BALANCE CAPACITY WITH VARIABILITY CAUSED BY HUMAN
FACTOR: AN APPLICATION IN A LINE WITH MONTE CARLO SIMULATION
Augusto Sandes Mendes
Federal Institute of São Paulo – Suzano Campus, Brazil
Email: augusto_sandes1986@hotmail.com
Adriano Maniçoba da Silva
Federal Institute of São Paulo – Suzano Campus, Brazil
Email: adrianoms@ifsp.edu.br
Luiz Teruo Kawamoto Júnior
Federal Institute of São Paulo – Suzano Campus, Brazil
Email: luizteruo@hotmail.com
Submission: 31/03/2016
Accept: 31/03/2016
ABSTRACT
The variation in processing times due to the human factor between the
working stations of a production line can generate queues resulting in a higher
cost to the productive process. The objective of this study was to apply Monte
Carlo simulation to balance the capacity of a production line with stations
suffering variability in processing time due to the human factor. Simulations
of the current situation of the production line were performed by comparing it
with a proposal to align capacity with the production restriction in order to
reduce inventories process while maintaining full capacity of the line. To
develop the study, the selection involves the case of a company’s production
line in the metal industry that produces machinery and products for metalworking
area. The results allowed pointing suggestions for the company to reduce
inprocess inventory, keeping then total capacity of the line.
Keywords:
Line balancing; Production line; Monte Carlo simulation.
1. INTRODUCTION
Aiming to optimize its
business operations companies have had an increasingly proactive stance in
improvement activities that add value to the final product. Although many
internal processes, especially concerning to physical management, are not under
direct customer evaluation, its performance directly affects market
preferences. In this context, the excess of intermediate stocks and queuing in
a production process, which can impact significantly the final cost.
Production Engineering is
aimed at the management of production systems in order to maximize all
available resources generating satisfactory results, then making the system
competitive in today's globalized market.
This scenario puts pressure
so that the production management includes in the process of decision making
important aspects such as raw material entrance rate in production process, as
this rate directly influences production capacity of the company, in the
balancing of production lines, in waiting inventory, and materials under
processing (WIP  work in process).
Another relevant issue is
the variability in production activities time for manual tasks, mainly due to
the worker's pace during the work period. This rate directly influences
production capacity, becoming indispensable a study to investigate variations
in this parameter.
Among the several ways to determine productive
capacity, subject to variation, the simulation performed by experiments based
on historical data has proven a useful technique for this purpose. Monte Carlo
simulation has been recognized as an important tool for decision makers,
therefore, allows a problem investigation based on experiments with random
number generation (JUNQUEIRA; PAMPLONA, 2002). This method is because the
relative frequency of a certain phenomenon occurrence approximates the probability
of the same, when the mathematical experiment is repeated several times.
From the importance of capacity
studies on a production line and the growing importance of Monte Carlo
simulation has received in recent years, it is stated the following question
problem: how to balance a productive process which neck has variable processing
time? Thus, this study will aim to analyze the ability to balance on a
production line that rely on human labor pace proposing changes based on Monte
Carlo simulation. The next section deals with the literature review..
2. LITERATURE REVIEW
In this section important concepts
for the study development were reviewed, treating issues like line balancing,
Theory of Constraints, necks, Simulation and Monte Carlo method.
2.1.
Production Lines and the Theory of Constraints
The Theory of Constraints (TOC) is a
scientific method designed by Israeli physicist Eliyahu Goldratt to solve
organizational problems susceptible to necks. TOC considers that the production
capacity of a “neck constraint” defines the maximum production capacity of a
system, that is, a process with the lowest capacity in a production line.
Following this approach, this constraint should be located and improved so that
the system's production capacity is optimized (GOLDRATT; COX, 2006).
According to Nunes (2004), a system
of constraints is made up of resources that limit their ability to achieve
better performance in relation to its goal. For the author, the whole system
involving flows between different seasons or jobs have at least one
restriction.
Goldratt and Cox (2006) suggest a
method for improving the necks guided on the following principles:
a) A system works like a chain, and the weakest link
determines the overall strength, so it should be found and strengthened.
b) The maximum overall system performance is not equal
to the sum of the maximum of all the links.
c) All system works in a relationship of cause and
effect. Among the adverse events observed, some are causers and some are
effects.
d) Undesirable effects are not considered problems but
indicators. They are results and hidden causes that should be located and
treated.
e) A solution is perishable. It deteriorates with time.
f) Most of the constraints stems from policies rather
than physical factors. The political constraints are of more complex
identification and addressing.
g) Ideas are not solutions. The best ideas do not have
potential until their implementation. Most of the ideas still fail in the
deployment process.
Goldratt and Cox (2006) compare a
production line with a walk of a Boy Scout troop in single file. Each have
their walking pace as well as production processes have their capacity. If the
fastest scout is placed in the front, the group tends to disperse. One solution
is to group the scouts so that the slower coordinate the walk. Another solution
would be to tie the scouts with a rope to make them walk the same pace, on the
speed of the slowest, namely the constraint pace. The challenge is to reduce
the dispersion of activities without increasing the total time to complete the
cycle.
The Theory of Constraints considers
that the system neck capacity defines its maximum production, for that reason
its disposal should be sought in order to speed up the system.
According to Goldratt and Cox
(2006), the necks of a production line can be identified by the previous
semifinished material accumulation to a certain process. For the authors,
efficiency, downtime, and use of this resource should be frequently monitored
to avoid losses in the rest of the production process.
In an industrial process, studies to
eliminate necks can also be accompanied by financial analyses. The existence of
neck involves costs caused by waiting or by the intermediary stock in view of
this waiting. However, there is the risk of replacing costs caused by necks for
some other kind of cost, not observed, while necks are seen as the main cause.
The decision for improvement in relation to a neck is closely linked to
improving the process cost. It is therefore necessary to define the neck
resource cost and its modifications within the activity to choose the best way
of treating this problem. The next section deals with the influence of human
behavior in modeling.
2.2.
Human behavior influence in modeling
Many tasks in the productive
environment require greater or lower amount of operators’ manual work. Human
labor can have important effects in the production process such as reduced
production rates due to fatigue. Factors considered in the composition of
fatigue are: physical exertion, mental stress and monotony. Physical exertion
is the physiological wear and tear to a muscle activity. The mental effort is
the physiological wear due to a mental activity in which the work the operator
performs requires focused attention. Monotony is the routine work (EHRHARDT et
al., 1994).
According to Baines et al. (2004),
computer simulations have traditionally guided in technologies systems (e.g.
machines, conveyors), then represented by deterministic or stochastic data.
However, such simulations often overestimate the manufacturing systems capacity
because they do not consider the human factor. This can cause serious problems
when the proposed system is implemented, and then does not meet the above
expectations to the model generation.
One of these omissions is the relationship
between a person's performance and factors affecting this performance. This is
particularly apparent when modeling industrial systems that have high
proportion of manual operations (ERNHARDT; SCHILLING, 1997). Consequently, to
improve the simulation accuracy is necessary to represent those more
realistically with the inclusion of delays resulting from behavioral aspects.
The next section deals with the simulation theme.
2.3.
Simulation
The simulation consists in
structuring a model that aims to represent an operation or realworld
situation. This model uses several parameters, detailing the system under
review with some fidelity. The purpose of this technique is to provide support
for decisions when conducting pilot studies or actual testing is not feasible,
for either security, financial, technological resources or time reasons
(AMANIFARD et al., 2011). However, the quality of the analysis generated by
simulated models as well as its results are directly linked to the entrance
data quality and model structure (CATELLI, 2010). Thus, to perform data
simulation correctly representing the problem is something essential.
The simulation can also be
understood as a process that makes possible the development of a useful model
for analyzing a real experience. For Moreira (2010), the simulation is based on
building a model that approaches the reality, which is operated several times,
always analyzing the results from a certain level of manipulation and control.
The use of computers facilitates this trial, allowing greater accuracy of
results due to the possibility of carrying out numerous interactions on the
system at hand.
According to Garcia, Lustosa and
Barros (2010), simulation models can be divided into deterministic and
probabilistic. The first group involves analysis of accurate settings to obtain
specific results. The second uses statistical assumptions, which incorporate
probabilistic behavior involved in the system variables behavior.
For Andrade (2009), the simulation
makes possible to perform deductions on the system behavior through
experiments. For Ehrlich (1985), the simulation method is used to analyze a
system performance by devising a model that deals with similar characteristics
to the original system. Possible problem responses can provide a reliable model
(HARRELL, 2002).
However, the use of simulation is a
step preceding the new policies and decision alternatives draft. For the
problem formulation data collection is required, which should be enough and
meaningful to the decisionmaking process (ANDRADE, 2009).
Once the model is established, it is
necessary to know the efficiency possible to obtain from the simulation
results. One should also perform tests that could demonstrate the propositions
consistency (ANDRADE, 2009).
Thus, by reviewing historical data,
it is possible to create a model to study the capacity variation and possible
queues on a production process by simulation methods. The next section deals
with Monte Carlo simulation.
2.4.
Monte Carlo simulation method
The origin of the term Monte Carlo
dates back to a parallel with a casino roulette located in the principality of
Monaco. Von Neumann, around 1944, was one of the term farmers used to name the
mathematical technique for solving nuclear physics problems, which was also
used for the creation of the nuclear bomb (LOESCH, HEIN, 2009; GARCIA, LUSTOSA
; BARROS, 2010).
The Monte Carlo method stems from
the probabilistic model that performs random events simulations (GARCIA,
LUSTOSA; BARROS, 2010). According Loesch and Hein (2009), Monte Carlo technique
consists in the operation of a hypothetical roulette leading to random results,
which is controlled so that the results lead to a certain interpretation.
For Moreira (2010), Monte Carlo
method focuses on probabilistic variables behavior simulation by generating
random values so that it has a set of possible occurrence of the phenomenon.
According to Garcia, Lustosa and Barros (2010), for the implementation of Monte
Carlo method, some basic steps are needed, such as: (1) defining variables and
collecting historical data; (2) identifying the collected variables
distribution; (3) modeling the probability distribution for the defined
variables; (4) defining intervals of random numbers; (5) generating random
numbers and; (6) simulating experiments.
As for Morais (2010), Monte Carlo
method comprises the following steps: (1) identification of probability
distributions with respect to the variables addressed; (2) establishment of the
cumulative probability distributions for each variable identified; (3)
definition of the random numbers ranges for each variable; (4) generation of
random numbers; and (5) experiments simulation.
The random numbers, according to
Moreira (2010), should be allocated from sets of numbers compatible with the
range extension to which they belong in the real context, keeping a
relationship between the set of random numbers and the frequencies.
As discussed in previous sections,
in a production line the flow should be adjusted by the neck. In this study, as
the studied process has variable processing rate, it is viable to state the
following research hypothesis:
H1 – In a production line with work station which neck
has variable production time, capacity should be adjusted from this process
including variation.
Next section presents the
methodology of the study.
3. METHODOLOGY
To prepare this study the case study
method was used, because it is a methodological approach to research, when
aiming to understand, explore or describe events and complex contexts in which
several factors are involved. Yin (2001) argues that this approach fits when
the researcher seeks answers to the "How?" and "Why?"
So, Yin (2001) defines "case
study" based on the study characteristics phenomenon and based on a set of
characteristics associated with the data collection process and analysis
strategies thereof.
As for approach methods, this
research is classified as qualitative and quantitative. The need for
qualitative interpretation of data obtained through information accessed during
the case study. Quantitative because data quantification through mathematical
tools provides better comprehension of the factors involved (GIL, 1999).
Regarding the purpose, this research
is classified as descriptive, that is the one which sets clear and well
outlined features of a given population or phenomenon. For this, it involves
standardized and structured techniques of data collection and is primarily
motivated by the need to solve problems concretely and more immediate.
Therefore, it has practical purpose, as opposed to pure research, motivated
primarily by intellectual curiosity of the researcher and located mainly in the
speculation level (VERGARA, 2006).
The research was conducted in four
stages. The first step was to characterize the company's production line,
specifically the line where there is heavy reliance on manual labor and that
there is great variability in production rates due to the pace of work,
identifying, establishing and defining the items probability distributions. The
second stage consisted of data processing and modeling from the production
system in Excel® software in order to get the random data generator as
probability distributions.
The third stage was the data
simulation into a set of 160 experiments, followed by 1,000 replications equivalent
to monthly charge of producing 160 hours. With data of the line current
situation and the proposed leveling with the capacity of the neck. Finally, the
fourth stage was the analysis and comparison of the two simulations, cited in
the third stage. The next section presents the results analysis.
4. RESULTS ANALYSIS
4.1.
Characterizing case and production line
The company chosen for the case
study is a Japanese multinational organization, manufacturer of machinery and
equipment for the metalmechanic sector, headquartered in Suzano, Brazil.
The studied process was an
intermediate production line in the components machining sector, it has a
demand of 10,000 items/month and time available in one round of 160
hours/month. The production line has 3 milling machines with intermediate
inventory, earlier at each process, in which there is dependence of the
processes precedence, as shown in Figure 1.
Note:
E: Intermediate inventory for operation on station i;
OP= Operation on station i;
i: Work
station = i=1, 2, 3.
Figure 1: Production line processes mapping
Capacity and variability data were
collected from company reports and operations chronoanalysis. The variability
in the entrance rate of the items on the production line has been converted
into probability as shown in Table 1.
Table 1: Relative
probability in entrance rate of the production line
Entrance
rate (items/hour) 
Relative
probability 
100 
20% 
84 
20% 
68 
60% 
Total:
252 
Total: 100% 
Source: Authors of the study
The Station 1 operation has 80
items/hour of production capacity, and may be flexible in increase and decrease
of 20% capacity. Operation at station 2 has constant production capacity of 200
items/hour, due to the fact of using an automated and relatively modern
equipment than the other stations. At Station 3, there is also variability in
production capacity due to the high degree of manual operations utilization.
Table 2 presents probability data related to the Station 3operation capacity.
Table 2: Relative
probability in operation productive capacity on Station 3
Capacity
Station 3 (items/hour) 
Relative
probability 
60 
12% 
54 
88% 
Total:
114 
Total: 100% 
Source: Authors of the study
The monthly demand of the company in
the reported period (July 2015) was 10 thousand items. With the time data available
of monthly demand, the average capacity required was calculated as shown in
Equation 1.
(1)
From the presented data, it is
identified that the Station 3 does not meet the demand of 10,000 items/month,
that is, the position is the production line neck, because it is not shown in
any of the cases of relative probability higher or equal to the calculated
average capacity, and it limits the total capacity of the line as the number of
items processed in Station 3, which is 51.12 items/hour on average. The next
section explains the simulation model.
4.2.
Data treatment and system modeling
With data from the characterization
of the production line, it was developed, in Excel® software, data processing
and modeling of the system to be simulated.
For generation of random numbers,
the entrance and the Station 3 capacity rates, the array was obtained with the
relative probabilities on the production history, Tables 1 and 2 and cumulative
probability for the correct assignment of the distribution of numbers to be
generated. Table 3 shows the distribution of accumulated probabilities.
Table 3: Accumulated
distribution of the model variables
(a) Entrance rate 
(b) Capacity on Station 3 

Probability 
Accumul.
Probability 
Entrance
rate 
Probability 
Accumul.
Probability 
Capacity 
0,2 
0 
100 
0,12 
0 
60 
0,2 
0,2 
84 
0,88 
0,12 
54 
0,6 
0,4 
68 

1 
54 
1 
68 

Source: Authors of the study
The production system modeling was
developed as shown in Table 4, with the entrance, waiting, missing, cumulative
waiting, cumulative absence, and work in process (WIP) rates for each working
station.
Table 4: Simulation Modeling (Station 1)
(1) Hour 
(2) Entrance rate 
(3) Absence 
(4) Waiting OP1 
(5) Cumulative Absences 
(6) Cumulative Waiting 
(7) Line OP1 
(8) Cap. OP1 
(9)WIP OP1 
1 
~Dist (Table 3a) 
Max (82;0) 
Max (28;0) 
∑_{3} 
∑_{4} 
Max (65;0) 
80 
Min (2;8) 
... 

160 
Source: Authors of the study
For calculating the input rate and
OP3 Queue random numbers were used to generate simulation from the cumulative
distributions in Table 3. The molded items were simulated for 160 hours, which
is the time available in one turn for one month of production. The absence was
obtained from the subtraction between the maximum station capacity and the
input rate and zero. Conversely, the wait was obtained by the maximum by subtracting
the entry fee for the ability and zero.
The following variables were
analyzed: (1) Total of items that the entrance rate resulted; (2) Maximum
number of items in the queue at Station 1 (Queue OP1); (3) Maximum number of
items in the queue at the Station 3 (Queue OP3); and (4) Total items processed
at Station 3. The next section presents the simulation results.
4.3.
Simulation results of the production line current
situation
Result simulation for total items
that the entrance rate resulted is shown in Table 5.
Table 5: Total items
resulted by entrance rate
Total
items 
12.784 
Average
(items/hour) 
79,90 
Standard
deviation (items/hour) 
13,93 
The result showed that the total
items that the input rate, working at current rates, even with variability
demand, is greater than 10,000 items. The maximum number of items in the
Station 1 queue has resulted in 30 pieces, which presents a very small result
in the total of items that entered the line, with an average of 1 unit on the
OP1 row.
The maximum number of items in
Station 3 queue, showed a maximum queue of 3,367 items that accumulate along
the simulation, presenting an approximately linear behavior, as shown in Figure
2.
Figure 2: Line behavior on Station OP3
This occurred because queue 3
capacity is reduced, according to Table 6, from the simulation results.
Table 6: Total items Station
3 produced on current situation simulation
Total
items 
8.742 
Average
(items/hour) 
54,64 
Standar
deviation (items/hour) 
1,85 
Due to limitations on investments related to the capacity
increase of the OP3 station, the company works with overtime schedule to make
up the difference between demand and capacity constraint of the OP3 station.
From these results, where the neck of the production process has been
identified, the next section presents the result of the equilibration process
for the production line.
4.4.
Simulation with proposed values for neck capacity
balance
Values with the input rate change to
those shown in Table 3 were simulated. The decrease of 16 batches of items of
the input rhythm were performed in each probability, as it is the standard
batch the one processed in previous queues. Thus, the new cumulative
distribution table can be seen in Table 7.
Table 7: Modified entrance
rate
Probab. 
Accumul. Probability 
Entrance
rate 
0,2 
0 
84 
0,2 
0,2 
68 
0,6 
0,4 
52 
1 
1 
52 
With these changes in entrance rate, total items on
simulation of 160 hours are presented in Table 8.
Table 8: Total items
entrance rate resulted with modifying simulation
Total
items 
10.096 
Average
(items/hour) 
63,10 
Standar
deviation (items/hour) 
13,31 
The result shows that even with the rhythm decrease in
the entrance rate, it still shows the total items near the demand of 10,000
items.
The same simulation was performed to decrease the
capacity of the Station 1 from 80 items/hour to 60 items/hour in order to align
the average input rate of items, because it is flexible due to the quantities
to be processed, so there is no lack of items on the OP3 station and it loses
capacity if there is a shortage, and in an attempt to decrease in the station
queue 3.
The maximum number of items in the OP1 queue was 88 items
representing a very small value in relation to entrance rate, with an average
of 14 items in the line of OP1 station.
The maximum number of items in the OP3 station queue,
showed a maximum queue of 567 items that accumulate over the simulation,
showing an increasing trend, as shown in Figure 3.
Figure 3: Line behavior on station OP3 with changes
on entrance rate and capacity on Station 1.
Total items processed in station OP3 is shown in Table 9
together with the simulation results with changes proposal.
Table 9: Total items Station
3 produced in the changes proposal simulation
Total items 
8.742 
Average (items/hour) 
54,64 
Standar deviation (items/hour) 
1,85 
The results presented in total items processed in Station
3 is identical to those shown in simulation with the condition, that is, there
was no lack of pieces in Station 3, even with decrease of entrance rate and of
Station 1 capacity rhythm.
Aiming to verify variation sensibility of OP3 capacity
and the Queue effect, the study conducted replications of the simulation
carried out from Station 1 processing variance capacity. According to the
exposed in Figure 4, there is convergence of the values simulated in the
replications.
Figure 4: Average Queue replications in Station 3
Once values established, it was possible to analyze
average queue behavior in function of the variance on processing time of
Station 1. Assuming what literature preconizes about, if stations have similar
processing time, there will not have queue, it could be verified queue
sensibility, in the sense that a maximum capacity of standardization was analyzed
in Station 1, noting that Station 3 has variance.
In order to investigate this result, a binary
codification was used every time Station 3 did not show queue, this is when
condition would be zero, and one in the opposite situation. The result of this
counting is shown in Figure 5.
Figure 5: Relation between OP1 and OP3 queue
From the understanding of Figure 5, it is possible to
state that when Station 1 capacity is equal to Station 3 (average of 54), there
is no queue in simulated hours, that is, the codification carried out is 0 in
all observations. When Station 1 capacity varied between 55 and 60 units, the
amount of hours representing queue is stable in 20. At last, from 61 units all
the simulated hours start generating queues.
The result is shown in Figure 5, allowing to discuss some
important aspects, what is done in the next section.
5. RESULTS DISCUSSION
The study results allow affirming that, in a production
line with working stations using different processing times, preceding
processes should be balanced in the station where the neck is located. This
way, the study result is according to what Goldratt and Cox (2006) stated, in
regards to the system identification and parameterization in relation to the
neck.
As stated Nunes (2004), the studied production system did
not show constratints limiting total capacity because constraint was in Station
3. Moreover, it was possible to model productive process variability coming
from human behavior that would represent eventual manual Works performed in the
operations environment (BERNHARDT; SCHILLING, 1997).
Monte Carlo simulation was a useful tool to investigate
particularities of the problem analyzed in regards to the variability of
entrance and processing rates and its effect on the processing queue
corresponding to productive neck. As announced by Andrade (2009) and Harrel
(2002), the system trustily allowed to replicate, considering the limitations
from simplification, so that production system could be modelled for analysis.
It is believed that the main result arises from the
analysis of a production line which neck has variation in its processing rate.
Especially the foregoing in Figure 5, it should be parameterize the foregoing
processes to the neck so that their processing rates do not exceed the maximum
variation of the neck processing rate.
There is a usefulness of the result obtained by the fact
that, as the examined example, if the Station 1 was parameterized with 55
processing rate, this result would not be efficient because a parameterization
with 60 would result in the same amount of idle time in production process. The
next section presents the findings.
6. CONCLUSIONS
The results of this study allow us to reaffirm the
usefulness of Monte Carlo simulation method, to generate random rates and
capacities in the range of accumulated probability as getting inputs as field
data obtained through reporting production and chronoanalysis.
The proposal of aligning capacity to the productive neck,
which is located in the premise of the theory of constraints, it proved to be,
in fact, the maximum capacity that can be achieved with the system. Thus, all
or any effort capacity variation should focus on previous or subsequent cases.
Based on the results shown in the simulations, by making
comparisons between current line status and the proposal of aligning capacity
to the neck, there were significant results in the possibility of producing
excessive reduction in entrance rate from 12,784 items to 10,096 items (21%
reduction) and in Station 3 queue, which resulted in the current condition
simulation in 3,367 items at the end of 160 hours of simulation, for the result
of the proposed condition of 567 items (83% reduction of items waiting to be
processed).
This study allows the model to be replicated in similar
cases of productive necks, which have as essential difficulty the entrance
rates variability, capabilities for predictions and capacity simulations,
allowing even comparisons with similar models and simulations with events
discrete.
It is concluded that in simulation models, the human
resource should not be statistically treated in the same way that automated
features. The results indicate significant variations (in 5 processing units),
and therefore should be considered in the analysis model.
The limitations verified are associated to the fact that
the process has been simulated using Monte Carlo simulation in discrete time,
since the latter form considers the dynamic view of the item in question. Also
another limiting factor may have been the amount of stations in the production
process analyzed, 3 stations, a fact that may compromise the results of the
conclusions and generalizations.
Future studies may lean on the balance of the production
line capacity with a bigger amount of stations, as well as in the presence of
greater number of variability sources, because in this study, only one was
identified 1, the OP3 station. Furthermore, it is necessary to perform the
analysis using discrete simulation.
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