22nd International Conference on Production Research
ASSEMBLY LINE BALANCING USING EIGHT HEURISTICS
R.B. Breginski, M.G. Cleto, J.L. Sass Junior
Department of Production Engineering, Universidade Federal do Paraná, Cel. Francisco
Heráclito dos Santos, 210, Curitiba, Paraná, Brazil
Abstract
The assembly line balancing is a critical activity for industries. It enhances their competitiveness in a market
that increasingly demands agreater diversity of products. This work aimed to evaluate eight assembling lines
balancing heuristics by applying them in a large-scaled automotive enterprise, located in the Metropolitan
Region of Curitiba, Paraná, Brazil. There was only a little difference among the results of the applied balancing
methods, however there was a greater variation in the results of the methods when the manner of performing
the balancing was different, either when considering each station individually, or whencontemplating the line as
a whole.
Keywords:
assembly line balancing, heuristics, automotive industry.
1
INTRODUCTION
Industries that utilize the assembly line to obtain their
products currently go through great challenges. The first is
the need to assemble a large number of product models
and their variants in their lines, due to the variety required
by the market. Another challenge is the need to maintain
an adequate level of manpower occupation and other
utilized resources.
In this scenario the activity of balancing operations
appears. In order to increase the efficiency and reduce the
operating costs of the line, balancing activities among
workstations are performed. They can be done by different
methods, such as: exact, heuristics, meta-heuristics
methods, or simulation. In assembly lines that produce
more than one model, total and individual assembly times
are often different among models, so the operation times of
each station vary from model to model.
The balancing in lines that produce more than one model
can be performed by using the weighted averages of the
times of the different models. Another possibility is to use
an objective function that considers the unbalance among
the models and try to minimize it.
Using real data from an assembly line meets the need of a
greater amount of practice research in assembly lines
balancing, because according to Boysen, Fliedner and
Scholl [1], researches using real data represented only 5%
of the work on assembly lines balancing.
The application of different methods of balancing and the
comparison among them will be a further indication of
which alternative best serves the large-scaledenterprises
in the automotive industry, which rely on assembly lines
with the same characteristics as the ones of the enterprise
being studied in this present work.
A well-balanced assembly line reduces wastes, such as
operator idleness, the need of fluctuating operators, stock,
and faulty products, it also decreases the production costs
of the unit for the company and allows the company to
reduce the price of their products.
The objective of this study is to evaluate eight methods of
mixed model assembly lines balancing, by applying them
to an assembly line of a large-scaledenterprise in the
automotive industry.
The limitation of this study was the inability to access the
real balancing method used by the enterprise, which uses
the Maximum Task Time method, however it was not
possible to make a comparison between it and the
theoretical result.
2
ASSEMBLY LINES
Mass production allows a lower cost production due to the
large amount of produced units of the same product, and it
is only possible by the division of labor [2]. The great
production increase resulting from the division of labor is
due to three factors: increased dexterity of each worker;
reduced wasted time when going from one type of work to
another, and the invention of a large number of machines
that facilitate working, allowing one person to do the job of
many [3].
The assembly line became popular with the mass
production of automobiles, when Henry Ford began
assembling the T model in the "Highland Plant"factory in
1913. In an assembly line system, the raw material enters
and moves progressively through a series of workstations
while being processed into the desired product [4]. The
total amount of work in the assembly process is divided
into elementary operations, called tasks, which require a
time to be performed. The tasks follow a precedence
relationship, in such an order that, to accomplish a task, all
its predecessors have to have already been executed [2],
[5]. Kimms [6] states that, to ensure the full production of
each model that passes through the line, each station must
be equipped with machines, robots andtrained people. The
number of stations and station equipment is called line
configuration.
All of the work content of the assembly process is divided
among the workstations, which repeat the operations at
every certain time interval, called cycle time, without
violating the assembly precedence relationships [2], [5],
[4]. The problem of optimizing the division of tasks among
workstations is known as Assembly Line Balancing
Problem - ALBP [7].
For Magatão et al. [8], Farnes and Pereira [9] and
Falkenauer[10], the basic concept of line balancing is to
either assign tasks to workstations in a line to get the
desired index of production (or cycle time)with fewer
workstations (employees), or to minimize the cycle time for
a given number of employees. The number of stations or
the time cycle is a performance measurement to be
optimized.
Regarding the number of products, the assembly lines can
be classified into three basic types [5], [11]:
Single-model assembly line: used in mass production of a
single product, as in Figure 1a. Mixed-model assembly
line: used to produce several models of a basic product,
without the need to setup (or with a very littlesetup time).
22nd International Conference on Production Research
Figure 1b shows an example of this type of line. Multimodel assembly line: used when there are significant
differences in the production processes of each model. To
minimize the inefficiency of the setup time between
models, batches are used, and it originates the batch
sizing problem. This line type is illustrated in Figure 1c.
Figure 1 - Assembly lines for single and multiple products
[5].
Following, the types of existing problems will be presented
together with the suggested approaches, techniques, and
proposals for their solutions.
Simple assembly line balancing problem
One of the most studied balancing problems is called the
Simple Assembly Line Balancing Problem - SALBP. In this
case, some considerations are made: production of only
one product, all tasks are processed in a certain manner
(there are no alternatives); assembly lines with fixed cycle
time, the line is considered serial, no supply lines or
parallel; processing sequence of tasks must follow the
precedence constraints, the times of the tasks are
deterministic, the only restrictions to assign the tasks
should be of precedence, a task cannot be split into two or
more workstations, all stations are also equipped with
machinery and operators [12], [7].
According to Cristo [13] the solution of all other problems
of assembly line balancing are derived from SALBP.
Although this case has been increasingly studied, real
situations that meet the nine conditions are practically
nonexistent.
The problems that do not meet the nine previous
conditions are classified as Generalized Assembly Line
Balancing Problem - GALBP [5].
The SALBP can be divided into four types, as seen on
Table 1. The first, called SALBP-F, checks the feasibility
problem for a given cycle time and number of stations. The
SALBP-1 minimizes the number of stations for a given
cycle time, while SALBP-2 minimizes the cycle time for a
certain number of stations. The SALBP-E is the most
general problem, maximizing line efficiency, minimizing
cycle time and number of stations [1], [5].
Table1 – Versions of SALBP [5].
Cycle
time
Given
Minimize
No. of
stations
Given
SALBP-F
SALBP-2
Minimize
SALBP-1
SALBP-E
Multiple optimization models that seek to support the
decision process have been emerging under the term
Assembly Lines Balancing. The first mathematical
formalization was made by Salveson in 1955, and
academic papers are mainly focused on the allocation of
tasks to workstations ever since [12]. Recently more
studies have increasingly attempted to expand the problem
by incorporating aspects such as: U lines, stations in
parallel, alternative processing, and mixed production lines
[5].
2.1 Difficulties for application of SALBP
The SALBP does not possess much applicability in real
cases, and this can be verified by the difficulties that
industries face to apply the theoretical models of assembly
lines balancing, identified by Falkenauer [10]:
a)
No balancing, but rebalancing: many studies
consider that the line will still be built, however the most
frequent cases areof rebalancing of existing lines.
b)
Workstations have an identity: as in most cases
the lines already exist, stations already have their space
constraints, equipment, certain capacity of features, and
restrictions of processes that can be performed.
c)
Fixed operations and zoning restrictions: fixed
operations can only be performed in a given station, and
zoning restrictions occur when the operation can be
performed at determined stations.
d)
Impossibility
of
eliminating
stations:
the
elimination of stations can only occur at the beginning or at
the end of the existing line.
e)
The need to balance the workload: after reaching
the desired cycle time, the goal is to minimize the square
of workload differences among stations.
f)
Multiple Operators: the stations can have more
than one operatorsimultaneously working on the product.
g)
Operations of multiple operators: some activities
require a second operator who helps in the process.
h)
Ergonomic restrictions: the ergonomic constraints
may be station or operators related.
i)
Multiple products: the assembling of only one
product is extremely rare.
2.2 Precedence graph
The precedence graph is constructed to help visualize the
predecessor tasks. The work elements are indicated by
circles, with the time required to perform them under each
circle. Arrows lead from the immediate predecessors to the
next element of the work [14].
The mixed-model study began in 1970 with Thomopoulos
[15]. For Gehardt [16], the most important contribution of
Thomopoulos was the possibility of unitingthe precedence
diagrams for each model in an equivalent precedence
graph, resulting in areduction in the work amount inequality
along the line.
The union of the precedence graphs may be performed
only if there are no conflicts of precedence between the
models, for example, a model requires that task A is
performed before task B, then no other model must
request that task B be performed before A [17]. In Figure 2
two examples of precedence graphs are shown [16].
When constructing the equivalent precedence graph, the
equivalent processing times are computed from the
production rate of each model within a given time period
(the sum of the production rates of all the models have to
be equal to one). By multiplying the task execution time of
each model by the percentage of the model demand and
making the sum for each task, the equivalent time is
obtained [18].
22nd International Conference on Production Research
added to the station, operatorsare added when necessary,
and the station utilization is calculated by equation 1.
Tasks are added at the used station until its utilization is
100%, or until a reduction occurs, considering the new task
and another operator when necessary. Then, a new station
is considered, and the procedure is repeated on the next
workstation for the remaining tasks [21].
Utilization, also called efficiency, is the percentage of time
that the production line, or station, works, and is calculated
by equation1, where:
= number of stations;
= cycle
time;
= total time required to assemble each unit [14],
[22]:
(1)
Figure 1 - Precedence graph for (A) Model A and (B)
Model B [16].
Figure 3 contains the equivalent precedence
graph for models A and B.
1
2
6
3
7
9
4
5
8
Figure 2 - Equivalent precedence graph [16].
2.3 Mathematical model
The balancing problems are generally formulated with a
binary formulation problem, in which the variable xik is
equal to 1, if the task
(task group) is allocated at
station
(station group), otherwise it is equal to 0 [13],
[19].
Mathematical models generate optimal solutions,
howeverwithin bigger problems, as those encountered in
the industries, the required time to obtain a solution makes
them difficult to use. They are used either for minor
problems, or for major problems with some considerations,
in order to simplify them.
2.4 Heuristics
For Hillier and Lieberman [20], a heuristic method is a
procedure that can find a good feasible solution for a given
class of problems, but which is not necessarily an optimal
solution.
According to Gaither and Frazier [21], heuristic methods,
or the ones based on the simple rule, have been used to
develop good solutions tobalancing problems of assembly
lines. In spite of not resulting into optimal solutions, the
obtainedsolutions are very advantageous. Below some
heuristic ruleswill be presented.
The Incremental Utilization Heuristic adds tasks to a
workstation in a precedence task order. To each task
Another heuristic also described by Gaither and Frazier
[21] is the Maximum Task Time Heuristic. In this rule, tasks
are allocated to a workstation, one at a time, following the
order of precedence of tasks. If there are two or more
allocabletasks at the same place, the one with the longest
duration is chosen. This has the effect of designating tasks
that are more difficult to fit at a workstationas soon as
possible. Tasks with shorter durations are reserved to
improve the solution, filling the idle times at stations [21].
This rule follows these steps [21]:
1. Suppose that i = 1, in whichi is the number of the
workstation that is being formed.
2. Make a list of all the candidatetasks to be assigned to
that workstation. For a task to be in that list, it must
satisfy all of these conditions:
a. It may not have been previously designated
to that one or to any other workstation.
b. The immediate predecessors must have
been assigned to this workstation or to an
earlier one.
c. The total duration of this task and all other
task durations already assigned to the
workstation must be less than or equal to the
duration of the cycle. If no candidate can be
found, go to Step 4.
3. Assign the task in the list that has the longest duration
to the workstation.
4. Stop assigning tasks to workstation i. This can occur
in two manners. If there is no task in the list of
candidates for the workstation, but there are still tasks
to be assigned, set i = i +1 and return to Step 2. If
there are no more unassigned tasks, the procedure is
complete.
Slack, Chambers and Johnston [23] quote a rule that
follows the same first two steps and the fourth step of
Maximum Task Time Heuristic, however the chosen task,
performed in the third step, should be based on the
amount of subsequent tasks, which is the task with the
greatest number of tasks that can only be allocated after it.
This rule is called the Number of Followers Heuristic.
Farnes and Pereira [9] also use a heuristic that changes
the task choice step, the Positional Weight Heuristic, which
considers the sum of the time of subsequent tasks. Tasks
are allocated in descending order of positional weight.
Grzechca[24] compares eight heuristic techniques to
determine their efficiency within the time problems of the
tasks, and three others to the problem of labor costs.
Among the eight techniques compared in the time
problems, the only one that achieved the optimal solution
was the Number of Immediate Followers Heuristic. Other
heuristics were used: Backward Positional Weight
Heuristic, similar to Positional Weight, inwhich the sum of
the time of predecessor tasks and Number of
Predecessors are considered, and the task choice is made
22nd International Conference on Production Research
based on the amount of predecessor tasks. According to
the author, minimizing both cost and time is important so
that the final product becomes more competitive.
The COMSOAL heuristic was developed by Chrysler and
reported by Arcus in 1966 in the article "COMSOAL - A
Computer Method of Sequencing Operations for Assembly
l.ine." This method randomly assigns tasks to workstations,
and toeach iteration, it compares the current solution to the
previous one and keeps the best solution [25]. To Togawa,
Paula and Alvares [26], the COMSOAL method is efficient
and simplewhen compared to other balancing methods.
Heuristics tend to have a more simple use than the exact
method or meta-heuristics, and can be implemented by
utilizing tools such as spreadsheets, widely used in
industries. Therefore, this work will be performed using
eight heuristics: Incremental Utilization, Maximum Task
Time, Number of Followers, Positional Weight, Number of
Immediate Followers, Backward Positional Weight,
Number of Predecessors and COMSOAL.
2.5 Meta-heuristics
According to Sanches [27], the major problem of heuristic
methods is the possibility of the method to get stuck in
regions oflocal optimums, notexploring regions with also
efficient solutions, or the optimal solution. The metaheuristics have been developed to solve this problem. The
logic is to improve procedures for certain heuristic, in order
to avoid stagnation in areas of localoptimum.
The meta-heuristics can be divided into two categories: the
first is the local search technique, which starts from an
initial solution and explores neighbor solutions. Taboo
Search and Simulated Annealing are examples of this
technique. The second technique is the population search,
which begins from a set of initial solutions, called the initial
population. In this technique, operators are applied,
attempting to generate new and better individuals for the
population. Scatter Search and Genetic Algorithm are
examples of this technique [28].
The different existing meta-heuristics tend to be versatile,
because they are general solving methods, and can be
applied to different kinds of problems. They possess
advantages over heuristics for trying to minimize the
stagnancy in areas of localoptimum. Regarding the
mathematical formulation, its advantage is the lower time
to obtain good solutions.
2.6 Simulation
Banks [29] defines the simulation as the imitation of the
real operation, process, or system for a period of time.
Simulation is used to describe and analyze the behavior of
a system, and it helps the system design and answer
questions like "what if" about possible changes in the real
system.
For Santoro and Moraes [30] some applications for the
simulationwithin the production are: design and analysis of
material handling systems, manufacturing assembly lines
andautomated storage systems.
For Law and McComas [31] one of the disadvantages of
the simulation is that it is not an optimization technique.
The analyst simulates some numbers to the system
configuration and chooses those with the best result.
Some software that can be used for simulation is Arena,
Promodel, Witness and SIMUL8 [27].
The simulation has a great utility when the objective is to
test different possibilities, without the need to use the real
system. But the simulation is performed only for the data
chosen by the analyst, and a system optimization should
be done separately if desired.
3
CASE STUDY
The case study was conducted at a large multinational
enterpriseof the automotive industry, located in the state of
Paraná. For reasons of information confidentiality, specific
characteristics of the enterprise and its products will not be
detailed.
The data that will be used is from one assembly line that
produces four different types of vehicles, performing 208
different activities to complete the assembly. The assembly
line consists of five stations, where 23 operators work.
Tasks are distributed among the stations according to
Table 2. The balancing done by the company uses the
Maximum Task Time Heuristic method, but the result of
this application was not provided by the company.
Table 2 – Number of tasks by station.
Number of Tasks
Station 1
Station 2
Station 3
Station 4
Station 5
63
29
39
44
33
The eight methods of assembly lines balancing were
computationally implemented using the language Visual
Basic for Applications - VBA, due to the extensive use of
electronic spreadsheets by industries.
For the COMSOAL method, the number of iterations was
chosen by considering Togawa, Paula and Alvares [26],
who used 100 iterations in their work, however, in order to
ensure better results, the value used for the calculation in
this work was of 1.000 iterations.
The data from tasks and times used in this study were
collected from the information system of the enterprise.
Some activities that should be performed in sequence
were grouped into only one task. The same task may have
different assembly times in different models or may not be
performed on all models.
Precedence relationships of the tasks were collected at the
assembly line. The assembly times were multiplied by a
conversion factor, to protect enterprise data. The cycle
time of 80 UT (units of time) was used in the calculations.
The demand of each model is required to calculate the
equivalent assembly times, and their values are in Table 3.
Table 3 – Demandof each model.
Demand
Model 1
Model 2
Model 3
Model 4
10.51%
51.25%
17.79%
20.45%
The criteria used for the comparison of results were the
number of operators required for assembling and
utilization, which is calculated using equation 1.
4
RESULTS
The balancing was performed using the task times and
precedence relationships collected in the case study. The
eightbalancing heuristics were executed in two different
manners: the first one considered each workstation
individually, and also the tasks currently performed in it,
and the second one used all 208 assembly tasks
conducted on the five stations of the assembly line to
perform the balancing.
22nd International Conference on Production Research
The resultsobtained by the application of the eight methods
were compared and are presented in Table 4. Each
assembly station and total columns show the balancing
performed using the first manner for the five stations. The
"All Tasks" column shows the balancing performed
usingthe second manner.
The comparison was performed using the number of
operators required for the different used methods. From
the number of operators, it is possible to calculate the
utilization of them by dividing the total time of assembly by
the time available to assemble (number of operators
multiplied by the cycle time).
Figures 4 to 6 illustrate the graphics completed by the used
balancing heuristic for each workstation, a total of five
workstations, and for all 208 tasks. The columns
representing each method are divided between the
assembly time per cycle time (station time) and idle time.
Table 4:Comparison between the result of balancing among the eight methods and the one used by the enterprise.
Station 1
Maximum
Task Time
Number of
Immediate
Followers
COMSOAL
Incremental
Utilization
Positional
Weight
Number of
Followers
Backward
Positional
Weight
Number of
Predecessors
Number of
Operators
Utilization
Number of
Operators
Utilization
Number of
Operators
Utilization
Number of
Operators
Utilization
Number of
Operators
Utilization
Number of
Operators
Utilization
Number of
Operators
Utilization
Number of
Operators
Utilization
Station
2
Station
3
Station 4
Station 5
Total
All Tasks
6
5
4
4
4
23
21
75.82%
6
70.16%
5
68.27%
4
78,75%
4
73,84%
4
73,44%
23
80,44%
21
75.82%
6
70.16%
4
68.27%
4
78.75%
4
73.84%
4
73.44%
22
80.44%
21
75.82%
6
87.70%
5
68.27%
4
78.75%
4
73.84%
4
76.78%
23
80.44%
20
75.82%
6
70.16%
5
68.27%
4
78.75%
4
73.84%
4
73.44%
23
84.46%
20
75.82%
6
70.16%
5
68.27%
4
78.75%
4
73.84%
4
73.44%
23
84.46%
20
75.82%
6
70.16%
5
68.27%
4
78.75%
4
73.84%
4
73.44%
23
84.46%
21
75.82%
6
70.16%
5
68.27%
4
78.75%
4
73.84%
4
73.44%
23
80.44%
21
75.82%
70.16%
68.27%
78.75%
73.84%
73.44%
80.44%
The eight methods used for balancing showed the same
result, utilization of 75.82% of station 1. This means that
for 24.18% of the cycle time, the station is idle. This idle
time may occur due to tasks that own a long assembling
time and cannot be divided among the operators of the
station, leaving some available time for operators. Another
reason for the idle time may be a need to perform a long
time task before other tasks with shorter times.
The equality in the solution of the eight methods at station
1 may be due to the characteristics of theused data. The
characteristics that may have affected the solutions are:
distribution of the time of tasks and the precedence graph
form of these tasks. Both may have restricted the choices
of tasks in the balancing calculations, not allowing the
methods to present different solutions.
Figure 4 shows the graph of the heuristics: Maximum Task
Time, Number of Immediate Followers, Backward
Positional Weight and Number of Predecessors. These
four heuristics presented the same results for the five
stations and for all tasks. However, the second manner (all
tasks) was greater than the total of the first manner,
obtaining respectively 80.44% and 73.44% of utilization of
the assembly line.
Figure 3– Solution of Maximum Task Time, Number of
Immediate Followers, Backward Positional Weight and
Number of Predecessors heuristics.
22nd International Conference on Production Research
Figure 5 shows the COMSOALheuristic graph. This was
the only heuristic that presented a different result for the
balancing using each assembly station individually, with
total utilization of the five stations of 76.78%, while the
other heuristics achieved a 73.44%. However, the
allocation of the second manner was also higher (80.44%
of utilization) than the first manner (76.78% of utilization).
operators are needed for the second manner.This should
have happened by the highest number of possibilities of
choices among tasks when balancing is performed by the
second manner.
As Falkenauer [10] comments, one of the greatest
difficulties of getting the assembly line to balance is that
the rebalancing isactuallyperformed. The difference
between the two manners used to produce the balance,
either considering each station, or considering all 208
tasks, the eight heuristics occur due to: the identity of the
stations – each station has its own equipment, tools, space
constraints and processes, precluding any change of
station tasks, and the tasks of final stations can be
allocated in the initial stations, filling the working time ofthe
operators.
It is important to remark that within the two manners of
performing the balancing, the results of the used methods
depend on the existingprecedence, on the distribution of
tasks by their length (longer or shorter) during the
assembly process, not to mentionthe possibilities of
breaking such tasks if they are of excessive length in
relation to the cycle time.
5
Figure 4 - Solution of COMSOAL heuristic.
Figure 6 shows the graph of the heuristics: Incremental
Utilization, Positional Weight and Number of Followers.
These three heuristics showed the same results for the
different balancing performed, considering both individual
stations and all tasks. The results in balancing using all
tasks were the best for these heuristics, obtaining
assembly line utilization of 84.46%, since other heuristics
had a utilization of 80.44%. However COMSOAL heuristics
obtained the best utilization value (76.78%) when the
balancing was performed by the first manner.
This work presents a theoretical referential on assembly
lines and the Assembly Line Balancing Problem. This was
motivated by the importance of the issue, balancing
assembly lines, for industries in the region and the data
provided by one of these enterprises.
In the balancing, eight heuristics methodswerecompared,
which were implemented computationally using electronic
spreadsheets in order to facilitate future use by industries.
The balancing was performed in two different manners,
one by separating the tasks of assembly stations where
they belong, considering each station individually, and
another considering the 208 tasks.
The results of the heuristics varied little among
themselves, but the two manners to perform the balancing
showed greater variation (7%). This is due to some factors
that cannot be considered in the implementation of
balancing heuristics. Some studies fall into some of these
factors in the calculation of the balancing meta-heuristics.
As recommendations for future work, it can be mentioned
the comparison between balancing heuristics and metaheuristics, considering the results obtained and the
computational time needed. The balancing by inserting
some of the factors that influence the balance that is found
in the practice, such as the place of an activity in the
vehicle, and the necessary tools, can be performed. A
study on the influence of times and the precedence graph
formatof the tasks in the results of balancing methods is
another recommendation.
6
Figure 5 - Solution of Incremental Utilization, Positional
Weight and Number of Followers heuristics.
The balancing using 208 tasks, the second manner, when
compared withthe total of thebalancing by workstations,
the first manner, requires fewer operators for assembling
tasks. Subject to the result of the best method in each
case, the first manner requires 22 operators, whereas 20
CONCLUSIONS AND DIRECTIONS FOR FUTURE
RESEARCH
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22nd International Conference on Production Research
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