Balancing of Manual Reconfigurable Assembly Systems with

Learning and Forgetting Effects

Maria Angela Butturi

, Francesco Lolli and Chiara Menini

Department of Science and Methods for Engineering, University of Modena and Reggio Emilia,

Via Amendola 2, Reggio Emilia, Italy

Keywords: Learning-forgetting Curves, Reconfigurable Assembly Systems, Line Balancing.

Abstract: Within the paradigm of Industry 4.0, digital reconfigurable manufacturing and assembly systems can rapidly

adapt to dynamic market demand, modifying their capacity and functionality. In manual or hybrid

reconfigurable assembly systems, the rapid and frequent variations in the performed tasks subject workers to

a significant cognitive load, making relevant the learning-forgetting phenomenon. In fact, the operators carry

out the assigned activities for a short time before a reconfiguration of the system takes place, assigning them

tasks often different from those just performed. This paper aims at investigating how the tasks’ execution time

varies for operators working along a reconfigurable assembly line, depending on the learning forgetting effect.

We applied a Kottas-Lau algorithm, considering the expected execution times updated according to a

learning-forgetting curve. A numerical example, considering with five successive reconfigurations, allows to

analyse the expected execution time trend for each operator-task pair and the variation in costs obtained as

the operators learning rate and the variability of the operations change.

1 INTRODUCTION

The increased variability of market demand, both in

the product range and the required quantity, is

pushing forward the development of reconfigurable

manufacturing and assembly systems.

“Reconfigurability” signifies a system’s capability of

converting and modifying its processes in order to

rapidly respond and adapt to market changing needs.

This capability is supported by the utilization of

digital manufacturing technologies, making the

reconfigurable manufacturing and assembly systems

part of the Advanced Manufacturing Solutions, the

first of the Industry 4.0 key enabling technologies

(Bortolini, Galizia, & Mora, 2018).

A reconfigurable system is a dynamic system,

combining the strength of dedicated hard automation

and flexible systems, generating a good compromise

between functionality, production capacity and costs.

Manual systems are the reconfigurable assembly

systems (RAS) with the highest level of

reconfigurability, since human being is highly

flexible and can easily deal with changes and manage

uncertainties (Bi, Wang, & Lang, 2007). Thus, in

https://orcid.org/0000-0003-1639-6065

manual RAS the workers are requested to frequently

move between cells and to rapidly change their tasks,

making learning and forgetting mechanisms relevant

to the assembly cycle time (Wang & Abubakar,

2017). The complexity of RAS, as well as the line

balancing challenges have been widely investigated

(ElMaraghy & ElMaraghy, 2016), however only a

few authors studied the influence of workers’ learning

and forgetting effects on line balancing.

At the best of our knowledge, this is the first paper

focusing on the balancing of manual RAS, analysing

the influence of frequent line reconfigurations on the

learning and forgetting of the workers, as well as the

effect of the learning-forgetting on the line total costs.

A model combining the Kottas-Lau heuristic for line

balancing and the learning and forgetting curves is

developed and analysed through a numerical

example, demonstrating the importance of

considering the human factor influence.

2 RESEARCH BACKGROUND

A literature review, bringing together the three main

124

Butturi, M., Lolli, F. and Menini, C.

Balancing of Manual Reconﬁgurable Assembly Systems with Learning and Forgetting Effects.

DOI: 10.5220/0010174901240131

In Proceedings of the International Conference on Innovative Intelligent Industrial Production and Logistics (IN4PL 2020), pages 124-131

ISBN: 978-989-758-476-3

research fields concerning this paper, provides the

research background of the study. As a result of the

performed literature review, we found that no studies

have yet been carried out on learning and forgetting

applied to RAS balancing.

2.1 Reconfigurable Assembly Systems

According to Koren and Shpitalni (2010)

reconfigurable assembly systems are systems that can

rapidly change their capacity (quantities assembled)

and functionality (product type, within a product

family) to adapt to market demand.

A RAS is a key component of reconfigurable

manufacturing systems (RMS), and must possess

three of the six core characteristics of a RMS:

customization, convertibility, and scalability. To

meet the increasing challenging complexity raised by

the mass individualization paradigm, allowing the

production of cost-effective highly personalized

products, a RAS must combine the advantages of

machine/robot precision and repeatability and human

adaptability. In this hybrid configuration, the time

needed for the worker to complete her/his task is

variable (Koren, Gu, & Guo, 2018).

2.2 Learning and Forgetting

Learning Curves were first studied and modelled by

Wright (1936). The formulation allows to describe

the variations in the performance of operators due to

the repetition of the same task performed:

memorization of the performed movements and

familiarity with the tools allow to reduce the time to

perform the same operation.

In learning models, different indicators can be

used as a dependent variable that measures the

performance of operators: the time to produce a single

unit, the number of units produced in a time interval,

the cost to produce a single unit or the percentage of

non-compliant units (Lolli et al., 2016a). The main

models can be classified as univariate and

multivariate; a review of the learning curves and

models can be found in (Anzanello & Fogliatto,

2011).

On the other hand, in recent years the impact of

the workers’ forgetting on the manufacturing process

has been recognized (Lolli et al., 2016b). The

forgetting phenomenon occurs when the operator

must stop performing a task (due to illness, a

vacation, a strike or a change in in product

specifications). The operator, once the execution of a

task has been interrupted for a long enough period,

will take a longer production time than what was

necessary before the task was interrupted. According

to Nembhard and Osothsilp (2001), the main factors

influencing the phenomenon of forgetting are the

length of the interruption, the amount of experience

learned before the interruption, the nature of the task

(procedural or motor), the type of activity carried out

during the interruption. Hoedt et al. (2019), have been

suggested that the activity that the worker performs

during the forgetting phase, does affect the level of

retention: a more similar job results in a better

retention of the reference job. It has also been shown

that operators who learn quickly are the same ones

who tend to forget just as quickly (M.Y. Jaber &

Kher, 2002). A classification of the models describing

the forgetting are presented in the review compiled by

Nembhard and Osothsilp (2001).

2.3 Assembly Line Balancing Problem

with Learning and Forgetting

Although it is now recognised that learning is a key

factor, influencing both the line total costs and the

correct line balancing, there are still few discussions

on these issues in the literature. The first study on

learning phenomena within an assembly line

balancing is proposed by Chakravarty and Shtub

(1988), and only recently the definition of “Assembly

Line Balancing Problem with Learning Effects” has

been given for the first time (Otto & Otto, 2014).

An overview of the main publications that aim at

combining the two topics are presented below,

classified according to the type of problem addressed.

2.3.1 Minimization of the Number of

Stations

Among the earliest studies on learning along

assembly lines are those carried out by Cohen et al.

(1998), to find the minimum number of stations that

allows to minimize the costs and to maximize the

profit. Toksari et al. (2008) implemented the learning

phenomenon within the study of simple and U-shaped

assembly lines, to minimize the number of stations

during line balancing and update the execution times.

By applying the algorithm to the well-known Jackson

11 problem (Jackson, 1956), they show that the

inclusion of the learning effects allows to open fewer

stations than theoretically foreseen. A mixed non-

linear mathematical model can solve the proposed

problem, introducing the concept of task deterioration

(Toksari, Işleyen, Güner, & Baykoç, 2010).

Otto & Otto (2014) tackle the ALBP-1 problem

by introducing a learning rate for each task to be

executed, thus defining a different decreasing rate of

Balancing of Manual Reconﬁgurable Assembly Systems with Learning and Forgetting Effects

125

the execution time for each task. Here, the authors

focus their attention on minimizing the number of

stations and propose a heuristic to allocate the tasks

to stations on the basis of a decreasing priority rule.

Lolli et al. (2017), for the first time, investigate

the role of learning in the stochastic balancing

problem of an assembly line with repetitive tasks

through the use of the Kottas-Lau (1973) heuristic. To

consider the effects of operator learning in manual

assembly lines, the authors implement the Kottas-Lau

algorithm, in which the expected execution times of

the tasks follow the power law with plateau learning

curve, while the variance changes keeping constant

its ratio with the mean time. To include the human-

machine collaboration, Lolli et al. (2018)

implemented a new learning curve, to allow the

subdivision of tasks into subtasks performed partly

manually and partly in an automated way.

2.3.2 Minimization of the Cycle Time

Cohen (2006) studies the optimal allocation of tasks

within the stations, taking into account a

homogeneous learning, in order to minimize the

makespan in a production of numerous products, each

with relatively low demand. To do this, the author

proposes a non-linear programming model and

demonstrates how homogeneous learning and small

batch sizes make a non-homogeneous task allocation

between stations more efficient than a balanced one.

Furthermore, he shows that the savings that occur

from balancing the line, increase with the number of

stations in the line, with the constant learning and

with the reduction of batch sizes.

2.3.3 Multi-objective Optimization

In considering the balancing of assembly lines with a

learning effect, many scholars have used a multi-

objective perspective, to evaluate the optimality of

the solutions.

Hamta et al. (2013) deal with the multi-objective

optimization of a balancing problem of a single model

assembly line; in the line the operating times, which

depend on the learning of the operator or the machine,

are not known, but only the upper and lower limits of

them, for each task, are known. In this problem, the

objectives considered simultaneously are the

minimization of the cycle time, the minimization of

the total cost of the equipment and the minimization

of the smoothness index. The problem is addressed by

the authors with a new solving approach that

combines the particle swarm with the variable

neighbourhood search metaheuristics.

Chutima and Naruemitwong (2014) solve the

problem of mixed model sequencing along a two-

sided assembly line, in which learning effects are also

taken into account, through the Pareto optimization

based on biogeography. They consider three

contrasting objectives: the minimization of the

variance of the production rate, the minimization of

the total utility work and the minimization of the total

set-up time depending on the chosen sequence.

3 PROBLEM FORMULATION

We consider a manual reconfigurable assembly line,

where frequent changes occur.

The operators are then subject to a phenomenon

of learning by doing, and to the forgetting

phenomenon if the task is not carried out for a certain

period. Thus, the time necessary for carrying out the

task must be therefore continuously updated.

A single-station manual assembly line is considered,

in which one and only one operator is assigned to each

station, fixed during all reconfigurations. Each

operator is characterized by a learning rate; the

learning rate value is the same for all operators,

independent from the type and number of tasks

assigned, and by the previous training and experience.

Each operator performs only the tasks assigned to

her/his station and, when the station is not needed

along the line, the operator is reassigned to another

task for the necessary time.

3.1 The Learning-forgetting Model

For characterizing the learning-forgetting effect we

used the learn-forget curve model (LFCM) presented

by Jaber and Bonney (1996), where the learning

component is modified by the assumption made by

Lolli et al. (2017). The LFCM combines the Wright’s

power learning curve (Wright, 1936), with the

forgetting curve relation introduced by Carlson and

Rowe (1976), and allows to estimate the future

performance of an operation within an intermittent

production.

In our model, for the learning component we

consider a modified Wright’s curve with a plateau (1)

according to (F. Lolli et al., 2017):











1r



∙





∙n





r∙



(1)

where y

ink

is the expected time for the task i after n

products have been assembled by the station k; n is

the number of products assembled; Y

is the initial

expected time for the task i (the standard task time);

is the positive learning rate related to each

assembly station k; r is the fraction, fixed for all the

IN4PL 2020 - International Conference on Innovative Intelligent Industrial Production and Logistics

126

stations and tasks, of Y

that is unaffected by the

learning process. The learning curve will then

converge to the plateau value rY

for all stations, that

is to the invariable part of the average processing time

of each task.

The forgetting curve relation (2) assumed is the

following:

















(2)

where T





is the time for the x-th unit of lost

experience; x is the amount of output that would have

been produced if interruption did not occur; T





is the

equivalent time for the first unit of the forgetting

curve; and f is the forgetting slope. The LFCM model

considers both the intercept 





and the slope f of the

forgetting curve variable.

3.2 Line Balancing Assumptions

The balancing of the reconfigurable assembly line

uses a Kottas-Lau heuristic (Kottas & Lau, 1973).

Alongside the standard assumptions for the

method (a to e), 4 extra assumptions (f to i) are

considered to introduce the learning-forgetting effect:

a) The cycle time and the priority between operations

are the only constraints considered when assigning

the tasks.

b) An operation can only be initiated if all the

preceding and following operations have been

completed.

c) Each operator of the line is equally paid.

d) The tasks and their execution times t

follow the

normal probabilistic curve (3) and are independent of

each other.



Nμ



,σ







(3)

where 

is the expected time to execute the k-th

operation and 

the standard deviation. The average

time μ

is characterized by a variable part, subject to

learning, and by a fixed part, which represents the

minimum time necessary to perform the task.

e) Whenever a task is incomplete, the unit keeps

moving along the line and all operations with no

priority constraints are completed. All incomplete or

unexecuted operations are completed offline at a

specific cost I

for each k-th operation.

f) The learning and forgetting effects are described by

eq. (1), where learning and forgetting effects are

applied to a fraction of the average initial time of each

task, the variable part of μ

, while the fixed part forms

the plateau of the curve.

g) The trend of the execution time of the tasks, due to

learning and forgetting, affects the parameter μ

for

each operation k. According to (F. Lolli et al., 2017),

the variance σ

(4) is defined so that its ratio to the

processing time of the k-th operation remain constant:





s∙t



(4)

where s is the variability rate defined for the

configuration and t

is the execution time of the

operation for the considered station. This definition

allows the variance to adjust following the changes in

the expected cycle time value, thus avoiding an

unrealistic increase in the variability of the execution

time following the learning effects.

h) The assembly line is completely manual and each

station is assigned only one operator.

i) Each worker has her/his own learning rate and it

depends only on the individual, and it is not

influenced by external factors.

3.3 Solution Approach

According to the Kottas-Lau heuristic, once set the

cycle time, the algorithm aims at establishing the

minimum number of stations that guarantee the

requested productivity. The novelty of this study is

the inclusion of the learning-forgetting effect on the

execution times, to use the methodology for

balancing manual reconfigurable assembly lines. The

algorithm has been implemented using Java language,

in an Eclipse integrated development environment.

Together with the standard input data for the

Kottas-Lau heuristic, the general parameters of

learning and forgetfulness are added for each worker

and task: the learning rate LR, the total forgetting

time t

, and the operations variability rate s.

Furthermore, the fraction of the processing not

subject to learning is provided.

The updating of the execution time due to the

learning-forgetting phenomenon is regulated

according to four possible cases:

1) the operation under consideration is assigned to a

station for the first time; the worker has no

experience. The time that this operator will take to

carry out the same operation in the future is updated

(5) on the basis of the learning that has taken place in

the configuration just completed:







1r





∙



d1





rT



(5)

where the expected initial execution time is (1- r)T

2) the operation has been assigned to a station where

it was previously processed; two sub-cases can take

place:

2.a) the operation is assigned to the same station in

which it was carried out in the previous configuration;

in this case, if the task was operating with

interruptions a factor , accounting for the

Balancing of Manual Reconﬁgurable Assembly Systems with Learning and Forgetting Effects

127

remembered rate of experience (Jaber M.Y &

Bonney, 1996), must be added (6).







1r



T



∙









1





rT



(6)

2b) the operation is assigned to a station where it has

already been carried out, but not in the previous

configuration; after updating the accumulated

demand in the previous period, the (6) applies.

3) the operation is not assigned to a station in which

it has not yet been entered; the execution time of this

operation equal to the average time provided by the

input data (7), as no learning or forgetting

phenomenon has yet occurred on it.



T



(7)

4) the operation is not assigned to a station from

which it has already been processed previously;

according to the modelled forgetting phenomenon by

(Jaber M.Y. & Bonney, 1997), the time needed to

rerun the task for the first time after the break

occurred is then updated (8):











1r



T



∙



α1





rT



(8)

Lastly, the algorithm that updates the time, considers

also the case in which a station, opened in a past

configuration, is not opened in the current

configuration. In this case, it is updated only the break

time of all the operations that have been allocated to

this station in the past configurations, at least once.

4 NUMERICAL EXAMPLE

The developed algorithm has been tested

implementing five successive reconfiguration of a

manual assembly system with six stations and twelve

operations; a set of realistic data has been used for

four configurations of the line, while for one of them

we decided to use the data proposed by the Jackson

11 problem, to compare our line balancing including

learning-forgetting effects with the results obtained

without considering these effects.

To investigate the effect that the learning-

forgetting phenomenon, firstly we balanced the line

with fixed learning-forgetting parameters. We then

performed the line balancing analysing the variation

of the production costs as a function of the operations

execution time variability rate s, with a fixed learning

rate, and as a function of different learning rates with

fixed s.

4.1 Line Balancing with Fixed

Learning-forgetting

The input data representing the five successive

reconfigurations are as in table 1 (variable data) and

in table 2 (fixed data).

The five precedence diagrams are shown in the

appendix (Figure A1), while the input data for each

station are available upon request.

Table 1: Production time and market demand variations for

the five configurations.

Config. 1 2 3 4 5

Production

time

5040

8400 6300 5880 4620

Deman

560

700 630 588 462

Table 2: Fixed input data for all the configurations.

Hourl

cost 30.0

Hourl

cost for inactivit

60.0

Cost for opening a station 25.0

Learning rate 0.9

Break time for total forgetting 300000.0

Variabilit

rate of the o

erations 0.1

After each reconfiguration the performed

calculation provides the line balancing and the

production costs. Moreover, at the end of each

configuration, for each open station the execution

times are updated to the value they will assume in the

next configuration.

The first balancing of the assembly is

implemented without any variation of the data, as no

learning or forgetting phenomenon has yet occurred.

For each operation, the operator to whom the task has

been assigned is affected by learning, and the related

execution time recalculated according to the eq. (5).

Starting from the second reconfiguration, the effects

of the forgetting are present. Where learning has

taken place, the recalculated execution time is lower

than the previous one, while where forgetting

occurred, as the stations that previously performed

the task, did not performed it during the last

configuration, the execution time increases.

In the third line reconfiguration we consider the

Jackson 11 problem. In this case, the line balancing is

clearly affected by the learning- forgetting effect

since the algorithm allocated all the tasks within 5

stations, unlike the classical solution of the Jackson

11 problem which provides for the opening of 6

stations, allowing a significant reduction in costs and

greater efficiency for the system. It is interesting to

notice that task 9, executed by station 3, had already

been processed by the same station during the 1st

IN4PL 2020 - International Conference on Innovative Intelligent Industrial Production and Logistics

128

configuration. The execution time by operator 3 for

this operation is therefore updated using the equation

(6).

After the fourth line balancing, the execution of

the task 8 by the station 5, after starting in the 1st

configuration, is interrupted for a time period (during

the 2nd and 3rd configuration) and finally it is

reallocated to the same operator in the current

configuration. In this case, the execution time is

updated considering the accumulated production

demand without interruption of the 1st configuration

to calculate the number of equivalent units

remembered after the interruption occurred during the

2nd and 3rd configurations and then applying the

equation (6).

In the last configuration we have the possibility to

study the long-term effects of the phenomenon of

learning and forgetting, since a significant number of

reconfigurations of the system have already occurred.

Figure 1: Task 1 execution time in the station 1.

Figure 2: Execution time of the task 9 in the station 3.

Conversely, the operator 3 carries out operation 9

in alternate configurations: for this operator,

therefore, there is a learning process followed by the

forgetting of the considered task, due to the

interrupted activity. This process is represented in

figure 2, that reminds the trend of the learning and

forgetting curves presented in (Jaber M.Y. & Bonney,

1996).

4.2 Production Costs vs s

In this scenario, the line balancing has been

performed considering a fixed low learning rate

(LR=9), and setting four classes for s, corresponding

to a variance (σ

, as defined in (4)) equal to 5% (low

variability), 10%, 20%, 30% (high variability) of the

average processing time.

The increase in the variability of operations

generates an increase in the total costs of the assembly

line, as can be seen in the figure 3. The cost growth

starts from a constant cost component due to the fixed

costs of the line, and grows until it reaches a plateau.

Figure 3: Cost trend as a function of the variability of the

operations.

4.3 Production Costs vs LR

The line balancing has been performed considering

s=0.1 and five levels of learning: LR=1 (no learning),

LR=0.9, LR=0.8, LR=0.7, and LR= 0.6 (high

learning rate). The costs incurred increase (figure 4)

as the operators’ learning rate increases, that

corresponds to a decreasing of the operators’ learning

capacity.

Figure 4: Cost trend as a function of the learning rate.

This is due to the fact that, since the operators are

slower to learn for the same number of units worked,

the operators take longer to carry out the tasks, thus

increasing labour costs and, in the event that this

involves opening a station, the fixed costs related to

the stations. The greatest total cost occurs when the

operators' learning and forgetting are not considered

(LR = 1). In fact, in this case the execution times are

constant and this implies higher costs.

Balancing of Manual Reconﬁgurable Assembly Systems with Learning and Forgetting Effects

129

5 CONCLUSIONS

The reconfigurable assembly systems are key

components of a manufacturing system complying

with the paradigm of mass individualization. In this

study, we propose a model to take into account the

workers’ learning and forgetting to make a more

precise allocation of the tasks within a given

configuration, with respect to the present workforce,

maximizing the efficiency of the system. We

combined a learning-forgetting model with the

Kottas-Lau heuristic to show how the learning and

forgetting phenomena affect the balancing of a

manual RAS and the related line costs. A preliminary

numerical application allowed to test the model, and

the use of the Jackson 11 problem showed that it is

crucial taking into account these phenomena. This is

only a first validation step, but, due to the relevance

of the obtained preliminary results, we will apply the

developed algorithm to a case study in industrial

environment, to further improve and validate the

methodology.

In addition, various research developments can

extend the study presented in this paper. Among

these, the possibility of considering specific learning

rates for each operator will be investigated. To fully

take advantage of the RAS capabilities, the problem

of designing a reconfigurable layout and assigning

tasks between operators and machines in an

interdisciplinary way should be addressed. Then, the

developed methodology should be adapted and

applied to hybrid RAS, including new technologies

such as autonomous robots that can help operators to

better adapt to sudden system reconfigurations.

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APPENDIX

The five reconfigurations precedence diagrams are

shown in the figure A1.

Figure A1: The five reconfigurations precedence diagrams.

Balancing of Manual Reconﬁgurable Assembly Systems with Learning and Forgetting Effects

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