Natália Cibele
De Sousa Santos
Federal
Technological University of Paraná (UTFPR), Brazil
E-mail: nataliaaeng.producao@gmail.com
Daniel
Ribeiro Gomes
Postgraduation
and Graduation Institute (IPOG), Brazil
E-mail: daniel.gomes@gruposinagro.com.br
Jarbas Ancelmo
Da Silva Júnior
Federal
Technological University of Paraná (UTFPR), Brazil
E-mail: jarbasjunior@alunos.utfpr.edu.br
Stella
Jacyszyn Bachega
Federal
University of Goiás (UFG), Brazil
E-mail: stella@ufg.br
Dalton Matsuo
Tavares
Federal
University of Goiás (UFG), Brazil
E-mail: dalton_tavares@ufg.br
Submission: 3/3/2020
Revision: 5/13/2020
Accept: 6/3/2020
ABSTRACT
Given an increase in consumer demand for product
quality, companies need to continually improve their means of production. The
use of computational resources assists companies to choose an ordering system
that best suits their reality. In this sense, the present study aims to analyze
and compare the performance of the Paired-cell Overlapping Loops of Cards with
Authorization (POLCA) system, according to pre-established parameters in a real
automobile company case, which has a flow-shop production environment. In order
to do this, the research has a hypothetical-deductive scientific explanation.
Also, the quantitative approach, and the experimental research procedure were
employed due to the use of simulation and optimization. The computer simulation
was performed using ProModel®. The initial
model was optimized, and the results of the two elaborated scenarios were
compared. It was verified that the optimized scenario showed improvement in the
average total output of the system. The simulation of the optimized model
presented an increase in production of approximately 95.29% when compared to
the initial scenario. Nevertheless, trade-offs were verified. It is noticeable
in the scenario analyzed that to increase the production of axles, the use of
intermediate stocks must be increased. Finally, the present research
contributes to the academic community since it proposed the study of an
ordering system that has a limited number of studies, mainly in Brazil. It also
contributes to the business community by encouraging the use of simulation in
companies so that a better performance analysis of ordering systems can be performed
prior to actual deployment.
Keywords: POLCA; simulation-based optimization; ordering systems
1.
INTRODUCTION
Computer simulation is
a technique that has been increasingly used for problem solving and decision
making (SARGENT, 2010). This technique is advocated by several authors such as
Buffa and Sarin (1987), Berends and Romme (1999), Chwif and Medina
(2007), Freitas Filho (2008) and Law and Kelton (2000).
According to Lahiani et al. (2014), simulation has often been used by
researchers for many applications in researching different topics such as
productivity, introduction of new technologies, transportation, among others.
However, a simple assessment does not provide enough detail for optimal
decision making. Consequently, the simulation-based optimization technique is
recommended to improve the performance of the studied systems. To optimize the
model, an approach is proposed in which the simulation model is coupled to an
optimization algorithm.
In the literature, this
technique is called simulation-based optimization or simulation optimization,
which is defined as an approach whereby an optimization mechanism provides
input factors for the simulation program (Rogers, 2002). For Carson and Maria
(1997), simulation-based optimization can be defined as the process of finding
the best values for input variables among all possibilities, without explicitly
evaluating each possibility. Phatak et al. (2014)
also reported on the procedure.
In the context of
production control are the Ordering Systems, as named by Burbidge (1983, 1990).
Such systems are intended to assist in monitoring or controlling the release of
production and purchase orders on the shop floor. Some of the Ordering Systems
presented in the literature are the CONWIP (Constant Work in Process), TBC
(Two-boundary Control), OPT (Optimized Production Technology), Kanban, MRP
(Material Requirements Planning) and POLCA (Paired-cell Overlapping Loops of
Cards with Authorization), the latter being the focus system of the present
article.
Computer simulation is
a technique that can and is applied within production systems, including
production control activities. Thus, the importance of simulation in the
context of Ordering Systems is highlighted since the choice of an ordering
system is extremely important for companies and the aforementioned technique
can help in choosing the best ordering system for the reality of the company.
Simulation applications for Ordering Systems' performance study were performed
by authors such as Ghrayeb, Phojanamongkolkji
and Tan (2009) and Khojasteh-Ghamari (2009) and Wang,
Cao and Kong (2009). It is also possible
to find in the literature several authors who used simulation-based
optimization such as Bachega (2013), Bachega and Tavares (2013), Ehrenberg and Zimmermann
(2012), Gansterer, Almeder
and Hartl (2014) and Melouk
et al. (2013).
Based on this context,
the research question of the present paper is: how to apply the
simulation-based optimization technique to the reality of an automobile company
operating in a flow-shop production environment? Flow-shop is defined by Pinedo (2001) as a group of machines placed in series where
each job follows the same processing route.
Thus, the research
problem is the simulation-based optimization of the Paired-cell Overlapping Loops
of Cards with Authorization (POLCA) ordering system, considering the case of an
automobile company. This approach was proposed because the importance of
studying a real production system applying this technique was noted so that it
was possible to reduce the gap between theory and practice.
Therefore, the
objective of the present article is to analyze and compare the performance of
the POLCA system according to pre-established parameters in a real case that
has a flow-shop production environment. The present research is justified by
the importance of the theme as observed in the works of Brighenti
(2006), Harrell et al. (2002), Krishnamurthy and Suri (2003), Kabadurmus (2009) and Riezebos
(2010). Organizations can use system simulation to find the Ordering Systems
that best fits their production system to analyze and improve their
performance.
2.
THEORETICAL REFERENCE
2.1.
Simulation Based Optimization
Luo and Lim (2013)
define simulation-based optimization as one of the fastest growing research
areas in the last two decades. Many studies have been conducted to obtain
optimal or sufficient solutions for simulation-based optimization problems
efficiently with limited computing efforts.
According to Carson and
Maria (1997), some of the simulation software that includes special search
procedures to guide a series of simulations to reveal optimal or near optimal
scenarios are the ProModel®, AutoMod®, Micro Saint®, LayOPT® and FactoryOPT®.
In addition, Ólafsson and Kim (2002) state that
simulation and optimization applications have become more common because
different simulation software vendors have offered it as part of their
simulation packages. For example, the AutoStat®,
OptQuest®, OPTIMIZ®, SimRunner®, and WITNESS Optimizer®
have already been incorporated into commercial simulation packages.
Simulation-based
optimization methods can be categorized based on the nature of the problem
being analyzed. Fu, Glover and April (2005) conducted a descriptive review of
the main approaches to perform simulation-based optimization, as follows: i) Ranking & Selection; ii) Response Surface
Methodology - RSM (Response Surface Methodology); iii) Gradient-Based
procedures; iv) Random Search (random search algorithms); v) Sample Path
Optimization (stochastic counterpart optimization or approximation of the
sample mean); vi) Metaheuristics.
The optimization module
present in the ProModel® simulator
software used in the present research is the SimRunner
Optimization®. This module consists of two features for analyzing
and optimizing ProModel® simulation
models. The first feature is a factorial design of experiments that reveal the
effect of a change in the input factor on the objective function. The second
feature is a multivariate optimization that tries various combinations of input
factors to arrive at the combination that yields the best objective function
value.
Harrel,
Ghosh and Bowden (2000) propose steps to conduct experiments using the SimRunner®, namely:
(a) Step 1: Create, verify, and validate
a simulation model using the ProModel®,
and then create a macro that is included in the runtime interface for each
input factor that is believed to influence the output of the simulation model.
(b) Step 2: Select the input factors you
want to test. For each input factor, the numeric data type (integer or real)
and its lower limit (lowest possible value) and upper limit (highest possible
value) must be defined.
(c) Step 3: An objective function is
defined to measure the utility of the solutions tested by the SimRunner®. The objective function is
constructed using terms extracted from the output report generated at the end
of the simulation run.
(d) Step 4: The optimization profile is
selected, which defines the population size of the evolutionary algorithm.
Population size defines the number of solutions measured by the algorithm
during each generation of your search.
(e) Step 5: Finally, the best solution
found was evaluated, and the SimRunner®
will inform the data of all experiments conducted and these will be classified
based on their utility measured by the objective function.
2.2.
POLCA
Faced with the growing
demand for customized products worldwide, Suri (1998) developed the POLCA
emission of ordering system which is part of a method also developed by Suri
(1998) called Quick Response Manufacturing (QRM). POLCA was developed to serve
companies operating in markets specializing in custom products which mostly
operate in environments with high demand variation and require effective
material control on the shop floor (Suri, 1998).
The POLCA system seeks to
combine the main features of the MRP (Material Requirements Planning) and
Kanban systems, thus it is classified as a hybrid system. The POLCA system has
basically four characteristics according to Suri (1998):
· Material Release is performed
through a system named the HL / MRP (Higher Level Material Requirements
Planning).
· The control method is performed
through cards, called a POLCA card, which are used for communication and
control between cells.
· POLCA cards are assigned to a pair
of cells instead of being specifically assigned to a product, as they do in
pull production systems. If the routing of any order goes from cell X to cell
Y, then a POLCA X/Y card is created and so on for the other processing steps.
Working with cells in pairs makes the POLCA card ensure that one cell will only
work on one task for which the target cell has available capacity.
· The POLCA card, for each pair of
cells, remains with the task throughout its execution through both cells and
then returns to the first cell when processing in the second cell is completed,
allowing the first cell to begin a new task.
Figure 1 shows a
schematic representation of the operation of POLCA in a production system
consisting of four sets of production cells - X, Y, Z and W cells. In the example
in question, the product will be made following the X1, Y2, Z3 and W1 path.
Figure 1: POLCA system operation
Source: Prepared by the
authors
Referring to Figure 1,
the procedure starts at the X1 Cell provided that raw material is available at
X1 and a POLCA X1 / Y2 card is sequenced to the Y2 Cell. This happens
sequentially for the other cards specified in this process. After a cell
completes its operations, the task product and POLCA X1 / Y2 card go to the Y2
Cell input buffer, determining that further movement is required or material is
available for a next operation.
Once you get to the Y2
Cell, since this task is assigned to the Z3 Cell, it is critical that you have
a POLCA Y2 / Z3 card available to begin this operation. It is noteworthy that
in the operation of the POLCA system the X1 / Y2 card remains with the task
along the Y2 Cell along with the Y2 / Z3 card. Demonstrating that in the Y2
Cell there will be 2 cards for that particular task as part of 2 card cycles.
That way each task in the Y2 Cell will carry 2 POLCA cards with it. After the
completion of work in the Y2 Cell, two situations occur:
· The X1 / Y2 card is removed from the
task and returns to the beginning of the X1 Cell;
· The task is sent to the Z3 Cell
input buffer with the Y2 / Z3 card still visibly attached to the material being
processed.
The same process is
performed for the Z3 mounting cell, which requires an available Z3 / W1 card to
begin the task in the cell. Upon completion of the task, it goes to the input
buffer of W1 at the same time as the Y2 / Z3 card returns to the beginning of
the Y2 Cell. Since W1 is the last cell of the script, there will be no POLCA
card waiting to start production and the task can be posted to W1 whenever the
cell is ready to start another task. When the job in W1 is finished, it is
dispatched (assuming the W Cell is a shipping cell) and card Z3 / W1 returns to
the beginning of Z3, thus completing the journey of the POLCA cards for this
production order.
According to the
operation described, each cell will only begin its work, except the first and
last cell, if there is a card that relates the cell in question to the previous
cell, and a card that relates this cell to the later cell, besides having the
work authorized by the HL / MRP system according to Suri (1998). Using POLCA
cards implies that cells work on tasks for which they are capable and also make
sure that the back cell is capable of performing them.
According to Suri
(1998), the POLCA card must clearly demonstrate the source cell and destination
cell, aiming to demonstrate to workers which route should be followed. The
number of POLCA cards to be used for each loop must be defined using Little’s
Law application. The number of cards is determined by Equation (1).
(1)
LT (A) and LT (B)
indicate the estimated average waiting time (in days) of the A and B Cells over
the planning horizon, ie is the lead in time of the A and B Cells,
respectively. Also, NUM (A, B) is the total WIP (Work in process) number that
goes from the A Cell to the B Cell during the planning horizon. Finally, D
represents the number of working days in the planning horizon. If the equation
results in a fractional number, the result must be rounded to the next integer
value.
Suri (1998) lists some
advantages of using the POLCA system, such as preventing an already overloaded
cell from receiving new tasks, making sure that each cell works only on tasks
they are destined for, designating cells that should be able to perform them.
Another advantage is that the system allows products to be produced only when
there is demand for them, through the authorization of HL / MRP, avoiding
unnecessary stocks.
The good performance of
the POLCA was noted in some works that used simulation. Among them, Riezebos
(2006) carried out experiments with models of order of arrival, demand
variation, lot size, product mix, occurrence of malfunctions or breaks, aiming
to demonstrate the effect of the number of POLCA cards on the crossing time in
a productive system. It was found that the number of POLCA cards is an
important measure in the project, and the simulation results showed that
reducing the number of POLCA cards reduces the lead time and the number of
stocks.
Kabadurmus (2009) compares the POLCA
and CONWIP systems via simulation. For scenarios that were simulated, the POLCA
system had better performance than the CONWIP because the CONWIP did not adapt
well in environments with unstable demand and processes with high variability.
3.
METHODOLOGY
The present research has a
hypothetical-deductive scientific explanation, because from a research problem, a
proposition was elaborated which was verified to be corroborated or falsified.
According to Carvalho (2000), the scientific explanation of the
hypothetical-deductive type is an evolution of the deductive scientific
explanation. Such evolution seeks the truth, testing the falsity of a
proposition and eliminating errors (Carvalho, 2000). Thus, it is assumed that
if the POLCA is adapted, it can be used in flow-shop production environments.
This proposition is based on the studies by Fernandes (2007) and Stevenson,
Hendry and Kingsman (2005). POLCA's proposal, according to Suri (1998), is the
application in job-shop environments. The adaptation proposed in the present
research aims to verify the behavior of the POLCA in a flow shop environment.
The research approach used is the
quantitative one. Bryman (1989) lists some features of this approach: i)
causation demonstration, presenting why things are the way they are, ii) the
hypotheses to be tested present concepts that need to be meticulously measured,
iii) investigations should have characteristics of replication by using the
procedures employed in other studies to check the validity of the results of
the first investigation.
The experimental research procedure
was still employed. This procedure seeks to verify the cause and effect
relationships of a given fact, and at the same time enables the researcher to manipulate
the independent variables. This favors the observation of eventual changes
contained in the results due to these manipulations (Creswell, 1994). According
to Bryman (1989), this research procedure is more appropriate for quantitative
approaches and also features mathematical modeling and computer simulations.
Due to the use of simulation and optimization, this procedure was the one used
in the present research.
The simulation was mathematical,
numerical and stochastic (Law & Kelton, 2000). According to Harrel et al.
(2002), simulation can be defined as a technique of experimentation of a
particular model of a real system, aiming to determine how the system will
behave in face of changes made in its structure, environment, characteristics
and parameters. Given the complexity of a simulation study, Law and Kelton
(2000) suggest 10 steps, which helped the present study: i) Problem formulation
and study planning; ii) Data collection and model definition; iii) Model
validation; iv) Construction and verification of the computer program; (v)
Conducting pilot executions; vi) Validation of the programmed model; vii)
Design of the experiments; viii) Realization of simulation runs; (ix) Analysis
of results; x) Documentation, presentation and implementation of results.
The computer simulation was
performed using the ProModel® Professional SP4 software version 8.6
and the optimization was performed using the SimRunner® tool which
is integrated in the simulator due to the friendly interface for the
researchers and the availability for university use. To use the optimizer, the
considerations of Harrel et al. (2000) were followed. As a basis for scenario
design, data from a car company with flow-shop production and high production
volume were used.
To guide the elaboration of the
computational model, a conceptual model was made using the IDEF-SIM technique
developed by Leal, Almeida and Montevechi (2008), which promotes better
integration between the conceptual model and the computational model due to the
use of terminologies common to the simulation area.
For the analysis of the results, a
95% confidence level was defined and the half-width limit of up to 10% of the
sample mean was established to obtain greater precision. This parameter is set
by the researchers. According to Kelton, Sadowski and Sadowski (2002), in the
configuration presented, 95% of replications must be within the range of the
mean achieved plus the half-range. The comparison of the scenarios was made in
the Minitab® v.17 software where the paired t-test was used.
4.
RESULTS AND DISCUSSIONS
4.1.
Characteristics of the developed scenario
The data to perform the simulation was collected in a production line of
a car company. The studied line belongs to the production of rear axles. Thus,
a production order was represented in the model with seven types of axles
(models), which were named axle 1, axle 2, axle 3, axle 4, axle 5, axle 6 and
axle 7. The conceptual model is illustrated in Figure 2.
The production line has five
workstations (WS A through WS E), and each is tasked with doing a set of
activities for assembling the shafts. For the POLCA reproduction, four POLCA
card posts were placed. An initial stock (I. Stock) was also represented, in
which the raw material to be used at the first workstation and throughout the
process arrives at equal times established by the company. Finished axles are
routed to a final stock (F. Stock), which has also been represented, plus four
intermediate stocks (IS 1 through IS 4), which are used only when the next
workstation is unavailable.
Thus, the entities (rear axle
models) are sent to the initial stock. Therefore, when an A / B card post (CP A
/ B) is available at workstation A (WS A), it indicates that workstations A and
B (WS B) are available for production. Production of the models is then started
by sending the raw material that is in the initial stock (I. Stock) to WS A.
Then, after processing at WS A, if the B / C card is available at WS B (CP B /
C), the product goes to WS B, similarly to other workstations. The existence of
the card next to the workstation part characterizes its processing. An axle can
only be released to move to another workstation when a card for the destination
station is available.
Figure 2: Conceptual model of the POLCA system
Source: Prepared by the authors
The time required for
production is 8.63 hours, so this value symbolizes the workday in the model.
Thus, the model was designed and analyzed according to the terminal system
classification, and the objective of the simulated model is to examine the
system performance on a normal working day following the operation of the POLCA
system. Figure 3 shows an image of the ongoing simulation for the POLCA
scenario.
Figure 3: Simulation in progress
Source: Prepared by the authors
It should be noted that for the initial scenario (POLCA scenario adapted
for a flow-shop environment), it was calculated according to Equation 1
proposed by Suri (1998), the amount of one card in each card post (CP A/B to CP
D/E), being one AB card (CP A/B), one BC card (CP B/C), one CD card (CP C/D)
and one DE card (CP D/E).
4.2.
Results of the POLCA scenario adapted to a flow shop environment
Considering the results for the average production quantities of each
axle type and the average total manufactured axles, due to the use of a fixed
production order of the workday, the quantity reached was exactly the same in
each replication. The total manufactured axles were 63 units. From the results
obtained, it can be analyzed that all types of axles (from one to seven) did
not show variation between the mean, maximum and minimum values because the
value of the standard deviation was null for all axles.
Table 1 shows the percentage of
workstation utilization. Average, maximum, minimum, standard deviation and
half-width values are shown. It is observed that workstation D had the highest
average utilization of 49.47% of the useful time for production. Workstation A
had the lowest average utilization, with 34.21% of the working time.
The intermediate stocks were not used, which points to a positive
feature of the POLCA system for the flow shop environment. Therefore, the data
related to the percentage of utilization of intermediate stocks regarding the
mean, maximum, minimum percentage, standard deviation and half-width values are
zeroed.
Table
1: Workstation Utilization
Placement |
Mean (%) |
Maximum (%) |
Minimum (%) |
Standard deviation |
Half-width |
Workstation A |
34.21 |
34.75 |
33.48 |
0.34 |
0.12 |
Workstation B |
43.86 |
44.25 |
43.37 |
0.22 |
0.08 |
Workstation C |
42.02 |
42.49 |
41.42 |
0.27 |
0.1 |
Workstation D |
49.47 |
50.15 |
48.78 |
0.35 |
0.13 |
Workstation E |
38.65 |
39.21 |
38.63 |
0.11 |
0.04 |
Source: Prepared by the authors
4.3.
Scenario Optimization
For the scenario optimization
reproduced in the present article, the following steps are described below:
(a) Define the variables that will
influence the model responses which will be tested by the optimization
algorithm: the variables defined in the present work were the number of outputs
(number of axles produced) and the number of cards used at the stations to
increase the number of total outputs.
(b) Determine the type of variable (real
or integer) and define the lower and upper limits: the variable in the present
study is the integer type, and the limits are from one to eight cards at each
POLCA card post.
(c) Define the objective function that
will evaluate the solutions tested by the algorithm: the purpose of the model
is to optimize the production line, taking into account the improvement of the
total system outputs. In the set of Equations 2 the defined objective function
is described according to the language used by the SimRunner®.
Entity:Max: 1.00 * axle_1 - Total Exits
Entity:Max: 1.00 * axle_2 - Total Exits
Entity:Max: 1.00 * axle_3 - Total Exits
Entity:Max: 1.00 * axle_4 - Total Exits
Entity:Max: 1.00 * axle_5 - Total Exits
Entity:Max: 1.00 * axle_6 - Total Exits
Entity:Max: 1.00 * axle_7 - Total Exits (2)
(d) Define the population size of the evolutionary
algorithm (this value affects the reliability and the precise time for the
search management): in the population size, the cautious option was selected
since it provides a large population but causes a longer time for processing.
The confidence level employed was 95%. As for the number of replications, we
used the same adopted in the simulation phase, i.e. 30 replications.
(e) Analyze the data according to the
search performed by the optimizing algorithm.
After 542 experiments, the optimizer presented the top ten solutions
which are presented in Table 2. Table 2 shows that from solution 1 to solution
5, the objective function values and the upper and lower confidence intervals
remained the same, and only the number of cards available at each card post was
changed. For the present research, the solution chosen for implementation in
the POLCA's optimized scenario was solution 3, since the DE post had the
smallest number of cards, which implies a reduction in the intermediate stock.
Table
2: Optimization values performed
Solutions |
FO value |
N° of cards AB |
N° of cards BC |
N° of cards CD |
N° of cards DE |
Lower CL 95% |
Upper CL 95% |
1 |
121.667 |
5 |
3 |
6 |
7 |
121.440229 |
121.893104 |
2 |
121.667 |
5 |
3 |
6 |
6 |
121.440229 |
121.893104 |
3 |
121.667 |
5 |
3 |
6 |
4 |
121.440229 |
121.893104 |
4 |
121.667 |
5 |
3 |
6 |
5 |
121.440229 |
121.893104 |
5 |
121.667 |
5 |
3 |
6 |
8 |
121.440229 |
121.893104 |
6 |
121.600 |
5 |
3 |
3 |
6 |
121.348104 |
121.851896 |
7 |
121.600 |
5 |
3 |
3 |
7 |
121.348104 |
121.851896 |
8 |
121.600 |
6 |
7 |
6 |
4 |
121.348104 |
121.851896 |
9 |
121.600 |
5 |
3 |
3 |
5 |
121.348104 |
121.851896 |
10 |
121.600 |
5 |
3 |
3 |
4 |
121.348104 |
121.851896 |
Source: Prepared by the authors
4.4.
Optimized Scenario
After the optimization, the scenario
was simulated with the optimized quantity of POLCA cards at the card stations
so that it was possible to make a comparative analysis of the results before
and after the optimization. In the optimized scenario, we used the following
number of cards: five AB cards, three BC cards, six CD cards and four DE cards.
Again 30 replications were performed. The confidence semi- intervals
(half-widths) found were less than 10% of the sample means, indicating that the
number of replications performed in the simulation was satisfactory.
The results are shown in Table 3. The values pertaining to the average
production quantities of each axle type and the average total axles produced
can be observed, as well as the results of the minimum, maximum, standard
deviation and confidence semi-interval (half-width). The average total
manufactured axles were approximately 123 axles, with the largest production of
type 5 axles (average of 48.93 axles).
Table
3: Result of shaft production
Axle
Type |
Mean
(%) |
Maximum
(%) |
Minimum
(%) |
Standard
deviation |
Half-width |
Axle 1 |
3 |
3 |
3 |
0 |
0 |
Axle 2 |
7 |
7 |
7 |
0 |
0 |
Axle 3 |
4 |
4 |
4 |
0 |
0 |
Axle 4 |
34 |
34 |
34 |
0 |
0 |
Axle 5 |
48.93 |
49.00 |
48.00 |
0.25 |
0.1 |
Axle 6 |
15 |
15 |
15 |
0 |
0 |
Axle 7 |
11.10 |
12.00 |
11.00 |
0.31 |
0.11 |
Total axles
produced |
123.03 |
124 |
122 |
0.56 |
0.21 |
Source: Prepared by the authors
Table 4 refers to the percentage of workstation utilization. It can be
verified that the D workstation presented the highest average use of the
production time, accounting for 99.76%. Meanwhile, the first workstation had
the lowest average utilization, 67.93% of the useful time for production.
Table
4: Use of workstations
Placement |
Mean (%) |
Maximum (%) |
Minimum (%) |
Standard deviation |
Half-width |
Workstation A |
67.93 |
68.70 |
67.15 |
0.38 |
0.15 |
Workstation B |
88.23 |
89.24 |
87.23 |
0.46 |
0.18 |
Workstation C |
85.17 |
86.15 |
84.44 |
0.39 |
0.15 |
Workstation D |
99.76 |
99.84 |
99.65 |
0.05 |
0.02 |
Workstation E |
76.31 |
77.07 |
75.79 |
0.28 |
0.11 |
Source: Prepared by the authors
Table 5 refers to the
percentage of utilization of intermediate stocks. Note that stocks 1 and 3 were
more used. Due to the increase in cards available at the POLCA card stations,
the use of intermediate stocks was expected to increase. Since the purpose of
the optimized model was to maximize total system outputs, intermediate stocks
were required. This fact is not a desirable feature of the original POLCA, however,
in adapting to use in a flow shop system, the use of these stocks improved the
system performance. It should be noted that even so, intermediate stocks had
low utilization, which is a desirable feature.
Table
5: Utilization of intermediate stocks
Placement |
Mean (%) |
Maximum (%) |
Minimum (%) |
Standard deviation |
Half-width |
Intermediate stock 1 |
25.74 |
26.10 |
25.17 |
0.23 |
0.08 |
Intermediate stock 2 |
1.27 |
1.50 |
0.95 |
0.13 |
0.05 |
Intermediate stock 3 |
25.03 |
27.20 |
21.83 |
1.23 |
0.46 |
Intermediate stock 4 |
2.36 |
2.52 |
2.20 |
0.08 |
0.03 |
Source: Prepared by the authors
4.5.
Comparative analysis
between non-optimized and optimized POLCA scenarios
When comparing the
results obtained in the scenarios, one can notice some differences related to
their performance. Table 6 presents the values related to the average total
axles produced and Table 7 shows the average times in the system.
Table
6: Comparative results regarding the average
total output
Axles |
Initial
scenario |
Optimized
scenario |
Variation
percentage (%) |
Axle 1 |
3 |
3 |
0.00 |
Axle 2 |
4 |
7 |
75.00 |
Axle 3 |
4 |
4 |
0.00 |
Axle 4 |
15 |
34 |
126.67 |
Axle 5 |
23 |
48.93 |
112.74 |
Axle 6 |
7 |
15 |
114.29 |
Axle 7 |
7 |
11.10 |
58.57 |
Total axles produced |
63 |
123.03 |
95.29 |
Source: Prepared by the authors
Table
7: Comparative results (average time in the
system)
Average system time |
||
Initial scenario |
Optimized
scenario |
Variation
percentage (%) |
21.00 mins |
45.86 mins |
118.38 |
Source: Prepared by the authors
4.6.
Paired t-tests
The paired t-test was
used to compare all performance measures before and after optimization.
According to Magalhães and Lima (2008), the t-test for paired samples is
appropriate when there is dependence between the elements of the tested
samples. In the case of the scenarios analyzed, the same workstations and the
same intermediate stocks were used before and after optimization, so there is a
dependency between the elements.
When making such a
comparison, a hypothesis test is performed, having a null hypothesis of
H0: = 0, which states that there is no
difference between the averages analyzed and the alternative hypothesis
Ha: ≠ 0, which states that there
is a difference between the means that are under review. According to Devore
(2006), when the p-value is lower than the significance level, being in the
present research less than 0.05, the null hypothesis is rejected.
Table 8 presents the
conclusions obtained through the paired t-test. Regarding the total outputs
from the initial scenario compared to the optimized one, axles 1, 2, 3 and 6
presented identical values in both columns analyzed, while axles 4, 5 and 7 are
significantly different since the p -value equals zero.
Regarding the average use
of workstations, it is noted that all measures were considered statistically
different in the comparisons between the initial versus optimized scenarios.
Concerning the average utilization of intermediate stocks, for the comparison
between the initial and optimized scenarios, the values are also statistically
different since the p-values of all stocks are equal to zero. Regarding the
average time in the system of the initial scenario compared to the optimized
one, these are considered statistically different since both have p-values
equal to zero, as can be seen in Table 8.
Table
8: Results of the paired t-test
Performance
measures |
Initial Scenario versus Optimized Scenario |
Axle 1 average total output |
All values are identical |
Axle 2 average total output |
All values are identical |
Axle 3 average total output |
All values are identical |
Axle 4 average total output |
Statistically different. P-value = 0 |
Axle 5 average total output |
Statistically different. P-value = 0 |
Axle 6 average total output |
All values are identical |
Axle 7 average total output |
Statistically different. P-value = 0 |
Average use of
workstation A |
Statistically different. P-value = 0 |
Average use of
workstation B |
Statistically different. P-value = 0 |
Average use of
workstation C |
Statistically different. P-value = 0 |
Average use of
workstation D |
Statistically different. P-value = 0 |
Average use of
workstation E |
Statistically different. P-value = 0 |
Average
utilization of intermediate stock 1 |
Statistically different. P-value = 0 |
Average
utilization of intermediate stock 2 |
Statistically different. P-value
= 0 |
Average
utilization of intermediate stock 3 |
Statistically different. P-value
= 0 |
Average
utilization of intermediate stock 4 |
Statistically different. P-value
= 0 |
Average system time |
Statistically different. P-value
= 0 |
Source: Prepared by the authors
5.
FINAL CONSIDERATIONS
Modeling, simulation and
parameter optimization were performed in a model of the POLCA ordering system,
and the best configuration was determined considering the maximization of the
total system outputs. The original proposal of the POLCA system, according to
Suri (1998), is to apply it in environments with job-shop production. The
present work applied the POLCA system in a flow-shop production environment,
which characterized an adaptation of the original system. Subsequently, the elaborated model was optimized, and the results of the
two elaborated scenarios were compared. With this, the proposed objective
was achieved.
The results showed
that, regarding the number of axles produced, the optimized model presented a
better performance. The simulation of the optimized model presented a
production increase of approximately 95.29%, compared to the initial scenario
that presented, on average, 63 axles produced at the end of the work shift. In
addition, the paired t-test proves the best performance of the optimized
scenario since it presented statistically different results in the comparison
between scenarios for the vast majority of performance measures analyzed.
However, trade-offs
were verified. In the initial model there was no use of intermediate stocks and
the average time of the axles in the system was lower compared to the optimized
scenario that presented an average time in the system of 45.86 minutes. Thus,
it can be seen in the scenario analyzed that to increase the production of
axles, the use of intermediate stocks must be increased.
The present research
contributes to the academic community since it proposed the study of an
ordering system that has a limited number of studies, mainly in Brazil. It also
contributes to the business community by encouraging the use of simulation in
companies so that a better performance analysis of ordering systems can be
performed prior to actual deployment.
Finally, it is
recommended as future research, to simulate other Ordering Systems in different
scenarios to verify and compare their behavior, as well as identify if they
apply to the reality of the productive system of the company chosen for a new
study.
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