# Hybridizations in line balancing problems: A comprehensive review on new trends and formulations

Olga Battaïa, Alexandre Dolgui

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## To cite this version:

Olga Battaïa, Alexandre Dolgui. Hybridizations in line balancing problems: A comprehensive review on new trends and formulations. International Journal of Production Economics, 2022, 250 (22), pp.108673. 10.1016/j.ijpe.2022.108673. hal-03981865

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Distributed under a Creative Commons Attribution 4.0 International License
Hybridizations in line balancing problems: a comprehensive review on new
trends and formulations

Olga Battaïa<sup>a</sup> and Alexandre Dolgui<sup>b</sup>

<sup>a</sup> Kedge Business School, Talence, France,
olga.battaia@kedgebs.com

<sup>b</sup> IMT Atlantique, LS2N-CNRS, Nantes, France
alexandre.dolgui@imt-atlantique.fr
# Hybridizations in line balancing problems: a comprehensive review on new trends and formulations

## Abstract

In the research on production economics, line balancing is an intensively studied combinatorial optimization problem. In our previous comprehensive survey on line balancing problem published in 2013 in the International Journal of Production Economics, we compared input data modelling approaches, constraints and objective functions used in more 300 studies mostly published from 2007 to 2012. Ten years after, line balancing problems still attract high attention from both academia and practice. The aim of this review is to analyse actual problem formulations that are more and more frequently hybridized with other optimization problems such as process planning, workforce planning and/or resource scheduling in order to create efficient solutions for customized production environments adapted for volatile markets. This presentation of the state of the art is based on a review of more than 500 articles published in refereed journals between 2012 and 2022.

*Keywords: Assembly line balancing, process planning, workforce planning, resource scheduling.*

## 1. Introduction

As an important part of the Supply Chains, manufacturing systems must respond to product and market changes (Ortega-Jimenez et al., 2020). The path from the product design to its delivery lies through several decision steps both in the design and operation of Supply Chain and Production system, such as, to cite only few, process planning, supplier selection, production system design and planning, product distribution, etc. Line balancing problem (initially known as assembly line balancing) is one of the important steps in this decision-making process.

According to the classification of Dolgui et al. (2022), it occupies the level of tactical decision making for production systems. In general terms, the objective of the line balancing problem is to decide how the product will be manufactured in the production system (represented by a set of workstations) by assigning tasks to resources (workstations) in order to meet some given requirements and to achieve efficiency through optimising one or several chosen objectives. At the step of line balancing, the layout of the line is generally known as chosen in a previous decision step. Each layout provides proper constraints to be respected while assigning tasks to workstations. Among frequently encountered layouts we can cite straight lines, line with multiple workplaces (two-sided lines is a particular case of such a layout, this case is discussed here below in details), U-lines (Fattahi et al., 2014; Li et al., 2017b, 2021b)
and lines with a circular transfer (Battaïa et al. 2014b, 2015, 2017a,b). Any combination of the above layouts may exist when parallel lines are employed.

Historically, the first line balancing problems addressed the case of a single product to be processed. Nowadays, line balancing and rebalancing is one of the effective tools to adapt the existing production system to evolved product design or new market condition. It also one of powerful mean for product customization. Multiple models of product (variants) can be planned for manufacturing in the same line either in *mixed-model mode* (Ilgin et al., 2017, Kucukkoc et al. 2013, Sadeghi et al., 2018) or in *multi-model mode* (Pereira, 2018a). In a *mixed-model mode*, there are several products (variants of a product); all products are processed at the line at the same time within a mixed sequence. In a *multi-model mode*, the *line* is used for one product at the same time and undergoes a setup to be prepared to switch to the next product model (variant). More information on product-mix performance portrait of serial lines can be found in the article by Alavian et al. (2017). A new mode of “multiple-piece-flow” assembly line has been considered by Otto and Li (2020) where several products move from station to station at the same flow. It should be noted that generally the information about a product or products is at least partially defined at the step of line balancing. This information may be partially not precise, stochastic or fuzzy, but in order to be able to assign tasks to workstation a minimal information should be known about tasks and resources available (or that can be available) in workstations.

Because of its importance, the line balancing problems have been intensively studied in the literature. Initially introduced for assembly lines, they have been also considered for machining and disassembly lines. Some studies even consider both assembly and disassembly tasks in the same line (Guo et al. 2021, Mete et al. 2018). McGovern and Gupta (2015) proposed a unified assembly-and-disassembly-line model formulae and discussed the inherent differences between the two processes.

In 2013, we proposed a taxonomy for line balancing problems creating a common framework for these diverse industrial contexts. Our research attracted interest in the field and the paper even has been the most cited in IJPE in 2018. During the last decade, more than 500 new contributions to line balancing field have been published in the literature. The objective of this review is to analyse the trends in this abundant literature and to discuss how the new developments support the transformation of production lines under the influence of global trends such as technology evolution related to the concepts of Industry 4.0, sustainability issues and product customization. In this study, we provide a comprehensive state of the art and original view on line balancing approaches from evolutions of application domains perspectives in different industrial environments including machining, assembly and disassembly and discuss next directions for academicians and practitioners.
A number of reviews on line balancing problems have been published in the last decade. Here below we discuss the most significative publications and compare them with the scope and approach adopted in the present paper.

First, we discuss the reviews that were limited to the assembly lines. Sivasankaran and Shahabudeen (2014) presented a literature review of assembly line balancing problems based on only three parameters, i.e. the number of models (single-model and multi-model), the nature of task times (deterministic and probabilistic) and the type of assembly line (straight-type and U-type). The scope was limited to assembly context and only essential elements of assembly lines.

Li et al. (2017a), Make and Razali (2017) focused their review articles on two-sided assembly line balancing problems. The former evaluated only heuristics and meta-heuristics. Razali et al. (2019) emphasised in their survey advances in mixed-model assembly line balancing.

Chutima (2020) discussed research trends in assembly line balancing problems between 2014 and 2018. The scope of the analysis was limited both by the time period and assembly context.

Eghtesadifard et al. (2020) analysed with a specific software tool the articles on assembly line balancing published between 1990 and 2017 and selected from the Web of Science database. They determine the collaborative network between researchers, the most frequently used keywords and analyse citations.

Boysen et al. (2021) reviewed the advances in assembly line balancing during last fifteen years following the classification scheme they introduced in 2007. As previously, the scope of their study was limited to assembly environment and according to our observation; many important recent publications were missing in their analysis, since the survey only covers about 300 articles published since 1967.

Jiao et al. (2021) reviewed 89 articles and classify the assembly line balancing problems according to the number of models (i.e. the number of different products), the layout shape of the assembly line, and the data of task time and analyze the solution methods developed for each category.

Chutima (2022) analysed about thirty studies dedicated to robotic assembly line balancing problem, which considered both fully automated systems and the use of collaborative robots interacting with human operators. Daneshmand et al. (2022) also reviewed robotic assembly and disassembly but through lenses of process planning, including studies on line balancing integrating this aspect. The review on optimization models and applications in robotic manufacturing systems of Vaisi (2022) also included a section on line balancing problems in robotic assembly and disassembly.

Several reviews on solution methods that can be used for line balancing problems are also available in the literature. For the simple assembly line balancing, Pape (2015) compared 12 heuristics and 9 lower bounds, Fathi, et al (2018) evaluated 20 constructive heuristics for straight and U-shaped assembly lines, Pereira (2015) provided an empirical evaluation of lower bounding methods for the simple
assembly line balancing problem, Li et al. (2020a) performed a comparative study of exact methods. Fattahi and Turkay (2015) compared MILP models developed for the U-shaped assembly line balancing problems and discussed possible infeasibility of solutions found. Hamzas et al. (2015) reviewed the existing evolutionary algorithms for multi-objective two-sided assembly line balancing problems. Gen et al. (2017) analysed the hybrid evolutionary algorithms developed for multi-objective manufacturing scheduling. Ramli and Ab Rashid (2021) reviewed assembly line balancing problems with energy consideration using meta-heuristic algorithms.

The analysis of literature shows that no recent review uses a common framework on line balancing
in assembly, machining and disassembly contexts to analyse global trends in manufacturing. The
objective of this paper is to analyse the whole scope of production line balancing problems in order to
derive managerial insights from the available body of knowledge as well as to develop future research
directions. However, since the development of solution methods has already widely discussed in the
existing reviews, e.g. Eghtesadifard et al. (2020), Boysen et al. (2021), we do not focus on this point in
the present study.

The paper is organized as follows. In Section 2, we briefly recall the structure of the taxonomy proposed and recall the trends perceived 10 years ago in (Battaïa and Dolgui, 2013). In Sections 3-6, we compare these trends with the actual development of the research field during last decade on the basis of more than 500 articles published since 2012. In Sections 7-9, we derive new insights and trends from this literature. In Section 10, we summarize our fundings and discuss how the hypotheses for future research directions expressed in (Battaïa and Dolgui, 2013) have been supported (or not) by research community. In Section 11, we provide conclusions and future research perspectives.

## 2. Trends and insights from our previous review

The literature attributes the introduction of assembly line balancing problem to Salveson (1955). A historical perspective on this formulation can be found in Wilson (2014). The basic version of this problem deals with a set of tasks $I=\{1,2,...,i,...,|I|\}$ that need to be assigned to a set of linearly ordered workstations $M=\{1,2,...,k,...,m\}$. Such an assignment must respect precedence constraints among the tasks and a cycle time that imposes that the sum of processing times of tasks assigned to each workstation must not exceed a given limit. The initial optimisation objective is to minimise the number of workstations required for the assignment of all tasks under given constraints.

Contemporary line balancing problems in industrial environments differ a lot from this basic
definition due to different structures of lines, details of their functioning, their constraints as well other
practical elements which vary from an application to another. Since different types of lines and their
elements can be modelled with the same mathematical tools, we proposed a taxonomy based on the
mathematical structure of the line balancing problems and not on the practical aspects. This taxonomy
is based on the following elements:

(i) Number of lines to be balanced: *one line; several independent lines with identical or different configurations; lines with multi-line workstations or workers performing tasks for more than one line; parallel lines with crossovers.*

(ii) Task attributes *T*(i): *task attributes with constant values; task attributes with dynamic values;*
*task attributes with uncertain values; task attributes with assignment-dependent values.*

(iii) Workstation attributes *W*(k): *workstation scalar-attributes, workstation vector-attributes.*

(iv) Constraints to be respected by a feasible solution: *assignment constraints; constraints concerning workstation attributes; constraints on performance measures calculated for workstations; cycle time constraint.*

(v) Optimisation criteria: *number of workstations, line cycle time, line efficiency, line smoothness,*
*probability of on-time completion, cumulative function based on workstation or tasks attributes, etc.*

Our previous study (Battaia and Dolgui, 2013) revealed the following research trends:

1. Simple versions of ALBP were still of high interest for researchers.

2. At the same time, more and more researchers considered integrated problem formulations where a line balancing problem was jointly solved with another optimisation problem such as process planning, line design or task scheduling.

3. A shift has been observed from single to multi-objective optimisation for simple problem formulations, but in many cases due to a joint consideration of several optimisation problems and integration of their objectives.

4. In terms of solution methods, a development of Branch and Bound techniques and a frequent use of metaheuristics (in particular for multi-objective formulation) have been reported.

5. The consideration of ergonomic aspects and environmental issues was a fast-developing trend.

In that study, we have also reported on the underdeveloped topics such as rebalancing problem and
robust optimisation under uncertainty of input data. We underlined the need for reliable data sources for
effective optimisation and the analysis of stability of solutions if such sources remain unavailable in
practice.

In order to discuss the evolution of these trends during the last decade, we analyse each of them in
the following sections: Section 3 – Simple version of ALBP, Section 4 – hybridization with other
optimisation problems, Section 5 – Multi-objective optimisation, Section 6 – Sustainability issues. As
it has already been mentioned, since the development of solution methods has already been widely
discussed in the existing reviews, we did not focus on this point in the present study. In consequent
sections, we discuss other trends observed in the literature: Section 7 – need for robustness, Section 8 –
need for resilience, Section 9 – Technological advancement and cobotisation, finally, Section 10 summarizes funding in closing discussion and Section 11 reports the final conclusions.

### 3. Simple version of ALBP: time for assessment

As in 2012, a number of recent publications still deal with the simple assembly line balancing problems, but their global number has been decreasing during the last decade. The last original contributions mostly propose an approximate method to solve SALBP-1 or SALBP-2 such as a particle swarm algorithm (Dou et al. 2013), genetic programming approach (Baykasoğlu and Özbakır, 2015), a hybrid genetic algorithm (Álvarez-Miranda et al. 2021b), a genetic algorithm with variable neighborhood search (Fathi et al. 2020;), beam ant colony optimisation (Huo et al. 2018), differential evolution (Nearchou and Omirou, 2017; Zhang et al. 2016). Nourmohammadi et al. (2019b) studied the landscape of the SALBP and concluded that it was flat for workload smoothness index, i.e. local optima are uniformly scattered over the search space. According to their conclusions, for meta-heuristics, the exploration of the search space has a higher priority than its exploitation to make sure that different local optima are found and compared with each other.

Only few new exact methods for SALBP-1 and 2 have appeared during this period. Vilà and Pereira (2013) proposed an enumeration procedure for the assembly line balancing problem based on branching by non-decreasing idle time. In parallel, the branch, bound and remember algorithm was developed for SALBP-1 by Sewell and Jacobson (2012) and tested by Morrisson et al. (2014) on a new benchmark data set proposed by Otto et al. (2013). Due to its outstanding performances, this algorithm has been adapted by many researchers and applied to many other formulations:

* manual mixed-model line with overtime costs (Li and Gao, 2014);

* mixed-model assembly lines with adjacent task duplication (Yang et al, 2014);

* robotic assembly line balancing Borba et al. (2018);

* U-shaped assembly line balancing problem (Li et al., 2018b);

* assembly line balancing considering uncertain task time with information (Li et al., 2018c);

* simple disassembly line balancing problem (Li et al., 2019);

* two-sided assembly line balancing problem (Li et al., 2020b);

* simple assembly line balancing problem of type II (Li et al., 2021f).

Ritt and Costa (2018) suggested an improved integer programming model for simple assembly line balancing and related problems such as the U-shaped assembly line balancing problem and bin packing problem with precedence constraints. Pereira (2016) studied a bin packing problem with precedence constraints which only differs by their form from SALBP-1: while the precedence relations in SALBP-
1 correspond to inequality constraints (≤), the precedence constraint in BPP-P correspond to strict inequality constraints (<).

Finally, Bukchin and Raviv (2018) designed and tested a constraint programming approach for SALBP 1 and 2. This approach is highly popular for scheduling problems, but the work of Bukchin and Raviv (2018) seems to be the first published attempt to employ it for SALBP. With the need to schedule the tasks and manage limited resources in assembly lines as in *Resource Constrained Project Scheduling problem*, the use of this approach is becoming more frequent (Lovato et al 2022).

The development of solution methods allowed an improvement of the resolution of SALBP-E considered in several recent studies (Corominas et al., 2016; Cerqueus and Delorme, 2019; García-Villoria and Pastor, 2013; Esmaeilbeigi et al., 2015;).

Several studies dealing with comparisons of different techniques for the simple assembly line balancing problems (SALBP) have been presented: Pape (2015) compared 12 heuristics and 9 lower bounds for SALPB-1; Fathi et al. (2018) evaluated 20 constructive heuristics for straight and U-shape SALBP; Pereira (2015) provided an empirical evaluation of lower bounding methods for the simple assembly line balancing problem; Li et al. (2020a) performed a comparative study of exact methods; Otto and Otto (2014a) discussed the generation of priority rules for SALBP. In 2019, Álvarez-Miranda and Pereira published a note on the complexity of SALBP where they analyse how other researchers assess the complexity of SALBP and refer to it.

In many studies, the authors also refer to simple assembly line balancing problem (SALBP) if all elements fit its standard formulation except for the objective function. Other studies considered “variants” of SALBP which can be also considered as a generalization of SALBP. Álvarez-Miranda et al. (2021a) considered a variant of the SALBP with parallel workstations and the objective of minimising the number of parallel stations required to obtain the maximum theoretical efficiency of the line. Azizoğlu and Imat (2018) considered SALBP with the objective of workload smoothing. Ozcan et al. (2017) proposed an alternative MILP model for SALBP-2 and for makespan minimization on assembly lines and compared proposed models on benchmark instances. Khalid and Yusof (2021) in addition to the line efficiency function dealt with the shifting bottleneck identification. Fathi et al. (2020) considered the minimization of the total number of workstations and secondarily the maximization of the workload smoothness, this objective has been also considered by Hazır et al. (2021) and Walter et al. (2021a,b). Rossi et al. (2016) used as the objective the robustness of the obtained solution.

Koltai et al. (2014) showed how the application of the results of simple assembly line balancing models could be used in practice. Wellington and Lewis (2018) presented an interactive excel-based procedure for line balancing for educational purpose. Education is an important step for bridging the gap between academy and practice. The digitalisation of industrial processes flourished in the last
decade, also helped companies to improve their line balancing procedures and either to apply an
available commercial decision tool or to develop their own application.

The analysis of the recent contributions shows that the standard formulation of SALBP was extensively studied in the literature. The majority of the contributions during the last decade dealt either with a comparison of existing methods or a multi-objective variant of SALBP. Only few new solution methods were developed showing that the focus in the field has shifted to more complex and relevant in practice line balancing problems as discussed in the next session.

4. Hybridization with other optimisation problems: a major trend

We can observe that this trend has not only been confirmed but also significantly intensified during the last decade. Making several decisions simultaneously along with line balancing leads to better final line performance and effectiveness. However, this hybridization also increases the number of decision variables to be managed and thus the complexity of the optimization problem to be solved.

**4.1. Line balancing and task sequencing at each workstation**

In the original version of SALBP, the tasks do not need to be sequenced within each station due to their one per one execution and cumulative station time. These two factors ensure that if the total task duration is inferior to the cycle time of the line, a sequence respecting the precedence constraints can be always found. The task sequencing within stations becomes necessary when order-dependent setup times exist between tasks and their duration is not negligible in comparison to the line cycle time, so there is a need to verify that a sequence of tasks respecting the cycle time exist. However, if there is no parallel task execution, task sequencing i.e. only task order is sufficient to verify this constraint. Task scheduling becomes necessary only when parallel resources can act on tasks and the satisfaction of precedence constraints become only possible by comparing the start and end times of the tasks.

In the case of task sequencing within stations, line balancing is combined with the total setup time minimisation that is equivalent to the search for the shortest path for a travelling salesman problem with precedence constraints. In the majority of the cases, the authors search for an optimal order of tasks developing a number of solution procedures (Akpinar et al., 2013; Akpinar and Baykasoğlu, 2014a,b; Furugi, 2022; Hamta et al., 2013; Kalayci and Gupta, 2013a,b,c, 2014; Kalayci et al., 2015a,b, 2016; Lahrichi 2021a,b; Lu and Yang, 2016; Nilakantan et al., 2019; Wang et al., 2019a; Yang and Cheng, 2020a,b). It should be noted that in presence of a single resource performing tasks and absence of another type of constraints as breaks, an optimal sequence of tasks produces an optimal schedule. The opposite is also true, an optimal schedule corresponds to an optimal task sequence if the overall objective function remains the same. Modelling of the task sequencing problem with scheduling concepts is also possible,
in this case the solution methods adapted for scheduling problems can be used (Esmaeilbeigi, 2016, Özcan, 2019).

## 4.2. Process planning and line balancing.

Singer et al. (2014) presented a new three-stage technique to fill the gap between product planning and production. In practice, process planning deals with the selection of tasks to be performed in order to complete the desired product and line balancing deals with the assignment of these tasks to stations. However, if the process planning is realised with the objective of total time minimization, the obtained solution does not necessarily lead to the optimal line configuration neither in terms of cycle time or cost. When it is possible to consider optional processes for task execution at the same time as task assignment to workstation, the final performance of the line can achieve much better results.

In the current literature, the main field for application of joint process planning and line balancing is disassembly. It is particularly relevant when there is no need to complete all the tasks as in assembly or machining. The most frequently used tool for introducing process alternatives is so-called “and” and “or” precedence graph which consists of two types of arcs: “and” for strict precedence and “or” for alternatives. Such a precedence graph has been used in numerous studies on disassembly line balancing, under assumption of complete disassembly as in Aydemir-Karadag and Turkbey, 2013; Bentaha et al., 2014a,b, c, 2015a, b, 2018, 2022; Çil, 2021; Ren et al., 2020; Riggs et al., 2017; Xiao et al., 2021. and under assumption of partial disassembly, such as in Aydemir-Karadag and Turkbey, 2013; Bentaha et al., 2018; Li et al., 2018d; Ren et al., 2017; Wang et al., 2019b,c 2021; Xia et al., 2020; Xiao et al., 2021; Yin et al., 2021b, 2022; Zhu et al., 2020a. A review on disassembly sequence planning was presented by Ong et al. (2021). The studies with the process selection with line balancing are much less frequent for assembly (Leiber et al., 2021; Papakostas et al., 2014) and machining lines (Battaïa et al., 2017).

Under global trend of product customization in manufacturing, the integration of process planning and line balancing seems to be an efficient tool in order to optimize the final performances of the line. Due to this problem hybridization, the common and particular tasks between the different models of the product can be efficiently spread in the line assuring a late differentiation of the products which is also known as a factor increasing the robustness of the line to the variations of customer demand. We believe that the customization in manufacturing will strengthen the interest of academicians to this hybridization.

## 4.3. Line design and balancing
Historically, line balancing refers to the assignment of tasks to stations, while line design includes decisions on the line configuration and also defines the equipment to be used in each workstation. The joint problem belongs to the overall framework of design for manufacturing and assembly/disassembly: joint design of products and production systems, a recent overview of existing studies has been presented in (Battaïa et al., 2018). The line design includes several decisions depending on the type of the lines (manual, automated, etc). In the literature, such decisions as worker assignment, equipment selection and even design of particular elements of the line such buffers of part feeding system can be hybridized with line balancing. They are discussed here below.

### a) Line balancing and worker assignment or equipment alternatives/equipment selection

In many cases, the hybridization of line balancing with worker assignment is equivalent to the hybridization of line balancing with equipment selection. It is true when only task attributes (such as time, cost, etc) depend on the choices made on the resources to be assigned to each workstation. The problems are only different when specific resource constraints are considered.

As already mentioned in (Battaïa and Dolgui, 2013), if multiple resources are assigned to the same workstation, then also a scheduling problem needs to be solved in order to avoid disturbances when these resources work in parallel. In many cases, this leads to solving a line balancing problem among the workstations and Resource Constrained Project Scheduling problem (RCPSP) at the level of each workstation. RCPSP assigns tasks to resources (operators or machines) taking into account precedence and resource constraints. The skills of operators can be easily modelled in this context. This is particularly relevant for big size products where the available space permits a teamwork (Zennaro et al., 2019) such as aircraft (Arkhipov et al., 2015a,b; Biele and Mönch, 2018; Battaia et al., 2019; Buergin et al., 2019; Gómez et al., 2016; Lovato et al., 2022). When only one worker or one piece of equipment is chosen for each workstation or multiple resources are selected but have not interaction between them, then they can be considered as "scalar attributes" of a workstation, see (Bataïa and Dolgui, 2013).

It should be also noted that in recent studies, the workers are not necessarily assigned to a workstation, they can move between the workstations (Battaïa et al., 2015; Biele and Mönch, 2018) not constantly as in bucket brigades (Koo, 2020) but having a precise schedule for visiting different workstations. This more flexible assignment improves the line capacities of the adaptation to the customization and changing demand and makes the line more scalable (Koren et al., 2017) and reconfigurable (Hashemi-Petroodi et al., 2021).

Worker assignment problem without RCPS was considered in the following studies as Akyol and Baykasoğlu, 2019; Borba and Ritt, 2014; Campana et al., 2021; Fattahi et al., 2016; Liu et al. 2022; Oksuz, et al 2017; Pereira, 2018; Polat et al., 2016; Ramezanian and Ezzatpanah, 2015; Salehi et al.,
2018, 2020; Samouei et al., 2016; Sungur and Yavuz, 2015; Vilà and Pereira, 2014; Zacharia and Nearchou, 2016. The availability of worker considered by Ritt et al. (2016), is closely related to the rbalancing problem discussed in Section 8.

Oesterle et al. (2019) presented a comparative study of multi-objective algorithms for the assembly line balancing and equipment selection problem under consideration of Product Design Alternatives. Recently, equipment alternatives have been considered in the following studies: Atasagun et al., 2019; Borisovsky et al. 2013, 2014; Bukchin and Raviv, 2018; Jayaswal and Agarwal, 2014; Lahrichi et al., 2021a,b; Ogan and Azizoglu, 2015; Pereira, 2018.

## b) Line balancing and RCPSP

This type of problem arises in multi-manned or multi-robots environments. The workers can be assigned to workstations or be flexible and move among workstations (Biele and Mönch, 2018).

The case of two-sided lines is a particular case of multi-manned lines where the number of resources is limited by definition to 2. Li et al. (2017) presented a comprehensive review and evaluation of heuristics and meta-heuristics for a two-sided assembly line balancing problem. For these lines, if tasks only can be done from one side, the partition of the set of tasks assigned to a station between two sides is straightforward. However, it is necessary to solve the corresponding scheduling problem in order to verify precedence constraints between the tasks realized on the different sides of the line. It should be noted that two-sided lines attracted a lot of interest from researchers during the last decade, we can cite more than 60 of them, therefore, we consider it as a major trend in the field (Cevikcan et al, 2020; Chutima and Prasert, 2018; Çil, 2020; Çil and Kizilay, 2020; Delice, 2019; Delice et al., 2016, 2017; Delorme et al., 2019; Gansterer and Hartl, 2018; Faccio et al., 2016; Fattahi et al., 2016; Huang et al., 2021; Kellegöz, 2017; Kellegöz and Toklu, 2012, 2015; Kucukkoc et al., 2018; Kucukkoc and Zhang 2015a,c, 2016a, b; Lei and Guo, 2016; Li et al. 2016a,b 2019c,d, 2020, 2021b,e; Li and Coit, 2018; Liang et al., 2021a,b; Lopes et al, 2019a, 2020b; Michels et al., 2019, 2020; Naderi, 2019; Pearce et al., 2019; Roshani and Giglio, 2017, 2020; Roshani and Nezami, 2017; Roshani et al, 2021; Şahin and Kellegöz, 2019a,b; Sternatz, 2014; Tang, 2017; Yadav et al., 2020b; Yadav and Agrawal, 2022; Yang and Cheng, 2020b; Yılmaz and Yazıcı, 2021; Yılmaz and Yılmaz, 2015, 2016, 2020; Wang et al., 2014; Zamzam and Elakkad, 2021; Zhang et al., 2018, 2020a,b, 2021c).

Because of such a significant number of contributions is not possible to discuss each of them detailly in this review, rather a focused review on this trend should be performed. Hashemi-Petroodi et al. (2021) have already discussed multiple aspects of workforce assignment strategies in manufacturing systems but this review can be complemented with a general performance evaluation of the developed methods on available benchmark instances.
We can provide some general observations on this body of literature: many of these studies consider
settings that have been already discussed for a straight or U-shape lines. However, the necessity to
manage multiple resources within each workstation and to schedule tasks considerably increases the
number of decision variables involved and therefore the complexity of the problem. As a consequence,
adapted methods capable of managing scheduling part are required to solve the problem. Due to the
necessity to include scheduling part in the decision process, we can observe a much frequent use, in
comparison to other formulations of line balancing, of a constraint programming approach (Arkhipov et
al., 2015a,b; Çil, 2020; Çil and Kizilay, 2020; Lovato et al., 2022; Pınarbaşı et al., 2016; Stecke and
Mokhtarzadeh, 2022).

c) Design of other elements of the line

In addition to workstations and resources assigned to them such as human operators, robots, cobots and piece of equipment, other elements as specific stations, specially designed equipment, buffers, feeding system, conveyor are defined during the line design. In recent literature, we can observe a number of studies which consider the design and optimization of “other” elements of the line, but in many cases there are only few or even one study available in the literature for each type of element. Since these elements have an important impact on the performances of the line, their further consideration is expected in next future.

Among such elements, we can cite:

- special resources positioned in stations: *positions for resources* (Leiber and Reinhart, 2021), *rework stations* (Cavdur and Kaymaz, 2020; Cavdur et al, 2021; Hossain and Sarker, 2015); combined *assembly/disassembly stations* (Mete et al., 2018), *underground workstations* (Kucukkoc et al., 2018), *specially designed multi-spindle machines* (Battaïa, et al 2014 a,b, 2015, 2017a, 2020, 2021);

- elements of internal logistics: *part feeding/material supply* (Battini et al., 2017; Calzavara et al., 2021; Chen et al., 2021; Nourmohammadi and Eskandari, 2017; Nourmohammadi et al., 2019; Schmid, 2021; Sternatz, 2015; Rabbani et al., 2017); *component picking* (Bortolini et al., 2017); *conveyor scheduling* (Calleja et al., 2013, 2014, 2016; Fleszar, 2017; García-Villoria et al., 2015, 2018).

- **buffers** (Lopes et al., 2020a, d; Romero-Silva, and Shaaban, 2019; Romero-Silva et al., 2019; Tiacci, 2017). Hybridization between line balancing and *buffer allocation* have been also considered (Lopes et al., 2020c; Oesterle et al., 2016; Shaaban and Romero-Silva, 2021; Shao et al., 2020; Tiacci, 2015; Xuemei et al., 2017) and in some studies also hybridized with model sequencing in (Lopes et al., 2020c), and equipment selection (Oesterle et al., 2016);
The hybridization of line balancing problem with a different optimisation problem often has an impact on the objective function considered for the joint problem. In particular, it often leads to position the problem in multi-objective perspective. The use of multi-objective optimisation for line balancing is discussed in the next section.

## 5. Multi-objective optimisation

An objective or goal function evaluates the quality of feasible solutions and is used to choose the best one. The following three goal functions are widely used for SALBPs:

* Minimize the *number of workstations* *m* to be installed (SALBP-1);

* Minimize *line cycle time* *c* (SALBP-2);

* Maximize *line efficiency* (SALBP-E), i.e. the value *m*c (Su et al., 2014).

Among others, the following other objective functions are also frequently used:

* Maximize the "system utilization" *U* which is another measure of "line efficiency" and can be calculated as the ratio of the minimum required number of workers to those actually assigned;

* Minimize line smoothness (SI) measures, not necessarily only processing times (Azizoğlu and Imat, 2018, Hazır et al., 2020,2021, Walter et al 2021a,b), e.g. workstation ergonomic risks;

* Minimize $\sum_{k=1}^{m} dimW^v(k)$ if workstation vectorial attributes are employed

* Maximize the probability of on-time completion of all tasks used for stochastic task times. This objective can be also expressed as a minimization of non-completion probabilities of each station;

* Maximize the cohesion of the tasks (IWR) assigned to the same workstations. This goal is used if the tasks related to the same product's function should be assigned to the same workstation;

* Minimize or maximize $Cum= \sum_{k=1}^{m} f_1(T(k)) + \sum_{k=1}^{m} f_2(W(k))$, calculated on the basis of task ($T(k)$) and workstation ($W(k)$) attributes, where Cum stands for cumulative objective function. Functions $f_1$ and $f_2$ are not always linear. They can be cost-oriented to be minimized or benefit-oriented to be maximized;

* Minimize the reconfiguration cost, denoted by Re, which can be expressed by setup costs (Kovalev et al., 2012), difference between initial and new solutions (Gamberini et al., 2006, 2009), number of transferring operations (Grangeon et al., 2011) or cost for the retraining of operators (Yang et al., 2012).

Table 3 compares the use of these objective functions in multi-objective context for the last decade.
<table><caption>Table 3. Objective functions considered jointly</caption><thead><tr><th>References</th><th>M</th><th>Σ dimW<sup>v</sup>(k)</th><th>c</th><th>Seq</th><th>SI</th><th>E</th><th>IWR</th><th>Cum</th><th>Re</th><th>Pr</th></tr></thead><tbody><tr><td>Zhu et al. 2020a</td><td>+</td><td>+</td><td>+</td><td>+</td><td>+</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Chutima and Yothaboriban, 2017, Chutima and Jirachai, 2020, Pastor et al. 2015, Buyukozkan et al., 2016, Kucukkoc et al., 2019</td><td>+</td><td>+</td><td>+</td><td>+</td><td>+</td><td>+</td><td></td><td></td><td></td><td></td></tr><tr><td>Zhang et al. 2021, Zhu et al 2020b</td><td>+</td><td>+</td><td></td><td></td><td>+</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Salehi et al. 2018</td><td>+</td><td>+</td><td></td><td></td><td></td><td></td><td></td><td>+</td><td></td><td></td></tr><tr><td>Yang et al. 2019</td><td>+</td><td></td><td>+</td><td>+</td><td>+</td><td></td><td></td><td>+,+</td><td></td><td></td></tr><tr><td>Paksoy et al. 2013</td><td>+</td><td></td><td>+</td><td>+</td><td>+</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Alavidoost et al., 2016, Su et al. 2014, Cerqueus and Delorme, 2019, Cao et al. 2020</td><td>+</td><td></td><td>+</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Kalayci and Gupta, 2014, Kalayci et al 2016, Liu and Wang, 2017, Seidi and Saghari, 2016</td><td>+</td><td></td><td></td><td>+,+</td><td>+</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Ren 2020, Zhu et al 2018</td><td>+</td><td></td><td></td><td>+</td><td>+</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Pistolesi et al 2017</td><td>+</td><td></td><td></td><td>+</td><td></td><td></td><td></td><td>+</td><td></td><td></td></tr><tr><td>Alavidoost et al., 2015, 2017</td><td>+</td><td></td><td></td><td></td><td>+,+</td><td>+</td><td></td><td></td><td></td><td></td></tr><tr><td>Fathi et al 2019</td><td>+</td><td></td><td></td><td></td><td>+,+</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Sternatz 2014</td><td>+</td><td></td><td></td><td></td><td>+</td><td>+</td><td></td><td></td><td></td><td></td></tr><tr><td>Liang et al. 2021a, Meng and Zhang, 2020</td><td>+</td><td></td><td></td><td></td><td>+</td><td></td><td></td><td>+</td><td></td><td></td></tr><tr><td>Fathi et al 2016</td><td>+</td><td></td><td></td><td></td><td>+</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Chica et al 2013, 2015, 2016, 2019, Zhou and Wu 2020, Kovalev et al. 2017</td><td>+</td><td></td><td></td><td></td><td></td><td></td><td></td><td>+</td><td></td><td></td></tr><tr><td>Fang et al. 2019</td><td></td><td>+</td><td>+</td><td></td><td></td><td></td><td></td><td>+,+</td><td></td><td></td></tr><tr><td>Çil and Kizilay, 2020, Fang et al 2020b, Liu et al, 2021</td><td></td><td>+</td><td>+</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Fang et al. 2021</td><td></td><td></td><td></td><td>+</td><td>+,+</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hamta,et al 2013, Yılmaz and Yazıçı, 2021</td><td></td><td></td><td>+</td><td>+</td><td></td><td></td><td></td><td>+</td><td></td><td></td></tr><tr><td>Moreira et al 2017, Qian 2022, Zacharia and Nearchou, 2016</td><td></td><td></td><td>+</td><td>+</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Bortolini et al 2017, Nilakantan, et al. 2015, Li et al 2021c, Ozdemir et al 2021, Li et al 2016a, Rabbani et al 2016, Triki et al. 2017</td><td></td><td></td><td>+</td><td></td><td></td><td></td><td></td><td>+</td><td></td><td></td></tr><tr><td>Fang et al 2020a</td><td></td><td></td><td>+</td><td></td><td></td><td></td><td></td><td>+,+</td><td></td><td></td></tr><tr><td>Zhang et al 2017, 2020c, Li et al, 2016a, Nilakantan et al 2015, Zhang et al 2018</td><td></td><td></td><td>+</td><td></td><td></td><td></td><td></td><td></td><td>+</td><td></td></tr><tr><td>Li, et al 2019</td><td></td><td></td><td>+</td><td></td><td></td><td></td><td></td><td></td><td>+</td><td></td></tr><tr><td>Kazancoglu and Ozturkoglu, 2018</td><td></td><td></td><td></td><td>+,+,+<br>+</td><td></td><td></td><td></td><td>+,+;+,+<br>+</td><td></td><td></td></tr><tr><td>Liang et al. 2021b</td><td></td><td></td><td></td><td></td><td>+,+</td><td></td><td></td><td>+</td><td></td><td></td></tr><tr><td>Li et al 2016b, Nourmohammadi et al. 2013, 2019c,d</td><td></td><td></td><td></td><td></td><td>+</td><td>+</td><td></td><td></td><td></td><td></td></tr><tr><td>Zhang et al. 2020a</td><td></td><td></td><td></td><td></td><td>+</td><td></td><td></td><td></td><td>+</td><td></td></tr><tr><td>Nilakantan et al 2017a, b</td><td></td><td></td><td></td><td></td><td></td><td>+</td><td></td><td>+</td><td></td><td></td></tr><tr><td>Finco et al. 2021, Li et al, 2016a, Tao et al 2019</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>+,+</td><td></td><td></td></tr></tbody></table>
The multi-objective optimisation is intimately linked to a global trend and enormous challenge not only in manufacturing: the need for sustainability of human activities. Sustainability is commonly defined on its three pillars: economic, environmental, and social. Until now we have mostly discussed the first one and in the next section is dedicated to the discussion about how the remaining two pillars, social and environmental have been considered in line balancing.

# 6. From ergonomic constraints to sustainability issues

The concept of sustainability is linked to the triple bottom line including economics, social and environmental dimensions. In recent years, businesses play more and more attention to these dimensions including in production lines where the social aspects are most frequently related to the use of manual power and the environmental aspects are mostly related to energy consumption, carbon footprint and waste generation including hazardous and not hazardous materials. A detailed classification of sustainability criteria has been presented by Kazancoglu and Ozkan-Ozen (2020). Renna and Materi (2021) presented a literature review of energy efficiency and sustainability in manufacturing systems.

## 6.1. Human factors and social aspects

In manual production lines, the consideration of human factors is of high importance. Although they were not taken into account in the original formulation for SALBP, recently many efforts were undertaken in order to provide safe and comfortable working conditions in production lines. Among all human factors, the first category that has been discussed for assembly line balancing was *physical ergonomic risks*. The ergonomic risks can play negative role in the development of musculoskeletal disorders. Otto and Battaïa (2017) presented a review of the assessment methods, modelling and minimization of physical ergonomic risks at assembly lines by line balancing and job rotation. Indeed, in practice the reduction of ergonomic risks can be achieved either by line balancing or job rotation (Boenzi et al., 2015; Mossa et al., 2016), or both. The consideration of physical ergonomic risks was also included in line balancing problems in the following studies: Akyol and Baykasoğlu, 2019; Battini et al., 2017; Bautista et al., 2016; Bautista-Valhondo and Alfaro-Pozo, 2018; Bortolini et al., 2017; Cheshmehgaz et al., 2012; Digiesi et al., 2018; Kara et al., 2014; Mokhtarzadeh et al., 2021; Ozdemir et al., 2021; Sgarbossa et al., 2016; Stecke and Mokhtarzadeh, 2022; Tiacci and Mimmi, 2018; Zhan et al., 2020c.

Another measure frequently used for evaluating physical strain of workers is *fatigue* also measured by *energy expenditure* (Abdous et al., 2022; Battini et al., 2016; Finco et al., 2020, 2021 Xu and Hall, 2021). This measure can be worker-dependent due to the use of coefficient that can take into account the age and physical condition of the worker. The measurement of fatigue is often related to the
calculation of rest allowance, idle time that is used in between the execution of two tasks in order to recover from the physical exertion. Work overload, legal working conditions and saturation limits in the context of line balancing were discussed by Bautista et al. (2015).

More generally, the *age and physical condition* of workers may impact not only the fatigue but also the time required to complete tasks. Therefore, the same task can take different amount of time depending on the worker who performs it. The impact of ageing workforce was considered by Boenzi et al., 2015 and Calzavara et al., 2020. Other *worker differences including disabilities and skills* were also studied in the literature (Borba and Ritt, 2014; Campana et al., 2021; Cao et al., 2020; Fattahi et al., 2016; Katiraee et al., 2021; Lovato et al., 2022; Salehi et al., 2018; Samouei et al., 2016).

Literature on production line balancing discusses less the cognitive exertion of manufacturing work in production lines. Only few studies exist that take into account the *human errors* related to the assembly process in line balancing (Arkhipov et al., 2018b; Fast-Berglund et al., 2013). The *learning effect* on task execution time is probably the most frequently considered cognitive human factor in line balancing (Hamta et al., 2013; Koltai and Kalló, 2017; Li and Boucher, 2017; Otto and Otto, 2014).

Several existing reviews provide useful insights on human factors in manufacturing. Glock et al. (2019) analyzed the applications of learning curves in production and operations management. Sgarbossa et al. (2020) discussed the place of human factors in production and logistics systems of the future, and Dolgui et al. (2022) in the design and management of assembly systems 4.0. Vijayakumar et al. (2022) proposed a framework for incorporating human factors into production and logistics systems. Xu and Hall (2021) reviewed the consideration of human fatigue in personnel scheduling and operations.

The human factors cited here below relate to the social pillar of sustainability. In the next section, we discuss the factors that relate to the environmental pillar of sustainability.

## 6.2. Environmental issues

On the contrary to the ergonomic risks mainly considered in manual lines, the environmental issues are principally treated for automatic lines and concern: the *energy consumption* (Fang et al 2019, 2020a, Li et al, 2016a, Liang et al., 2021b, Nilakantan et al 2015, Tao et al 2019, Zhang et al 2019b, Zhou and Wu, 2020) and related to the energy consumption, *carbon footprint* (Nilakantan et al 2017a, Yang et al. 2019).

Another topic highly concerned by environmental issues is remanufacturing. In disassembly lines, *hazardous materials* can be manipulated and need to be safely removed both for operators (human factors) and for a proper treatment (environment issue). In disassembly lines, the maximisation of recycling rate may be one of the objective functions. Ilgin et al. (2015) discussed the use of multi-
criteria decision-making (MCDM) techniques in environmentally conscious manufacturing and product recovery. Tolio et al. (2017) reviewed the methods for design, management and control of demanufacturing and remanufacturing systems. Rizova et al. (2020) presented a systematic review of decision-making in remanufacturing. The use of hazardous materials was considered in numerous studies such as Bentaha et al., 2014a, b, 2015a, 2018, 2022; Li et al., 2018d; Liang et al., 2021a,b; Liu and Wang, 2017; Liu et al., 2022; Meng and Zhang, 2020; Ren et al., 2020; Wang et al., 2019c; Zhu et al., 2018, 2020a. Kazancoglu and Ozturkoglu (2018) considered in addition the issue of *solid waste*. Igarashi et al. (2016) measured the *recycling rate*.

The analysis of the literature shows that currently the factors related to the social and environmental pillars of sustainability are mainly considered separately for manual and automatic lines, respectively. However, there is an exception: the management of hazardous materials in disassembly lines has been regarded from social and environmental perspectives.

According to a recent study of Simon-Kucher & Partners “Globally, sustainability is rated as an important purchase criterion for 60 percent of consumers. While attitudes vary across generations, countries, and industries, 85% of consumers have become ‘greener’ in their purchasing in recent years. Companies must act now to avoid obsolescence in the future”. Since the manufacturing process represents an important part of the product footprint, the sustainability consideration must be taken into account at all steps of decision process including line balancing. We believe that existing modelling base is mature enough to include additional indicators related to the sustainability measurement into line balancing, however, the difficulty may come from the availability of reliable data to be used at this step of decision process. The uncertainty management in line balancing is one of major trend in the field discussed in the next section.

## 7. Need for stability: uncertainty management

In practice, decision makers do not generally possess exact data about the product, customer demand, workforce characteristics and manufacturing process at the step of line balancing, especially when the line is balanced for the first time.

In order to deal with uncertainty of the data, several approaches were developed in the literature. A number of studies consider an uncertain demand, which results in uncertain takt time. It can be considered that the demand lies in a defined interval and this information is used for line balancing (Breckle et al., 2021; Cao et al., 2020; Samouei and Ashayeri, 2019). Lopes et al. (2021a) considered assembly line balancing for two cycle times as alternative to re-balancing. The modelling of interval-defined demand gives line configurations that are more robust to the changes of the demand within the expected interval and particularly suits customized production environments. Liu et al., 2021a; Chica et
al., 2013, 2016, 2019 considered uncertain demand and developed several robustness metrics and a visualisation tool to help decision makers. Mondal et al. (2013) developed a measurement system for robustness in a serial multi-stage manufacturing system, which combines statistical regression, Taylor series expansion, the root-sum-squares method and a variation model. Lopes et al. (2022) proposed to consider fractionable tasks where it is technically possible, and show that this relaxation leads to more robust solutions under demand uncertainty. Mönch et al. (2022) considered the case of variable takt time groups and workload equilibrium. Zhang et al. (2021a) proposed a robust mixed integer programming program (MILP) model with cycle time relaxation and robust objective function for mixed-model multi-manned assembly line balancing under uncertain demand. Zhang et al. (2021b) considered the disruptions related to preventive maintenance and proposed to use a set of pre-calculated solutions for the cases of disruptions. Stability measures for obtained solutions were considered by Freiheit and Li (2017) and Lai et al. (2016).

The intervals were also used for definition of task attributes, for example task processing time was interval defined in the following studies: Fang et al., 2020a; Gurevsky et al., 2013b; Hamta et al., 2013; Hazır and Dolgui, 2013, 2015; Moreira et al., 2015; Pereira, 2018b; Pereira and Álvarez-Miranda, 2018; Xiao et al., 2021; Zhang, 2019a.

Several authors use *fuzzy numbers* in order to represent task attributes, fuzzy theory for problem modelling and fuzzy algorithms for their solution, e.g. Alavidoost et al., 2015, 2016, 2017; Babazadeh and Javadian, 2019; Cheshmehgaz et al., 2012; Chutima and Yothaboriban, 2017; Liang et al., 2021b; Salehi et al., 2018; Samouei et al., 2016; Sarwar, 2019; Seidi and Saghari, 2016; Zacharia and Nearchou, 2016; Zhang et al, 2017a.

If historical data is available, task attributes can be modelled as *stochastic variables* as it was done in the following studies: Altekin et al., 2016; Aydemir-Karadag and Turkbey et al., 2013; Aydoğan et al., 2019; Dong et al., 2014, 2018; Bentaha et al., 2014a,b, c, 2015a, b, 2018, 2022; Chiang et al., 2016; Colledani and Battaia, 2016; Delice et al., 2016, 2017; Celik et al., 2014; Faridanifar and Samouei, 2022; Foroughi and Gokcen, 2019; Ozcan, 2018; Li et al., 2019; Fathi et al., 2019; Guo et al., 2021; Li, 2017; Li and Boucher, 2017; Li et al. 2020c; Serin et al., 2019; Tang et al., 2017; Zhang et al., 2017; Zhu et al., 2020b. Altekin (2017) compared piecewise linear programming formulations for stochastic disassembly line balancing. Pınarbaşı et al. (2016) considered not only stochastic task times but also flow stochasticity and used a constraint programming (CP) and queueing models for the problem solution.

In the past, historical data was used to define the distribution of probability for such stochastic variables. However, recent studies e.g. He et al., 2020, 2021; Hu et al., 2021; Li et al., 2018, 2019; Liu et al., 2020, 2021b,c, 2022; Zheng et al., 2018 considered line balancing problems with uncertain task
times, where the distributional information was limited, i.e. only the mean values and standard
deviations were given, sometimes an upper bound for a task attribute, due to the lack of data. Liu et al.
(2020) considered robust disassembly line balancing with ambiguous task processing times and
developed an approximated mixed integer second-order cone programming model as well as a two-stage
parameter-adjusting heuristic.

When the robustness of the line is not sufficient to meet new environmental conditions or react to disruptions, then, in practice, it is needed to rebalance the line in order to adapt to new data, constraints and/or objectives. This research topic is considered in the next section.

8. Need for resilience: from line balancing to line rebalancing

The analysis of the literature shows that the number of studies dedicated to rebalancing problem substantially increased in recent years as we expected in (Battaia and Dolgui, 2013). The rebalancing of a line is needed when the current manufacturing process cannot be continued because of a disruption or because of poor performances (e.g. demand changes). The main difference between balancing and rebalancing problems lies in the fact that the latter usually takes into account the existing assignment of tasks to stations. Even if the changes are needed, each change in the established manufacturing process is a source of possible errors or not expected problems, as a consequence, one of the considered objectives for rebalancing usually measures the magnitude (Girit and Azizoglu, 2021; Makssoud et al. 2015; ) or the cost (Belassiria et al. 2018; Celik et al. 2014; Serin et al. 2019; Yang et al., 2013; Zhang et al. 2018) of modifications in the initial line and seeks to minimize it. Usually, this is one objective function for a multi-objective formulation. Other objectives are as discussed in Section 5. In machining lines, where the rebalancing may lead to replacement of equipment, the objective may be to reuse the existing equipment as much as possible (Makssoud et al. 2014). However, a disruption can be so important that the main objective becomes to find a feasible solution at any price of changes.

In the recent literature, we can distinguish two contexts in which rebalancing was considered. One is the conventional production lines which were not designed for rebalancing. In such systems, rebalancing can be an urgent issue, since economic burden can exist for non-productive period of time (Lovato et al., 2022). In this case, the time for rebalancing can be limited and only fast optimisation procedures can be used in this case except the small size problems where exact methods can be applied (Sancı and Azizoğlu, 2017). In practice, even mixed-model assembly lines designed for a mix of products need to be rebalanced if the mix of products changes (Yang et al., 2013).

The second context for rebalancing is reconfigurable manufacturing systems which are designed to be reconfigured and rebalanced. In this case, the rebalancing problem can be considered at the design phase in order to prepare the possible system configurations that will be used later. Consequently, the
time available for optimisation can be longer. In the current literature, the studies on rebalancing in conventional production systems are more frequent (Battaïa et al., 2019; Belassiria et al., 2018; Celik et al., 2014; Faridanifar and Samouei, 2022; Girit and Azizoğlu, 2021; Li, 2017; Li and Boucher, 2017; Li et al., 2021f; Makssoud et al. 2014, 2015; Mete et al., 2019; Michels et al., 2021; Sancı and Azizoğlu, 2017; Serin et al., 2019; Sikora et al., 2017; Yang et al., 2013; Zhang et al., 2018, 2020a) than for reconfigurable manufacturing systems (Yadav et al., 2020a, Yuan et al., 2019; Kristianto et al., 2014; Huang et al., 2019; Huang and Yan, 2019; Liu et al., 2021a). However, since the reconfigurable manufacturing systems are seen as an important manufacturing trend due to their capacities of being adapted to changing market and product conditions and particularly adapted for customization, we expect that the studies dedicated to the reconfigurable manufacturing systems will flourish in coming years.

Ortega Jimenez et al. (2015) described the shift from flexible to reconfigurable systems in production for improved responsiveness. Koren et al. (2018) discuss principles, design methods, and future trends for reconfigurable manufacturing systems. Yelles-Chaouche et al. (2021) described reconfigurable manufacturing systems from an optimisation perspective. Morgan et al. (2021) discussed Industry 4.0 smart reconfigurable manufacturing machines. Dubey et al. (2017) explained the impact of reconfigurable manufacturing systems on environmental performance.

Huo et al. (2020a,b) presented real time control procedure in order to capture the changes in real time and to rebalance the line in consequence. Smart technologies are currently transforming the means for control of production systems providing more reliable data for further improvement on the design stage. In the next section, we discuss the changes introduced by the technological advancement in production lines and their balancing.

## 9. Technological advancement and cobotisation

The fourth industrial revolution, namely Industry 4.0 drives the development of technologies as intelligent industrial robots, information technologies (IT) to share information among workpiece, equipment, and machines, artificial intelligence for the analysis of information and support self-adapting activities, etc. These technologies enable a station of automated flow line to perform different operations on different products without the need of a time-consuming and costly setup. Several authors analysed the major trends in the production systems driven by Industry 4.0. Neumann et al. (2021) discussed the importance of human factors for the development of Industry 4.0. Cohen et al. (2019) positioned the assembly systems in Industry 4.0 era. Daneshmand et al. (2022) focused on the use robotic assembly and disassembly in the context of Industry 4.0 and circular economy. Vaisi (2022) presented a review
of optimization models and applications in robotic manufacturing systems within the context of Industry 4.0 and beyond.

A comprehensive review of robotic assembly line balancing problem was presented by Chutima (2022). In comparison to our previous review (Battaïa and Dolgui, 2013), where only 3 articles were included considering the case of robotic lines, the number of studies on this topic has significantly increased last ten years, here we can cite about 30 contributions: c.f. Aghajani et al, 2014; Borba et al, 2018; Chutima and Khotsaenlee, 2022; Çil et al., 2017, 2020; Kammer Christensen et al, 2017; Koltai et al. 2014; Li et al., 2016a, 2018a, 2019c, 2021a,c, 2017; Lopes et al., 2017; Michels et al., 2018; Müller et al., 2017, 2018; Nilakantan et al., 2015, 2016, 2017a,b, 2019; Pereira et al., 2018; Rabbani et al, 2016; Jordan et al., 2021; Yadav and Agrawal, 2022; Zhang et al. 2019b; Zhou and Wu, 2020. In the past, robotic lines were considered to be too expensive for disassembly context in practice, but the technology progress makes it possible and the studies considering such a setting become more numerous (Fang et al. 2019, 2020a,b; Liu et al. 2018; Ying et al. 2022).

One of the major changes and opportunity in the organization of assembly and disassembly lines in the context of Industry 4.0 is the possibility to use collaborative robots (cobots) alongside with human operators (Boschetti et al., 2021; Chutima and Khotsaenlee, 2022; Çil et al. 2020; Dalle Mura and Dini, 2019; Gil-Vilda et al., 2017; Gjeldum et al., 2021; Gualtieri et al., 2021; Li et al., 2021c; Nugraha et al., 2021; Stecke and Mokhtarzadeh, 2022; Weckenborg et al., 2020, 2022; Xu et al., 2021). It should be noted that then a collaboration on the common tasks exists between cobots alongside with human operators, then the problem may become equivalent to the hybridization of line balancing with worker assignment or equipment selection. Instead of employing resources of the same type as discussed in Section 4.3, cobotization deals with multi-resources of different type with possibly constraints of different nature for each type of resources. However, it also brings the necessity to manage multiple resources within each workstation and to schedule tasks between cobots and human operators as we discussed in Section 4.3. It considerably increases the number of decision variables involved and therefore the complexity of the problem.

Hashemi-Petroodi et al. (2020) analysed operations management issues in design and control of hybrid human-robot collaborative manufacturing. Quenehen et al. (2022) discussed economic and ergonomic performance enhancement due to human-robot collaboration. Robla-Gómez et al. (2017) and Gualtieri et al. (2021) focused on safety and ergonomics issues in such a collaboration. Simões et al. (2022) focused on the design of workplaces for such a collaboration. Hjorth and Chrysostomou (2022) reviewed the human-robot collaboration in disassembly.

It should be noted that despite the technology development and progress done within Industry 4.0, at the same time, in other environments, highly manual, the gap for acquiring right data is still high as
shown in the study of Cannas et al. (2018) where the complexity reduction and kaizen events to balance
manual assembly lines was discussed.

In the next section, we summarize funding presented in Sections 3-9 and discuss additional emerging
topics I the field.

**10. Discussion**

First, we can affirm that line balancing is a vivid and fertile field of research. More than 500
contributions were made during the last decade and this number continues to grow. However, the
dynamics is different for existing various directions.

The original and historical version of ALBP, SALBP even if it has still been relatively present in
publications these recent years, will probably be less discussed in coming years except the development
of breakthrough methodologies based on machine learning or quantic computing for integer
programming.

On the opposite, the hybridization of line balancing with other optimisation problems will continue
to attract interest of researchers introducing even more complex problem formulations and integrating
more decisions in order to improve the global performances of the production lines. During the last
decade, one of the fast-developing field was the worker assignment in line balancing and this
development can continue under perspective of Industry 5.0 by integrating more worker-dependent
attributes in particular in relation to the physical and cognitive exertion of the performed work. The
issue of ageing workforce in manufacturing systems will also continue to attract interest since according
to recent estimations; the working-age population is expected to rise by 9.4% in the following 40 years
along with the fact that the average retirement age in many countries is rising as well (Berti et al. 2021).

Along with several optimization problems integration, the literature more and more addresses the
design of multiple lines. Dolgui et al. (2021) evaluated the profitability of a multi-model manufacturing
line versus multiple dedicated lines. Hemig et al. (2014) studied the link between single and parallel
lines and the impact on staff planning. Aguilar et al. (2020) reviewed the existing formulation for
balancing of parallel assembly lines. Indeed, within the scope of multiple lines consideration, the case
of parallel lines remains the most frequently addressed during the last decade, as in following studies:
Ağpak and Zolfaghari, 2015; Araújo et al., 2015; Chutima and Yothaboriban, 2017; Chutima and
Jirachai, 2020; Chutima and Khotsaenlee, 2022; Çil et al., 2017; Hezer and Kara, 2015; Kucukkoc and
Zhang, 2015a,b,c, 2014a,b, 2017; Ozcan, 2018, 2019; Otto and Li, 2020; Tapkan et al., 2016. The design
of merging lines was considered much less frequently (Romero-Silva and Shaaban, 2019; Romero-Silva
et al., 2019, 2021). Therefore, we can conclude that many configurations of multiple lines have not
sufficiently addressed yet and represent an important research direction to explore more flexible and
responsive system configurations.

The sequencing of multiple products in mixed-model balancing models has been also frequently considered jointly with line balancing (Cortez and Costa, 2015; Hamzadayi and Yildiz, 2012, 2013; Kucukkoc and Zhang, 2014a,b, 2016a,b, 2017b; Lu and Yang, 2016; Rashid et al., 2019; Yang et al., 2013; Yin et al., 2021). Using this approach, the performances of the line can be optimized for a given product mix, but rebalancing may be required if the mix of products changes. In such a situation, it is important for managers to find a trade-off between frequent rebalancing of the line or a more robust solution, which is adapted to frequent changes in the product mix in customized production environment, but less performant for each particular mix. This trade-off can be searched between the robustness of the line and the setup cost (Dolgui et al., 2014).

We can also observe that during the last decade the researchers were interested in the design of unpaced lines (Hudson et al., 2015; Jeong and Jeon, 2021; Lopes et al, 2018, 2019b, 2022; Öner-Közenet al., 2017; Schlüter and Ostermeier, 2022; Tiacci and Mimmi, 2018; Urban and Chiang, 2016) and specific lines for printed circuit board (Koskinen et al, 2020; Mmumtaz et al., 2020; Toth et al., 2022). Hottenrott and Grunow (2019) considered the production line where the stations are no longer arranged serially and no longer linked by a paced transportation system but by automated guided vehicles. To achieve more flexibility and be resilient to external changes, in future, the production lines will certainly be transformed in their layout organization in order to have more mobile structure and better adapt the resources to the changing demand and product mix. The reconfigurable manufacturing systems will also occupy a more important place on work floor in the future. This transformation will call for new mathematical modeling for the initial assignment of tasks to resources but also for developing efficient tools capable of fast adaptation to the changing parameters.

As an important part of the Supply Networks, manufacturing systems must respond quickly and
efficiently to product and market changes. For this reason, several authors recently considered line
balancing problems in the Supply Network or Chain design models (Hamta et al., 2015, 2016; Koç,
2017; Pereira and Vilà, 2016; Sun and Wang, 2019). The context of reverse Supply Chain design used
for products' end-of-life treatment has been also explored (Özceylan and Paksoy, 2013; Özceylan et al.,
2014). Kannan et al. (2017) studied a problem of reverse logistics network from the perspective of the
third party integrating the disassembly line balancing. Yolmeh and Saif (2021) proposed a
decomposition approach for a closed-loop supply network design integrated with assembly and
disassembly line balancing under uncertainty. In link with the Supply Chain activities, several authors
considered assembly line design and balancing with connection to distribution (for assembly lines) and
collection (for disassembly lines) problems: e.g. Habibi et al. (2017a,b; 2019), Kenger et al. (2020), thus, including routing problems. Due to the digitalization, supply chains become more connected and with fast and efficient communication, the decisions can be spread out efficiently in the chain. This topic will certainly attract more attention of researchers in the future.

Since the complexification of line balancing problem via integration of decisions from other decision levels will continue to achieve globally optimized performances, the multi-objective optimization modelling and methods will remain relevant for their solution. Naturally, the advances in the field will benefit from the development of multi-objective methodology in combinatorial optimization.

With declaration of United Nation Sustainable Goals, the ssustainability became a global issue impacting all sectors of human activities. Despite of first studies in the field of line balancing, still a significant progress should be realized in order to address all aspects of sustainability at the level of the design of the line, its balancing and operation. Currently, the existing studies consider mostly separately social issues for manual lines and environmental aspects in particular energy consumption and carbon footprint for automated and robotic lines. This should be improved in the future by developing a holistic view on sustainability of production lines.

The actual manufacturing context calls both for robustness and resilience of production line face to a large spectre of uncertainty. The control of production lines will be in future be possible due to digital twins of the line where an important number of disruptions and breakdowns as well as the solutions to overcome the problems occurred will be anticipated and available for managers in order to support them in fast decision making.,

The development of technology and cobotisation will also transform practices in production lines. Only first steps are done in this direction in the field of line balancing and more contributions are needed in order to support managers in this fast developing domain.

The solution methods have not been detailly discussed in this review, since they were extensively analysed in a number of recent surveys, some of them also provide a comparison of method performance on numerical experiments. However, we can note an increased use of Benders decomposition (Akpinar et al., 2017; Bentaha et al., 2018a; Furugi, 2022; Hazır and Dolgui, 2013, 2015; Huang et al., 2021; Michels et al., 2019, 2020; Zohali et al., 2022) and a much more frequent use of simulation (Lopes et al., 2020a; Lv et al., 2019; Neungmatcha and Boonmee, 2021; Öner-Közenet al., 2017; Portioli-Staudacher et al., 2020, Rane et al., 2016; Romero-Silva and Shaaban, 2019; Romero-Silva et al., 2019, 2021; Renna, 2019; Samant et al., 2018; Tiacci, 2015a,b). We believe that this is in line with the development of digital twins and willing to have a digital model corresponding to the physical one in order to support the decision-making process. A recent state of the art on the use of simulation in the design and operation of manufacturing systems can be found in (Mourtzis, 2020). The development of
AI based digital twins for process design and planning, line balancing, production planning and scheduling is presented in (Castané et al., 2022).

## 11. Conclusion

In this paper, we presented a recent bibliography on line balancing in assembly, machining and disassembly environments. More than 500 papers published during last 10 years were analyzed. We observed that the insights about existing trends in the field revealed in our previous review (Battaïa and Dolgui, 2013) have been followed by the community and many contributions were brought to these topics during the last decade. Even if simple versions of assembly line balancing were still of high interest for scholars, more and more researchers considered integrated problem formulations where a line balancing problem was jointly solved with another optimisation problem such as process planning, task scheduling, line design, model sequencing and supply chain design with collection and distribution activities. Multi-objective optimisation has also gained in frequency of employment more suitable for integrated optimisation problems. For these formulations, the use of metaheuristics is still the most popular solution approach. However, decomposition techniques have also gained in popularity as well as simulation approaches. The researchers pay more and more attention to the sustainability of the production lines, but often its different aspects are considered separately: human factors in manual lines, carbon footprint in energy-intensive lines as well as the treatment of hazardous material in disassembly lines. A more holistic view on all aspects of sustainability should attract attention of academicians and practitioners in next future.

In our previous study (Battaïa and Dolgui, 2013), we have also reported on the underdeveloped topics such as rebalancing problem and robust optimisation under uncertainty of input data. The analysis of the recent literature showed that significant advances have been made in these directions. Several solution methods were developed for rebalancing problems. Various mathematical models were elaborated to take into account the uncertainty of the data, including distribution free modelling of historical data. These efforts will be continued in order to achieve digital twins of production lines capable of supporting fast decision making face to uncertainty.

We have also observed such new trends in the literature as formulations related to the development of Industry 4.0 technologies, the more frequent design of parallel, unpaced and reconfigurable lines in order to achieve a better flexibility in production systems and to create efficient solutions for customized production environment adapted for volatile markets.
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