works that study different break placement methods, and analyze the impacts on the produced schedules. For example, Bechtold (1979) proposes several models of fatigue and rest periods in the context of workforce scheduling. Rekik et al. (2008) study the modeling of both time windows and work-stretch duration. Thompson and Pullman (2007) study the comparison between scheduling breaks in advance and doing so in real time.

**Other HFs.** The detailed modeling of the break scheduling rules may come from the factors related to the industrial application at hand, for example, heat exposure (Yi and Chan, 2015; Sadeghi-Dastaki and Afrazeh, 2018) or hazard exposure in contaminated areas (Janiak and Kovaliyov, 2006, 2008; Sawik, 2010).

### 6.1.3. Shift scheduling

In the Shift Scheduling Problem (SSP), the main decision is to allocate the employees of a given workforce to different work shifts over a certain time horizon, usually weeks or months (Lodree et al., 2009). Each shift is characterized by a staff requirement, given by a number of employees to be scheduled in the shift, often with the associated skill set required to perform the operations that are planned. The objective is often to minimize the cost of the plan with penalties, that can be applied to favor aspects desired in the solution: equity between employees, workers' preferences, overtime (Lodree et al., 2009). The corresponding studies are presented in Table 10, and focus on skills, working hours regulations and psychosocial factors.

**Skills.** Considering the nature of the SSP and the scope of the present review, it is not surprising that skills are one of the main HFs considered in SSP (Akbari et al., 2013; Cai and Li, 2000; Eitzen et al., 2004). Skills are seen as different qualifications for the employees: the manufacturing system cannot run during a shift if certain jobs are absent from the production site, or are not in a sufficient number. This is well illustrated in industrial case studies. For example, Shuib and Kamarudin (2019) study an SSP in a power station, and the skills correspond to the different positions: chief charge engineer, senior/junior block operators, first/second patrolmen, control operators, etc.

**Working hours regulations.** The manufacturing systems modeled with an SSP are often running on a 24 h schedule, thus including the shift scheduling aspect. And as such, working hours regulations are of foremost importance in the industrial context. In optimization models, this can be modeled with forward/backward constraints (Nishi et al., 2014; Knust and Schumacher, 2011; Prot et al., 2015) or forbidden sequence constraints (Cheng and Kuo, 2016; Pan et al., 2010).

**Psychosocial factors.** Another important class of HFs considered in SSP relates to the psychosocial risk factors, the most popular being employee preferences and equity. In the 24 h shift work, some shifts are more draining than others (i.e., night shifts). If applicable, some work periods are less preferred than others (i.e., weekends, public holidays). For a manager, it is crucial to account for these aspects to ensure fairness between employees and keep the workforce satisfied. In the mathematical models, several works integrate the shift preferences of the employees. In this case, each employee gives its preferred shifts, either with scores or via a ranking system (Cheng and Kuo, 2016; Knust and Schumacher, 2011; Pan et al., 2010). In some models, the maximization of preferences is the sole objective (Akbari et al., 2013; Shuib and Kamarudin, 2019). The equity concerns in the SSP literature are not limited to preferences, other measures are used to balance the workload between employees, like the total working time, or the assigned shifts on public holidays (Prot et al., 2015; Lapegue et al., 2013; Cheng and Kuo, 2016).

**Other HFs.** Fatigue may be considered in SSP (Akbari et al., 2013; Dewi and Septiana, 2015). It is indeed particularly relevant for industrial cases running on a 24 h schedule.

### 6.2. Workforce management

#### 6.2.1. Workforce planning

In this section, we focus on workforce planning problems. In this class of problems, the main decision is, for each period, to assign the employees to a set of tasks to be performed. The difference with
<table><caption>**Table 11**
Workforce 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>Stewart et al. (1994)</td><td></td><td>SO</td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Bordoloi and Matsuo (2001)</td><td>✓</td><td>MO-Ho</td><td></td><td></td><td>S</td><td>Skills</td></tr><tr><td>Wirojanagud et al. (2007)</td><td></td><td></td><td>TC</td><td></td><td>S, LR</td><td>Skills</td></tr><tr><td>Fowler et al. (2008)</td><td>✓</td><td></td><td>TC</td><td></td><td>S, LR</td><td>Skills</td></tr><tr><td>Aryanezhad et al. (2009a)</td><td></td><td>MO-Ho</td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>McDonald et al. (2009)</td><td>✓</td><td>MO-Ho</td><td>CC</td><td>VQ</td><td>S</td><td>Skills</td></tr><tr><td>Othman et al. (2012)</td><td></td><td>MO-He</td><td></td><td></td><td>S, PP, CPP</td><td>Skills, motivation</td></tr><tr><td>Kim et al. (2013)</td><td></td><td>MO-Ho</td><td></td><td></td><td></td><td>Total cost function</td></tr><tr><td>Attia et al. (2014)</td><td></td><td>MO-He</td><td>CC</td><td>VTT</td><td>S, LR</td><td>Skills, learning</td></tr><tr><td>Nembhard and Bentefouet (2014)</td><td></td><td></td><td></td><td>VTT</td><td>S, LR</td><td>Skills, learning</td></tr><tr><td>Hewitt et al. (2015)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Mehdizadeh et al. (2016)</td><td></td><td>MO-Ho</td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Valeva et al. (2017)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Wang et al. (2018)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Shahbazi et al. (2019)</td><td></td><td>MO-He</td><td></td><td>VTT</td><td>S</td><td>Skills, psychosocial</td></tr><tr><td>Cavagnini et al. (2020)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Ruf et al. (2022)</td><td></td><td>MO-Ho</td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Jaillet et al. (2022)</td><td></td><td>MO-Ho</td><td></td><td></td><td>S</td><td>Skills</td></tr><tr><td>Rafiee et al. (2022)</td><td></td><td>MO-Ho</td><td>CC</td><td></td><td>S</td><td>Skills, learning</td></tr><tr><td>Doan et al. (2022)</td><td>✓</td><td>MO-He</td><td>CC</td><td></td><td>S, P</td><td>Skills, satisfaction, equity</td></tr></tbody></table>

the workforce scheduling problem lies in the planning horizon. The workforce planning process is located at the tactical level, therefore the planning horizon is rather long (e.g., weeks or months). This larger horizon means that tactical decisions (e.g., the size of the workforce) become available for the planner (De Bruecker et al., 2015). The hiring and firing processes are usually considered in these models, both coming at a monetary cost. In most problems, the skill pool of the workforce should remain sufficient to fulfill the requirement of each work period. Table 11 presents the works on the topic, with a focus on skills, and skill development. The interested reader is directed to De Bruecker et al. (2015) for a detailed literature review on workforce planning with skill considerations.

**Skills.** The most common HF in this class of problems is skills. They can be modeled with compatibility constraints, where only qualified employees can be assigned to certain tasks when individual assignments are modeled (McDonald et al., 2009). Another modeling approach is with resource constraints: In this case, employees are not modeled individually, the number of employees at a given skill level is considered as a resource, that needs to be above a certain requirement in each planning period (Fowler et al., 2008). Skills can also be modeled with varying task times (see Section 7.3.1), where the productivity of an employee improves with his/her skill level (Wang et al., 2018). More than productivity, the output quality level can vary with the skill of an employee (McDonald et al., 2009).

**Skill development.** With the tactical planning horizon, hiring and firing are not the only ways to adapt the skill set of the workforce. Some works explicitly consider human resource planning, where training can be scheduled to improve the skill level of an employee. In this case, the training comes at a monetary cost, either directly, or indirectly when an employee is unavailable due to training (Othman et al., 2012; Mehdizadeh et al., 2016). Fowler et al. (2008) and Wirojanagud et al. (2007) are interested in the General cognitive ability of employees, affecting the required training time to pass from one skill level to another. The skill development does not necessarily come with training, but also via individual (i.e., autonomous) learning. More details on the difference between induced and autonomous learning are provided in Prunet et al. (2024), Learning. This is also considered in several works on workforce planning, where the repetition of tasks requiring a given skill increases the proficiency of an employee at this skill. Learning curves are used to model this autonomous learning (Nembhard and Bentefouet, 2014; Cavagnini et al., 2020).

### 6.2.2. Workforce assignment

In this section, we study the workforce assignment. This is not a unified class of problems, but we chose to regroup problems that assign a set of operators to a set of jobs or workstations. Generally speaking, this assignment decision is not the focus of these works per se, but one aspect of the decision-making process. Table 12 presents the works on the topic, with a focus on skills and psychosocial factors.

**Skills.** An important class of problems refers to the cellular manufacturing organization, where machines and processes are grouped into cells that produce a specific output. In this context, one step of the process is the assignment of workers to the set of cells. As usual, when dealing with problems related to workforce optimization, skills are a very common HF (Wu et al., 2018; Lian et al., 2018). Norman et al. (2002) focus their modeling of the skill aspect on both technical and human skills. Skill improvement can be considered through training (Norman et al., 2002), which is unusual with problems without a time horizon. In this example, a maximum training time is allowed to get the desired skill set in the workforce. For a person/job assignment problem, Sayin and Karabati (2007) use a 2-stage model to assign workers between several departments. The model is multi-period with the first stage consisting of assigning employees to departments by minimizing labor shortage, and the second stage aiming at maximizing skill development in the workforce.

**Psychosocial factors.** Several papers that study a general person/job assignment with a security concern (Zhang et al., 2019b), while accounting workers' sensitivity to risk (Lazzerini and Pistolesi, 2018), or accounting for cognitive aspects of the job and various human resources strategies (Fini et al., 2017). Brusco (2015) focuses on employees' preferences as a second objective function to determine the optimal person/job assignment.

**Other HFs.** Learning is also considered in this class of problems, for instance (Nembhard, 2001) studies a basic model of two jobs and workers with different learning rates. The author performs simulations under different experimental conditions to design a heuristic policy that maximizes total productivity. Equity is another common concern, where the aim is to balance the workload among employees (Lian et al., 2018; Wu et al., 2018).

## 7. Mathematical programming considerations

This section presents an analysis of the reviewed material from a mathematical programming perspective. The integration of HFs is
<table><caption>**Table 11**
Workforce 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>Stewart et al. (1994)</td><td></td><td>SO</td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Bordoloi and Matsuo (2001)</td><td>✓</td><td>MO-Ho</td><td></td><td></td><td>S</td><td>Skills</td></tr><tr><td>Wirojanagud et al. (2007)</td><td></td><td></td><td>TC</td><td></td><td>S, LR</td><td>Skills</td></tr><tr><td>Fowler et al. (2008)</td><td>✓</td><td></td><td>TC</td><td></td><td>S, LR</td><td>Skills</td></tr><tr><td>Aryanezhad et al. (2009a)</td><td></td><td>MO-Ho</td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>McDonald et al. (2009)</td><td>✓</td><td>MO-Ho</td><td>CC</td><td>VQ</td><td>S</td><td>Skills</td></tr><tr><td>Othman et al. (2012)</td><td></td><td>MO-He</td><td></td><td></td><td>S, PP, CPP</td><td>Skills, motivation</td></tr><tr><td>Kim et al. (2013)</td><td></td><td>MO-Ho</td><td></td><td></td><td></td><td>Total cost function</td></tr><tr><td>Attia et al. (2014)</td><td></td><td>MO-He</td><td>CC</td><td>VTT</td><td>S, LR</td><td>Skills, learning</td></tr><tr><td>Nembhard and Bentefouet (2014)</td><td></td><td></td><td></td><td>VTT</td><td>S, LR</td><td>Skills, learning</td></tr><tr><td>Hewitt et al. (2015)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Mehdizadeh et al. (2016)</td><td></td><td>MO-Ho</td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Valeva et al. (2017)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Wang et al. (2018)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Shahbazi et al. (2019)</td><td></td><td>MO-He</td><td></td><td>VTT</td><td>S</td><td>Skills, psychosocial</td></tr><tr><td>Cavagnini et al. (2020)</td><td></td><td></td><td></td><td>VTT</td><td></td><td>Learning</td></tr><tr><td>Ruf et al. (2022)</td><td></td><td>MO-Ho</td><td>CC</td><td></td><td>S</td><td>Skills</td></tr><tr><td>Jaillet et al. (2022)</td><td></td><td>MO-Ho</td><td></td><td></td><td>S</td><td>Skills</td></tr><tr><td>Rafiee et al. (2022)</td><td></td><td>MO-Ho</td><td>CC</td><td></td><td>S</td><td>Skills, learning</td></tr><tr><td>Doan et al. (2022)</td><td>✓</td><td>MO-He</td><td>CC</td><td></td><td>S, P</td><td>Skills, satisfaction, equity</td></tr></tbody></table>

the workforce scheduling problem lies in the planning horizon. The workforce planning process is located at the tactical level, therefore the planning horizon is rather long (e.g., weeks or months). This larger horizon means that tactical decisions (e.g., the size of the workforce) become available for the planner (De Bruecker et al., 2015). The hiring and firing processes are usually considered in these models, both coming at a monetary cost. In most problems, the skill pool of the workforce should remain sufficient to fulfill the requirement of each work period. Table 11 presents the works on the topic, with a focus on skills, and skill development. The interested reader is directed to De Bruecker et al. (2015) for a detailed literature review on workforce planning with skill considerations.

**Skills.** The most common HF in this class of problems is skills. They can be modeled with compatibility constraints, where only qualified employees can be assigned to certain tasks when individual assignments are modeled (McDonald et al., 2009). Another modeling approach is with resource constraints: In this case, employees are not modeled individually, the number of employees at a given skill level is considered as a resource, that needs to be above a certain requirement in each planning period (Fowler et al., 2008). Skills can also be modeled with varying task times (see Section 7.3.1), where the productivity of an employee improves with his/her skill level (Wang et al., 2018). More than productivity, the output quality level can vary with the skill of an employee (McDonald et al., 2009).

**Skill development.** With the tactical planning horizon, hiring and firing are not the only ways to adapt the skill set of the workforce. Some works explicitly consider human resource planning, where training can be scheduled to improve the skill level of an employee. In this case, the training comes at a monetary cost, either directly, or indirectly when an employee is unavailable due to training (Othman et al., 2012; Mehdizadeh et al., 2016). Fowler et al. (2008) and Wirojanagud et al. (2007) are interested in the General cognitive ability of employees, affecting the required training time to pass from one skill level to another. The skill development does not necessarily come with training, but also via individual (i.e., autonomous) learning. More details on the difference between induced and autonomous learning are provided in Prunet et al. (2024), Learning. This is also considered in several works on workforce planning, where the repetition of tasks requiring a given skill increases the proficiency of an employee at this skill. Learning curves are used to model this autonomous learning (Nembhard and Bentefouet, 2014; Cavagnini et al., 2020).

### 6.2.2. Workforce assignment

In this section, we study the workforce assignment. This is not a unified class of problems, but we chose to regroup problems that assign a set of operators to a set of jobs or workstations. Generally speaking, this assignment decision is not the focus of these works per se, but one aspect of the decision-making process. Table 12 presents the works on the topic, with a focus on skills and psychosocial factors.

**Skills.** An important class of problems refers to the cellular manufacturing organization, where machines and processes are grouped into cells that produce a specific output. In this context, one step of the process is the assignment of workers to the set of cells. As usual, when dealing with problems related to workforce optimization, skills are a very common HF (Wu et al., 2018; Lian et al., 2018). Norman et al. (2002) focus their modeling of the skill aspect on both technical and human skills. Skill improvement can be considered through training (Norman et al., 2002), which is unusual with problems without a time horizon. In this example, a maximum training time is allowed to get the desired skill set in the workforce. For a person/job assignment problem, Sayin and Karabati (2007) use a 2-stage model to assign workers between several departments. The model is multi-period with the first stage consisting of assigning employees to departments by minimizing labor shortage, and the second stage aiming at maximizing skill development in the workforce.

**Psychosocial factors.** Several papers that study a general person/job assignment with a security concern (Zhang et al., 2019b), while accounting workers' sensitivity to risk (Lazzerini and Pistolesi, 2018), or accounting for cognitive aspects of the job and various human resources strategies (Fini et al., 2017). Brusco (2015) focuses on employees' preferences as a second objective function to determine the optimal person/job assignment.

**Other HFs.** Learning is also considered in this class of problems, for instance (Nembhard, 2001) studies a basic model of two jobs and workers with different learning rates. The author performs simulations under different experimental conditions to design a heuristic policy that maximizes total productivity. Equity is another common concern, where the aim is to balance the workload among employees (Lian et al., 2018; Wu et al., 2018).

## 7. Mathematical programming considerations

This section presents an analysis of the reviewed material from a mathematical programming perspective. The integration of HFs is
<table><caption>**Table 12**
Workforce assignment 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>Nembhard (2001)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Norman et al. (2002)</td><td></td><td>MO-Ho</td><td>CC</td><td>VQ</td><td>S, CPP</td><td>Skills</td></tr><tr><td>Sayin and Karabati (2007)</td><td></td><td>MO</td><td></td><td></td><td>S</td><td>Skills, learning</td></tr><tr><td>Sueer and Tummaluri (2008)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills, learning</td></tr><tr><td>Egilmez et al. (2014)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Brusco (2015)</td><td></td><td>MO-He</td><td></td><td></td><td>S, P</td><td>Skills, satisfaction</td></tr><tr><td>Niakan et al. (2016)</td><td></td><td></td><td>CC, TC</td><td></td><td>S</td><td>Skills, noise</td></tr><tr><td>Ferjani et al. (2017)</td><td>✓</td><td>MO-He</td><td>CC</td><td></td><td>S</td><td>Skills, fatigue effect</td></tr><tr><td>Azadeh et al. (2017)</td><td></td><td>MO</td><td></td><td></td><td>CPP</td><td>Psychosocial</td></tr><tr><td>Fini et al. (2017)</td><td>✓</td><td>SO</td><td></td><td></td><td>S, PP, CPP</td><td>Cognitive, psychosocial</td></tr><tr><td>Lazzerini and Pistolesi (2018)</td><td>✓</td><td>MO</td><td></td><td></td><td>CPP, P</td><td>Satisfaction, expert collaboration</td></tr><tr><td>Wu et al. (2018)</td><td></td><td>MO-He</td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Lian et al. (2018)</td><td></td><td>MO</td><td></td><td>VTT</td><td>S</td><td>Skills, equity</td></tr><tr><td>Zhang et al. (2019b)</td><td>✓</td><td>MO-Ho</td><td>TC</td><td></td><td></td><td>Expert collaboration</td></tr><tr><td>Yilmaz (2020)</td><td></td><td>MO</td><td></td><td>VTT</td><td>S</td><td>Equity</td></tr><tr><td>Lee et al. (2022)</td><td>✓</td><td></td><td>CC</td><td></td><td></td><td>Hazard exposure</td></tr><tr><td>Daş et al. (2022)</td><td></td><td>MO-He</td><td></td><td></td><td>S, CPP</td><td>Skills, psychosocial</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Popularity of existing modeling techniques.</figcaption></figure>

mainly performed through the objective function (see Section 7.1), constraints (see Section 7.2), or parameters (see Section 7.3). This section highlights the impact of HAMs on the structure and complexity of mathematical models and solution methods. Modeling approaches are linked to the most classical HAMs they are applied with. Examples are provided for illustration purposes, but mostly links are made toward topics discussed in Prunet et al. (2024). Fig. 2 shows the popularity of the modeling techniques found in the collected material. Note that the different techniques within the same category (e.g., constraints) are not mutually exclusive, as one paper may use several of those.

## 7.1. Objective function

In this section, we study models where HFs are integrated via an objective function. This is achieved either with a single human-aware objective function (see Section 7.1.1), or with the integration of a human-related objective function alongside other economic-related objectives (see Section 7.1.2).

### 7.1.1. Single objective optimization

A single ergonomic objective is very straightforward to handle from a mathematical point of view. However, considering only a HF-related objective is rarely sufficient while neglecting existing (economic) objectives. Since costs are not included in the objective, this modeling

approach refers mainly to problems where the cost is fixed or bounded, and other quantities are balanced between employees/zones. This class of problems is mainly related to job rotation (Otto and Scholl, 2013), assembly line balancing (Bautista et al., 2016a), or storage assignment in warehousing (Otto et al., 2017). It can also be encountered in driver scheduling models (Otto et al., 2017). Mathematical models involving a single HF-related objective are used mainly in two cases: (i) for special-purpose models, or (ii) when dealing with equity concerns.

**Special-purpose models.** Special-purpose models heavily depend on the problem under study. One can cite (Stewart et al., 1994), where different training strategies lead to different objective functions related to the workforce (e.g., minimizing the training cost, maximizing the workforce flexibility). Sometimes the objective is to minimize the total ER of a plan without computing it for individual employees (Diefenbach et al., 2020).

**Single equity objective.** The main application found in the literature is to deal with equity between employees or lines in an assembly context. This is relevant for problems where the number of resources is already decided, and the goal is to balance these resources efficiently. It is in assembly line balancing or job rotation to find an assignment of operations that balances the workload *evenly* between the park of workstations. In the case of HAMs, this workload is, however, defined in terms of physical workload for the employees, or work-related injury
<table><caption>**Table 12**
Workforce assignment 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>Nembhard (2001)</td><td></td><td></td><td></td><td>VTT</td><td>LR</td><td>Learning</td></tr><tr><td>Norman et al. (2002)</td><td></td><td>MO-Ho</td><td>CC</td><td>VQ</td><td>S, CPP</td><td>Skills</td></tr><tr><td>Sayin and Karabati (2007)</td><td></td><td>MO</td><td></td><td></td><td>S</td><td>Skills, learning</td></tr><tr><td>Sueer and Tummaluri (2008)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills, learning</td></tr><tr><td>Egilmez et al. (2014)</td><td></td><td></td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Brusco (2015)</td><td></td><td>MO-He</td><td></td><td></td><td>S, P</td><td>Skills, satisfaction</td></tr><tr><td>Niakan et al. (2016)</td><td></td><td></td><td>CC, TC</td><td></td><td>S</td><td>Skills, noise</td></tr><tr><td>Ferjani et al. (2017)</td><td>✓</td><td>MO-He</td><td>CC</td><td></td><td>S</td><td>Skills, fatigue effect</td></tr><tr><td>Azadeh et al. (2017)</td><td></td><td>MO</td><td></td><td></td><td>CPP</td><td>Psychosocial</td></tr><tr><td>Fini et al. (2017)</td><td>✓</td><td>SO</td><td></td><td></td><td>S, PP, CPP</td><td>Cognitive, psychosocial</td></tr><tr><td>Lazzerini and Pistolesi (2018)</td><td>✓</td><td>MO</td><td></td><td></td><td>CPP, P</td><td>Satisfaction, expert collaboration</td></tr><tr><td>Wu et al. (2018)</td><td></td><td>MO-He</td><td></td><td>VTT</td><td>S</td><td>Skills</td></tr><tr><td>Lian et al. (2018)</td><td></td><td>MO</td><td></td><td>VTT</td><td>S</td><td>Skills, equity</td></tr><tr><td>Zhang et al. (2019b)</td><td>✓</td><td>MO-Ho</td><td>TC</td><td></td><td></td><td>Expert collaboration</td></tr><tr><td>Yilmaz (2020)</td><td></td><td>MO</td><td></td><td>VTT</td><td>S</td><td>Equity</td></tr><tr><td>Lee et al. (2022)</td><td>✓</td><td></td><td>CC</td><td></td><td></td><td>Hazard exposure</td></tr><tr><td>Daş et al. (2022)</td><td></td><td>MO-He</td><td></td><td></td><td>S, CPP</td><td>Skills, psychosocial</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Popularity of existing modeling techniques.</figcaption></figure>

mainly performed through the objective function (see Section 7.1), constraints (see Section 7.2), or parameters (see Section 7.3). This section highlights the impact of HAMs on the structure and complexity of mathematical models and solution methods. Modeling approaches are linked to the most classical HAMs they are applied with. Examples are provided for illustration purposes, but mostly links are made toward topics discussed in Prunet et al. (2024). Fig. 2 shows the popularity of the modeling techniques found in the collected material. Note that the different techniques within the same category (e.g., constraints) are not mutually exclusive, as one paper may use several of those.

## 7.1. Objective function

In this section, we study models where HFs are integrated via an objective function. This is achieved either with a single human-aware objective function (see Section 7.1.1), or with the integration of a human-related objective function alongside other economic-related objectives (see Section 7.1.2).

### 7.1.1. Single objective optimization

A single ergonomic objective is very straightforward to handle from a mathematical point of view. However, considering only a HF-related objective is rarely sufficient while neglecting existing (economic) objectives. Since costs are not included in the objective, this modeling

approach refers mainly to problems where the cost is fixed or bounded, and other quantities are balanced between employees/zones. This class of problems is mainly related to job rotation (Otto and Scholl, 2013), assembly line balancing (Bautista et al., 2016a), or storage assignment in warehousing (Otto et al., 2017). It can also be encountered in driver scheduling models (Otto et al., 2017). Mathematical models involving a single HF-related objective are used mainly in two cases: (i) for special-purpose models, or (ii) when dealing with equity concerns.

**Special-purpose models.** Special-purpose models heavily depend on the problem under study. One can cite (Stewart et al., 1994), where different training strategies lead to different objective functions related to the workforce (e.g., minimizing the training cost, maximizing the workforce flexibility). Sometimes the objective is to minimize the total ER of a plan without computing it for individual employees (Diefenbach et al., 2020).

**Single equity objective.** The main application found in the literature is to deal with equity between employees or lines in an assembly context. This is relevant for problems where the number of resources is already decided, and the goal is to balance these resources efficiently. It is in assembly line balancing or job rotation to find an assignment of operations that balances the workload *evenly* between the park of workstations. In the case of HAMs, this workload is, however, defined in terms of physical workload for the employees, or work-related injury
risk. The HAMs used to estimate the ER to balance in a single optimization objective, include most observational methods (Bautista et al., 2016a), especially with lifting activities via the NIOSH-equation (Otto et al., 2017) or the JSI (Carnahan et al., 2000), but also with noise exposure (Tharmmaphornphilas and Norman, 2004).

Karsu and Morton (2015) provide a review of the different equity metrics found in the OR literature, i.e., the different functions that can be used to assess if a quantity is well balanced between a set of entities. In the works surveyed in the current review, where a single equity objective is used, the basic min-max balancing criterion is the most common. Here, a set of tasks $N$, each with an associated ER $p_i$, $i \in N$ has to be balanced between a set of employees $W$ over a planning horizon $T$. The assignment decision variable $x_{iwt}$ is equal to 1 if task $i \in N$ is assigned to employee $w \in W$ during period $t \in T$. Then the objective is to minimize the maximal accumulated risk over the planning horizon for the employees, as shown in the following equation:

$$ \min_{w \in W} \max_{i \in T} \sum_{t \in T} \sum_{i \in N} p_i x_{iwt} $$

For further analysis, the interested reader is directed to Karsu and Morton (2015).

### 7.1.2. Multi-objective optimization

Multi-criteria optimization is commonly used to include human well-being and safety in mathematical optimization because it allows taking into account both economic and ergonomic objectives at the same time. Despite the ease of modeling, the challenge of multi-criteria optimization resides in the handling of multiple (and often conflicting) objectives. We distinguish three possibilities to simultaneously handle multiple criteria:

*   **Multiple objectives:** In this case all objective functions are fully considered in the model, and the aim is to compute, or estimate, the so-called Pareto-front. This approach is the most sound in terms of modeling, as no assumption is made on the preferences of the decision-maker.

*   **Aggregation of heterogeneous objectives:** Another possibility is to work with objective functions expressed by heterogeneous quantities (like money and work-related ER), and to aggregate them nonetheless. The decision-maker then has to position the objective function of interest in relation to its relative importance. In this case, the considered objectives are aggregated with weights, which need to be tuned to look at the desired area of the Pareto front. This is, however, non-trivial and often requires a fair amount of work (Branke et al., 2008).

*   **Aggregation of homogeneous objectives:** In this case, objectives are expressed as homogeneous quantities (like money) that are comparable. Therefore, multiple criteria can be added to the objective without requiring additional information.

**Multiple objectives.** Multi-objective optimization is a rather common way to account for HFs. It is used in various areas of logistics: assembly (Battini et al., 2016a), job rotation (Botti et al., 2020), warehousing (Larco et al., 2017), routing (Liu, 2016), scheduling (Lu et al., 2019), or lot sizing (Andriolo et al., 2016). In terms of HFs accounted for, the list is also diverse but mostly focused on ER assessment methods that are reduced or balanced. It includes energy expenditure, manual handling risk assessment methods, posture assessment, or general workload equity concerns.

Dealing with multiple criteria decision-making has an impact both in terms of complexity and choice of solution approaches (Branke et al., 2008). The multi-criteria aspect leads to several non-dominated optimal solutions with respect to the considered criteria, the so-called Pareto front. This approach is especially relevant for industrial applications, as the Pareto front provides a convenient visual representation for the decision-maker. To compute an estimate of this front or some

of its particular points, two methods are mainly used: population-based metaheuristics, and non-interactive mathematical programming approaches.

Population-based metaheuristics are well-studied and have proven their efficiency in dealing with large-scale multi-criteria optimization problems (Branke et al., 2008). Several solutions are kept in memory at all times, with consideration for the population diversity, thus enabling the generation of a set of non-dominated solutions at the end. The most common metaheuristics found are variants of genetic algorithms (Sana et al., 2019; Al-Zuheri et al., 2016), as the NSGA-II algorithm (Rabbani et al., 2020; Azadeh et al., 2017). More seldom, other metaheuristics frameworks have been used, like the artificial bee colony (Li et al., 2018a), the particle swarm optimization (Cui et al., 2020), or the Grey Wolf optimization (Lu et al., 2019).

As far as mathematical programming is concerned, several common multi-criteria methods have been used in the context of this literature review. The most common one is the $\epsilon$-constraint method, which enables the computation of several points of the Pareto front by optimizing over one objective, while the others are constrained by a given value (Bortolini et al., 2017; Finco et al., 2020a). A more basic version of this method is the optimization using lexicographic objectives, where one objective is first optimized and then constrained to its optimal value, then another objective is optimized, and so on. Compared to $\epsilon$-constraint, this approach is more straightforward in its design and implementation but provides less information on the Pareto front (Lehuédé et al., 2020; Liu, 2016).

**Aggregation of heterogeneous objectives.** This modeling approach is fairly common since it is the most basic way to deal with economic and ergonomic objectives. In the retrieved corpus, it has been used in various areas of logistics and manufacturing. These include assembly line balancing (Otto and Scholl, 2011; Bautista et al., 2016b), job rotation (Diego-Mas et al., 2009), workforce scheduling (Yoon et al., 2016; Othman et al., 2012), and vehicle routing (Kim et al., 2006).

A naive method to construct an aggregate objective is, for a feasible solution $x \in X$, to associate with each objective function $g_i(x)$ a weight $0 < w_i < 1$, $i \in \{1, 2, ..., n\}$. These weights are usually normalized so that their sum is equal to one. The aggregate objective function is then the weighted sum of $n$ objectives:

$$ g(x) = \sum_{i=1}^{n} w_i g_i(x) $$

This is analytically and computationally rather easy to do. However, the fine-tuning of these weights is far from trivial to translate well the preferences of the decision maker into quantified trade-offs. Its ease of use has made the weighted sum method fairly popular in the present corpus. One can cite (Bhadury and Radovilsky, 2006; Bautista et al., 2016b) or Diego-Mas et al. (2009) with up to 45 criteria aggregated in a weighted sum. Goal programming is another widely used method to aggregate heterogeneous objectives. The idea is, for each objective function $g_i$ to set a target value $g_i^*$, which corresponds to the desired value for the decision maker. Then the aggregate objective function is to minimize the weighted sum of the deviations from the target values. The advantage of goal programming over the weighted sum approach is that the target values have a concrete interpretation for the decision maker, and are therefore easier to compute. Furthermore, these targets provide natural values for the weights in the sum, by normalizing the deviation to the target value as a percentage. The objective function would then be:

$$ g(x) = \sum_{i=1}^{n} w_i \frac{|g_i^* - g_i(x)|}{g_i^*} $$

An alternative exists, where the Chebyshev distance metric is used instead, i.e., the objective is to minimize the maximum (weighted) deviation from the target values. Goal programming has been used, for instance, in Choi (2009), Sungur et al. (2017) and Mokhtari and Hasani (2017).
risk. The HAMs used to estimate the ER to balance in a single optimization objective, include most observational methods (Bautista et al., 2016a), especially with lifting activities via the NIOSH-equation (Otto et al., 2017) or the JSI (Carnahan et al., 2000), but also with noise exposure (Tharmmaphornphilas and Norman, 2004).

Karsu and Morton (2015) provide a review of the different equity metrics found in the OR literature, i.e., the different functions that can be used to assess if a quantity is well balanced between a set of entities. In the works surveyed in the current review, where a single equity objective is used, the basic min-max balancing criterion is the most common. Here, a set of tasks $N$, each with an associated ER $p_i$, $i \in N$ has to be balanced between a set of employees $W$ over a planning horizon $T$. The assignment decision variable $x_{iwt}$ is equal to 1 if task $i \in N$ is assigned to employee $w \in W$ during period $t \in T$. Then the objective is to minimize the maximal accumulated risk over the planning horizon for the employees, as shown in the following equation:

$$ \min_{w \in W} \max_{i \in T} \sum_{t \in T} \sum_{i \in N} p_i x_{iwt} $$

For further analysis, the interested reader is directed to Karsu and Morton (2015).

### 7.1.2. Multi-objective optimization

Multi-criteria optimization is commonly used to include human well-being and safety in mathematical optimization because it allows taking into account both economic and ergonomic objectives at the same time. Despite the ease of modeling, the challenge of multi-criteria optimization resides in the handling of multiple (and often conflicting) objectives. We distinguish three possibilities to simultaneously handle multiple criteria:

* **Multiple objectives:** In this case all objective functions are fully considered in the model, and the aim is to compute, or estimate, the so-called Pareto-front. This approach is the most sound in terms of modeling, as no assumption is made on the preferences of the decision-maker.

* **Aggregation of heterogeneous objectives:** Another possibility is to work with objective functions expressed by heterogeneous quantities (like money and work-related ER), and to aggregate them nonetheless. The decision-maker then has to position the objective function of interest in relation to its relative importance. In this case, the considered objectives are aggregated with weights, which need to be tuned to look at the desired area of the Pareto front. This is, however, non-trivial and often requires a fair amount of work (Branke et al., 2008).

* **Aggregation of homogeneous objectives:** In this case, objectives are expressed as homogeneous quantities (like money) that are comparable. Therefore, multiple criteria can be added to the objective without requiring additional information.

**Multiple objectives.** Multi-objective optimization is a rather common way to account for HFs. It is used in various areas of logistics: assembly (Battini et al., 2016a), job rotation (Botti et al., 2020), warehousing (Larco et al., 2017), routing (Liu, 2016), scheduling (Lu et al., 2019), or lot sizing (Andriolo et al., 2016). In terms of HFs accounted for, the list is also diverse but mostly focused on ER assessment methods that are reduced or balanced. It includes energy expenditure, manual handling risk assessment methods, posture assessment, or general workload equity concerns.

Dealing with multiple criteria decision-making has an impact both in terms of complexity and choice of solution approaches (Branke et al., 2008). The multi-criteria aspect leads to several non-dominated optimal solutions with respect to the considered criteria, the so-called Pareto front. This approach is especially relevant for industrial applications, as the Pareto front provides a convenient visual representation for the decision-maker. To compute an estimate of this front or some

of its particular points, two methods are mainly used: population-based metaheuristics, and non-interactive mathematical programming approaches.

Population-based metaheuristics are well-studied and have proven their efficiency in dealing with large-scale multi-criteria optimization problems (Branke et al., 2008). Several solutions are kept in memory at all times, with consideration for the population diversity, thus enabling the generation of a set of non-dominated solutions at the end. The most common metaheuristics found are variants of genetic algorithms (Sana et al., 2019; Al-Zuheri et al., 2016), as the NSGA-II algorithm (Rabbani et al., 2020; Azadeh et al., 2017). More seldom, other metaheuristics frameworks have been used, like the artificial bee colony (Li et al., 2018a), the particle swarm optimization (Cui et al., 2020), or the Grey Wolf optimization (Lu et al., 2019).

As far as mathematical programming is concerned, several common multi-criteria methods have been used in the context of this literature review. The most common one is the $\epsilon$-constraint method, which enables the computation of several points of the Pareto front by optimizing over one objective, while the others are constrained by a given value (Bortolini et al., 2017; Finco et al., 2020a). A more basic version of this method is the optimization using lexicographic objectives, where one objective is first optimized and then constrained to its optimal value, then another objective is optimized, and so on. Compared to $\epsilon$-constraint, this approach is more straightforward in its design and implementation but provides less information on the Pareto front (Lehuédé et al., 2020; Liu, 2016).

**Aggregation of heterogeneous objectives.** This modeling approach is fairly common since it is the most basic way to deal with economic and ergonomic objectives. In the retrieved corpus, it has been used in various areas of logistics and manufacturing. These include assembly line balancing (Otto and Scholl, 2011; Bautista et al., 2016b), job rotation (Diego-Mas et al., 2009), workforce scheduling (Yoon et al., 2016; Othman et al., 2012), and vehicle routing (Kim et al., 2006).

A naive method to construct an aggregate objective is, for a feasible solution $x \in X$, to associate with each objective function $g_i(x)$ a weight $0 < w_i < 1$, $i \in \{1, 2, ..., n\}$. These weights are usually normalized so that their sum is equal to one. The aggregate objective function is then the weighted sum of $n$ objectives:

$$ g(x) = \sum_{i=1}^{n} w_i g_i(x) $$

This is analytically and computationally rather easy to do. However, the fine-tuning of these weights is far from trivial to translate well the preferences of the decision maker into quantified trade-offs. Its ease of use has made the weighted sum method fairly popular in the present corpus. One can cite (Bhadury and Radovilsky, 2006; Bautista et al., 2016b) or Diego-Mas et al. (2009) with up to 45 criteria aggregated in a weighted sum. Goal programming is another widely used method to aggregate heterogeneous objectives. The idea is, for each objective function $g_i$ to set a target value $g_i^*$, which corresponds to the desired value for the decision maker. Then the aggregate objective function is to minimize the weighted sum of the deviations from the target values. The advantage of goal programming over the weighted sum approach is that the target values have a concrete interpretation for the decision maker, and are therefore easier to compute. Furthermore, these targets provide natural values for the weights in the sum, by normalizing the deviation to the target value as a percentage. The objective function would then be:

$$ g(x) = \sum_{i=1}^{n} w_i \frac{|g_i^* - g_i(x)|}{g_i^*} $$

An alternative exists, where the Chebyshev distance metric is used instead, i.e., the objective is to minimize the maximum (weighted) deviation from the target values. Goal programming has been used, for instance, in Choi (2009), Sungur et al. (2017) and Mokhtari and Hasani (2017).
Overall, a heterogeneous aggregation of several objectives is much easier to handle than true multi-objective optimization, both analytically and computationally. However, information is lost since a single solution is found instead of a set of non-dominated ones. This can make an actual implementation trickier to fine-tune to the decision maker's preferences.

**Aggregation of homogeneous objectives.** Another way to deal with multiple objectives is to convert them into homogeneous quantities. This way they are comparable, and the trade-off is easier to find. The big advantage of this kind of modeling is that the model has only one objective, thus being analytically and computationally easier, without requiring the decision maker to quantify his/her needs to fine-tune an implementation of the model. However, to be feasible, the considered objectives should be expressed in homogeneous quantities, which, depending on the context, can be rather difficult. Usually, the aggregated objective is expressed as a total cost since it is a rather common concern for companies to quantify the direct and indirect economic impacts of their decisions. Note that, to use this modeling, a HAM should be convertible to a monetary cost, which limits the applicability.

This modeling approach is interesting to use since it combines both accuracy in the decision-making process and ease of computation. However, the problem at hand should be compatible with such modeling, which is not always the case. It is used in different areas of logistics and manufacturing, such as lot sizing (Battini et al., 2017c), assembly line balancing (Kara et al., 2014), workforce scheduling (Jamshidi and Seyyed Esfahani, 2014) or warehousing (Battini et al., 2017b).

A common approach is based on fatigue with energy expenditure and rest allowance. The general idea is that when the fatigue level of an employee increases, the ER increases accordingly. Therefore, for each work period, one can compute a rest allowance corresponding to a break period enabling the recovery, which can easily be translated into a cost using the hourly wage of the employee since it corresponds to paid unproductive time (Battini et al., 2017c; Condeixa et al., 2020; Glock et al., 2019c). A high level of fatigue also leads to a rise in the error rate, which can easily be quantified as a cost and integrated into the objective function (Kuo et al., 2014).

Another common modeling refers to the WMSD risk. A high level of work-related injuries might impact indirectly several cost items of a company. Sobhani et al. (2017), Sobhani and Wahab (2017) and Sobhani et al. (2019) try to quantify this monetary impact. The objective function they use is expressed in terms of a monetary cost and includes several terms that correspond to different cost items, potentially impacted by poor working conditions: performance loss, injury leave costs, increased insurance costs, hiring and firing costs for replacement short-term employees or to compensate a high turnover rate, etc. Another interesting approach is to account for the cost of risk-mitigation measures when faced with a hazardous work environment. For example, Razavi et al. (2014) account for noise control in a manufacturing environment, and their objective function includes personal and machine equipment to keep the noise-related risks at an acceptable level.

Finally, when considering employees' skills, it is possible to link the skill level to productivity rate (Norman et al., 2002), error rate (McDonald et al., 2009) and, of course, wages (Moon et al., 2009). All these aspects impact the cost structure.

## 7.2. Constraints

Another widespread way to consider human-related factors in optimization models is across constraints. Several types of human-aware constraints can be identified within the collected material: compatibility constraints, threshold constraints, forbidden sequence constraints, and work-stretch duration constraints.

**Compatibility constraints.** Compatibility constraints are one of the most basic ways to integrate human considerations into mathematical models. They are mostly used when the aim is to assign a set $W$ of human resources (often employees) to a set $\mathcal{N}$ of tasks in accordance with the skills of employees. Compatibility constraints are mostly used to model the skills and qualifications for workforce scheduling (Pan et al., 2010) or assembly line balancing (Manavizadeh et al., 2013), more seldom, for vehicle routing when drivers scheduling is integrated (Anoshkina and Meisel, 2020).

To better reflect practical considerations, additional modeling layers can be added to the problem. The idea behind this is always that a subset of assignments is forbidden. For example, each worker $w \in W$ is associated with a set $\mathcal{N}(w)$ of tasks he/she is able to perform, or with the opposite view each task $i \in \mathcal{N}$ is associated with a set $W(i)$ of workers that can perform it. When skills are explicitly accounted for, the problem definition contains a set $S$ of skills that can represent either different competencies or qualifications, a single competence with different proficiency levels, or both at the same time. In this case, each employee $w$ is associated with a set $S(w)$ of skills he/she is able to perform, and each task $i$ requires a set $S(i)$ of competences to be operated (e.g., Pan et al. (2010)). Then an assignment is possible when the employee possesses the skills required for the task. Sometimes several employees can be assigned to a task, and the skill requirement applies to the group as a whole, and not to each individual. This is found in problems dealing with cell formation in manufacturing (Aryanezhad et al., 2009a), or technician routing problems (Mathlouthi et al., 2018), where the teams should have a broad skill set.

From a complexity perspective, these constraints do not significantly change the problem. With fewer feasible assignments, the problem becomes more constrained. It could therefore be more complicated to find feasible solutions, depending on the number of constraints applied to a specific instance. However, in the reviewed papers, the main challenge is the optimization of the problem since the skill resources are not scarce enough to make feasibility challenging. This modeling requires considering a heterogeneous workforce, slightly increasing the problem size depending on the granularity of the skill set (i.e., the number of skills considered). This modeling is, apart from early work, used mostly in addition to other human aspects that are computationally more challenging to consider in mathematical models.

**Threshold constraints.** Threshold constraints are mostly used when assigning or scheduling tasks. The idea is that each task is associated with an ER. Then there is a threshold value for accumulated ER for an employee over a shift. This modeling is mostly used when dealing with risk estimation methods, like WMSD risk assessment methods or energy expenditure. Sometimes it is also applied to environmental factors that are also linked to occupational risks, like noise or heat exposure. It is applied to various kinds of logistics and manufacturing problems related to assembly line balancing (Otto and Scholl, 2011), job rotation (Mossa et al., 2016), warehousing (Zhao et al., 2019), scheduling (Yi and Wang, 2017) or vehicle routing (Rattanamanee et al., 2015).

Threshold constraints are very classical in the OR literature, often called “capacity constraints”. A set $\mathcal{N}$ of tasks has to be assigned to a set $W$ of workers. Each task $i \in \mathcal{N}$ has a risk score $p_i > 0$. An assignment variable $x_{i,w} \in \{0, 1\}$ is equal to 1, if task $i \in \mathcal{N}$ is assigned to worker $w \in W$ during the shift. A threshold value $p_{max}$ is given and should not be violated by the accumulated ER of tasks assigned to each employee, ensuring the risk remains at an acceptable level. Then, the threshold constraint is of the form:

$$ \sum_{i \in \mathcal{N}} p_i x_{i,w} \le p_{max} \quad \forall w \in W. \quad (1) $$

The modeling of the assignment task/employee can be more sophisticated, especially when considering the scheduling of the tasks, where time is accounted for. Usually, in this family of constraints, the sequencing of tasks does not matter. Often the risk level of a task
Overall, a heterogeneous aggregation of several objectives is much easier to handle than true multi-objective optimization, both analytically and computationally. However, information is lost since a single solution is found instead of a set of non-dominated ones. This can make an actual implementation trickier to fine-tune to the decision maker's preferences.

**Aggregation of homogeneous objectives.** Another way to deal with multiple objectives is to convert them into homogeneous quantities. This way they are comparable, and the trade-off is easier to find. The big advantage of this kind of modeling is that the model has only one objective, thus being analytically and computationally easier, without requiring the decision maker to quantify his/her needs to fine-tune an implementation of the model. However, to be feasible, the considered objectives should be expressed in homogeneous quantities, which, depending on the context, can be rather difficult. Usually, the aggregated objective is expressed as a total cost since it is a rather common concern for companies to quantify the direct and indirect economic impacts of their decisions. Note that, to use this modeling, a HAM should be convertible to a monetary cost, which limits the applicability.

This modeling approach is interesting to use since it combines both accuracy in the decision-making process and ease of computation. However, the problem at hand should be compatible with such modeling, which is not always the case. It is used in different areas of logistics and manufacturing, such as lot sizing (Battini et al., 2017c), assembly line balancing (Kara et al., 2014), workforce scheduling (Jamshidi and Seyyed Esfahani, 2014) or warehousing (Battini et al., 2017b).

A common approach is based on fatigue with energy expenditure and rest allowance. The general idea is that when the fatigue level of an employee increases, the ER increases accordingly. Therefore, for each work period, one can compute a rest allowance corresponding to a break period enabling the recovery, which can easily be translated into a cost using the hourly wage of the employee since it corresponds to paid unproductive time (Battini et al., 2017c; Condeixa et al., 2020; Glock et al., 2019c). A high level of fatigue also leads to a rise in the error rate, which can easily be quantified as a cost and integrated into the objective function (Kuo et al., 2014).

Another common modeling refers to the WMSD risk. A high level of work-related injuries might impact indirectly several cost items of a company. Sobhani et al. (2017), Sobhani and Wahab (2017) and Sobhani et al. (2019) try to quantify this monetary impact. The objective function they use is expressed in terms of a monetary cost and includes several terms that correspond to different cost items, potentially impacted by poor working conditions: performance loss, injury leave costs, increased insurance costs, hiring and firing costs for replacement short-term employees or to compensate a high turnover rate, etc. Another interesting approach is to account for the cost of risk-mitigation measures when faced with a hazardous work environment. For example, Razavi et al. (2014) account for noise control in a manufacturing environment, and their objective function includes personal and machine equipment to keep the noise-related risks at an acceptable level.

Finally, when considering employees' skills, it is possible to link the skill level to productivity rate (Norman et al., 2002), error rate (McDonald et al., 2009) and, of course, wages (Moon et al., 2009). All these aspects impact the cost structure.

## 7.2. Constraints

Another widespread way to consider human-related factors in optimization models is across constraints. Several types of human-aware constraints can be identified within the collected material: compatibility constraints, threshold constraints, forbidden sequence constraints, and work-stretch duration constraints.

**Compatibility constraints.** Compatibility constraints are one of the most basic ways to integrate human considerations into mathematical models. They are mostly used when the aim is to assign a set $W$ of human resources (often employees) to a set $N$ of tasks in accordance with the skills of employees. Compatibility constraints are mostly used to model the skills and qualifications for workforce scheduling (Pan et al., 2010) or assembly line balancing (Manavizadeh et al., 2013), more seldom, for vehicle routing when drivers scheduling is integrated (Anoshkina and Meisel, 2020).

To better reflect practical considerations, additional modeling layers can be added to the problem. The idea behind this is always that a subset of assignments is forbidden. For example, each worker $w \in W$ is associated with a set $N(w)$ of tasks he/she is able to perform, or with the opposite view each task $i \in N$ is associated with a set $W(i)$ of workers that can perform it. When skills are explicitly accounted for, the problem definition contains a set $S$ of skills that can represent either different competencies or qualifications, a single competence with different proficiency levels, or both at the same time. In this case, each employee $w$ is associated with a set $S(w)$ of skills he/she is able to perform, and each task $i$ requires a set $S(i)$ of competences to be operated (e.g., Pan et al. (2010)). Then an assignment is possible when the employee possesses the skills required for the task. Sometimes several employees can be assigned to a task, and the skill requirement applies to the group as a whole, and not to each individual. This is found in problems dealing with cell formation in manufacturing (Aryanezhad et al., 2009a), or technician routing problems (Mathlouthi et al., 2018), where the teams should have a broad skill set.

From a complexity perspective, these constraints do not significantly change the problem. With fewer feasible assignments, the problem becomes more constrained. It could therefore be more complicated to find feasible solutions, depending on the number of constraints applied to a specific instance. However, in the reviewed papers, the main challenge is the optimization of the problem since the skill resources are not scarce enough to make feasibility challenging. This modeling requires considering a heterogeneous workforce, slightly increasing the problem size depending on the granularity of the skill set (i.e., the number of skills considered). This modeling is, apart from early work, used mostly in addition to other human aspects that are computationally more challenging to consider in mathematical models.

**Threshold constraints.** Threshold constraints are mostly used when assigning or scheduling tasks. The idea is that each task is associated with an ER. Then there is a threshold value for accumulated ER for an employee over a shift. This modeling is mostly used when dealing with risk estimation methods, like WMSD risk assessment methods or energy expenditure. Sometimes it is also applied to environmental factors that are also linked to occupational risks, like noise or heat exposure. It is applied to various kinds of logistics and manufacturing problems related to assembly line balancing (Otto and Scholl, 2011), job rotation (Mossa et al., 2016), warehousing (Zhao et al., 2019), scheduling (Yi and Wang, 2017) or vehicle routing (Rattanamanee et al., 2015).

Threshold constraints are very classical in the OR literature, often called “capacity constraints”. A set $N$ of tasks has to be assigned to a set $W$ of workers. Each task $i \in N$ has a risk score $p_i > 0$. An assignment variable $x_{i,w} \in \{0, 1\}$ is equal to 1, if task $i \in N$ is assigned to worker $w \in W$ during the shift. A threshold value $p_{max}$ is given and should not be violated by the accumulated ER of tasks assigned to each employee, ensuring the risk remains at an acceptable level. Then, the threshold constraint is of the form:

$$ \sum_{i \in N} p_i x_{i,w} \le p_{max} \quad \forall w \in W. \quad (1) $$

The modeling of the assignment task/employee can be more sophisticated, especially when considering the scheduling of the tasks, where time is accounted for. Usually, in this family of constraints, the sequencing of tasks does not matter. Often the risk level of a task
is weighted by the time spent performing this task, according to a given ER assessment method. Nevertheless, this family of constraints is ultimately equivalent to the basic form of Inequalities (1). The value of the threshold $p_{max}$ is often derived from the risk assessment method and is set to an acceptable risk level for the shift. The risk assessment method can be: the OCRA index (Mossa et al., 2016), the NIOSH-equation (Mateo et al., 2020), the energy expenditure (Zhao et al., 2019), or the DND (Razavi et al., 2014). Sometimes the threshold value is set with respect to legal constraints about employees' exposure, e.g., related to toxic substance exposure (Villeda and Dean, 1990). In Ruiz-Torres et al. (2015), the opposite constraint is used, where each employee satisfaction level should be above a given threshold.

**Forbidden sequence constraints.** Forbidden sequence constraints are used to avoid some successions of tasks/shifts when designing a schedule. Indeed, when performing a physical task of high intensity, the ER increases with the duration of the task. In observational risk estimation methods, the exertion duration is often a key parameter. A forbidden sequence constraint ensures a maximum number (often one) of successive strenuous tasks scheduled for a given operator. The threshold constraints are a suitable method to limit the risk exposure of an employee on his/her shift. However, they miss a key component of the risk estimation, namely, the duration of the uninterrupted exertion. Forbidden sequence constraints are a way to bring more refinement and accuracy to models that already have mechanisms to limit/balance the ER over a shift (see e.g., Moussavi et al. (2019)). Naturally, forbidden sequence constraints are mostly found in job rotation models (Moussavi et al., 2019; Yoon et al., 2016), or work-rest scheduling problems, since they account for the sequence of assigned tasks to a workstation or an employee (Gärtner et al., 2001; Aravindkrishna et al., 2009).

In terms of complexity, these constraints are rather straightforward to handle from a modeling point of view. However, the problem becomes significantly more constrained. Moreover, the insertion of these constraints in an existing model might lead to infeasibility, and overall feasibility becomes more complicated to ensure. One should note that the reduction of successive high workloads is also commonly found as an objective function instead of a constraint (Asensio-Cuesta et al., 2012b; Botti et al., 2020). Modeling this aspect as an objective addresses the aforementioned drawbacks of the forbidden sequence constraints, however, other difficulties might arise with the handling of several objectives (see Section 7.1).

**Time window constraints.** The time window constraint is a widely used modeling technique in OR (see Fig. 2). It applies mostly when scheduling a set of activities, that need to be performed in a given time frame. In these problems, decisions have to be made related to the start time of a given set $N$ of operations. For a given activity $i \in N$, a time window constraint ensures that the activity $i$ starts during a given time window $[a_i, b_i]$. With $t_i$ the decision variable defining the start time of the activity, the mathematical constraint is then $a_i \le t_i \le b_i$.

In the scope of this review, the activities concerned with time window constraints are work breaks. There are indeed several ways to model the integration of breaks in a workforce schedule, the most basic one being through time windows. It corresponds to mostly early work on the topic, where a meal break has to be scheduled in the work shift with a flexible start time (Thompson, 1990). However, the meal break should happen roughly at mealtime, thus the time window. In the retrieved corpus, this modeling is mostly found in workforce scheduling problems (Brusco, 2008; Brusco and Jacobs, 2000), but also within the routing literature when driver meal breaks need to be scheduled (Kim et al., 2006; Coelho et al., 2016).

In terms of complexity, time window constraints are often easy to integrate. This modeling adds a number of activities to schedule (the breaks) on top of the productive tasks, which constraint slightly the problem. Although the consideration of time window constraints was challenging in the early literature on the topic (Solomon and Desrosiers, 1988), they are nowadays common and well-studied features in various

classes of problems. In most applications, they do not provide a significant algorithmic challenge compared to the other constraints in the model.

**Forward-backward constraints.** Forward-backward constraints are commonly used when dealing with break scheduling. With this approach, a set of rules is defined to ensure that the quantity, duration, and/or placement of breaks comply with either work regulations or company policies. The objective is to give the mathematical models more flexibility than using time windows while prohibiting schedules that are of poor interest in practice. For example, scheduling a break just after the shift starts, or scheduling all the breaks one after another. In practice, rest breaks should be spread over the work shift to enable recovery. The rules defining the forward-backward constraints vary from one paper to another, more details can be found in Prunet et al. (2024), *Regulatory breaks and Work-stretch durations*, but some examples would be: "The first break should be scheduled at least 2 h after the shift starts", "A shift should contain one lunch break of a minimum duration of 1h" or "The work duration between two consecutive breaks must be at least 2 h, and at most 4h".

A more theoretical and general description of forward-backward constraints can be found in Widl and Musliu (2014) and Rekik et al. (2008). There are two main areas of application to forward-backward constraints: shift scheduling and vehicle routing. In vehicle routing, these rules are usually aligned with official regulations. Several countries have legislated on truck drivers' working times. The rules depend on the country, but follow the same framework (Goel, 2009; Prescott-Gagnon et al., 2010; Rancourt et al., 2013). Work-rest scheduling is the other main application area of forward-backward constraints. There is no regulation to comply with in this case, however, the flexibility allowed by this modeling is still worth considering (Gärtner et al., 2001; Restrepo et al., 2012; Quimper and Rousseau, 2010).

The flexibility gained from this modeling approach often leads to better quality solutions compared to time window constraints (Rekik et al., 2008, 2010). However, this flexibility comes at a cost in terms of complexity. One common technique to deal with this complexity is to consider break placement implicitly. This can be done directly in the formulation (Rekik et al., 2010), or these aspects can be convexified in the subproblem within a decomposition framework (Prescott-Gagnon et al., 2010; Ceselli et al., 2009).

### 7.3. Parameters

The HFs might be integrated directly in the parameters of the problem, either with *varying task time*, *varying quality*, or a *heterogeneous workforce*. The impact on optimization models varies depending on which aspect is considered and how it is integrated. Nevertheless, one can assume that considering heterogeneous characteristics will often increase the computational burden that follows by the need to consider extra dimensions in the mathematical models. These extra dimensions may be the time needed to capture the change of a parameter over the shift. It can also be the explicit consideration of employees to take into account their different skills. Finally, the model can be stochastic in nature.

#### 7.3.1. *Varying task time*

Varying task time is one of the main ways to model HFs in optimization models (see Fig. 2). It is indeed a very flexible tool, which can be adapted to a wide range of HFs, and fits well in the OR frameworks. The idea is rather simple: instead of being a fixed parameter, the processing time of a task performed by a human operator varies. This variation can be purely stochastic to model the intrinsic variability of the performance of a human operator (Chiang and Urban, 2006; Egilmez et al., 2014; Sotskov et al., 2015). However, most of the time, processing times are deterministic and depend on the characteristics of the operator (e.g., skill, fatigue level). In terms of application fields, this
is weighted by the time spent performing this task, according to a given ER assessment method. Nevertheless, this family of constraints is ultimately equivalent to the basic form of Inequalities (1). The value of the threshold $p_{max}$ is often derived from the risk assessment method and is set to an acceptable risk level for the shift. The risk assessment method can be: the OCRA index (Mossa et al., 2016), the NIOSH-equation (Mateo et al., 2020), the energy expenditure (Zhao et al., 2019), or the DND (Razavi et al., 2014). Sometimes the threshold value is set with respect to legal constraints about employees' exposure, e.g., related to toxic substance exposure (Villeda and Dean, 1990). In Ruiz-Torres et al. (2015), the opposite constraint is used, where each employee satisfaction level should be above a given threshold.

**Forbidden sequence constraints.** Forbidden sequence constraints are used to avoid some successions of tasks/shifts when designing a schedule. Indeed, when performing a physical task of high intensity, the ER increases with the duration of the task. In observational risk estimation methods, the exertion duration is often a key parameter. A forbidden sequence constraint ensures a maximum number (often one) of successive strenuous tasks scheduled for a given operator. The threshold constraints are a suitable method to limit the risk exposure of an employee on his/her shift. However, they miss a key component of the risk estimation, namely, the duration of the uninterrupted exertion. Forbidden sequence constraints are a way to bring more refinement and accuracy to models that already have mechanisms to limit/balance the ER over a shift (see e.g., Moussavi et al. (2019)). Naturally, forbidden sequence constraints are mostly found in job rotation models (Moussavi et al., 2019; Yoon et al., 2016), or work-rest scheduling problems, since they account for the sequence of assigned tasks to a workstation or an employee (Gärtner et al., 2001; Aravindkrishna et al., 2009).

In terms of complexity, these constraints are rather straightforward to handle from a modeling point of view. However, the problem becomes significantly more constrained. Moreover, the insertion of these constraints in an existing model might lead to infeasibility, and overall feasibility becomes more complicated to ensure. One should note that the reduction of successive high workloads is also commonly found as an objective function instead of a constraint (Asensio-Cuesta et al., 2012b; Botti et al., 2020). Modeling this aspect as an objective addresses the aforementioned drawbacks of the forbidden sequence constraints, however, other difficulties might arise with the handling of several objectives (see Section 7.1).

**Time window constraints.** The time window constraint is a widely used modeling technique in OR (see Fig. 2). It applies mostly when scheduling a set of activities, that need to be performed in a given time frame. In these problems, decisions have to be made related to the start time of a given set $N$ of operations. For a given activity $i \in N$, a time window constraint ensures that the activity $i$ starts during a given time window $[a_i, b_i]$. With $t_i$ the decision variable defining the start time of the activity, the mathematical constraint is then $a_i \le t_i \le b_i$.

In the scope of this review, the activities concerned with time window constraints are work breaks. There are indeed several ways to model the integration of breaks in a workforce schedule, the most basic one being through time windows. It corresponds to mostly early work on the topic, where a meal break has to be scheduled in the work shift with a flexible start time (Thompson, 1990). However, the meal break should happen roughly at mealtime, thus the time window. In the retrieved corpus, this modeling is mostly found in workforce scheduling problems (Brusco, 2008; Brusco and Jacobs, 2000), but also within the routing literature when driver meal breaks need to be scheduled (Kim et al., 2006; Coelho et al., 2016).

In terms of complexity, time window constraints are often easy to integrate. This modeling adds a number of activities to schedule (the breaks) on top of the productive tasks, which constraint slightly the problem. Although the consideration of time window constraints was challenging in the early literature on the topic (Solomon and Desrosiers, 1988), they are nowadays common and well-studied features in various

classes of problems. In most applications, they do not provide a significant algorithmic challenge compared to the other constraints in the model.

**Forward-backward constraints.** Forward-backward constraints are commonly used when dealing with break scheduling. With this approach, a set of rules is defined to ensure that the quantity, duration, and/or placement of breaks comply with either work regulations or company policies. The objective is to give the mathematical models more flexibility than using time windows while prohibiting schedules that are of poor interest in practice. For example, scheduling a break just after the shift starts, or scheduling all the breaks one after another. In practice, rest breaks should be spread over the work shift to enable recovery. The rules defining the forward-backward constraints vary from one paper to another, more details can be found in Prunet et al. (2024), Regulatory breaks and Work-stretch durations, but some examples would be: "The first break should be scheduled at least 2 h after the shift starts", "A shift should contain one lunch break of a minimum duration of 1h" or "The work duration between two consecutive breaks must be at least 2 h, and at most 4h".

A more theoretical and general description of forward-backward constraints can be found in Widl and Musliu (2014) and Rekik et al. (2008). There are two main areas of application to forward-backward constraints: shift scheduling and vehicle routing. In vehicle routing, these rules are usually aligned with official regulations. Several countries have legislated on truck drivers' working times. The rules depend on the country, but follow the same framework (Goel, 2009; Prescott-Gagnon et al., 2010; Rancourt et al., 2013). Work-rest scheduling is the other main application area of forward-backward constraints. There is no regulation to comply with in this case, however, the flexibility allowed by this modeling is still worth considering (Gärtner et al., 2001; Restrepo et al., 2012; Quimper and Rousseau, 2010).

The flexibility gained from this modeling approach often leads to better quality solutions compared to time window constraints (Rekik et al., 2008, 2010). However, this flexibility comes at a cost in terms of complexity. One common technique to deal with this complexity is to consider break placement implicitly. This can be done directly in the formulation (Rekik et al., 2010), or these aspects can be convexified in the subproblem within a decomposition framework (Prescott-Gagnon et al., 2010; Ceselli et al., 2009).

### 7.3. Parameters

The HFs might be integrated directly in the parameters of the problem, either with varying task time, varying quality, or a heterogeneous workforce. The impact on optimization models varies depending on which aspect is considered and how it is integrated. Nevertheless, one can assume that considering heterogeneous characteristics will often increase the computational burden that follows by the need to consider extra dimensions in the mathematical models. These extra dimensions may be the time needed to capture the change of a parameter over the shift. It can also be the explicit consideration of employees to take into account their different skills. Finally, the model can be stochastic in nature.

#### 7.3.1. Varying task time

Varying task time is one of the main ways to model HFs in optimization models (see Fig. 2). It is indeed a very flexible tool, which can be adapted to a wide range of HFs, and fits well in the OR frameworks. The idea is rather simple: instead of being a fixed parameter, the processing time of a task performed by a human operator varies. This variation can be purely stochastic to model the intrinsic variability of the performance of a human operator (Chiang and Urban, 2006; Egilmez et al., 2014; Sotskov et al., 2015). However, most of the time, processing times are deterministic and depend on the characteristics of the operator (e.g., skill, fatigue level). In terms of application fields, this
modeling is mostly used in operational problems, where the granularity of the modeling allows us to consider individual execution times. Scheduling problems are a natural application, for example, production scheduling (Lee and Wu, 2009; Gong et al., 2020b), workforce scheduling (Yilmaz, 2020), or assembly lines (Ostermeier, 2020). Other applications are found in logistics, such as warehousing (Matusiak et al., 2017), or vehicle routing (Yan et al., 2019). Furthermore, this topic has also been studied from a more theoretical perspective with complexity studies (Janiak and Rudek, 2010; Lee and Wu, 2009; Wu and Lee, 2008).

Several factors are found to affect the processing time of tasks, as the workforce skills (Akyol and Baykasoğlu, 2019; Azizi et al., 2010), or the position of the task in the shift schedule (Biskup, 1999; Otto and Otto, 2014). The task time depending on its position in a shift is a very common modeling approach for problems related to employee learning since the repetition of a similar task improves the efficiency of the operator. However, it is also used to model a fatigue effect, where the productivity of an operator decreases as fatigue increases toward the end of a work shift (Sanchez-Herrera et al., 2019; Wang et al., 2020). Another very similar modeling technique is to adjust the processing time of a task depending on the sum of the processing times of tasks scheduled before. This is a very common modeling approach to the learning process (Zhang and Gen, 2011; Wang et al., 2019). It is also used when dealing with fatigue, where the productivity of an employee decreases according to a given function that depends on the time passed since the last rest break. In some papers, learning and fatigue effects are considered together, with their opposite effects on processing time (Givi et al., 2015b; Ostermeier, 2020).

The impact on optimization models varies depending on which aspect is considered, and how it is integrated. Nevertheless, one can assume that considering varying task times will often increase the computational burden of the models. It is however interesting that for scheduling models the problems seem to stay polynomial in several cases (Wu and Lee, 2008; Lee and Wu, 2009).

### 7.3.2. Varying quality

Some researchers consider that the quality level of the production is not a fixed exogenous parameter, but depends on the characteristics of the employee operating the given task. Several factors can be used to measure the quality level of production. The most common one is the skill level of the employee performing the task (De Bruecker et al., 2015). A varying quality level is mainly used when dealing with workforce planning when it depends on the skill level (Norman et al., 2002; McDonald et al., 2009). Learning, as the determining factor of the quality level, has also been used in the literature. One can especially cite (Givi et al., 2015b) and Givi et al. (2015a), who extend the learning forgetting fatigue recovery model to account for a quality improvement in the learning process. Another possibility is to model the error rate through a probabilistic framework. Khan et al. (2012) and Khan et al. (2014) study the human error taxonomy and classification with associated probabilities. In some other applications, errors are modeled using random variables with known density functions (Shin et al., 2018; Gilotra et al., 2020).

Employee fatigue is another major source of errors, and several empirical studies show a clear link between human fatigue and production quality (Yung et al., 2020). This source of errors is, for instance, a common consideration in warehousing studies focusing on order picking (Zhao et al., 2019; Grosse et al., 2017b).

### 7.3.3. Heterogeneous workforce

Other models worth mentioning are those considering a heterogeneous workforce. Historically, the homogeneity of the workforce is a common assumption in OR models. It is indeed generally very convenient from a mathematical point of view, and the hypothesis is valid for a number of applications. However, in some cases, a finer granularity in the modeling of the workforce is necessary to consider certain effects.

This modeling is not attached to a particular HAM and is most of the time used within another modeling approach (e.g., objective function, or constraints). An interested reader is referred to Katiraee et al. (2021) for a dedicated review on the topic.

A heterogeneous workforce is naturally encountered when dealing with skills, otherwise all employees would have the same skill set. This case is denoted *S* in the result tables. The underlying idea of integrating skills in an optimization model can be twofold: (i) Employees as a heterogeneous set of resources. In this case, the skills represent different jobs or qualifications, enforced via compatibility constraints (Calzavara et al., 2019a; Hochdörffer et al., 2018; Joo and Kim, 2013), or (ii) Employees as a single set of resources, yet with different throughput/cost. In this case, the skills represent the proficiency of the employee on a set of tasks, enforced with varying task times, or varying quality (Hong, 2018; Khan et al., 2012; Matusiak et al., 2017). Note that neither case is exclusive to each other.

Related to skills, learning rates can also vary between employees. This case is denoted *LR* in the result tables. When working with learning curves, it is reasonable to suppose there is some discrepancy between employees in terms of learning rates. This modeling is mostly used in studies that focus on modeling with more accuracy the performances and their variations in a workforce. It has mainly seen use in workforce-focused problems, like workforce planning (Fowler et al., 2008; Attia et al., 2014), but also warehousing (Grosse and Glock, 2015; Grosse et al., 2013), machine scheduling (Marichelvam et al., 2020), shift scheduling (Gans and Zhou, 2002), and job rotation (Ayough et al., 2020).

The heterogeneity of the workforce can also be based on other intrinsic properties of its components. In the result tables, this is referred to as *PP* for Physical Properties, and *CPP* for Cognitive and Psychosocial Properties. These parameters are mostly risk factors for developing WMSD and are accounted for when computing the estimation of the ER of a work situation. It is indeed known that individuals have different chances of developing occupational diseases when facing a given work situation (Bridger, 2018). This can depend, for example, on the age of the person (Yi and Wang, 2017), his/her lifting capabilities (Carnahan et al., 2000), the physical fatigue he/she can safely sustain (Rattanamanee et al., 2015) or even its smoking and drinking habits (Yi and Chan, 2015). However, most of the time the individual physical parameters can be seen as *skills* in the sense that they affect the processing times of tasks or learning characteristics. Concerning psychosocial characteristics, they can be used to create teams with compatible decision-making styles (Azadeh et al., 2017), to account for the carefulness of the employees in a context of hazardous work environment (Lazzerini and Pistolesi, 2018), or to consider the motivation and personality of individuals when assigning tasks (Othman et al., 2012).

The last parameter that can differ between employees is their individual work preferences, noted *P* in the result tables. This parameter is used when accounting for the satisfaction of the workforce, either as an objective function, or threshold constraints that enforce a minimal satisfaction level for each employee, in a search for equity (Ruiz-Torres et al., 2015, 2019; Akbari et al., 2013).

Modeling the workforce as heterogeneous might have a substantial impact on decision models. The most obvious one is that a parameter that was constant over the workforce now depends on the concerned individual. This means that the decision variables should be able to model the individual assignment/schedule of the employees. Note that this is most of the time already the case in the problems studied in this review, especially the workforce-related ones. This individual-dependent parameter can add some complexity to an existing model. However, it also breaks symmetries, which is often beneficial for the performance of solution approaches, especially when using mathematical programming-based methods (Margot, 2010).
modeling is mostly used in operational problems, where the granularity of the modeling allows us to consider individual execution times. Scheduling problems are a natural application, for example, production scheduling (Lee and Wu, 2009; Gong et al., 2020b), workforce scheduling (Yilmaz, 2020), or assembly lines (Ostermeier, 2020). Other applications are found in logistics, such as warehousing (Matusiak et al., 2017), or vehicle routing (Yan et al., 2019). Furthermore, this topic has also been studied from a more theoretical perspective with complexity studies (Janiak and Rudek, 2010; Lee and Wu, 2009; Wu and Lee, 2008).

Several factors are found to affect the processing time of tasks, as the workforce skills (Akyol and Baykasoğlu, 2019; Azizi et al., 2010), or the position of the task in the shift schedule (Biskup, 1999; Otto and Otto, 2014). The task time depending on its position in a shift is a very common modeling approach for problems related to employee learning since the repetition of a similar task improves the efficiency of the operator. However, it is also used to model a fatigue effect, where the productivity of an operator decreases as fatigue increases toward the end of a work shift (Sanchez-Herrera et al., 2019; Wang et al., 2020). Another very similar modeling technique is to adjust the processing time of a task depending on the sum of the processing times of tasks scheduled before. This is a very common modeling approach to the learning process (Zhang and Gen, 2011; Wang et al., 2019). It is also used when dealing with fatigue, where the productivity of an employee decreases according to a given function that depends on the time passed since the last rest break. In some papers, learning and fatigue effects are considered together, with their opposite effects on processing time (Givi et al., 2015b; Ostermeier, 2020).

The impact on optimization models varies depending on which aspect is considered, and how it is integrated. Nevertheless, one can assume that considering varying task times will often increase the computational burden of the models. It is however interesting that for scheduling models the problems seem to stay polynomial in several cases (Wu and Lee, 2008; Lee and Wu, 2009).

### 7.3.2. Varying quality

Some researchers consider that the quality level of the production is not a fixed exogenous parameter, but depends on the characteristics of the employee operating the given task. Several factors can be used to measure the quality level of production. The most common one is the skill level of the employee performing the task (De Bruecker et al., 2015). A varying quality level is mainly used when dealing with workforce planning when it depends on the skill level (Norman et al., 2002; McDonald et al., 2009). Learning, as the determining factor of the quality level, has also been used in the literature. One can especially cite (Givi et al., 2015b) and Givi et al. (2015a), who extend the learning forgetting fatigue recovery model to account for a quality improvement in the learning process. Another possibility is to model the error rate through a probabilistic framework. Khan et al. (2012) and Khan et al. (2014) study the human error taxonomy and classification with associated probabilities. In some other applications, errors are modeled using random variables with known density functions (Shin et al., 2018; Gilotra et al., 2020).

Employee fatigue is another major source of errors, and several empirical studies show a clear link between human fatigue and production quality (Yung et al., 2020). This source of errors is, for instance, a common consideration in warehousing studies focusing on order picking (Zhao et al., 2019; Grosse et al., 2017b).

### 7.3.3. Heterogeneous workforce

Other models worth mentioning are those considering a heterogeneous workforce. Historically, the homogeneity of the workforce is a common assumption in OR models. It is indeed generally very convenient from a mathematical point of view, and the hypothesis is valid for a number of applications. However, in some cases, a finer granularity in the modeling of the workforce is necessary to consider certain effects.

This modeling is not attached to a particular HAM and is most of the time used within another modeling approach (e.g., objective function, or constraints). An interested reader is referred to Katiraee et al. (2021) for a dedicated review on the topic.

A heterogeneous workforce is naturally encountered when dealing with skills, otherwise all employees would have the same skill set. This case is denoted *S* in the result tables. The underlying idea of integrating skills in an optimization model can be twofold: (i) Employees as a heterogeneous set of resources. In this case, the skills represent different jobs or qualifications, enforced via compatibility constraints (Calzavara et al., 2019a; Hochdörffer et al., 2018; Joo and Kim, 2013), or (ii) Employees as a single set of resources, yet with different throughput/cost. In this case, the skills represent the proficiency of the employee on a set of tasks, enforced with varying task times, or varying quality (Hong, 2018; Khan et al., 2012; Matusiak et al., 2017). Note that neither case is exclusive to each other.

Related to skills, learning rates can also vary between employees. This case is denoted *LR* in the result tables. When working with learning curves, it is reasonable to suppose there is some discrepancy between employees in terms of learning rates. This modeling is mostly used in studies that focus on modeling with more accuracy the performances and their variations in a workforce. It has mainly seen use in workforce-focused problems, like workforce planning (Fowler et al., 2008; Attia et al., 2014), but also warehousing (Grosse and Glock, 2015; Grosse et al., 2013), machine scheduling (Marichelvam et al., 2020), shift scheduling (Gans and Zhou, 2002), and job rotation (Ayough et al., 2020).

The heterogeneity of the workforce can also be based on other intrinsic properties of its components. In the result tables, this is referred to as *PP* for Physical Properties, and *CPP* for Cognitive and Psychosocial Properties. These parameters are mostly risk factors for developing WMSD and are accounted for when computing the estimation of the ER of a work situation. It is indeed known that individuals have different chances of developing occupational diseases when facing a given work situation (Bridger, 2018). This can depend, for example, on the age of the person (Yi and Wang, 2017), his/her lifting capabilities (Carnahan et al., 2000), the physical fatigue he/she can safely sustain (Rattanamanee et al., 2015) or even its smoking and drinking habits (Yi and Chan, 2015). However, most of the time the individual physical parameters can be seen as *skills* in the sense that they affect the processing times of tasks or learning characteristics. Concerning psychosocial characteristics, they can be used to create teams with compatible decision-making styles (Azadeh et al., 2017), to account for the carefulness of the employees in a context of hazardous work environment (Lazzerini and Pistolesi, 2018), or to consider the motivation and personality of individuals when assigning tasks (Othman et al., 2012).

The last parameter that can differ between employees is their individual work preferences, noted *P* in the result tables. This parameter is used when accounting for the satisfaction of the workforce, either as an objective function, or threshold constraints that enforce a minimal satisfaction level for each employee, in a search for equity (Ruiz-Torres et al., 2015, 2019; Akbari et al., 2013).

Modeling the workforce as heterogeneous might have a substantial impact on decision models. The most obvious one is that a parameter that was constant over the workforce now depends on the concerned individual. This means that the decision variables should be able to model the individual assignment/schedule of the employees. Note that this is most of the time already the case in the problems studied in this review, especially the workforce-related ones. This individual-dependent parameter can add some complexity to an existing model. However, it also breaks symmetries, which is often beneficial for the performance of solution approaches, especially when using mathematical programming-based methods (Margot, 2010).
# 8. Discussion and future research

The analysis of the collected material brings out a large variety of works on the topic of integrating HFs into decision models for logistics and manufacturing systems, both in terms of studied problems, modeling approaches, and considered HFs. However, in light of the insights gained from the cross-analysis performed in both parts of the review, some gaps still remain to be filled. In this section, we discuss the collected material and propose some research directions that appear promising for future works, namely the relationship between HFs and fields of application (Section 8.1), the under-represented decision problems (Section 8.2), and the modeling of modern industrial practices (Section 8.3). The reader interested in a study of the different modeling of a HF depending on the field of application is referred to the second part of this work (Prunet et al., 2024).

## 8.1. Discussion on the relationship between HFs and fields of application

Upon reviewing the collected material, it becomes evident that the preponderance of the studied HFs varies between logistics and manufacturing problems, as illustrated by Table 13 that highlights the relationships between decision problems and HFs. This observation can be mainly explained by two factors: either the combination is irrelevant to the study, or the topic has not been thoroughly exploited and presents a direction for future research.

**Learning.** While extensively studied in some applications (e.g., production planning and scheduling), learning is seldom integrated into other scheduling problems where it could be relevant. This is especially true for applications where employees perform different kind of tasks, and thus where learning and forgetting occur when the task assignment changes: assembly line balancing, job rotation, and work-rest scheduling. Accounting for learning in job rotation would allow to discriminate equivalent solutions in terms of painfulness (Ayough et al., 2020). Vehicle routing is another field where learning is largely absent, despite the relevance of the learning process of drivers. Few works in the literature account for driver learning (Battini et al., 2015; Ulmer et al., 2020; Bakker et al., 2021), yet driver familiar with the roads may anticipate traffic jams and use alternative routes, thereby reducing the travel time. The learning process also applies to the customer locations, where service times might be reduced when drivers become more familiar with the locations.

**Fatigue.** The topic is studied in almost all fields, often using different HAMs. Although several fields extensively study the fatigue phenomenon via different HAMs, the explicit consideration of when to schedule rest breaks is mainly prevalent in vehicle routing and work-rest scheduling, despite being a powerful tool to reduce fatigue. The use of work-stretch duration to explicitly schedule rest breaks is a promising research direction in areas like warehousing or job rotation. The routing literature is another research direction for fatigue considerations. Although this interaction is profusely studied, it is almost exclusively using hours of service regulations. The work of Fu et al. (2022) is the only exception, as it accounts for biological indicators to schedule drivers' breaks. Further studies on vehicle routing with alternative fatigue HAMs would enrich the literature on the topic. Finally, energy expenditure is only used twice in the job rotation corpus, despite providing a convenient indicator to estimate the ER to balance between employees.

**WMSD risk assessment methods.** A large class of problems integrates WMSD risk. Shift scheduling and workforce planning are the two notable exceptions, which is unsurprising as they consider longer time horizons. Despite being challenging to model, the balancing of the WMSD ER is, however, still relevant as the risk builds over time, and more works should pursue this direction (Caballini and Paolucci, 2020).

**Cognitive, psychosocial and perceptual factors.** These factors are overall understudied, despite being relevant for a large class of problems. Noise and vibration exposure, for example, would be worth investigating in all the applications involving heavy machinery, such as assembly line balancing, production scheduling and planning, work-rest scheduling, or job rotation. Although employee satisfaction is rarely considered in the workforce planning literature, it plays an important role in the rate of turnover that is often considered in this class of problems (Doan et al., 2022). Finally, boredom would be an interesting research direction for the literature on warehousing and assembly line balancing, given the highly repetitive nature of the corresponding jobs.

## 8.2. Under-represented decision problems

**Cases where the study is not relevant.** Some HFs may not be relevant to be studied within specific applications. The first example that comes to mind is perceptual and environmental factors: it does not make sense to study heat or noise exposure when they do not pose a risk factor in a particular application, similarly visual considerations are only relevant in some applications (e.g., when an operator spends an important portion of the time visually searching for items to pick). Other examples include the HFs that are relevant for the application at hand, but where the optimization problem cannot modify the associated risk. This is for instance the case for posture-related risk in the routing literature: while the prolonged sitting position may be harmful to drivers, their exposure level is only marginally affected by the routing plan. Finally, there are some cases where the HF is simply not applicable for some classes of problems. The most straightforward example is when studying problems that do not integrate time aspects, such as layout design or inventory management, where the scheduling of rest breaks is not applicable. To cite another example, skills constitute the most studied topic, but are not relevant when applied to production planning, as individual employees are not modeled. Hours of service regulations are almost exclusively studied in the routing literature, because of the complex legislation enforcing them (Prunet et al., 2024). When applied to other problems, similar fatigue considerations are modeled via work-stretch duration. Finally, fatigue can be considered as a “short-term” effect, and thus it is understandably under-studied in problems with long time horizons that do not decompose a shift (shift scheduling, workforce planning and assignment). The interested reader is referred to Prunet et al. (2024) for additional discussions on the cross-dependency between HF and application.

**Layout design problems.** The design of workstation layout is one of the main study directions in HF/E and is an important lever of ergonomic improvement in a work situation (Bridger, 2018). However, the OR literature on the topic is scarce. More than designing workstations per se, for instance, studied in Antonio Diego-Mas et al. (2017), optimization algorithms enable a cost-benefit analysis of different solutions. For example, Razavi et al. (2014) and Finco et al. (2020a) study the economic and ergonomic impacts of using protective equipment for, respectively, noise and vibration exposure. Within warehousing logistics, Glock et al. (2019a) study the possibility of rotating pallets to enable easier access to the stored items, and Calzavara et al. (2017) or (Calzavara et al., 2019a) study the design of the storage racks and assess the economic and ergonomic impacts of different technological solutions. Overall, more works should study the impact of different technological solutions by the means of optimization problems.

**Maritime logistics problems.** Despite being an important class of problems within logistics (Christiansen et al., 2007), the integration of HFs remains lacking with these problems. Actually, a single work has been retrieved by our search methodology (Caballini and Paolucci, 2020). Future research should determine which HFs are important for this research stream, and integrate them in models. For instance, fatigue and skills may be relevant considerations for ships sailing around the clock.
# 8. Discussion and future research

The analysis of the collected material brings out a large variety of works on the topic of integrating HFs into decision models for logistics and manufacturing systems, both in terms of studied problems, modeling approaches, and considered HFs. However, in light of the insights gained from the cross-analysis performed in both parts of the review, some gaps still remain to be filled. In this section, we discuss the collected material and propose some research directions that appear promising for future works, namely the relationship between HFs and fields of application (Section 8.1), the under-represented decision problems (Section 8.2), and the modeling of modern industrial practices (Section 8.3). The reader interested in a study of the different modeling of a HF depending on the field of application is referred to the second part of this work (Prunet et al., 2024).

## 8.1. Discussion on the relationship between HFs and fields of application

Upon reviewing the collected material, it becomes evident that the preponderance of the studied HFs varies between logistics and manufacturing problems, as illustrated by Table 13 that highlights the relationships between decision problems and HFs. This observation can be mainly explained by two factors: either the combination is irrelevant to the study, or the topic has not been thoroughly exploited and presents a direction for future research.

**Learning.** While extensively studied in some applications (e.g., production planning and scheduling), learning is seldom integrated into other scheduling problems where it could be relevant. This is especially true for applications where employees perform different kind of tasks, and thus where learning and forgetting occur when the task assignment changes: assembly line balancing, job rotation, and work-rest scheduling. Accounting for learning in job rotation would allow to discriminate equivalent solutions in terms of painfulness (Ayough et al., 2020). Vehicle routing is another field where learning is largely absent, despite the relevance of the learning process of drivers. Few works in the literature account for driver learning (Battini et al., 2015; Ulmer et al., 2020; Bakker et al., 2021), yet driver familiar with the roads may anticipate traffic jams and use alternative routes, thereby reducing the travel time. The learning process also applies to the customer locations, where service times might be reduced when drivers become more familiar with the locations.

**Fatigue.** The topic is studied in almost all fields, often using different HAMs. Although several fields extensively study the fatigue phenomenon via different HAMs, the explicit consideration of when to schedule rest breaks is mainly prevalent in vehicle routing and work-rest scheduling, despite being a powerful tool to reduce fatigue. The use of work-stretch duration to explicitly schedule rest breaks is a promising research direction in areas like warehousing or job rotation. The routing literature is another research direction for fatigue considerations. Although this interaction is profusely studied, it is almost exclusively using hours of service regulations. The work of Fu et al. (2022) is the only exception, as it accounts for biological indicators to schedule drivers' breaks. Further studies on vehicle routing with alternative fatigue HAMs would enrich the literature on the topic. Finally, energy expenditure is only used twice in the job rotation corpus, despite providing a convenient indicator to estimate the ER to balance between employees.

**WMSD risk assessment methods.** A large class of problems integrates WMSD risk. Shift scheduling and workforce planning are the two notable exceptions, which is unsurprising as they consider longer time horizons. Despite being challenging to model, the balancing of the WMSD ER is, however, still relevant as the risk builds over time, and more works should pursue this direction (Caballini and Paolucci, 2020).

**Cognitive, psychosocial and perceptual factors.** These factors are overall understudied, despite being relevant for a large class of problems. Noise and vibration exposure, for example, would be worth investigating in all the applications involving heavy machinery, such as assembly line balancing, production scheduling and planning, work-rest scheduling, or job rotation. Although employee satisfaction is rarely considered in the workforce planning literature, it plays an important role in the rate of turnover that is often considered in this class of problems (Doan et al., 2022). Finally, boredom would be an interesting research direction for the literature on warehousing and assembly line balancing, given the highly repetitive nature of the corresponding jobs.

## 8.2. Under-represented decision problems

**Cases where the study is not relevant.** Some HFs may not be relevant to be studied within specific applications. The first example that comes to mind is perceptual and environmental factors: it does not make sense to study heat or noise exposure when they do not pose a risk factor in a particular application, similarly visual considerations are only relevant in some applications (e.g., when an operator spends an important portion of the time visually searching for items to pick). Other examples include the HFs that are relevant for the application at hand, but where the optimization problem cannot modify the associated risk. This is for instance the case for posture-related risk in the routing literature: while the prolonged sitting position may be harmful to drivers, their exposure level is only marginally affected by the routing plan. Finally, there are some cases where the HF is simply not applicable for some classes of problems. The most straightforward example is when studying problems that do not integrate time aspects, such as layout design or inventory management, where the scheduling of rest breaks is not applicable. To cite another example, skills constitute the most studied topic, but are not relevant when applied to production planning, as individual employees are not modeled. Hours of service regulations are almost exclusively studied in the routing literature, because of the complex legislation enforcing them (Prunet et al., 2024). When applied to other problems, similar fatigue considerations are modeled via work-stretch duration. Finally, fatigue can be considered as a “short-term” effect, and thus it is understandably under-studied in problems with long time horizons that do not decompose a shift (shift scheduling, workforce planning and assignment). The interested reader is referred to Prunet et al. (2024) for additional discussions on the cross-dependency between HF and application.

**Layout design problems.** The design of workstation layout is one of the main study directions in HF/E and is an important lever of ergonomic improvement in a work situation (Bridger, 2018). However, the OR literature on the topic is scarce. More than designing workstations per se, for instance, studied in Antonio Diego-Mas et al. (2017), optimization algorithms enable a cost-benefit analysis of different solutions. For example, Razavi et al. (2014) and Finco et al. (2020a) study the economic and ergonomic impacts of using protective equipment for, respectively, noise and vibration exposure. Within warehousing logistics, Glock et al. (2019a) study the possibility of rotating pallets to enable easier access to the stored items, and Calzavara et al. (2017) or (Calzavara et al., 2019a) study the design of the storage racks and assess the economic and ergonomic impacts of different technological solutions. Overall, more works should study the impact of different technological solutions by the means of optimization problems.

**Maritime logistics problems.** Despite being an important class of problems within logistics (Christiansen et al., 2007), the integration of HFs remains lacking with these problems. Actually, a single work has been retrieved by our search methodology (Caballini and Paolucci, 2020). Future research should determine which HFs are important for this research stream, and integrate them in models. For instance, fatigue and skills may be relevant considerations for ships sailing around the clock.
<table><caption>**Table 13**

Cross-analysis of the human factors studied by field of application.</caption><thead><tr><th></th><th>Skills</th><th>Learning</th><th>Energy expenditure</th><th>Rest allowance</th><th>Fatigue effect</th><th>Learn forget fatigue recovery</th><th>Meal breaks</th><th>Hours of service regulations</th><th>Workstretch duration</th><th>Whole body</th><th>Manual handling</th><th>Working posture</th><th>Repetitive movements</th><th>Motivation and boredom</th><th>Satisfaction</th><th>Psychosocial factors</th><th>Cognitive factors</th><th>Noise exposure</th><th>Visual considerations</th><th>Heat exposure</th><th>Vibration exposure</th></tr></thead><tbody><tr><td>Warehousing</td><td>4</td><td>3</td><td>6</td><td>2</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>3</td><td>4</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>1</td><td></td><td></td></tr><tr><td>Vehicle routing</td><td>4</td><td>3</td><td>2</td><td></td><td>1</td><td></td><td>8</td><td>23</td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>1</td><td>3</td><td></td><td></td><td></td><td></td><td>1</td><td></td><td></td></tr><tr><td>Production scheduling</td><td>14</td><td>31</td><td>2</td><td>1</td><td>6</td><td>1</td><td>2</td><td></td><td></td><td>1</td><td>1</td><td>3</td><td>2</td><td>2</td><td>2</td><td></td><td></td><td>4</td><td>1</td><td></td><td></td><td>1</td><td></td></tr><tr><td>Assembly line balancing</td><td>20</td><td>2</td><td>8</td><td>2</td><td>1</td><td>1</td><td></td><td></td><td></td><td>1</td><td>4</td><td>6</td><td>6</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Production planning</td><td></td><td>18</td><td>4</td><td>4</td><td></td><td>1</td><td></td><td></td><td></td><td></td><td>2</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Design of systems</td><td>5</td><td>1</td><td>4</td><td></td><td>1</td><td>1</td><td></td><td></td><td></td><td></td><td>1</td><td>1</td><td>2</td><td></td><td></td><td>1</td><td>1</td><td>1</td><td>1</td><td></td><td></td><td>1</td><td></td></tr><tr><td>Job rotation</td><td>10</td><td>1</td><td>2</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>3</td><td>6</td><td>2</td><td>4</td><td>4</td><td></td><td></td><td></td><td>5</td><td></td><td></td><td></td><td></td><td>1</td><td></td></tr><tr><td>Work-rest scheduling</td><td>1</td><td></td><td>2</td><td>1</td><td>6</td><td></td><td>16</td><td>1</td><td>12</td><td></td><td></td><td></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>2</td><td></td></tr><tr><td>Shift scheduling</td><td>9</td><td>1</td><td>1</td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>1</td><td></td><td>1</td><td></td><td></td><td>5</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Workforce planning</td><td>16</td><td>6</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>1</td><td>1</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Workforce assignment</td><td>10</td><td>3</td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>2</td><td>3</td><td>1</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Total</td><td>93</td><td>69</td><td>31</td><td>11</td><td>18</td><td>4</td><td>26</td><td>24</td><td>12</td><td>5</td><td>19</td><td>16</td><td>15</td><td>8</td><td>12</td><td>8</td><td>3</td><td>12</td><td>4</td><td>3</td><td>3</td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>**Table 13**
Cross-analysis of the human factors studied by field of application.</caption><thead><tr><th></th><th>Skills</th><th>Learning</th><th>Energy expenditure</th><th>Rest allowance</th><th>Fatigue effect</th><th>Learn forget fatigue recovery</th><th>Meal breaks</th><th>Hours of service regulations</th><th>Workstretch duration</th><th>Whole body</th><th>Manual handling</th><th>Working posture</th><th>Repetitive movements</th><th>Motivation and boredom</th><th>Satisfaction</th><th>Psychosocial factors</th><th>Cognitive factors</th><th>Noise exposure</th><th>Visual considerations</th><th>Heat exposure</th><th>Vibration exposure</th></tr></thead><tbody><tr><td>Warehousing</td><td>4</td><td>3</td><td>6</td><td>2</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>3</td><td>4</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1</td><td></td><td></td></tr><tr><td>Vehicle routing</td><td>4</td><td>3</td><td>2</td><td></td><td>1</td><td></td><td>8</td><td>23</td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>1</td><td>3</td><td></td><td></td><td></td><td>1</td><td></td></tr><tr><td>Production scheduling</td><td>14</td><td>31</td><td>2</td><td>1</td><td>6</td><td>1</td><td></td><td>2</td><td></td><td></td><td>1</td><td>1</td><td>3</td><td>2</td><td>2</td><td>2</td><td></td><td>4</td><td>1</td><td></td><td>1</td></tr><tr><td>Assembly line balancing</td><td>20</td><td>2</td><td>8</td><td>2</td><td>1</td><td>1</td><td></td><td></td><td></td><td></td><td>1</td><td>4</td><td>6</td><td>6</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Production planning</td><td></td><td>18</td><td>4</td><td>4</td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>2</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Design of systems</td><td>5</td><td>1</td><td>4</td><td></td><td>1</td><td>1</td><td></td><td></td><td></td><td></td><td>1</td><td>1</td><td>2</td><td></td><td></td><td></td><td>1</td><td></td><td>1</td><td></td><td>1</td></tr><tr><td>Job rotation</td><td>10</td><td>1</td><td>2</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3</td><td>6</td><td>2</td><td>4</td><td>4</td><td></td><td>5</td><td></td><td></td><td>1</td><td></td></tr><tr><td>Work-rest scheduling</td><td>1</td><td></td><td>2</td><td>1</td><td>6</td><td></td><td>16</td><td>1</td><td>12</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Shift scheduling</td><td>9</td><td>1</td><td>1</td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>1</td><td></td><td>1</td><td></td><td></td><td>5</td><td>1</td><td></td><td></td><td></td><td></td></tr><tr><td>Workforce planning</td><td>16</td><td>6</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>1</td><td>1</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Workforce assignment</td><td>10</td><td>3</td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>2</td><td>3</td><td>1</td><td>1</td><td></td><td></td><td></td></tr><tr><td>Total</td><td>93</td><td>69</td><td>31</td><td>11</td><td>18</td><td>4</td><td>26</td><td>24</td><td>12</td><td>5</td><td>19</td><td>16</td><td>15</td><td>8</td><td>12</td><td>8</td><td>3</td><td>12</td><td>4</td><td>3</td><td>3</td></tr></tbody></table>
**Economic quantification of the indirect cost of poor ergonomics.** Some studies presented in this review integrate HFs with their models by computing the cost of poor working conditions, due to e.g., injuries or turnover, and account for this cost in the objective function (see Prunet et al. (2024), *Total cost function*). For example, in the model proposed by Sobhani et al. (2015, 2017) and Sobhani and Wahab (2017), a Markov chain is used to determine the steady state of the number of injured employees and consequent sick leaves. This value is then used to compute the indirect costs of such leaves. It accounts for performance loss, injury leave costs, increased insurance costs, hiring, training, and firing costs for replacing the injured employees with short-term workers, and, finally, to compensate for the higher turnover rate linked to the degraded working conditions. Further research in this direction could be beneficial for the community, helping to present more comprehensive models for decision makers and be the basis of cost/benefit analysis for the consideration of HFs in the optimization of logistics and manufacturing systems.

**Heterogeneous modeling of employees.** Human characteristics are intrinsically subjected to personal variability. This is the case when considering human performance estimation, where each individual will have different levels of productivity, depending on the task at hand, his/her age, experience, etc. Moreover, a task might present a high level of risk for an individual, and an acceptable risk for someone else. This could be affected by several characteristics of the individual, e.g., age, height, and health conditions. However, in the literature, the norm is mostly to consider the workforce as a homogeneous pool of employees. This assumption of homogeneity makes sense when not considering HFs, yet it leads to a net loss of accuracy in the modeling when human characteristics are involved. In HF/E, anthropometry (i.e., the study and measurement of the human body) is an important field of study (Pheasant and Haslegrave, 2018), as it provides help to design work situations that would be safe and adapted for a large part of the working population (e.g., suited for 95% of the concerned population).

**Integration of human-related variability.** There is an intrinsic variability in human performances. In this review, several works focused on the modeling of human aspects for performance evaluation, sometimes with sophisticated models. However, few works integrate stochasticity into their modeling, despite it being an appropriate tool for the modeling of the variability. Furthermore, stochastic optimization is a well-studied area of OR, which could lead to interesting developments, by using methods historically originating from OR to deal with HFs in models.

### 8.3. Modeling of modern industrial practices

The rise of Industry 4.0, followed by the beginning of Industry 5.0, has led to the development of new practices in the logistics and manufacturing industries. Some of these innovations change the way the operators interact with their work environment. Future research should aim at accounting for these new practices, to bridge the gap between theory and practice.

**Human-robot collaborative systems.** This kind of organization is becoming more and more present in industrial systems. Indeed, human operators are more suited to tasks that require dexterity or decision-making, whereas robots are adapted to tasks with poor ergonomic conditions (e.g., repetitive tasks, heavy material handling, and use of hazardous tools). Human-robot collaborative systems have been studied in the collected material (Hu and Chen, 2017; Zhang et al., 2022; Stecke and Mokhtarzadeh, 2022; Lee et al., 2022), but the topic is still under-represented in the literature considering its importance in manufacturing (Jahanmahin et al., 2022b) or warehousing (Pasparakis et al., 2023). Future research directions follow the question raised by human-robot collaboration: Which tasks should be performed by humans/robots? How to organize the process such that operators remain safe around robots? How to schedule such a system.

**Augmented workforce.** Related to the development of human-robot collaboration, the augmented workforce is becoming a reality for demanding tasks where automation is ineffective (Moencks et al., 2022). Operator assistance systems (OAS), such as exoskeletons, can increase productivity and reduce the ergonomic risk for employees. In the collected material, only (Weckenborg et al., 2022) model OAS. The authors integrate exoskeleton in an assembly line balancing problem. An interesting line of research would be to study the economic and ergonomic impacts of accounting for OAS in planning problems.

**Ageing workforce.** This topic is gaining more and more importance in the industry, due to a higher retirement age of the workforce (Calzavara et al., 2020). Older workers behave differently than younger ones, they have decreased physical and cognitive abilities, but more experience. These differences have impacts on decision models, for instance in terms of skill set, productivity, and rest break required. Few works in the collected material integrate these aspects (Berti et al., 2021; Battini et al., 2022), and more studies are needed to better adapt planning models to this population.

**Collaboration with HF/E practitioners for models' validation.** As the topic of this review is heavily influenced by HF/E, it is natural to highlight that an increment in collaborations between both disciplines would be beneficial: (i) First, to validate the relevance of the work of the OR community, and (ii) second, to guide the field toward modeling problems that are relevant in practice and the use of HAMs that make sense in a given situation. For instance, Ryan et al. (2011) study a production planning problem in a multidisciplinary approach. Insights are developed to guide the collaboration between OR and HF/E scientists. Moreover, it appears that it is sometimes challenging for an OR practitioner to work on real-life case studies. This will eventually raise the question of the validity of the work. Real-life applications provide opportunities and appropriate settings to validate OR work. Let us emphasize that this is even more critical in human-aware optimization due to its direct impact on humans. It would be beneficial to see more case studies where human-aware optimization models are implemented in industrial contexts, and the implications of such interventions are assessed. This kind of work could bring insightful feedback to the community and lead to new research directions guided by industrial needs. Substantial efforts have been made in this regard (Ryan et al., 2011; Yi and Chan, 2015; Bautista et al., 2016b; Battini et al., 2016a; Moussavi et al., 2019), but further work is needed. As a consequence, the amount of work using real-life data with risk assessment methods is scarce. It would be beneficial for the community to have access to datasets issued from fieldwork and collaborations with ergonomists. In this way, OR researchers could confront their work and solution methods to real data.

### 9. Conclusions

In the first part of this literature review, we have introduced the corpus of the reviewed material. It covers a large spectrum of classical logistics and manufacturing optimization problems, which shows the interest and continued need for designing human-aware models and solution methods. Pushed, in particular, by the sustainable development movement, human considerations are more and more involved in logistics and manufacturing systems, including: warehousing, vehicle routing, scheduling, production planning, and workforce scheduling and management. In the current part, we have studied the modeling systems of human aspects through the lens of mathematical programming, i.e.: Which HFs and how they are integrated into decision models from logistics and manufacturing fields? And, what is the impact induced by the integration of HFs into the available modeling approaches? Based on a cross-analysis of the current review, multiple opportunities for future research have also been discussed. Due to the broad scope of the study, the review methodology is semi-systematic, to keep the studied corpus of manageable size. As such,
**Economic quantification of the indirect cost of poor ergonomics.** Some studies presented in this review integrate HFs with their models by computing the cost of poor working conditions, due to e.g., injuries or turnover, and account for this cost in the objective function (see Prunet et al. (2024), *Total cost function*). For example, in the model proposed by Sobhani et al. (2015, 2017) and Sobhani and Wahab (2017), a Markov chain is used to determine the steady state of the number of injured employees and consequent sick leaves. This value is then used to compute the indirect costs of such leaves. It accounts for performance loss, injury leave costs, increased insurance costs, hiring, training, and firing costs for replacing the injured employees with short-term workers, and, finally, to compensate for the higher turnover rate linked to the degraded working conditions. Further research in this direction could be beneficial for the community, helping to present more comprehensive models for decision makers and be the basis of cost/benefit analysis for the consideration of HFs in the optimization of logistics and manufacturing systems.

**Heterogeneous modeling of employees.** Human characteristics are intrinsically subjected to personal variability. This is the case when considering human performance estimation, where each individual will have different levels of productivity, depending on the task at hand, his/her age, experience, etc. Moreover, a task might present a high level of risk for an individual, and an acceptable risk for someone else. This could be affected by several characteristics of the individual, e.g., age, height, and health conditions. However, in the literature, the norm is mostly to consider the workforce as a homogeneous pool of employees. This assumption of homogeneity makes sense when not considering HFs, yet it leads to a net loss of accuracy in the modeling when human characteristics are involved. In HF/E, anthropometry (i.e., the study and measurement of the human body) is an important field of study (Pheasant and Haslegrave, 2018), as it provides help to design work situations that would be safe and adapted for a large part of the working population (e.g., suited for 95% of the concerned population).

**Integration of human-related variability.** There is an intrinsic variability in human performances. In this review, several works focused on the modeling of human aspects for performance evaluation, sometimes with sophisticated models. However, few works integrate stochasticity into their modeling, despite it being an appropriate tool for the modeling of the variability. Furthermore, stochastic optimization is a well-studied area of OR, which could lead to interesting developments, by using methods historically originating from OR to deal with HFs in models.

### 8.3. Modeling of modern industrial practices

The rise of Industry 4.0, followed by the beginning of Industry 5.0, has led to the development of new practices in the logistics and manufacturing industries. Some of these innovations change the way the operators interact with their work environment. Future research should aim at accounting for these new practices, to bridge the gap between theory and practice.

**Human-robot collaborative systems.** This kind of organization is becoming more and more present in industrial systems. Indeed, human operators are more suited to tasks that require dexterity or decision-making, whereas robots are adapted to tasks with poor ergonomic conditions (e.g., repetitive tasks, heavy material handling, and use of hazardous tools). Human-robot collaborative systems have been studied in the collected material (Hu and Chen, 2017; Zhang et al., 2022; Stecke and Mokhtarzadeh, 2022; Lee et al., 2022), but the topic is still under-represented in the literature considering its importance in manufacturing (Jahanmahin et al., 2022b) or warehousing (Pasparakis et al., 2023). Future research directions follow the question raised by human-robot collaboration: Which tasks should be performed by humans/robots? How to organize the process such that operators remain safe around robots? How to schedule such a system.

**Augmented workforce.** Related to the development of human-robot collaboration, the augmented workforce is becoming a reality for demanding tasks where automation is ineffective (Moencks et al., 2022). Operator assistance systems (OAS), such as exoskeletons, can increase productivity and reduce the ergonomic risk for employees. In the collected material, only (Weckenborg et al., 2022) model OAS. The authors integrate exoskeleton in an assembly line balancing problem. An interesting line of research would be to study the economic and ergonomic impacts of accounting for OAS in planning problems.

**Ageing workforce.** This topic is gaining more and more importance in the industry, due to a higher retirement age of the workforce (Calzavara et al., 2020). Older workers behave differently than younger ones, they have decreased physical and cognitive abilities, but more experience. These differences have impacts on decision models, for instance in terms of skill set, productivity, and rest break required. Few works in the collected material integrate these aspects (Berti et al., 2021; Battini et al., 2022), and more studies are needed to better adapt planning models to this population.

**Collaboration with HF/E practitioners for models' validation.** As the topic of this review is heavily influenced by HF/E, it is natural to highlight that an increment in collaborations between both disciplines would be beneficial: (i) First, to validate the relevance of the work of the OR community, and (ii) second, to guide the field toward modeling problems that are relevant in practice and the use of HAMs that make sense in a given situation. For instance, Ryan et al. (2011) study a production planning problem in a multidisciplinary approach. Insights are developed to guide the collaboration between OR and HF/E scientists. Moreover, it appears that it is sometimes challenging for an OR practitioner to work on real-life case studies. This will eventually raise the question of the validity of the work. Real-life applications provide opportunities and appropriate settings to validate OR work. Let us emphasize that this is even more critical in human-aware optimization due to its direct impact on humans. It would be beneficial to see more case studies where human-aware optimization models are implemented in industrial contexts, and the implications of such interventions are assessed. This kind of work could bring insightful feedback to the community and lead to new research directions guided by industrial needs. Substantial efforts have been made in this regard (Ryan et al., 2011; Yi and Chan, 2015; Bautista et al., 2016b; Battini et al., 2016a; Moussavi et al., 2019), but further work is needed. As a consequence, the amount of work using real-life data with risk assessment methods is scarce. It would be beneficial for the community to have access to datasets issued from fieldwork and collaborations with ergonomists. In this way, OR researchers could confront their work and solution methods to real data.

### 9. Conclusions

In the first part of this literature review, we have introduced the corpus of the reviewed material. It covers a large spectrum of classical logistics and manufacturing optimization problems, which shows the interest and continued need for designing human-aware models and solution methods. Pushed, in particular, by the sustainable development movement, human considerations are more and more involved in logistics and manufacturing systems, including: warehousing, vehicle routing, scheduling, production planning, and workforce scheduling and management. In the current part, we have studied the modeling systems of human aspects through the lens of mathematical programming, i.e.: Which HFs and how they are integrated into decision models from logistics and manufacturing fields? And, what is the impact induced by the integration of HFs into the available modeling approaches? Based on a cross-analysis of the current review, multiple opportunities for future research have also been discussed. Due to the broad scope of the study, the review methodology is semi-systematic, to keep the studied corpus of manageable size. As such,
and despite our commitment of being as transparent as possible, the inclusion methodology is not fully reproducible, and thus constitutes a limitation of the work. The literature search is limited to papers published before the end of 2022, and more recent insightful works have been produced within this active research stream. The monitoring of the existing and emerging trends within the area constitutes an important research avenue for future research.

In the second part of this review (Prunet et al., 2024), we give a comprehensive presentation of the range of modeling frameworks found in the collected material dedicated to the representation and the quantification of both ergonomic risks and human characteristics. Each HAM is explained in detail, and links are made to its relevance in the industrial context.

## CRediT authorship contribution statement

**Thibault Prunet:** Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Validation, Visualization, Writing – original draft, Writing – review & editing. **Nabil Absi:** Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – review & editing. **Valeria Borodin:** Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – review & editing. **Diego Cattaruzza:** Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – review & editing.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

We kindly thank the two anonymous reviewers for their careful reading of the paper and their valuable comments that allowed to highly improve the quality of the manuscript. This work has been supported by the French National Research Agency, France through the AGIRE project under the grant ANR-19-CE10-0014.<fnref n="10" /> This support is gratefully acknowledged.

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Andriolo, A., Battini, D., Persona, A., Sgarbossa, F., 2016. A new bi-objective approach for including ergonomic principles into EOQ model. Int. J. Prod. Res. 54 (9), 2610–2627.

Anoshkina, Y., Meisel, F., 2020. Interday routing and scheduling of multi-skilled teams with consistency consideration and intraday rescheduling. EURO J. Transp. Logist. 9 (3).

Antonio Diego-Mas, J., Poveda-Bautista, R., Garzon-Leal, D., 2017. Using RGB-D sensors and evolutionary algorithms for the optimization of workstation layouts. Appl. Ergon. 65, 530–540, Place: Oxford Publisher: Elsevier Sci Ltd WOS:0004085974000053.

Anzanello, M., Fogliatto, F., 2010. Scheduling learning dependent jobs in customised assembly lines. Int. J. Prod. Res. 48 (22), 6683–6699.

Anzanello, M.J., Fogliatto, F.S., 2011. Learning curve models and applications: Literature review and research directions. Int. J. Ind. Ergon. 41 (5), 573–583, Place: Amsterdam Publisher: Elsevier WOS:000295242700019.

Anzanello, M., Fogliatto, F., Santos, L., 2014. Learning dependent job scheduling in mass customized scenarios considering ergonomic factors. Int. J. Prod. Econ. 154, 136–145.

Aravindkrishna, T., Balasubramanian, V., Narendran, T., 2009. Ergonomic risk incorporated schedules (ERIS)-scheduling using genetic algorithm to reduce operator fatigue in flow-shop based cells. Int. J. Enterpr. Netw. Manag. 3 (3), 184–200.

Aroui, K., Alpan, G., Frein, Y., 2017. Minimising work overload in mixed-model assembly lines with different types of operators: a case study from the truck industry. Int. J. Prod. Res. 55 (21), 6305–6326, Place: Abingdon Publisher: Taylor & Francis Ltd WOS:000412561900006.

Aryanezhad, M., Deljoo, V., Mirzapour Al-E-Hashem, S., 2009a. Dynamic cell formation and the worker assignment problem: A new model. Int. J. Adv. Manuf. Technol. 41 (3), 329–342.

Aryanezhad, M., Kheirkhah, A., Deljoo, V., Mirzapour Al-E-Hashem, S., 2009b. Designing safe job rotation schedules based upon workers' skills. Int. J. Adv. Manuf. Technol. 41 (1), 193–199.

Asadkhani, J., Mokhtari, H., Tahmasebpoor, S., 2022. Optimal lot-sizing under learning effect in inspection errors with different types of imperfect quality items. Oper. Res. 22 (3), 2631–2665, URL https://www.webofscience.com/wos/woscc/full-record/WOS:000631481900001, Place: Heidelberg Publisher: Springer Heidelberg WOS:000631481900001.

Asawarungsaengkul, K., Nanthavanij, S., 2008. Heuristic genetic algorithm for workforce scheduling with minimum total worker-location changeover. Int. J. Ind. Eng.-Theory Appl. Prac. 15 (4), 373–385, Place: Cincinnati Publisher: Univ Cincinnati Industrial Engineering WOS:000207714000005.

Asensio-Cuesta, S., Diego-Mas, J., Canós-Darós, L., Andrés-Romano, C., 2012a. A genetic algorithm for the design of job rotation schedules considering ergonomic and competence criteria. Int. J. Adv. Manuf. Technol. 60 (9), 1161–1174.

Asensio-Cuesta, S., Diego-Mas, J., Cremades-Oliver, L., González-Cruz, M., 2012b. A method to design job rotation schedules to prevent work-related musculoskeletal disorders in repetitive work. Int. J. Prod. Res. 50 (24), 7467–7478.

Attia, E.-A., Duquenne, P., Le-Lann, J.-M., 2014. Considering skills evolutions in multi-skilled workforce allocation with flexible working hours. Int. J. Prod. Res. 52 (15), 4548–4573.

Aykin, T., 1996. Optimal shift scheduling with multiple break windows. Manage. Sci. 42 (4), 591–602.

Aykin, T., 1998. A composite branch and cut algorithm for optimal shift scheduling with multiple breaks and break windows. J. Oper. Res. Soc. 49 (6), 603–615.

Ayough, A., Zandieh, M., Farhadi, F., 2020. Balancing, sequencing, and job rotation scheduling of a U-shaped lean cell with dynamic operator performance. Comput. Ind. Eng. 143, 106363, Place: Oxford Publisher: Pergamon-Elsevier Science Ltd WOS:000525872600003.

Azadeh, A., Ravanbakhsh, M., Rezaei-Malek, M., Sheikhalishahi, M., Taheri-Moghaddam, A., 2017. Unique NSGA-II and MOPSO algorithms for improved dynamic cellular manufacturing systems considering human factors. Appl. Math. Model. 48, 655–672, Place: New York Publisher: Elsevier Science Inc WOS:000403994400037.

Azizi, N., Zolfaghari, S., Liang, M., 2010. Modeling job rotation in manufacturing systems: The study of employee's boredom and skill variations. Int. J. Prod. Econ. 123 (1), 69–85.

<footnote n="10">¹⁰ https://anr.fr/Projet-ANR-19-CE10-0014.</footnote>
and despite our commitment of being as transparent as possible, the inclusion methodology is not fully reproducible, and thus constitutes a limitation of the work. The literature search is limited to papers published before the end of 2022, and more recent insightful works have been produced within this active research stream. The monitoring of the existing and emerging trends within the area constitutes an important research avenue for future research.

In the second part of this review (Prunet et al., 2024), we give a comprehensive presentation of the range of modeling frameworks found in the collected material dedicated to the representation and the quantification of both ergonomic risks and human characteristics. Each HAM is explained in detail, and links are made to its relevance in the industrial context.

## CRediT authorship contribution statement

**Thibault Prunet:** Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Validation, Visualization, Writing – original draft, Writing – review & editing. **Nabil Absi:** Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – review & editing. **Valeria Borodin:** Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – review & editing. **Diego Cattaruzza:** Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – review & editing.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

We kindly thank the two anonymous reviewers for their careful reading of the paper and their valuable comments that allowed to highly improve the quality of the manuscript. This work has been supported by the French National Research Agency, France through the AGIRE project under the grant ANR-19-CE10-0014.<fnref n="10" /> This support is gratefully acknowledged.

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* Anoshkina, Y., Meisel, F., 2020. Interday routing and scheduling of multi-skilled teams with consistency consideration and intraday rescheduling. EURO J. Transp. Logist. 9 (3).

* Antonio Diego-Mas, J., Poveda-Bautista, R., Garzon-Leal, D., 2017. Using RGB-D sensors and evolutionary algorithms for the optimization of workstation layouts. Appl. Ergon. 65, 530–540, Place: Oxford Publisher: Elsevier Sci Ltd WOS:0004085974000053.

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* Aravindkrishna, T., Balasubramanian, V., Narendran, T., 2009. Ergonomic risk incorporated schedules (ERIS)-scheduling using genetic algorithm to reduce operator fatigue in flow-shop based cells. Int. J. Enterpr. Netw. Manag. 3 (3), 184–200.

* Aroui, K., Alpan, G., Frein, Y., 2017. Minimising work overload in mixed-model assembly lines with different types of operators: a case study from the truck industry. Int. J. Prod. Res. 55 (21), 6305–6326, Place: Abingdon Publisher: Taylor & Francis Ltd WOS:000412561900006.

* Aryanezhad, M., Deljoo, V., Mirzapour Al-E-Hashem, S., 2009a. Dynamic cell formation and the worker assignment problem: A new model. Int. J. Adv. Manuf. Technol. 41 (3), 329–342.

* Aryanezhad, M., Kheirkhah, A., Deljoo, V., Mirzapour Al-E-Hashem, S., 2009b. Designing safe job rotation schedules based upon workers' skills. Int. J. Adv. Manuf. Technol. 41 (1), 193–199.

* Asadkhani, J., Mokhtari, H., Tahmasebpoor, S., 2022. Optimal lot-sizing under learning effect in inspection errors with different types of imperfect quality items. Oper. Res. 22 (3), 2631–2665, URL https://www.webofscience.com/wos/woscc/full-record/WOS:000631481900001, Place: Heidelberg Publisher: Springer Heidelberg WOS:000631481900001.

* Asawarungsaengkul, K., Nanthavanij, S., 2008. Heuristic genetic algorithm for workforce scheduling with minimum total worker-location changeover. Int. J. Ind. Eng.-Theory Appl. Prac. 15 (4), 373–385, Place: Cincinnati Publisher: Univ Cincinnati Industrial Engineering WOS:000207714000005.

* Asensio-Cuesta, S., Diego-Mas, J., Canós-Darós, L., Andrés-Romano, C., 2012a. A genetic algorithm for the design of job rotation schedules considering ergonomic and competence criteria. Int. J. Adv. Manuf. Technol. 60 (9), 1161–1174.

* Asensio-Cuesta, S., Diego-Mas, J., Cremades-Oliver, L., González-Cruz, M., 2012b. A method to design job rotation schedules to prevent work-related musculoskeletal disorders in repetitive work. Int. J. Prod. Res. 50 (24), 7467–7478.

* Attia, E.-A., Duquenne, P., Le-Lann, J.-M., 2014. Considering skills evolutions in multi-skilled workforce allocation with flexible working hours. Int. J. Prod. Res. 52 (15), 4548–4573.

* Aykin, T., 1996. Optimal shift scheduling with multiple break windows. Manage. Sci. 42 (4), 591–602.

* Aykin, T., 1998. A composite branch and cut algorithm for optimal shift scheduling with multiple breaks and break windows. J. Oper. Res. Soc. 49 (6), 603–615.

* Ayough, A., Zandieh, M., Farhadi, F., 2020. Balancing, sequencing, and job rotation scheduling of a U-shaped lean cell with dynamic operator performance. Comput. Ind. Eng. 143, 106363, Place: Oxford Publisher: Pergamon-Elsevier Science Ltd WOS:000525872600003.

* Azadeh, A., Ravanbakhsh, M., Rezaei-Malek, M., Sheikhalishahi, M., Taheri-Moghaddam, A., 2017. Unique NSGA-II and MOPSO algorithms for improved dynamic cellular manufacturing systems considering human factors. Appl. Math. Model. 48, 655–672, Place: New York Publisher: Elsevier Science Inc WOS:000403994400037.

* Azizi, N., Zolfaghari, S., Liang, M., 2010. Modeling job rotation in manufacturing systems: The study of employee's boredom and skill variations. Int. J. Prod. Econ. 123 (1), 69–85.

<footnote n="10">¹⁰ https://anr.fr/Projet-ANR-19-CE10-0014.</footnote>