Impact of limiting the ergonomic risk on the economic and productive efficiency of an assembly line

Note: Snapshot PDF is the proof copy of corrections marked in EditGenie, the layout would be different from typeset PDF and EditGenie editing view. Author Queries & Comments: Q1 : Funding details have been taken from information supplied with your manuscript submission. Please correct if this is inaccurate. Response: Resolved Q2 : Tables 3 and 4 was not cited in the text so a citation has been inserted. Please provide a correction if this is inaccurate. Response: Resolved Q3 : The disclosure statement has been inserted. Please correct if this is inaccurate. Response: Resolved Q4 : The reference "Battaïa and Dolgui 2013" is listed in the references list but is not cited in the text. Please either cite the reference or remove it from the references list. Response: Resolved Q5 : Please provide missing page range for reference "Bautista and Alfaro-Pozo 2020" references list entry. 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CM4 : Insert a space between parameter and the parenthesis CM5 : Insert a space between parameter and the parenthesis CM6 : Insert a space between equation 9a and the parenthesis CM7 : Insert a space between parameter and the parenthesis CM8 : Insert a space between parameter and the parenthesis CM9 : Insert a space between Equation 9b and the parenthesis CM10 : Eliminate the space and align with the rest of variables CM11 : If it's possible, justify the equations and add space between the equation and the index values. CM12 : If it's possible, use only one line for each equation CM13 : If it's possible, use only one line for each equation CM14 : remove last comma CM15 : change the "four meters" to the following equation: ${A_k^{max}= 4\textrm{ }({\forall k} )} ) CM16 : In the description of the figure put Xk^max=2 in equation format: ${\rm X}_k^{max} = 2\textrm{ }({\forall k} )$ CM17 : Change 1 to A1 CM18 : Change 2 to A2 CM19 : Change 3 to A3 Rocío Alfaro-Pozo, JoaquínBautista-Valhondo Departament d’Organització d’Empreses (DOE), Service and Industrial Robotics – Operation, Production and Enterprise (SIR-OPE), Institut d’Organització i Control de Sistemes Industrials (IOC), Escola Tècnica Superior d’Enginyeria Industrial de Barcelona (ETSEIB), Universitat Politècnica de Catalunya (UPC), Barcelona, Spain CONTACT Rocío Alfaro-Pozo [email protected] Departament d’Organització d’Empreses (DOE), Service and Industrial Robotics – Operation, Production and Enterprise (SIR-OPE), Institut d’Organització i Control de Sistemes Industrials (IOC), Escola Tècnica Superior d’Enginyeria Industrial de Barcelona (ETSEIB), Universitat Politècnica de Catalunya (UPC), Av. Diagonal, 647, Barcelona 08028, Spain History : received : 2022-12-14 accepted : 2023-11-1 Copyright Line: © 2023 Informa UK Limited, trading as Taylor & Francis Group ABSTRACT Considering ergonomics at the design phase can lead to assembly lines that protect and improve workers’ health and well-being. However, this may reduce efficiency and productivity. Evaluating the potential benefits of incorporating ergonomics into line design versus the additional costs associated with the number of extra stations required or increased idle time, as well as exploring other ergonomic design alternatives, is critical for decision-makers. An assembly line balancing problem considering time, space and ergonomics, is used to evaluate the impact of ergonomic considerations. A model for maximising line efficiency is proposed and linearised for solution by the solver CPLEX. The mixed-integer linear model is compared to an alternative linearisation approach in which a decision variable is parameterised and then iteratively solved. An example and a case study are used to observe the competitiveness of both solution methods, where the iterative approach is shown to be superior for real size problems. The results show that ergonomic evaluation in line design leads to safer but less productive lines, which in turn increases the number of workstations and costs. Specifically, limiting ergonomic risk to a moderate level for the engine assembly line examined in this study, means maximum daily drop of 27 engines. KEYWORDS Assembly line balancing efficiency ergonomics productivity mixed integer linear programming This work has been funded by the Ministry of Economy and Competitiveness of the Government of Spain through project OPTHEUS (ref. PGC2018-095080-B-I00), including European Regional Development Funds (ERDF).[Q1]Ministerio de Economía y Competitividad Assembly systems have been adapted to the evolution of the industrial environment. Technological innovation has made it possible to move from rigid production with large quantities of a single product at low cost to flexible production characterised by customised manufacture of a wide range of product types. These disruptive changes in manufacturing processes have not only improved productivity, but also the Impact of limiting the ergonomic risk on the economic and productive efficiency of an assembly line Recto running head : INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH Verso running head : R. ALFARO-POZO AND J. BAUTISTA-VALHONDO FUNDING 1. Introduction technical and economic performance and social development of the industry (Bortolini et al. 2017). Despite technological progress, however, efficient automation of all tasks and operations has not yet been fully realised. The presence of human resources at workstations is still indispensable, as their skills contribute significantly to value creation in terms of flexibility and adaptability. Improving production systems must therefore take into account not only economic and productive efficiency, but also the wellbeing of workers. Automotive sector is a clear example of production system where manual work is still needed. Vehicle or engine assembly operations, for example, involve manual handling and lifting, postural loads, and repetitive movements. Such actions and movements associated with manual tasks are physical risk factors due to inadequate ergonomics and are the main cause of musculoskeletal injuries among workers, according to the European Agency for Safety and Health at Work ., Musculoskeletal disorders affect millions of workers across Europe and represent a significant financial burden for employers, costing billions of euros. Despite the progress made in occupational safety and health at European level over the last 15 years, and despite a decrease of more than 50% in the incidence rate of non-fatal accidents, traditional ergonomic risks persist, at the same rate (European Agency for Safety and Health at Work 2023). According to the Third European Survey of Enterprises on New and Emerging Risks (European Agency for Safety and Health at Work 2019), repetitive hand/arm movements and heavy-load lifting and moving remain two of the most common risk factors identified in the EU28. In line with one of the three main objectives of the EU Strategic Framework on Health and Safety at Work 2021–2027 (European Commission 2021), it therefore seems crucial to take preventive measures and minimise risk factors in the workplace. One possible measure is to adapt the workplace by taking ergonomic considerations into account when designing or improving workstations. Indeed, the literature (Otto and Battaïa 2017) shows how, in the case of assembly lines, incorporating ergonomics into operational planning decisions can significantly reduce risks while ensuring process efficiency and worker well-being and physical integrity (Baykasoglu et al. 2017). As part of this research line, some studies (Abdous et al. 2023; Battini et al. 2015; Battini et al. 2017) have opted to reduce risks by including recovery time after demanding operations. Others (Bautista-Valhondo et al. 2013; Otto and Scholl 2011; Possan, Michels, and Magatão 2023) limit them by assigning operations to workstations and even by assigning operations to workers based on their skills (Katiraee et al. 2022). Others reduce risks by using collaborative robots (Stecke and Mokhtarzadeh 2022). Whichever approach is taken, in most cases, limiting or reducing ergonomic risks involves the use of additional resources or a deterioration in the productivity parameters of assembly lines (Battini et al. 2017). However, to our knowledge, the current literature lacks an assessment of the economic and productivity impacts of incorporating ergonomics into assembly line design. In this article, we argue that while it is important for workers’ well-being and safety to prioritise ergonomics, it is also crucial to assess the potential impact of risk mitigation measures on the overall productivity and economic performance of the company. Restricting task assignment at assembly stations to avoid exceeding certain ergonomic limits may result in the need to increase the number of stations on the line and consequently require a greater number of operators. In Europe and the US, where labour costs are high, this could lead to a significant increase in costs for the companies. Another possible impact is an increase in cycle time to provide recovery time for operators. However, this situation can lead to a loss of line productivity, which translates into economic losses for the company. Additionally, the increase in cycle time can also lead to an increase in unproductive time on the line, reducing overall efficiency. To illustrate the above, we propose a mixed-integer model for assembly line balancing that maximises efficiency while limiting the space required by workstations to perform assigned tasks and the maximum ergonomic risk these tasks pose to workers. Through a case study, we examine the impact of limiting ergonomic risk on the safety, productivity and efficiency of the resulting production lines. This study stems from a paper presented at the 13th International Conference on Industrial Engineering and Industrial Management, XXIII Congreso de Ingeniería de Organización (Bautista and Alfaro-Pozo 2020). The conference paper introduced a mixed-integer model for balancing assembly lines that takes into account both maximising productivity and limiting spatial and ergonomic risks at workstations. The proposed problem was solved for a demand plan using two mixed-integer linear models that minimise cycle time and imbalance between workloads assigned to workstations. In this study, we extend the model to include ergonomic evaluation using two different methods from the literature: the method proposed by Bautista, Alfaro-Pozo, and Batalla-García (2016), based on traditional observation methods, and the method proposed by Battini et al. (2016), based on the energy expenditure of tasks. In this study, starting from the mixed-integer model for the problem, we propose two linearisation methods, preserving the objective function of minimising the line’s non-productivity. Finally, we extend the computational experience by analysing a representative set of demand plans with different production mix compositions. A brief literature review is provided below in Section 2. This review focuses on studies that address the assembly line balancing problem and are concerned with maximising line efficiency or equivalent objectives, as well as those that consider ergonomic aspects in line balancing. We also present the main contributions of this study. In Section 3, we develop the proposed problem and formulate a mixedinteger model. We also explain the ergonomic estimation method used in this study and present two alternatives to linearise the proposed mixed-integer model. This section concludes with a small example to validate the functionality of the proposed general problem. In Section 4, we present a case study and the main results. In Section 5, we analyse the economic, social and managerial implications of limiting ergonomic risks in assembly line design. Finally, in Section 6, we summarise the main results of our study and suggest possible future research directions. This section is divided into two parts. First, it highlights the main studies on assembly line balancing, specifically those focussed on maximising line efficiency. Second, the review exclusively focuses on relevant studies addressing assembly line balancing problems with ergonomic considerations. Since Salveson (1955), the Assembly Line Balancing Problem (ALBP) has been extensively studied in the literature, progressively aligning it with real-world scenarios where factors affecting line balancing complexity increase (Didden et al. 2023). Baybars (1986) classified the problem into two categories based on the considered constraints: the Simple Assembly Line Balancing Problem (SALBP), which exclusively considers operation processing times and the execution order of tasks (precedence diagram) (Boysen, Fliedner, and Scholl 2007); and the General Assembly Line Balancing Problem (GALBP), which encompasses supplementary factors necessitating consideration during line balancing. A clear example of a GALBP is the Mixed Assembly Line Balancing Problem (MALBP). However, this problem can be treated as a SALBP depending on the solution approach used (Becker and Scholl 2006). Bautista and Pereira (2007) simplified the problem of variability in process times for different product types by considering average times based on the production mix composition. Additionally, the authors extended the SALBP proposed by Boysen, Fliedner, and Scholl (2007) by considering the linear space required for task execution, giving rise to a new balancing problem referred to in the literature as the Time and Space Assembly Line Balancing Problem (TSALBP). With this extension, line balancing not only considers cycle time and the number of line stations, but also accounts for spatial, resulting in eight types of problems based on optimisation criteria. TSALBP-m/c is one of these problems. Specifically, TSALBP-m/c is an extension of the less studied ALBP in the literature (Matondang and Jambak 2010; Tasan and Tunali 2008), known as the Type E problem. In this problem, balancing involves determining the cycle time and the number of stations that maximise line efficiency, considering the task precedence diagram and the maximum available and known linear area for workstations. To our knowledge, very few studies have been conducted on ALBP Type E. The nonlinearity of the problem and its consequent difficulty in resolution explain the limited number of studies on this problem and the preference for using heuristic procedures instead of exact procedures for its resolution. Table 1 summarises a brief review of the most relevant articles on the Type-E problem. Wei and Chao (2011) and Corominas, GarcíaVilloria, and Pastor (2016) proposed approaches based on iterative resolution of the Type-II problem. On the other hand, Macaskill (1972), Suwannarongsri and Puangdownreong (2008), and Gurevsky, Battaïa, and Dolgui (2012) proposed heuristic procedures. Hwang and Katayama (2010), Zacharia and Nearchou (2013), and Al-Hawari et al. (2015) solved different variants of the problem using genetic algorithms. Suwannarongsri, Limnararat, and Puangdownreong (2007), Özcan and Toklu (2009), and Belassiria et al. (2017) focussed on hybrid procedures. Only Esmaeilbeigi, Naderi, and Charkhgard (2015) and Bautista and Alfaro-Pozo (2020) proposed a linear mathematical formulation to solve the problem using standard linear solvers. 2. A review of the relevant literature 2.1. Assembly line balancing problems ALBP Type-E paper review.Table 1. Authors Line Type Objective approach Resolution method Macaskill 1972 Mixed Assembly Line Single objective: Maximisation of the line efficiency Heuristics procedure Suwannarongsri, Limnararat, and Puangdownreong 2007 Simple Assembly Line Single objective: Maximisation of the line efficiency Heuristic procedure and genetic algorithm Suwannarongsri and Puangdownreong 2008 Simple Assembly Line Single objective: Maximisation of the line efficiency; Multiobjective: (1) minimisation of the number of workstations (2) minimisation of the workload variance, (3) minimisation of the idle time, and (4) maximisation of the line efficiency Heuristics procedures Özcan and Toklu 2009 Simple and Ushaped assembly line Multiobjective: maximisation of the line efficiency and minimisation of the variation of workloads Hybrid heuristic procedure Hwang and Katayama 2010 Simple and Ushaped assembly line Single objective: Maximisation of the line efficiency and minimisation of variation of workload, simultaneously Genetic algorithm Wei and Chao 2011 Simple Assembly Line Single objective: Maximisation of line efficiency by minimising line capacity Iterative heuristic procedure based on solving the SALBP-2 for different numbers of workstations Gurevsky, Battaïa, and Dolgui 2012 Simple Assembly Line with task processing times having uncertain values Single objective: Maximisation of the line efficiency by minimising the line capacity Heuristics procedures Zacharia and Nearchou 2013 Simple Assembly Line with fuzzy processing times for the assembly tasks Single objective: Maximisation of the line efficiency by minimising the line capacity Genetic algorithm Al-Hawari et al. 2015 Simple Assembly Line Multiobjective: minimisation of number of workstations, maximisation of assembly line efficiency, and minimisation of workload variation between workstations Genetic algorithm Esmaeilbeigi, Naderi, and Charkhgard 2015 Simple Assembly Line Single objective: Maximisation of the line efficiency by minimising the total idle time for workstations Mathematical programming (Solver CPLEX) Corominas, García-Villoria, and Pastor 2016 Simple Assembly Line Single objective: Maximisation of the line efficiency by minimi szing line capacity Heuristics derived from an iterative procedure and enhanced iterative procedure based on solving the SALPBP-2 for different number of workstations. Belassiria et al. 2017 Simple Assembly Line Single objective: Maximising simultaneously the line efficiency and workload balance between workstations Hybrid genetics Algorithm Specifically, Bautista and Alfaro-Pozo (2020) studied line efficiency through two approaches: minimising the cycle time and minimising the dispersion between the allocated working time for the set of stations. All of this while considering the health and well-being of line workers. Other extensions of TSALBP that include ergonomic attributes of tasks can be found in Bautista, Batalla-García, and Alfaro-Pozo (2016), Bautista, Alfaro-Pozo, and Batalla-García (2016), and Bautista-Valhondo and Alfaro-Pozo (2018a; 2018b). Ergonomics has been a significant factor in assembly line balancing over the past four decades. Starting with Gunther, Johnson, and Peterson (1983), who introduced ergonomics by quantifying physical demand in terms of calorie consumption during tasks, various perspectives have integrated ergonomics into ALBPs. In terms of ergonomic estimation, methods such as observation techniques and calculation of energy expenditure have been some of the most common employed, as well as the consideration of different ergonomic parameters. Similarly, ergonomic considerations have been integrated into assembly line design from different perspectives. This includes the introduction of new constraints to mitigate risk levels or the modification of the objective function to minimise or maximise ergonomic factors. Recent research has explored the risk reduction through collaborative systems and the inclusion of rest intervals (Abdous et al. 2022). Otto and Scholl (2011) extended the SALBP in two distinct ways, by introducing ergonomic constraints and incorporating ergonomic risk assessment within the objective function. Xu et al. (2012) limited upper-extremity ergonomic risks by incorporating parameters such as exertion frequency, duty cycle, and vibration exposure and acceleration. Bautista, Batalla, and Alfaro (2013) expanded TSALBP by linking ergonomic risk constraints to workstation workloads. Bautista-Valhondo et al. (2013) investigated the effect of ergonomic risk reduction on the number of workstations. Later, Bautista, Batalla-García, and AlfaroPozo (2016) categorised tasks based on ergonomic estimates from the RULA, OCRA, and NIOSH methods. They classified tasks as acceptable or unacceptable and developed mathematical models within the TSALBP framework that considered this ergonomic categorisation. They also proposed a method to assess the line configuration robustness and employed various resolution methods for their proposed models (Bautista, Alfaro-Pozo, and Batalla-García 2015; Bautista, Alfaro-Pozo, and Batalla-García 2016; Bautista, Batalla-García, and Alfaro-Pozo 2015; Bautista-Valhondo and Alfaro-Pozo 2018a). Battini et al. (2016) formulated a multiobjective model based on the energy expenditure rate developed by Garg, Chaffin, and Herrin (1978). Similarly, Battini et al. (2015) introduced two approaches that consider ergonomic aspects in balancing problems. First, the authors simultaneously minimised the imbalance of both work distribution among workstations and physical load among workers. Second, they minimised the worktime imbalance of workers by converting the energy expenditure rate into rest intervals. Building upon the energy expenditure-based ergonomic estimation, Dalle Mura and Dini (2019) developed a genetic algorithm to minimise the station count and qualified worker number, factoring in their technical and physical capabilities. Barathwaj, Raja, and Gokulraj (2015) minimised the ergonomic risk estimated through the RULA checklist, together with the number of workstations and workload dispersion between the set of workstations within a mixed model assembly line. Sgarbossa et al. (2016) applied the first approach proposed by Battini et al. (2015) to a mixed model assembly line. Kara et al. (2014) and Weckenborg and Spengler (2019) incorporated ergonomics through constraints, solving line balance problems with economic considerations. The first authors incorporated psychological and physical strain, interdisciplinary workers, working postures and light level limitations. The second authors introduced collaborative robots alongside human resources, adjusting processing times with rest intervals to limit energy expenditure. Finally, several authors have merged ergonomic considerations with other real-world assembly line conditions, such as job rotations, parallel and U-lines, and part feeding (Battini et al. 2017). For further details, Otto and Battaïa (2017) and Boysen, Schulze, and Scholl (2022) offer comprehensive insights. This study examines the economic and productive implications of limiting ergonomic risk in TSALBP-m/c. In contrast to previous studies, a Bautista and Alfaro-Pozo 2020 Mixed assembly line treated as a single assembly line. Maximi szation of line efficiency by minimising the cycle time or minimising the imbalance of workstations workload Mixed integer linear programming for different values of the number of assembly line stations. 2.2. Ergonomics in assembly lines 2.3. Main contributions of this study mathematical model that is valid for various methods of ergonomic risk assessment is introduced. Furthermore, a linearisation of the model is proposed to enable direct resolution through Mixed-Integer Linear Programming (MILP). Moreover, an alternative linearisation of the problem is proposed to evaluate the performance of the MILP model. This approach iteratively addresses the problem while keeping the number of assembly line stations constant. The objective is to determine the Pareto frontier of potential line configurations based on feasible workstations. Both resolution methodologies are compared through a case study and a simple example to verify the problem’s adaptation to the two most prevalent ergonomic evaluation methods: energy expenditure calculation and task categorisation based on risk levels determined via observation techniques. As in prior studies, the estimation of ergonomic risk in the employed case study follows the categorisation method of tasks based on their risk levels (Bautista and Alfaro-Pozo 2020; Bautista, Batalla-García, and Alfaro-Pozo 2016). However, this study introduces a distinct approach to risk limitation. In prior studies, station risk was contingent on the ergonomic risk of tasks assigned to them, constrained by a maximum risk depending on the line’s cycle time. This approach remains valid solely for fixed cycle time problems. When the cycle time is variable, there is no guarantee that all stations will involve a risk category lower than the established maximum. For instance, if station workload is confined to a maximum risk of 360 ergo-seconds – equating to a minor/moderate risk category (Category 2) for a cycle time of 180 s – and the resulting cycle time is 120 s, the risk category for some stations might increase to high (Category 3). Consequently, the line poses a significant ergonomic risk to workers. Hence, given the variable cycle time in the studied problem, this study confines the maximum permissible risk category rather than capping the maximum risk of stations. This approach ensures that regardless of the resulting cycle time, every workstation meets the minimum ergonomic requirements. The main contributions of this study are as follows: Formulation of a comprehensive mathematical model for the TSALBP-m/c incorporating general ergonomic constraints. Adaptation of the mixed-integer model to two common ergonomic evaluation methods. Development of a mixed-integer linear model to solve the problem using standard solvers. Evaluation of the proposed model in comparison with the iterative implementation of the mixed-integer model, achieved by fixing the decision variable value linked to the number of assembly line stations. Application of both mixed-integer linear procedures considering distinct ergonomic estimation methods to a small illustrative example. Examination of the impact of integrating ergonomic considerations into the design of an assembly line through a case study. In this section, we provide a general formulation for the extension of TSALBP-m/c with ergonomic risk limitations associated with the operations assigned to workstations (Section 3.1). We explain the selected method for risk estimation (Section 3.2), propose two resolution procedures (Section 3.3), and present an example of the problem (Section 3.4). We consider a simple assembly line consisting of a set of stations arranged in series and connected by a conveyor belt that moves at a constant speed determined by the cycle time , c. This time represents both the time elapsed between two consecutive units of the products being assembled and the time available at each station to perform the assigned tasks as the product moves along the conveyor belt. In such conditions, we can define the efficiency of an assembly line, , as the relationship between the total worktime needed to assemble a product unit and the total time available at the line to work on the product unit (1). H(m,c) = 1 m×c |J| ∑ j=1tj Given that the sum of the processing times for the operations required for product assembly is constant ( ), efficiency can be maximised by maximising the productivity of assembly line (2), which is equivalent to minimising the product of the number of line stations, , and the cycle time, (Scholl and Becker 2006). In this study, we define this as line non-productivity. 3. Minimisation of non-productivity of an ergonomic assembly line 3.1. The mixed-integer model of TSALBP-m/c with ergonomics H |J| ∑ j=1tj=T m 1c max [H(m,c)] ≡ max 1 m×c |J| ∑ j=1tj min [m×c] Minimising non-productivity is the goal pursued by the problem studied in this research. Specifically, the TSALBP-m/c focuses on assigning the tasks required for product assembly among a set of workstations and for a cycle time such that the non-productivity is minimised, or equivalently, line efficiency is maximised. In addition, this assignment must consider the following: 1 The sequence in which the tasks must be performed, given by the technological restrictions of the production process and defined by the precedence diagram. 2 The space required for executing the tasks and the maximum space that the stations may have owing to spatial restrictions of the production plants. 3 The ergonomic risk that tasks pose to operators and the maximum risk to which the operators of workstations may be subjected throughout their working day without damaging their health and well-being. All of this is reflected in the mathematical formulation of the problem, whose decision variables and parameters are presented below. The binary variables indicate whether task is assigned to station ( ) or not ( ), integer variable determines the number of workstations, and real variable represents the cycle time of the line. The parameters of TSALBP-m/c with ergonomics are listed in Table 2. The mixed-integer model of TSALBP-m/c with ergonomics is as follows: Minimise Z=m×c Subject to: m≥mmin mmax ∑ k=1 xj,k= 1 (j= 1, …, |J|) mmax ∑ k=1 (kxj,k) ≤ m (j= 1, …, |J|) [ ] xj,kj k xj,k= 1 xj,k= 0 m c Parameters of TSALBP-m/c with ergonomics.Table 2. JSet of elemental tasks (j= 1,…, |J|) 2mmin Lower bound of number of line stations tjProcessing time of task jJ mmax Upper bound of number of line stations ajSpace required for task jJ Amax kMaximum available space at station k rjEstimation of the ergonomic risk of task jJ Rmax kErgonomic limit at the station k PjSet of tasks preceding task jJ  3 |J| ∑ j=1(tjxj,k) ≤ c(k= 1, …, mmax) |J| ∑ j=1(ajxj,k) ≤ Amax k(k= 1, …, mmax) |J| ∑ j=1(rjxj,k) ≤ Rmax k(k= 1, …, mmax) mmax ∑ k=1 k (xj,k−xi,k) ≥ 0({i,j}  J:iPj) xj,k {0, 1}(j= 1, …, |J|)Λ(k= 1, …, mmax) Objective function (3) minimises the product of the number of workstations and the cycle time (i.e. the non-productivity of the line). Equation (4) ensures a minimum number of workstations. Equation (5) indicates that each task can be assigned to only one workstation. Constraints (6) and (7) determine the number of workstations and cycle time of the line. Equations (8) and (9) impose the maximum linear area available for workstations and the maximum ergonomic risk, respectively. Constraint (10) guarantees the fulfilment of the precedence relationships between tasks. Finally, Equation (11) sets the domain of the variables. We use the method proposed by Bautista, Alfaro-Pozo, and Batalla-García (2016) to estimate the ergonomic risk of tasks, which allows us to simultaneously consider the three risk factors with the highest presence in assembly lines: postural loads, repetitive movements, and manual handling. This method classifies tasks into four levels of risk based on whether they require immediate attention because they pose a clear danger to the worker or, conversely, do not require any action because they pose no risk to the worker. Thus, based on the evaluation conducted by an expert ergonomist, tasks can be categorised as inescapable risk (Category 4) when the ergonomic risk posed by the task is very high and requires immediate action; high risk (Category 3) when the risk factor can cause short/medium-term harm; minor or moderate risk (Category 2) when it can cause long-term harm; and acceptable risk (Category 1) when the task poses no harm to the worker. The authors proposed that this categorisation of tasks based on their level of risk should be performed based on the preliminary evaluation obtained through different specific methods. Certainly, as detailed by Batalla, Bautista, and Alfaro (2015), their proposal integrates, into a single normalised risk level scale, the level scales of the RULA, OCRA, and NIOSH methods for assessing the ergonomic risk of any task. Once the tasks are categorised and under the assumption that the risk to which a worker is exposed increases with the duration of the task, the ergonomic risk associated with each task is determined by multiplying its category by its processing time, . Therefore, the risk that a worker bears when performing a Category 3 task with a duration of 30 s is lower than that a worker bears when performing a Category 3 task with a processing time of 60 s . Thus, given the workload of station , which represents the set of tasks assigned to station , the ergonomic risk of that station is calculated by summing up the risks associated with those tasks, . Similarly, given the ergonomic risk of a station and the cycle time of the line, the risk category of that station can be determined as follows: 3.2. Estimation of ergonomic risk χj(jJ) 4 rj=χjtj(jJ) 5(χj= 3) (tj= 30s) (χj= 3) (tj= 60s) Skk k (Sk= {jJ:xj,k= 1}) Rk= ∑ jϵSkrj Xk addition, the number of non-optimal solutions also increases. Influence of Ergonomic Limitation: The analysis of the results indicates a better computational performance of the mixed-integer model for TSALBP-m/c with a fixed number of stations when the ergonomic risk of the stations is considered. When the maximum category of stations is limited, the model yields a higher number of optimal solutions (55) compared with the case without ergonomic limitations (49), with a shorter average computation time (see CPU times in Table 6). Conversely, the proposed MILP model, which was designed for a single execution, does not reach an optimal solution for any demand plan. Some demand plans even failed to produce a feasible solution within the allotted CPU time for experimentation. Nonetheless, upon analysing the solutions obtained, we observe that, on average, the solutions without ergonomic limitations are approximately 8% off from the best bound found by the solver, whereas the solutions achieved under the ergonomic limitation are approximately 21% off. This suggests a possible, although inconclusive, negative impact of the limitation on the model’s performance. The line configurations obtained after running the models show a clear influence of the ergonomic limitations. In all cases, balancing by imposing gives rise to assembly lines with lower productivity, either because of the need to have more stations or a longer cycle time. Analysing the Pareto frontier of the efficiency values, which are calculated based on the cycle time obtained from each execution of the mixed-integer model for TSALBP-m/c across various station values (Figure 4), reveals an efficiency loss of approximately 10 points when limiting station risks. Specifically, the line configuration with the highest efficiency, when the station risk category is limited ( ), involves a productivity of 85.63% – equivalent to 25 workstations and a cycle time of 140 s for all demand plans. However, when the risk is not limited ( ), an average efficiency of 95.98% is achieved. In this case, the lines have 24 workstations and a cycle time of 130 s for all demand plans, except for plans #9 and #11, where the solution requires 25 workstations and a cycle time of 125 s. CPU times taken by the mixed-integer model of TSALBP-m/c with .Figure 3. m=mmax  16 Box-and-whisker plot showing the minimum, maximum, median, and first and third quartiles of time used to solve all demand plans in relation to the number of workstations. Blue boxes represent results without ergonomic limitations (E1), and red boxes represent results with Xk max = 2(k) (E2). Xmax k= 2 (k) Xmax k= 2 (k) Xmax k→ ∞ (k) Pareto frontier efficiency for line configurations given by the mixed-integer model for TSALBP-m/c with .Figure 4. m=mmax Graph depicting the efficiency values calculated for each demand plan based on the cycle time resulting from the execution of the mixedinteger model of TSALBP-m/c for the possible numbers of stations on the line. Similarly, even though the results are worse than those obtained with the mixed-integer model with station number parameterisation, the MILP also achieves solutions with lower productivity when the risk category of the stations is restricted (Figure 5). With this resolution procedure, an average productivity of only 77.55% is achieved when the station risk category is limited, compared to 91.08% when the risk is not limited. Graphs with the number of workstations and the percentage of efficiency of line configurations given for each demand plan. In any case, the loss of efficiency caused by the incorporation of ergonomic constraints is offset by a reduction in the risk level of the line. Indeed, the resulting line configurations, when ergonomics are not taken into account, have workstations with a risk category equal to three, which implies an immediate analysis and improvement of the station. However, this level of risk is reduced when ergonomic constraints are Solutions given by the MILP model of TSALBP-m/c with ergonomics.Figure 5. active. In this case, all obtained configurations have no stations with a risk above the minor/moderate level. Ensuring the health and well-being of workers is an essential aspect in any industrial environment. In fact, the reduction of risk factors has become a key objective within the EU’s strategic framework for health and safety at work 2021-2027. Assembly lines with a high incidence of manual operations are clear examples of production systems in which prevention can lead to significant cost savings for both companies and states. The direct relationship between manual operations and the presence of risk factors that can lead to the development of musculoskeletal disorders makes it necessary to include ergonomic analysis in the design phase of workstations. In this study, an assembly line balancing problem has been proposed with the aim of obtaining efficient designs that are also adjusted to space limitations and safe for workers. This safety has been achieved through the limitation of the risk at workstations, which has been accomplished through two approaches: 1 Expanding the assembly line with a higher number of workstations. 2 Extending the cycle time of the line, providing operators with more time between consecutive product units, and therefore recovery time between tasks with high ergonomic demands. In any case, this limitation of ergonomic risks negatively impacts the efficiency of the assembly line as defined in Equation 1. In this section, we analyse the economic and managerial implications of incorporating ergonomic conditions into the TSALBP-m/c. Specifically, based on the results obtained from the two proposed resolution procedures for all demand plans and the two possible scenarios regarding ergonomics, with and without risk limitation, various attributes are analysed. These attributes are linked to ergonomics (A1), productivity (A2), and efficiency (A3) of the assembly line: 1 Maximum level of risk at workstations in the resulting assembly line. 2 Number of workstations and cycle time of the resulting assembly line. 3 Idle time of workstations in the resulting assembly line. As expected, both procedures have provided assembly line configurations that meet the objective of attribute A1. Restricting the maximum risk category of workstations during line balancing has resulted in safe assembly lines for workers. In fact, limiting the risk category of workstations to has ensured that the workload assigned to each workstation corresponds to a minor/moderate risk level. On the other hand, considering has led to assembly lines with workstations carrying a higher risk level, requiring immediate analysis, improvement, and periodic controls of these workstations. Focusing on the best configurations in terms of line efficiency provided by the mixed-integer model for TSALBP-m/c with , the consideration of ergonomics in the line design would mean eliminating the subsequent analysis and improvement of eight workstations in the best-case scenarios (demand plans #3, #10, and #12), and eleven workstations in the worst-case scenarios (demand plans #1, #6, and #9). As example, Figure 6 shows the optimal solutions for demand plan #1, where the motor demand is uniformly distributed among the motor types. Specifically, it presents the solutions that lead to assembly lines with higher productivity in the two potential scenarios, without and with ergonomic limitations. 5. Economic and managerial implications  17  18  19 Xmax k= 2 (k) Xmax k→ ∞ (k) m=mmax Optimal solutions with higher productivity given by mixed-integer model of TSALBP-m/c with and without ergonomics.Figure 6. Based on attribute A1, we can conclude that the incorporation of ergonomic analysis in the assembly line design phase proves to be beneficial as it results in safer workstations. Furthermore, this proactive approach not only ensures worker safety and well-being from the outset but also helps save time and resources that would otherwise be spent on corrective actions. However, if we analyse the results regarding attribute A2, we observe that the ergonomic improvement achieved in the assembly line design is accompanied by a loss of productivity. This loss occurs either due to the need to increase the number of workstations in the line so that tasks can be distributed without exceeding the maximum allowed risk category or by extending the cycle time of the line, providing workers with recovery time to reduce accumulated risk. It is also possible that both situations occur simultaneously. In comparing the optimal solutions obtained with the mixed-integer model of TSALBP-m/c with , both with and , corresponding to the highest line productivity (solutions for demand plans #1, #3, #10, and #12), we observe that, in addition to requiring one more workstation in the line (24 versus 25), the risk level restriction results in a reduction of productivity by approximately 7%. Specifically, when analysing the particular case of demand plan #1, the incorporation of ergonomics in the balancing process adds one workstation to the line and increases the cycle time by 10 s (from 130 to 140 s). Therefore, considering the characteristics of the Nissan9Eng-I case, where there are two shifts of 6.75 effective hours each, this 10-second increase in the cycle time implies a decrease in production capacity equivalent to 27 motors per day. Taking into account that the Consolidated Operating Profit (COP) of the line is 10% of the price of a motor, and the price of a motor is 4000€, this could result in a daily loss exceeding 10,000€. Finally, if we analyse the results from an efficiency perspective of the assembly line (A3), we observe that restricting the risk at workstations during balancing leads to less efficient line designs. This decrease in efficiency is a result of the need for more workstations and an increase in idle time on the line. Specifically, when we refer back to the optimal solutions for each possible situation regarding ergonomic considerations, in all cases, an additional workstation is required, and the idle time on the line increases, ranging from 4% to 14% of the total working time. These findings highlight how incorporating ergonomic analysis in assembly line design can result in lines that not only require a higher number of resources, such as workstations and consequently more operators, but also may require more working time to accomplish the same production. It is crucial to carefully consider the trade-offs between worker safety, line efficiency, and overall financial performance when incorporating ergonomic factors. While prioritising worker well-being is essential, maintaining a balance between overall line productivity and resource utilisation is also critical for the long-term success and sustainability of the assembly line. Prioritising worker safety through ergonomic analysis is crucial for creating a work environment that safeguards employee well-being and Two tables, each with as many rows as workstations, displaying the corresponding assembly line configurations. Each station is shown with its assigned tasks, idle time, and risk category. m=mmax Xmax k→ ∞ (k) Xmax k= 2 (k) minimises the risk of work-related injuries. However, it is equally essential to assess the impact of ergonomic improvements on production efficiency and resource use. In this regard, we see how conducting a comprehensive evaluation will enable decision-makers to determine whether the initial investment required for considering ergonomics in line balancing outweighs the losses resulting from a less efficient line design. Throughout this study, the challenge of balancing efficiency with space limitations and ergonomic safety in assembly line design has been comprehensively addressed. The TSALBP-m/c problem has been studied by incorporating the ergonomic risk of tasks, recognising that it can be estimated using various evaluation methods. Indeed, a general mixed-integer model has been formulated for the problem and adapted to two ergonomic risk estimation methodologies from literature. Given the complexity of the problem, two MILP resolution procedures have been proposed. One of them is based on iteratively executing the mixed-integer model while fixing the number of stations, and the other formulates a new MILP model. Using a simple example, the validity of both procedures and their adaptability to different ergonomic estimation methods has been demonstrated. However, the superiority of the iterative procedure over the proposed MILP has also been evidenced through the Nissan-9Eng-I case study, especially with medium to large-sized datasets. The results demonstrate that within an average time of around 45 min (2578.49 s), the iterative procedure is capable of providing a Pareto front that enables decision-makers to identify the most efficient solutions in terms of the balance between productivity and worker wellbeing, considering the given constraints. The analysis of the results reveals that ergonomic improvement in assembly lines can be accompanied by economic and productive losses, either due to more workstations or even production declines. Specifically, as shown by the case study, the application of ergonomic risk limitation in assembly line balancing requires special attention as it can lead to significant efficiency loss in the line, with longer idle times and reduced production capacity. All these negative effects must be evaluated by decision-makers to achieve a balance between promoting a safe working environment and maintaining productivity and competitiveness. Clearly, this requires additional information, such as the costs derived from reduced absenteeism, occupational accidents, and work-related illnesses, as well as the costs that alternative approaches could entail to mitigate these negative effects, such as implementing shift rotation schedules or incorporating collaborative robots. By rotating tasks among workers or integrating collaborative robots into the production process, the ergonomic load on individual workers can be reduced, potentially enhancing their overall well-being and performance. Moreover, these alternative measures can lead to more efficient resource utilisation, ultimately offsetting potential cost increases. Studying risk reduction strategies and developing alternative resolution procedures are potential future works to strike the appropriate balance between ergonomic considerations and productivity improvements. All of this is aimed at creating a safe and efficient working environment, ensuring worker well-being, and maximising company success. Note 1 Average CPU time (in seconds) taken by the solver to complete all iterations of a specific demand plan. Disclosure statement No potential conflict of interest was reported by the author(s[Q3]). Notes on contributor Rocío Alfaro-Pozo is a Technical Industrial Engineering, specialising in Industrial Electronics (2007) from the Universitat de les Illes Balears, Industrial Engineering (2010), and a Ph.D. in Business Administration (2015) from the UPC and she also completed the Master’s degree in Evaluation and Quality Management in Higher Education (2021) at the UOC. She began her teaching career as an associate lecturer in the area of Business Organisation in 2010, and since then, she has been exercising his teaching work in 6. Conclusion and outlook various subjects related to Industrial Engineering at the Barcelona School of Industrial Engineering of the UPC. Accredited by the National Agency for Quality Assurance and Accreditation (ANECA) and by the Agency for Quality in the Catalan University System (AQU), from 2016 to 2022, she combined her teaching and research activities with the role of Deputy Dean for Quality and Accreditations at EAE Business School. Her research primarily focuses on production and logistics operations, specifically in sequencing and assembly line balancing. She has participated in various projects funded by the Spanish Government’s National R&D&i Plan and has published in various conferences and journals. Joaquín Bautista-Valhondo is an Industrial Engineer (1983) specialising in Energy Techniques and a Doctor of Industrial Engineering (1993) from the Polytechnic University of Catalonia (UPC) with an extraordinary doctorate award in Industrial Engineering (1995). In 1984 he obtained a pre-doctoral fellowship from the French Atomic Energy Commissioner (CEA), carrying out a research stay at the Division for the exploitation of prototype and experimental reactors of the Centre for Nuclear Studies in Grenoble. He has been a University Professor since 2002 in the area of Business Organisation, exercising his teaching work in various subjects related to Industrial Engineering at the Barcelona School of Industrial Engineering of the UPC. He has been an affiliate researcher of the European Centre for Soft Computing (2007) as well as Academic Director of the Nissan Motor Iberian Chair of Automotive Innovation at the UPC (2005). He has participated as a member of advisory committees in commissions and university quality agencies linked to the autonomous and central governments of Spain. 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