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SIMULATION OF A DAIRY PLANT PACKAGING

presented by

JAEMIN CHOI

has been accepted towards fulﬁllment
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SIMULATION OF A DAIRY PLANT PACKAGING LINE

By

Jaemin Choi

A THESIS

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

MASTER OF SCIENCE

School of Packaging

1 999

ABSTRACT
SIMULATION OF A DAIRY PLANT PACKAGING LINE
By

Jaemin Choi

Simulation is a powerful problem-solving technique. The optimization
process for a packaging line often can not be solved by an analytical method.
The proper selection of optimization method will result in higher productivity of
the packaging line. A simulation model for increasing the productivity of dairy
plant packaging lines was developed based on statistical analysis, using the
simulation software “Taylor II”. The computer simulation model was run for a
variety of system parameters and was found to accurately predict the
performance of the system.

There has been no implementation of the simulation to date. However, for
limiting cases, the simulation model of the current line agreed very well with

actual performance.

ACKNOWLEDGMENTS

The author wishes to express his thanks to his advisor, Dr. Harold A.
Hughes for his valuable sincere assistance and providing good research topic
and also the author gives thanks to the School of Packaging at Michigan State
University and College of Agriculture and natural Resources at Michigan State

University for providing the ﬁnancial assistance for this project.

The author is deeply indebted to people in the dairy plant in Detroit for
their sincere support, assistance and encouragement throughout this project,

though I am not liberty to reveal their names.

Genuine appreciation is extended to the members of the research guidance
committee, Drs. Gary Burgess and John Partridge for reviewing this manuscript.
Special thanks to go to Mr. Roger Hullinger at F&H Simulation Inc. for his sincere

help to use “Taylor ll” simulation software.
Last but not least, the author wishes to express deepest appreciation to his

parents, Mr. B. T. Choi and Mrs. H. S. Hwang and the best friend, Krittika

Tanprasert, for their love and support.

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................. vi
LIST OF FIGURES .............................................................................................. vii
INTRODUCTION .................................................................................................. 1
CHAPTER 1
LITERATURE REVIEW ........................................................................................ 3
1.1. Computer Simulation of a manufacturing/packaging line .................... 3
1.1.1. Deﬁnition ............................................................................... 3
1 .1.2. Classiﬁcation ......................................................... , ............... 4
1.1.3. Advantages and disadvantages of simulation ....................... 5
1.1.4. Requirements of simulation software ..................................... 7
1.2. Setting up a simulation study .............................................................. 8
1.2.1. Formulate problem and plan the study .................................. 9
1.2.2. Data collection and analysis ................................................ 10
1.2.3. Model building ..................................................................... 12
1.2.4. Model veriﬁcation and validation .......................................... 13
1.2.5. Experiments and output analysis ......................................... 16
1.2.6. Documentation, presentation, and
implementation of results ..................................................... 17
1.3. Probability Distribution ....................................................................... 18
1.3.1. Stochastic behavior of the system ....................................... 18
1.3.2. Theoretical distribution and empirical distribution ................ 19
1.3.3. Choosing a distribution ........................................................ 20
1.3.4. Common theoretical distribution .......................................... 22
1.4. Statistical Analysis of results ............................................................. 26
1.4.1. Terminating simulation and non-terminating simulation ....... 27
1.4.2. Statistical analysis for terminating simulations ..................... 29
1.4.3. Statistical analysis for non-terminating simulations ............. 29
CHAPTER 2
DEVELOPMENT OF THE SIMULATION MODEL .............................................. 33
2.1. Problem formulation -
Deﬁning the current problem of the dairy plant .................................. 33
2.2. Description of the system to be modeled .......................................... 34
2.2.1. Blow molding machines ....................................................... 35
2.2.2. Wire conveyor ...................................................................... 37
2.2.3. Filling machines ................................................................... 37
2.2.4. Case washer ........................................................................ 38
2.2.5. Caser ................................................................................... 38
2.2.6. Stacker ................................................................................ 38
2.2.7. Cooling Storage ................................................................... 38

2.3. Experimental alternatives .................................................................. 38

2.4. Gathering and analyzing the data ..................................................... 40
2.4.1. Mean Time between Failure (MTBF) and
Mean Time to Repair (M'ITR) .............................................. 41
2.5. Computer model building, veriﬁcation and validation ........................ 43
2.5.1. Model 1 - Model of blowmolding station .............................. 45
2.5.2. Model 2 - Model of blowmolding station and
wire conveyor I .................................................................... 50
2.5.3. Model 3 - Model of blowmolding station and
wire conveyor I and II .......................................................... 53
2.5.4. Model 4 - Model of blowmolding station and
wire conveyor I, II and ﬁlling machines ................................ 55
2.5.5. Model 5 - Further speciﬁcation ............................................ 56
CHAPTER3
EXPERIMENTS AND DATA ANALYSIS ........................................................... 58
3.1 Experiments ....................................................................................... 58
3.1.1. Changing the length of conveyor (experiment 1) ................. 59
3.1.2. Changing the speed of conveyor (experiment 2) ................. 60
3.1.3. Adding accumulators (experiment 3) ................................... 60
3.1.4. Changing the speed of casers and
stackers (experiment 4) ....................................................... 60
3.1.5. Adding the accumulators and changing
the speed of casers and stackers (experiment 5) ................ 61
3.1.6. Increasing the efﬁciency of
ﬁlling machines (experiment 6) ............................................ 61
3.1.7. Increasing the efﬁciency of casers (experiment 7) ............... 61
3.1.8. Increasing the efﬁciency of stackers (experiment 8) ............ 62
3.1.9. Increasing the efﬁciency of
blowmolding machines (experiment 9) ................................. 62
3.1 .10. Experimental Method ......................................................... 62
3.2. Results and Discussion ..................................................................... 63
CHAPTER4
CONCLUSION ................................................................................................... 65
APPENDICES ................................................................................................... 67
BIBLIOGRAPHY .............................................................................................. 122

LIST OF TABLES

Table 1. Detailed information of blowmolding machines ..................................... 37
Table 2. Theoretical distribution of elements. ..................................................... 43
Table A1. Machine element data ........................................................................ 69
Table B1. Raw data of time between failure and time to repair of blowmolding

machine #1 ......................................................................................................... 71
Table D1. Utilization of element ........................................................................ 110
Table DZ. Average blocked time of elements ................................................... 111
Table D3. Average busy time of elements ........................................................ 112
Table D4. Average down time of elements ....................................................... 113
Table D5. Average queue of elements .............................................................. 114
Table D6. Average idle time of elements .......................................................... 115
Table D7. Total number of produced of each element ...................................... 116
Table D8. Average number of produced bottles ............................................... 117
Table D9. Output of ANOVA test ...................................................................... 1 18
Table D10. Output of ANOVA test .................................................................... 120

vi

LIST OF FIGURES

Figure 1. Dairy plant packaging line .................................................................... 35
Figure 2. Line divider .......................................................................................... 36
Figure 3. Simulation model layout ....................................................................... 44
Figure 4. Model 1 - Model of blowmolding station ............................................... 45
Figure 5. Experiment analysis of Model 1 ........................................................... 49
Figure 6. Average queue of each element in Model 1 ......................................... 50
Figure 7. Model 2- blowmolding station and wire conveyor l .............................. 51
Figure 8. Model 3 — Model of blowmolding station and wire conveyor I and II ..... 54
Figure 9. Experimental Analysis of Model 3 ........................................................ 54
Figure 10. Model 4 - Model of blowmolding station and wire conveyor I, II and

ﬁlling machines ................................................................................................... 55
Figure 11. Model 5 - Further speciﬁcation ........................................................... 57
Figure 12. Average number of produced bottles for each experiment ................ 64

Figure B1. Theoretical distribution of mean time between failure of blowmolding
machine #1 ......................................................................................................... 72

Figure 82. Theoretical distribution of mean time to repair blowmolding machine
#1 ........................................................................................................................ 72

Figure BS. Theoretical distribution of mean time between failure of blowmolding
machine #2 ......................................................................................................... 73

Figure B4. Theoretical distribution of mean time to repair blowmolding machine
#2 ........................................................................................................................ 73

Figure BS. Theoretical distribution of mean time between failure of blowmolding
machine #3 ......................................................................................................... 74

Figure B6. Theoretical distribution of mean time to repair blowmolding machine
#3 ........................................................................................................................ 74

vii

Figure B7. Theoretical distribution of mean time between failure of blowmolding
machine #4 ......................................................................................................... 75

Figure B8. Theoretical distribution of mean time to repair blowmolding machine
#4 ........................................................................................................................ 75

Figure B9. Theoretical distribution of mean time between failure of conveyor.... 76
Figure B10. Theoretical distribution of mean time to repair conveyor ................. 76

Figure B11. Theoretical distribution of mean time between failure of ﬁlling
machine #1 ......................................................................................................... 77

Figure B12. Theoretical distribution of mean time to repair ﬁlling machine #1 .77

Figure B13. Theoretical distribution of mean time between failure of ﬁlling
machine #2 ......................................................................................................... 78

Figure B14. Theoretical distribution of mean time to repair ﬁlling machine #2 .78
Figure B15..Theoretical distribution of mean time between failure of caser ....... .79
Figure B16. Theoretical distribution of mean time to repair caser ...................... .79
Figure B17. Theoretical distribution of mean time between failure of stacker #1.80
Figure B18. Theoretical distribution of mean time to repair stacker #1 .............. .80
Figure B19. Theoretical distribution of mean time between failure of stacker #281
Figure 820. Theoretical distribution of mean time to repair stacker #2 .............. .81

Figure B21. Theoretical distribution of mean time between failure of cooling
storage ............................................................................................................... .82

Figure 322. Theoretical distribution of mean time to repair cooling storage ...... .82

viii

INTRODUCTION

There are several useful tools that are ﬁnding increasing application for
improving packaging line efﬁciency. Among them, simulation, which addresses
the dynamic interactions of line components and measures overall system
efﬁciency and control stability, is the most useful.

A packaging line simulation study consists of four basic steps: building a
model of a packaging line, simulating the model, analyzing the simulation results,
and making recommendations.

Building a packaging line model involves describing the line machinery
and the logic of its operations. Collection and interpreting data are critical steps in
the process'of making a useful and accurate simulation model.

Simulation does not necessarily provide accurate answers. However, the
technique does allow a simulation practitioner (and a client) to develop and test
various approaches to a problem and to quantify the efﬁciency gains for each.
Packaging lines can be evaluated under varying conditions and operating
characteristics without actually modifying the lines or building them if they do not
exist. Another advantage of simulation modeling is that it forces the user to gain
a full understanding of the process. Valuable insights can be gained even before
the model is built. In this study, a simulation model of a dairy plant was built
based on the data from real dairy plant1 in southeast Michigan and evaluated by

using the discrete simulation software “Taylor ll”.

 

' Speciﬁc plant not identiﬁed at request of management

The overall goal for this study was to ﬁnd the “best possible” solution to

increase the productivity of current system.

The speciﬁc objectives of this research were:
1. To collect and analyze data for the simulation study
2. To develop a model to identify bottlenecks in the system
3. To provide alternative solutions to increase production rate
4. To provide answers to ‘what if' questions such as ‘what if one more ﬁlling
machine is added into the system’, ‘what if the repair time of the blowmolding

machines is reduced’, etc.

CHAPTER 1

LITERATURE REVIEW
1.1. COMPUTER SIMULATION OF A MANUFACTURING/PACKAGING LINE

1.1.1. Deﬁnition

Simulation is the process of designing a model of a real system and
conducting experiments with the model for the purpose of obtaining a better
understanding of the behavior of the system or of evaluating various strategies
and alternatives for the operation of the system (Shannon 1975). In other words,
simulation is an experimental technique and an applied methodology which
seeks to describe and to understand the behavior of systems, to construct
theories or hypotheses that account for the observed behavior, and to use these
theories to predict future behavior or the effect produced by changes in the
operational input set (Pidd 1984; F&H Simulations, 1995).

Simulation is a tool used within a problem-solving process. Problem
solving processes are numerous and evolving. Examples include designing a
new packaging line, choosing a right sized buffer, right sizing and many other
popular processes. Often there is no pre-conﬁgured problem solving process, but
simulation is a tool which can process the decision making criteria in a timely and
cost efﬁcient manner. Simulation may not provide all of the answers. It is a tool to
help understand the system under study (Mott, 1996).

Many manufacturing/packaging systems are good examples of

“collections of interdependent elements portraying random but statistically

predictable behavior.” These systems are often of such size and complexity that
traditional design techniques are inadequate to guarantee that the resulting
design will have the desired cost and performance attributes. Simulation of a
proposed system design or designs can be thought of as a foretelling technique
that lets a system be tested before it has been built. Also when using simulation,
one can make mistakes and correct them ahead of time in a relatively easy and
inexpensive way. Over the years, simulation has become a technique of high
practicality. Many studies show it is one of the most effective tools which can be
used to help solve problems (Sahnnon et al 1980; Ledbetter and Fox 1977; Cook
and Russell 1976).

The actual process of simulation is simple and straightforward. A model of
the system’s operations is built on a personal computer or main-frame computer.
Once built, the simulation model serves as a tool in which proposed changes to
that system can be tested and studied. To give structure to this model building
process, a general purpose simulation language or manufacturing oriented
simulation package is usually used (Banks 1996). Examples of these languages
include SIMSCRIPT ll, GPSS, SLAM ll, AWESIM and MAP/1. Examples of the

software packages include Taylorll, Witness, Arena, Promodel and BPSimuIator.

1.1 .2. Classiﬁcation
Simulation is classiﬁed according to the type of system under study.
Hence, simulation can be either continuous or discrete. If all changes in the state

of a system occur at speciﬁc points in time, the system is of the discrete event

type. For example, a unit of work-in-process arrives at a machine. When all
changes in system state occur continuously over time the system is of the
continuous type. For example, the level of oil in a storage tank rises continuously
as oil is pumped into the tank.

Hybrid systems involve both discrete and continuous changes in system
state. Continuous changes in system state can often be represented by a series
of discrete approximations. Discrete-event techniques have been highly
successful in modeling a large number of systems (Law 1986).

Simulation is classiﬁed as either static or dynamic depending on whether
or not the model variables change over time. The checkout system in a retail
store is an example of a dynamic system. The number of customers in the queue
changes as new ones arrive and others complete the checkout process. All
queuing models are considered to be dynamic models. A ﬁnancial model in a
spreadsheet is generally a static model. One changes a variable, for example the
tax percentage, and studies the effect on the net proﬁt. In such a model, time has
no inﬂuence on the result. A static simulation model is called a Monte Carlo

simulation. (F&H Simulations 1995; Law 1986; Hoover and Perry 1989)

1.1.3. Advantages and disadvantages of simulation

The general beneﬁt of simulation is that it allows a simulation practitioner
to obtain a system wide view of the effect of changes on the system, whether it
exists or not. For example the effect of adding an additional accumulator to a

work station may be predicted by using simple queuing theory. However, the

technique probably is not robust enough to determine the effect the change will
have on the entire system. Increasing the throughput at one workstation might
cause bottlenecks to develop at one or more other workstations. Speciﬁc beneﬁts
of simulation in manufacturing are increased throughput, reduced in-process
inventories, improved utilization of machines and workers, increased on-time
deliveries and reduced capital requirements (Law 1986; Filmer 1994).

The simulation yields information on machine utilization, bottlenecks,
throughput and queue sizes along with the effects of unplanned occurrences,
such as machine breakdowns. A simulation model may be used to perform
experiments. A proposed system can be evaluated before actually implementing
it into a real system. Also an existing system can be “experimented on” without
disturbing it (Law 1986).

On the negative side, simulation is, innately, an imperfect technique.
Simulation produces statistical estimates, rather than exact results. Simulation is
not an optimization technique. It involves only a comparison of alternatives, as
contrasted with identiﬁcation of the optimal design. Models tend to become
unwieldy, involving many combinations of independent variables. Simulation may
be costly, requiring trained simulation model specialists. And, the building of
models is only part of a simulation project. Long modeling lead times can be
involved. The gathering of system details, collection and estimation of data,
building the computer model, verifying, and validating the model, and drawing
appropriate inferences from simulation runs, can consume months of time. Large

amounts of computer time may be needed even though the introduction of high

capacity computer hardware has shortened the simulation runtime. However new
manufacturing-oriented simulation languages and software systems are on the
market and their capabilities are improving. Software includes modeling
languages and includes other tools needed for a balanced simulation study, e.g.,
preparation of input data; graphical support for describing system layouts;
statistical analysis of output; data presentation. Personal computers have
contributed to reducing the cost of computing and shortened modeling lead times
by putting the computing resource under the control of the simulation practitioner

(Law 1986; Filmer 1994; Musselman 1984).

1.1.4. Requirements of simulation software

Software is of considerable importance in simulation and the following
requirements should be met.

1. Must be ﬂexible enough to model the most common characteristics of a
manufacturing system line without the need of a simulation language expert.

2. Must automatically generate detailed simulation output reports with the
statistics required to make design decisions.

The software should support the use of computer graphics to produce
animated, screen-based displays of the movement of entities through the
simulated system to make veriﬁcation and presentation easy. Among its several
advantages, simulation animation greatly enhances communication between the
simulation model builder and second parties responsible for the system being

simulated, for example, manufacturing engineers, managers, clients, etc.

Animation may help the simulation practitioners establish credibility for
themselves in the eyes of the second parties. The second parties can become
more involved in the modeling process, can more easily judge whether the model
simulates reality properly, and can more easily suggest modiﬁcations which
might be made in the system design to improve system performance (Swientek
1993; Carson 1986). Another advantage of watching the animated simulated
system at work is that this may trigger creative ideas about how the system might
be modiﬁed to improve system performance. However, simulation animation is
not a substitute for rigorous model veriﬁcation, model validation, and statistical

analysis of simulation output.

1.2. SETTING UP A SIMULATION STUDY

It has been proposed that there are six steps in a typical simulation study
(Martha 1996; Law 1986; Hoover and Perry 1989). These are listed below.
Commentary on various aspects of these elements follows throughout the rest of
this study.

1. Formulate problem and plan the study

2. Data collection and analysis

.0"

Model building

4. Model veriﬁcation and validation

9'

Experiments and output analysis

6. Documentation, presentation, and implementation of results

A simulation study usually starts when there is a problem with an existing
system, when it is not possible to experiment with an existing system, or when a
system is under design, that is, the system does not exist yet. After clearly
understanding and evaluating management needs and expectations, the
simulation practitioner should determine whether or not simulation is a proper
tool for the analysis of the system under observation. In some instances, an
analytical technique may provide a solution (F&H Simulations 1995).

If simulation modeling is the right technique, the practitioner should begin

by stating objectives clearly and describing the system to be studied.

1.2.1. FORMULATE PROBLEM AND PLAN THE STUDY

Problem formulation can have a signiﬁcant impact on the ultimate success
of the analysis and the implement of the results. Appropriate solutions to
inappropriately formulated problems can not be achieved (Urban 1974). In this
stage, the simulation practitioner deﬁnitively states the study's overall objectives,
how much detail should be included in the system and the speciﬁc issues to be
addressed based on preliminary data from the client, since the client or manager
may not know precisely. Also, the system conﬁgurations to be studied are
described. At this stage the modeler should decide whether to use a general
purpose language (C++, FORTRAN, BASIC), a simulation speciﬁc language
(SIMSCRIPT ll, GPSS, SLAM ll, Arena, or MAP/1), or a manufacturing oriented
simulation package (T aylorll, Witness, HighSpeedSim, Promodel, or

BPSimuIator). Manufacturing oriented simulation software usually has convenient

features like statistical distribution tools, data analysis tools and pre-conﬁgured
model entities (Banks 1996). Project goals should be set at this stage and checks
should be made to be sure that all agendas are underStood completely by all of

the parties involved. (Law 1997)

1.2.2. DATA COLLECTION AND ANALYSIS

During this step, the bulk of the data is collected, reduced, and analyzed
to make the model more explicit. lnforrnation on the system layout, operating
procedures and routing is collected. Information should be acquired from multiple
sources. No single person or document is sufﬁcient. Some people may provide
inaccurate information so true subsystem “experts” must be identiﬁed.

Data are collected to specify model parameters and input probability
distributions. Examples of the types of needed data are arrival times, processing
times, expected time between failures of machines, repair times, travel times,
and setup times (F&H Simulations 1995).

Data can be collected in many ways. Typical sources of data are (Carson
1986);

(1) If the system exists, properly designed time studies usually provide
the most accurate data.

(2) Historical records from earlier studies can be obtained from digital
forms or the production and downtime reports. Information from these sources
should be used carefully, because historical records are usually not designed to

be used for time studies, and because reports may show aggregated information

10

in such a way as to be misleading rather than the speciﬁc data needed for
simulation studies.

(3) The equipment vendor may be able to supply speciﬁcations and
projected performance characteristics (e.g., processing time, time to failure).
Such information can provide a useful starting point but should be used with
caution. Vendor claims are often based on ideal conditions, not the actual
production conditions.

(4) The client can provide estimates of data in some cases, such as
machine capacity, line speed, etc

(5) Based on experience, the simulation practitioner may be in a
position to estimate the statistical distribution form which data of various types
are likely to follow.

If possible, data should be collected on the performance of the existing
system. These data can be used to test the model. The level of model detail
depends on project objectives, performance measures, data availability,
credibility concerns, computer constraints, opinions of system "experts", and
time/money constraints. Data should be collected to suit the study’s objectives.
(Law 1986).

The data may be available in many places and in different formats. For
example, data may be on a production log, production order sheets, and or found
in a computerized data accumulation system. When there is no data available or
collected data are of poor quality, the modeler must measure, estimate and

assume (F&H Simulations, 1995). The modeler should consult with experts in the

11

plant or system before assuming or predicting. A client, management personnel
or decision-maker must participate during the data acquisition period. Usually,
they know the system better than anybody else. Throughout the study,
interaction with plant personnel or system experts is crucial for a successful
simulation project (Law 1997).

Some of the data used to deﬁne a model is deterministic, that is, known
with certainty, but much of it is probabilistic. In simulation, probability distributions
are introduced to describe the stochastic character of a system. Examples of
stochastic events are arrival of parts in a system, size of orders, breakdown
behavior of systems, etc. Often, the use of an appropriate theoretical distribution
is both revealing in the understanding of the system behavior and efﬁcient in the
running of the model (Law 1982; Centeno 1996; F&H Simulations 1995).
Determining the theoretical distribution will be discussed in chapter 2.3.

Discoveries found while collecting and analyzing data may prompt a return
to the problem formulation stage to recast the original problem (Hoover and Perry

1989).

1.2.3. MODEL BUILDING

After the conceptual model has been established and veriﬁed, and data
has been collected and analyzed, a computer-based model must be developed.
Computer program ﬂow charts can be used to deﬁne the ﬂow of the conceptual
logic of the simulation model (F&H Simulations 1995; Hoover and Perry 1989).
Usually it is useful to break the model into several small blocks and combine

those together into one big model later.

12

Too much detail can make a model bigger than necessary make
simulation runtime longer, and make the veriﬁcation and validation processes

more complex and difﬁcult.

1.2.4. MODEL VERIFICATION AND VALIDATION

Modelers, users of the information derived from the results of the
simulation experiments, and people affected by decisions based on such model
information, are all concerned with whether a model and its results are “correct”.
This concern is addressed through the processes of model veriﬁcation and
validation. Converting a conceptual model into a digital model is meaningless,
unless the digital model is thoroughly veriﬁed and validated. The reliability of the
digital model is directly affected by the quality of the veriﬁcation and validation
processes.

Veriﬁcation (or debugging) is the process a modeler uses to determine if a
conceptual model has been correctly translated into a computer program: Does
the model act as it was designed? Is the computer code correctly representing
the process ﬂow diagram? Validation is the process ensuring that the model
behaves the same as the real system and evaluating how much reliance can be .
placed on the predictions made by the model. A valid model can be used to
answer certain “what it” questions (Carson 1989; Sadowski 1989). A decision on
model validity is based on the degree to which the performance measures

predicted by the model and those observed in the real system are similar. In

13

reality, veriﬁcation is often regarded as a part of the validation. (F&H Simulations
1995)

Conceptually, if a simulation model is “valid," it can be used to make
decisions about the system similar to those that would be made if it were feasible
and cost-effective to experiment with the system itself. The ease or difﬁculty of
the validation process depends on the complexity of the system being modeled
and on whether the system currently exists. A simulation model of a complex
system can only be an approximation of the actual system. There is no absolute
model validity. Furthermore, the most valid model is not necessarily the most
cost-effective.

There are three basic approaches used in the validation process (Sargent
1994, 1996). The most common approach is to make a subjective decision based
on the results of various tests and evaluations conducted as part of the model
development process. Another approach is to use a third party to decide whether
the model is valid. The third party should be independent of the model
development team and client. The last approach is to use a scoring model. The
scoring technique is infrequently used.

Validation techniques include animation, comparison with other models,
extreme-condition tests, historical data validation, structured walkthroughs,
historical methods, and traces (Balci and Sargent 1982). Breaking down a big
model into several small sub-units can greatly improve the veriﬁcation and
validation quality. The ﬁnal veriﬁcation has to be performed on a complete model

and the ultimate test of the model’s validity must be how well the model

14

accurately predicts future events. Simulation programs with animation
capabilities can make the veriﬁcation task much easier. Animation allows the
modeler to display all signiﬁcant model elements on the screen to be observed,
show important interactions within the model and explain the nature of the
simulation model to management. Also, it can be used to debug a simulation
computer program. Animation, however, is not a substitute for a statistical
analysis of the simulation output and a "correct" animation is no guarantee of a
valid or debugged model (Law 1997). Validation can be difﬁcult and in some
cases impossible to perform. If the system currently exists, comparisons can be
made to ensure that the model represents the real world. If the system does not
exist, but similar ones do, the simulation results can be compared to similar
systems and, at least, a partial validation performed. If there is no real system to
be compared with the simulation, then validation cannot be performed. If this is
the case, it is recommended that the Turing Test be used, as suggested by Alan
Turing. The Turing test is based on principles of artiﬁcial intelligence. Those who
are familiar with the system design are asked to verify and validate simulation
output. (Schruben 1980; Carson 1989; Hoover and Perry 1989)

Validation and veriﬁcation should not be regarded as steps that can be
tacked onto the end of a project. They are an important part of a process that
starts at the beginning of the' project and evolve throughout model building and
into the period of implementing the experiments. Involving the client in a team
effort makes it more likely that the model will be efﬁcient and will be accepted

and used in the decision-making process.

15

1.2.5. EXPERIMENTS AND OUTPUT ANALYSIS

In this phase, a simulation model can provide answers to the questions
asked when the problem was originally formulated. The system conﬁgurations
that are to be simulated are selected. Experimenting is divided into three steps;
setting experiment conditions, canying out the simulation runs and registering
results (Law 1997). Output analysis is a statistical process that is aimed at
estimating a simulation model's (not necessarily the system's) measures of
performance. Topics of interest are length of each simulation run, wann-up -
period duration, and number of independent simulation runs.

The analysis of the data provided by the simulation model will depend on
the initial objectives of the study and on the type of system being modeled
(Sadowski 1993). There are two types of systems: terminating and non-
terrninating. Statistical experiments are designed to meet the objectives of the
study. Observing a model under one or two experiments usually provides
incomplete information. Therefore, a set of experiments must be analyzed within
the practical range of multiple experimental conditions. Objectives of a simulation
output analysis are determining performance of system conﬁgurations and
comparing alternative system conﬁgurations (Hoover and Peny 1989). Details
will be discussed in chapter 2.4.

By evaluating alternative system designs according to the measures of
performance produced by simulation output analysis, the best, or at least a very

good system design can be selected.

16

1.2.6. DOCUMENTATION, PRESENTATION, AND IMPLEMENTATION OF
RESULTS

Assumptions, computer programs, and results of projects should be
documented. No matter how good the results of the model experiments, if they
can not be communicated convincingly, they are essentially useless. The
documentation and presentation should be done to ensure that the client or
manager understands the results of the study, or at least has the impression that
the study has been carried out well. Usually, for a good presentation of results,
animation, graphics and a discussion of model building/validation process should
be included (Law 1997; F&H Simulations 1995).

All that remains is the implementation of the selected solution. It is obvious
that the users, clients, and manager will not realize the beneﬁts of a lengthy and
costly analysis without proper implementation and acceptance. Since
implementation appears at the end of any sequential list of elements in a
simulation study, it is often the case that implementation is not thought about, or
dealt with until the ﬁnal model or solution has been developed. However,
research suggests that this approach will almost assure failure (Perry et al 1986).
Reasons for unsuccessful implementation include the following: a communication
gap between modeler and user, the inability of users and managers to
understand the technical terminology of the modeler, the undertaking of
implementation too late in the analysis procedure, and resistance to change, or a
lack of coincidence of personal and organizational objectives. In dealing with
these potential obstructions, the general approach is adapted from techniques

used in developing and implementing information systems, namely treating the

17

entire project as a process of change and viewing the analyst as a change agent
(Lucas 1974). This approach requires full involvement of users and modelers
from the beginning of the simulation project. Lucas (1974) suggests the following
elements for Information Systems. These can be adapted as a change plan for
the simulation study:

. A design team consisting of users and analysts

0 An active role for users in the modeling process

0 User-initiated simulation study requests

0 Support of high level management

. Development of favorable attitudes toward study goals

0 Careful planning for implementation from the outset

0 Appropriate attention to training and user manuals.

Advances in personal computer hardware and software for simulation
study may narrow the traditional gap between users and modelers. The newly
found ease with which models can be constructed and experiments run may help
users to understand the simulation process but it may also cause users to draw

statistically toward the wrong conclusion.

1.3. PROBABILITY DISTRIBUTION
1.3.1 . STOCHASTIC BEHAVIOR OF THE SYSTEM

Most manufacturing systems contain one or more stochastic components

(random variables). Inter-arrival times of parts in a system, machine breakdown

18

time, machine repair times and the outcomes of inspecting jobs (e.g., good,
rework, or scrap) are examples of random factors in a manufacturing system. A
probability distribution indicates how the chances are divided. A simulation
engine generates random samples from these input probability distributions as
required throughout the simulation run. The output data from a simulation (e.g.,
daily throughputs, average queue in the system) are also random samples from
probability distributions. Therefore, it is important to correctly model the random
inputs to a simulation model and also to analyze simulation outputs in a proper

manner. (Law 1986)

1.3.2. THEORETICAL DISTRIBUTION AND EMPIRICAL DISTRIBUTION

A probability distribution is a theoretical set of values deﬁned by a set of
probabilities. The frequency with which a value occurs in a simulation depends
upon the probability distribution chosen for that variable. A probability distribution
is characterized by three quantities: the average, the standard deviation, and the
form of the distribution. In a simulation model, the correctness of the average is
the most important, followed by the correctness of the standard deviation and the
form of the distribution (Law 1997). That is, a 10 % error margin in the average is
worse than a 10 % error margin in the standard deviation. An error in the
standard deviation is worse than choosing the wrong distribution.

There are two approaches to determining distributions from data (F&H
Simulations 1995):
0 Use a theoretical probability distribution

. Use an empirical distribution

19

Usually a theoretical probability distribution is the preferred method for
selecting an input probability distribution. It is the often the case that historic data
is not available and an empirical distribution may give an incorrect description
without a fairly large amount of data. Determining an empirical distribution is
difﬁcult, especially when confronted with a large range of possible values. If a
theoretical distribution ﬁts the data adequately, it will represent the parent
population better than an empirical distribution. For example, an empirical
distribution may give a poor ﬁt to the parent distribution in one or both tails of the
distribution. On the other hand, the tails of distributions can not be estimated
accurately from a limited amount of data, whether a theoretical or an empirical
approach is being used to determine the distribution (F&H Simulations 1995).
There is considerable debate, however, about whether using theoretical

distribution is better than an empirical distribution (Fox 1981).

1.3.3. CHOOSING A DISTRIBUTION

The following methods are used in ﬁtting a theoretical distribution to the
data (Schriber 1974):
1) Select a distribution form (e.g., uniform, lognonnal, exponential, Weibull):

The selection can be accomplished by plotting a histogram of the acquired
data and visually comparing its form with the forms of known theoretical
distributions.

2) Estimate values for the parameters in the distribution:

20

Parameters can be estimated from the data. One or more parameters
might alternatively be provided in the form of estimates based on knowledge of
the process which gives source to the data.

3) Goodness-of-ﬁt test :

Goodness-of-ﬁt tests are designed to test whether a data set can be
considered to be a sample from a speciﬁed probability distribution. The two most
frequently used tests are the Pearson’s Chi-square goodness-of-ﬁt test and the
Kolmogorov-Smirnov (K-S) goodness-of-ﬁt test. If the proposed ﬁt is
unacceptable, the modeler can try one or more other distribution forms, or can
use an empirical distribution for the data (Hoover and Perry 1989).

When no data are available, the following procedures can be used (Law
1997):

1. Choose a typical distribution for the application

2. Use a Triangular distribution as a “ﬁrst cut”

3. Choose a distribution from based on knowledge or intuition.

Schriber (1974) suggested several useful methods of quantifying
probabilistic data based on estimates, since there are still a number of
possibilities for getting probabilistic estimates supplied by people (e.g.. vendors,
clients):

(1) Mean Only. If only the mean value (e.g.. mean time to failure) can be
estimated, then just the mean itself might be used: or a distribution centered on
the mean with a range taken as some percentage of the mean might be used: or
in some cases, an exponential distribution might be used.

(2) Range Only (Pessimistic and Optimistic Values). If only the range of
values (e.g., minimum time to failure: maximum time to failure) can be estimated,
then a uniform distribution spanning the range might be used: or a normal

21

distribution can be determined, centered on the midpoint and with a standard
deviation estimated by dividing the range by 6.

(3) Most Likely Value and Range. If these three values can be estimated,
then a triangular distribution can be used or, if the most likely value is at the
midpoint of the range, a normal distribution can be used.

(4) Most likely Value. 10th Percentile and 90th Percentile. If these three
values can be estimated, then a 10-90 triangular distribution can be used; or a
uniform distribution (extending appropriately beyond the 10th and 90th
percentiles) can be used: or, if the most likely value is at the midpoint of the 10-
90 range, a normal distribution (with standard deviation determined
appropriately) can be used.

(5) Mean Value Most Likely Value and Range. If these four values can be
estimated, then a Beta distribution can be used.

Statistical software packages are also commercially available to support
the process of ﬁtting distributions to data, e.g., UNIF IT, ExpertFit, and SIMSTAT

(Banks 1996).

1.3.4. COMMON THEORETICAL DISTRIBUTION

The following are selected descriptions and areas of application of
common theoretical distribution (Law 1997; Hoover and Perry 1989; Centeno
1996).

1. Uniform distribution

The uniform distribution is symmetrical and is used when lower and upper
limits are known, but very little is known about the distribution between these
limits. Intervals that fall outside the limits have a zero probability of occurring.
Within a lower and upper limit each value has an equal chance of occurring.

This distribution is often used in the early stages of a simulation analysis
until information is developed to construct some other distribution, as a

convenient and well understood source of random variation.

22

Parameters are lower limit a and upper limit b.

2. Normal distribution

The normal distribution is usually symmetrical (may be skewed) and 95%
of values are within 1.96 times the standard deviation.

It is used when the average is known and when most values occur near
the average. Numbers, weights, sizes, measurements, and deviations are often
assumed to be normally distributed. Processing times are sometimes normally
distributed, especially if they are manual actions with little variation in the
required time.

Parameters are mean and standard deviation.

3. Exponential distribution

This distribution is used for processes where intervals between events are
independent. The greater the value the less often an event occurs. Values less
than the mean occur more often. Values range from 0 to around 10 times the
mean. The standard deviation of the negative exponential distribution is equal to
the average. In practice, the exponential distribution is often the greatest form of
randomness. The exponential distribution has no memory.

The most important application for the distribution is its use for arrival
processes; customers placing orders, parts arriving at a system. If they are
independent events, the arrival process is exponential. For example, arrival of

customers at a post ofﬁce are independent of each other. Besides arrival

23

processes, there are many other processes that can be described with the
exponential distribution: time between two breakdowns (MTBF), order sizes,
processing times, etc.

Parameter is a mean.

4. Erlang distribution
The erlang distribution involves two parameters; a mean and a K factor.
With K=1 the distribution is a negative exponential. With large K values (about
10) or as K approaches inﬁnity, the distribution approaches a normal distribution.
Applications are processing times, repair times, manual tasks, handling

times and, sometimes, inter-arrival times.

5. Lognormal distribtion

This distribution has a taller “spike” than the erlang distribution. Standard
deviations larger than the mean are allowed.

The lognorrnal is often used as a model of the time to perform manual
tasks such as assembly, inspection, or repair, and has also been used as a
model of the time until failure.

The Iognonnal distribution involves two parameters; a mean and a

standard deviation.

6. Empirical Distribution

24

The empirical distribution allows the possibility of deﬁning multiple “peaks.
For each possible value, the modeler must specify the chance that the event will

occur. Historical data is needed to create an accurate empirical distribution.

7. Gamma distribution

Examples of the gamma distribution are the time to perform a manual
task, the monthly sales of an item, the seconds of CPU time a job will require,
and the deviation of a trajectory from its intended target.

It is characterized by two parameters: shape and scale.

8. Weibull distribution

The weibull distribution is used in reliability theory to model the distribution
of time until failure, particularly for devices where wear or usage is a factor such
as vacuum tubes, ball bearings, and springs.

It is characterized by two parameters: shape and scale.

9. Beta distribution
Common application of the beta distribution is the time to complete an
activity in a project consisting of multiple activities.

It is characterized by two parameters: shape and scale.

10. Logistic distribution

25

It is used for random variables which are constrained to be greater or
equal to 0.
The logistic distribution involves two parameters; a mean and a standard

deviation.

1.4. Statistical Analysis of results

After getting results from several simulation runs, statistical techniques are
used to analyze the results. Statistical analysis is used to estimate a simulation
model’s true measures of performance. Many simulation practitioners make a
single simulation run of somewhat arbitrary length and then treat the resulting
estimates as the true answer for the model (Law 1997). A result that comes from
one simulation run is usually different than the result from another simulation run.
These results are random variables themselves that may have large variances,
and differ greatly from the corresponding real answers. From a simple
experiment of throwing a die, one can not tell that each result has an equal
theoretical probability of 0.17 without a large number of replications. An inﬁnite
number of observations are needed to get exact results. However executing an
inﬁnite number of replications is impossible. Some simulation models of
manufacturing operations take a very long time to execute. The number of
observations in a simulation should large enough to result in the required
accuracy.

To get a number of observations, which is enough to provide required

accuracy, a simple method, “making a number of runs”, can be used (F&H

26

Simulations 1995). If four simulations are run and four outputs are obtained, the
average of the four outputs can be taken as the simulation results. However,
often more accurate methods are required.

A conﬁdence interval in the form of “the average output can be found
between 5,288 and 5,420 with a reliability of 95%” can be used to describe the
output of the simulation results. A large number of observations are needed to
produce a conﬁdence interval. These observations are acquired by repeating the
experiment or by dividing a long experiment into a number of subruns. Choosing
a proper method depends on the objectives of the simulation study and whether
the experiment involves a terminating or non-terminating system. Also warm-up
conditions and the subrun length play an important role in the gathering of

observations. (F&H Simulation 1995; Law and Kelton 1982)

1.4.1. Terminating simulation and non-tenninating simulation

“A terminating simulation is one for which there is a natural event E that
speciﬁes the length of each run (Law and Kelton 1982; Law 1997)”. The event E
often occurs at a time point that has one of the following properties:

. System is “cleaned out”

. Beyond which no useful information is obtained.

There may be reoccurring epochs, sometimes called points of
regeneration, but each epoch starts off fresh. In a terminating system, the ending
state of the previous epoch does not affect the starting state of the current epoch

(Hoover and Perry 1989). An example of a terminating system is a post ofﬁce.

27

When the ofﬁce opens in the morning, the queues are empty. At closing time, the
queues are being emptied.

A non-terminating system is one for which there is no natural event E to
specify the length (end) of a run. The discrete events driving the system continue
to occur indeﬁnitely. A single epoch of the system continues indeﬁnitely and there
is no terminating event. An example of a non-terminating simulation is a
manufacturing plant that never stops. Another example is a manufacturing plant
starts at 8 am. and closes 5 pm. But the products are not emptied. The plant
continues the following morning as it stopped the previous evening.

Closely related to the issues of terminating or non-terminating systems are
the transient and steady-state properties of systems (Sadowski 1993). The
steady state is the situation in which the system is ‘behaving normally”. In steady-
state, the probabilities of possible situations in the system are not inﬂuenced by
the time at which one measures. In terminating simulations, it is generally the
case that, the simulation practitioner is interested in transient behavior, but the
terminating event may occur when the system is behaving as it would in steady
state. In non-terminating simulations, the modeler is usually interested in the
steady-state behavior. Often, however, non-terminating systems never achieve a
steady-state behavior (Hoover and Perry 1989).

Almost every paper and book written on the analysis of simulation output
data deals with the non-terminating, steady state case. However, according to

Law and Kelton (1991), by surveying a large number of simulation practitioners it

28

was discovered that signiﬁcant proportions of simulations in the real world are

actually of the terminating type.

1.4.2. Statistical analysis for terminating simulations

Terminating systems are relatively easy to analyze. A simulation run takes
as long as the “open” times of the system under observation or, if necessary, a
little longer to clear out the system. In terminating simulations, each replication
produces an MD (independent identically distributed) “observation” (Law 1997).
Therefore constructing conﬁdence intervals is relatively simple. Suppose that we
would like to estimate the population mean u, when the random sample size is
reasonably large. Make n independent replications and let X1, X2, Xn be the

resulting "0 random variables. An approximate 100(1-a) percent conﬁdence
interval for H is given by TizsU—(I

Where, 2 = z(1-od2), 517} = f: (Neter et al 1992)

I:
When n becomes inﬁnitely large, the probability of exceeding limits
becomes equal to those of the normal distribution. With more than 30
observations, one may freely use the standard normal distribution (F&H

Simulation 1995).

1.4.3. Statistical analysis for non-terminating simulations
For non-terminating systems, it is necessary to bring the simulation model

to steady state before model generated data is analyzed. All of the data

29

generated before the model reaches steady state should be thrown away. Upon
reaching steady state, it is necessary to decide the length of the single replication
that is to be run. Usually, the method of batching is used to analyze this data
(Martha 1996). Batching refers to breaking the highly correlated, sequential
observations generated by the model, into groups or batches. These batches
would then be treated in the same fashion as replication in the case of
terminating systems.

A batch is based on the level of correlation between observations
separated by a given lag k. Statistical theory tells us that the farther apart two
correlated observations are, the smaller the correlation. So, it is necessary to
compute the correlation factor for various values of the lag k (20-500), graph the
correlation factor, and identify the lag value at which the correlation factor p is
approximately 0. From that process, the number of observations in the batch is
established taking into account that this is a random process, so a safety factor
needs to be added.

Once the batches are formed, each batch is treated as an independent
replication, and an analysis similar to that for a terminating system should be
done. Regardless of the type of system, the simulation practitioner should keep
in mind that the reporting point estimates of the measure of performance are not
particularly helpful. Conﬁdence intervals on critical measures of performance
should be constructed to add credibility and strength to the study.

When analyzing a non-terminating system, it is necessary to bring the

model to steady state before the data generated from the model is used in

30

analysis. Simulations of manufacturing/packaging systems often begin with the
system in an idle or empty state. This results in the output data from the
“beginning” of the simulation not being representative of the “normal” behavior of
the system. Therefore, simulations are often run for a certain amount of time, the
warm-up period, before the output data are analyzed to acquire the desired
measure of performance. This is also known as the starting run. In most cases,
systems with high utilization of machines and long sequences require very long
warm-up period. Including data from the long wann-up time data often results in
inaccurate results (F&H Simulation 1995). In the simple case of a bank
simulation, the queue starts with 0 at an early stage then grows.

There are a number of ways to determine the length of the warm up
period. One method is to simply plot a key simulation parameter as the
simulation repeats, and observe where the model starts repeating its output on
some consistent level. Another method for determining the warm up length with
fewer observations is the Welch method that is generally accepted today
(Stockdale 1997). This method is similar to the above. However, by eliminating
ﬂuctuations in the average, a reasonably smooth plot can be obtained with
relatively small number of observations.

The Welch graphical method is rather complex. It requires running multiple
full length replications of the model. For each replication, for time periods 1, 2...,
n, a key simulation parameter is averaged. Then, the data are plotted, one graph
for each denominator of the moving average, and inspected for its ﬂatness. As

with any other visual method, the Welch method is subject to graphical bias from

31

choosing axis intervals that distort plots by under or over ﬂattening moving
average curves (Welch 1983).

While the Welch graphical method is a good academic tool, modelers can
rarely invest the time required for this technique. Many simulation practitioners
ﬁnd that technique of determining the warm-up period is more complex and time
consuming than development of the model itself. The simple plot technique is
better than guessing, but visually observing output for the warm-up periods does

not present one with easy decision (Stockdale 1997).

32

CHAPTER 2

DEVELOPMENT OF THE SIMULATION MODEL

The research project consisted of the following phases: (F&H Simulation
1995; Martha 1996; Law 1986)

1. Problem formulation

2. Description of the system to be modeled

3. Experimental alternatives

4. Gathering and analyzing the data

5. Computer model building with veriﬁcation and validation

2.1. Problem formulation - Deﬁning the current problem of the dairy plant.

The dairy plant produced ﬁve kinds of milk: skim milk, low fat milk, one
percent, two percent, homogenized (whole milk) and chocolate milk. Milk was
bottled in one-gallon high-density polyethylene (HDPE) bottles and half gallon
HDPE bottles. Gable top cartons were used to bottle small portions.

The packaging machinery set for milk products was: blow molders, wire
conveyors, ﬁlling machines, casers, stackers, and case washers (Figure 1).
Since all of the machine components were linked together, either directly or
indirectly, it was very hard to deﬁne the cause of problems in the packaging line.
If the blowmolders and ﬁlling machines were running well, there often was a

shortage of cases or space for cooling storage. Of course, if the blow molders

33

were not working well, the rest of the line had to wait for bottles; i.e. operators
had to shut down the rest of the line and wait for bottles.

People in the plant have tried to ﬁx these problems, but the problems
appeared to be related and have no clear solutions. Frequently a problem is
caused by multiple factors and uncertainties which all inﬂuence one another.
Even if plant personnel identiﬁed a possible solution, they could not be sure of its
ﬁnancial merits. People at the plant have proposed replacing or overhauling the
old blowmolding machines because the blowmolders are at the start of
packaging line and have had many problems. It was reported that two ﬁlling
machines also had very low utilization of around 60 percent.

The following were the problems of the plant;

. Low productivity

0 Low utilization of ﬁlling machines and stackers

. Alternative possibility of overhauling of existing machine or purchasing

a new machine
In short, the plant wanted to ﬁnd a way to increase the productivity within

its ﬁnancial limit.

2.2. Description of the system to be modeled
The plant produces about 8,640 gallons of milk per hour (one-gallon
plastic bottles). It has an average bottled milk production of 100,000 gal/day.

There are seven pasteurized milk tanks with a total capacity of approximately

70,000 gallons. The factory (Figure 1) runs six days a week with two shifts;

approximately 8.5 hours per shift.

 

   

Filler

    

 

 

 

Caser I Stacker I

  
 

 

Cooling

  

 

 

Storage

      

Blow molders Case washer

out

 

 

 

 

 

Filler I Caser I Stacker I

Figure 1. Dairy plant packaging line

 

 

2.2.1. Blow molding machines

Four blowmolding machines produce one-gallon high-density polyethylene
bottles for milk. About every 7.5 seconds each blowmolding machine mold four
bottles using the “extrusion blow molder.” The process consists of extruding a
hollow tube, called a “parison,” between two halves of a mold. As the mold
closes, it closes the bottom of the parison, leaving the top open for the injection
of air. The warm, soft plastic stretches out under this pressure and forms the
shape of the mold interior. (Hanlon 1992)

After molding, the four bottles are placed on the cooling conveyor and
moved to the trimmer. After trimming, compressed air is blown into the bottle to
check for leakage. If leakage is found, the bottle is rejected and moved to the

grinding room for reuse. lf leaks are not found, the bottles from blowmolder 1, 2,

35

and 3 are moved on a stainless steel conveyor to the wire conveyor. The bottles
from machine 4 are transferred to the wire conveyor directly. Each blowmolder
has its own reject ratio of 1 to 10 percent. Speed and capacity of the blowmolding
machines are shown in Table 1.

The ﬁrst, second, and third blowmolders use the same conveyor, while the
fourth blowmolder uses a different conveyor. After traveling on each conveyor,
the bottles are merged onto a single conveyor in front of the raw milk storage
room. Line dividers are used to direct the ﬂow from blowmolders 1, 2, 3, and
machine 4. A divider blocks off the exit and allows only one line of milk bottles to
ﬂow through at a time. The back pressure on the bottles moves the bottles that
are in position onto the through lane, while keeping the other containers milling
around until each of them is in position (Davis 1994). Currently, the line divider is
set to open for 15 seconds for bottles from the ﬁrst, second, and third machines
and close for 4 seconds to clear up the path, then the divider is reopened for four
seconds for bottles from the fourth machine and closed for four seconds to clear

up the pathway. This procedure repeats throughout the production. (Figure 2)

 

 

 

 

 

 

oooooooo (>00on
0

‘ n ‘ o

O

 

 

 

 

Figure 2. Line divider

36

Table 1. Detailed information of blowmolding machines

 

 

 

 

 

 

 

 

 

Speed Capacity Reject ratio
Blowmolder 1 4 bottles/7 .6 sec 4 1 ~ 10%
Blowmolder 2 4 bottles/7 .8 sec 4 1 ~ 10%
Blowmolder 3 4 bottles/7 .5 sec 4 1 ~ 10%
Blowmolder 4 4 bottles/7 .4 sec 4 1 ~ 10%

 

Two operators run the machines and 4,000 ~ 7,000 bottles are produced

in an hour.

2.2.2. Wire conveyor

The wire conveyor transfers bottles with speed of 1 meter per second and

acts as an accumulator.

2.2.3. Filling machines

The ﬁlling machinery consisted of four components: labeler, date coder,

ﬁller and capper machines. The rotary ﬁllers had 26 ﬁlling heads and ran at the

speed of 4,320 bottles per hour. Filling machines 1 and 2 had the same speed

and capacity but different downtimes. One operator was needed to run each

machine.

37

 

2.2.4. Case washer

After trucks deliver and unload empty cases, the empty cases are cleaned
in the case washer. After cleaning, the cases are moved to one of the casers.
Two operators are needed for the case washer. One operator drives a forklift to
move pallet-loads of empty cases while the other runs the washing machine and

handles the trash in empty cases.

2.2.5. Caser

The caser loads four bottles from ﬁlling machine into each case.

2.2.6. Stacker
The stacker stacks two columns and six rows of cases into a unit (12

cases, 48 bottles).

2.2.7. Cooling Storage

The cooler can hold up to 25,000 cases (100,000 bottles). It maintains a

temperature 35°F. The cooler is connected to the dock area.

2.3. Experimental alternatives

Based on the preliminary study of the system, the following possible
solutions were considered.

. Changing the speed of the conveyor

. Changing the length of the conveyor (acting as an accumulator)

38

. Changing the speed of the ﬁlling machines
0 Minimizing the downtime of the ﬁlling machines
0 Minimizing the downtime of the casers

o Minimizing the downtime of the stackers

The simulation software “Taylor II’ was chosen after consideration of the
study objectives and availability. Taylor II is a product developed by F&H
Simulations. It runs under Microsoft Windows 3.1 and Windows 95, 98, and NT.
The process of using Taylor ll starts with building a model. All model building is
menu driven. A model in Taylor |I consists of four fundamental entities: elements,
jobs, routings, and products. The element types are in/out, machine, buffer,
conveyor, transport, path, aid, warehouse, and reservoir. One or more operations
can take place at an element. The three basic operations are processing,
transport, and storage. Deﬁning a layout is the ﬁrst step when building a model.
Layouts consist of elements. By selecting the elements in sequence, the product
path or routing is deﬁned. Routing descriptions may also be provided from
external ﬁles.

The next step is detailing the model. In this step the parameters are
provided. In addition to a number of default parameters, Taylor ll uses a macro
language called TLI for Taylor Language Interface. TLI is a programming
language that permits modiﬁcations of model behavior in combination with

simulation-speciﬁc predeﬁned and user-deﬁnable variables. TLI can also be used

39

interactively during a simulation run to make queries and updates. Interfaces to
different program language like C, Basic, or Pascal are also possible.

During simulation, zoom, pan, rotate, and pause are options. Modiﬁcations
can be made “on-the-ﬂy.” The time representation is fully user-deﬁnable (hours,
days, seconds, and can be mixed). Output analysis possibilities include
predeﬁned graphics, user-deﬁned graphics, predeﬁned tabular reports, and user-
deﬁned reports. Examples of predeﬁned graphics are queue histograms and
utilization pies. User-deﬁned outputs include bar graphs, stacked bars, and other
business graphics. Predeﬁned tables include job, element and cost reports.

Animation capabilities include both 2-D and 3-D. The 3-D animation can
be shaded. Standard indicators can be shown for elements. Icon libraries for both
2-D and 3-D animation are provided. Each of these libraries contains more than

50 icons.

2.4. Gathering and analyzing the data

There are two fundamental entities in Taylor II that are needed to build a
model: elements and products. Elements are the resources of the model and
products are the entities that are processed by the elements. Elements fall into
three categories: the element, the job, and the stage parameters. Properties that
are related to the physical part of the element are categorized in the element
parameters, such as the capacity, entry and exit condition and the failure rate
etc. Job parameters describe how an operation is done, for example: how long it

takes for the machine cycle, what the batch size is, etc. The deﬁnition of the

40

routing of products through the model is done with the stage parameters of an
element.

The following methods were used to gather data for this study: time
studies, historical records, vendors’ claims, and line managers’ “best guess”.
Some of the data was estimated, especially machine downtimes, repair times
and the arrival times of some of the machine elements. Another reason for
estimation was because of the machine operators’ occasional work overload.
Sometimes operators couldn’t ﬁnd enough time to measure and keep records of
downtimes or repair times. It will be noted when estimated data were used later
in this chapter.

Estimations of the conveyor lengths were made from scaled ﬂoor
drawings, so there is a possibility of some error in the lengths of the conveyors.
The model was based on a two-month span of the daily production log. Each

data element is listed in Appendix A.

2.4.1. Mean Time between Failure (MTBF) and Mean Time to Repair (MTI'R)
To interpret the stochastic behavior of the system, mainly for “Mean Time
between Failure (MTBF)” and “Mean Time to Repair (M'l'l'R)”, an analysis of the
historical data of machine down time was performed.
There are two approaches to determine the distributions from the data:
ﬁtting a theoretical distribution to the data and ﬁtting an empirical distribution to
the data. If a fairly large amount of data can be gained, an empirical distribution

can be used. Since the data set in this study, however, was collected only for two

41

months, the alternative approach, “ﬁtting a theoretical distribution to the data”
was used.

The following three methods were used to ﬁt a theoretical distribution to
the data.

1. Curve ﬁt actual data to a theoretical distribution form - This was done by
plotting a histogram from the data and visually comparing its form with the
forms of known theoretical distributions.

2. Determine the relative goodness of the ﬁtted distribution -This was done
by the statistical goodness-of-ﬁt test e.g. Chi-Square, Kolmogorovsmirnov.

3. Comparing results from 1 and 2 and built-in ﬁtting analysis functions in

Taylor ll.

Some of the data sets have a very small amount of data to ﬁt into a
theoretical distribution. In these cases, the distribution was selected based on the
modeler's knowledge or intuition. The theoretical distributions of MTBF and
MTTR for each element are shown in Table 2.

The simulation engine generated random samples from these distributions
as required throughout each simulation replication. Examples of raw data of
machines down times, repair times, and histograms are shown in Appendix B

(Table B1 and Figure B1 to B22).

42

Table 2. Theoretical distribution of elements.

 

 

 

Elements MTBF MTTR

Lognormal (3234.83,
Blowmolder 1 Beta (19453.45, 0.6, 1.5) 4025.16)
Blowmolder 2 Logistic (35129.47, 24120.27) Exponential (3568.42)

 

Blowmolder 3

Gamma (33438.39, 0.9)

Lognormal (2184.19,
3364.75)

 

 

 

Blowmolder 4 Weibull (35475, 0.7) Lognormal (3100.91 , 3794.6)
Lognormal (1090.43,

Conveyor Beta (53240.87, 0.6, 1.7) 1 153.79)

Filling machine . Lognormal (1605.52,

1 Werull (75868.97, 1.1) 2416.21)

 

Filling machine
2

Beta (30356.84, 0.5, 1.2)

Gamma (1654.74, 0.9)

 

 

 

Caser Weibull (19546.71, 0.5) Weibull (374.37, 0.9)
Stacker 1 Lognormal (284884339304) Lognormal (955.2, 1024.83)
Stacker 2 Gamma (4548429, 0.4) Logistic (996.43, 513.9)

 

 

Cooling storage

 

Logistic (1317935, 141889)

 

Exponential (21 10)

 

2.5. Computer model building, veriﬁcation and validation

The computer model building was split into three phases:

0 Building a layout

. Input of parameters, control logic, etc.

0 Further speciﬁcation

Before building the computer model, a conceptual model was built based

on the system study. It is shown on Figure 3.

43

 

 

 

 

r r I
l Blowmolder!“ I LBlowmoIder#2 I l Blowmolder#3 1 [ Blowmolder“ I

 

 

 

 

 

 

IL Conveyor : L Conveyor I

 

 

 

 

 

L| Llne divider II

I

I Conveyor 1

 

 

 

L Line divider 1
I

 

 

r r
[ Conveyor I [ Conveyor I

 

 

 

|r=iIIIng machine #1 I [Filling machine #2]

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Buffer ] I Buﬂer I
l l

I Calser I L Calser I

I Buffer I f Buffer I

[ Staiker I I StaLker I
F l

I Conveyor I I Conveyor ]

 

 

 

LLCoollng Storage l—l

Figure 3. Simulation model layout

To make veriﬁcation easier and more feasible, the model building process
was divided into several stages.
1. Model of blowmolding station
Model of blowmolding station and wire conveyor l

Model of blowmolding station and wire conveyor l and II

PS9.”

Model of blowmolding station and wire conveyor I, II and ﬁlling machines

5. Further speciﬁcation

2.5.1. Model 1 - Model of blowmolding station (Figure 4)

In Figure 4, element numbers 1, 5, 9, and 13, the in/out elements,
represented inputs of plastic resin. The default capacity was 2 with zero job time.
This means the resin will be supplied to the ﬁlling machines endlessly during the
simulation run. Element numbers 1, 5, 9 and 13 were assigned product codes
from 1 to 4. In reality there was no difference in bottles from each machines,
however, by assigning different product codes, the veriﬁcation and validation

processes could be done more easily.

mlnvlur ll [1|
E‘I]

 

 

 

Figure 4. Model 1 - Model of blowmolding station

45

Element numbers 2, 6, 10 and 14 represented the extrusion blow molding
machines. Each machine had the capacity of 4 with a production time of about 7
seconds per 4 bottles. Since 4 bottles were produced and sent out at the same
time, “batch” and “out batch” commands were used.

Element numbers 3, 7, 11 and 15, represented the cooling tables. Each
cooling table had the capacity of 20 bottles. During production, the cooling table
always had a stock of 16 bottles. To simulate this behavior, the TLI (Taylor
Language Interface) command of “elqueue“ was used. The “elqueue[x]” means
the current number of products available at element x. By adding “elqueue[3]>16”
in the “exit condition” section, the cooling table in the model always had enough
room for 16 bottles plus another 4 bottles to be produced from a blowmolding
machine.

Element numbers 4, 8, 12 and 16 represented the trimmers. The trimmers
have job times of 1.9 seconds with the capacity of 12 bottles. Again the
command, “elqueue[4]>8” was used in the “Exit condition” section to simulate the
stock of 8 bottles in the trimmer and the space for 4 bottles from the cooling
table. To simulate the reject ratio of bottles, a TLI command of “bernoulli[X,Y,Z]”
was introduced. The “bemoulli[X,Y,Z]” returns a value from a Bernoulli
distribution, which is: in x% of the cases y is returned, in (100 - x)% of the cases
2 is returned. So “bernoulli[90,19,17]” sent 90% of bottles to element number 19
and 10% of the bottles to the element number 17, the regrinder, for reuse of the

plastics. Each blowmolder had an individualized reject ratio.

46

Element number 17 represented the regrinder. After regrinding, resin was
put back into each blowmolding machines in the real system. But, in the
simulation, enough stock of resin was deﬁned (stock of 2 with processing time of
zero), so the plastic from the regrinder did not go back to the “In/Out” element for
the blowmolders in the model. Element number 18 represented the “In/Out"
element, a sinksource function, which is typically used at the beginning or at the
end of a line. It generated and ”ate” products.

Element number 19 represented the big buffer. All of the bottles, except
rejected bottles, from blowmolding machines 1, 2, 3 and 4 were sent to this
element. This element does not exist in the plants. For the purpose of
veriﬁcation, a short job time with a high capacity buffer was introduced.

Finally, element number 20 represented the “In/Out” which absorbs the
products from the previous elements. HDPE bottles, size of 15 centimeters, were
also deﬁned in the “Products” sub menu in the “Model” menu.

The route listing is shown in Appendix C. To verify the computer model, a
run time of ﬁve hours and replications of ten runs were executed.

From simple calculations, the production of bottles can be estimated.

Blowmolder number 1

4 bottles per 7.6 seconds = 0.52 bottles per second

0.52 bottles x 3,600 seconds = 1,894.7 bottles per hour

1,894.7 bottles per hour x 90 % = 1,705.2 bottles per hour

Blowmolder number 2

4 bottles per 7.8 seconds = 0.51 bottles per second

47

0.51 bottles x 3,600 seconds = 1,846.1 bottles per hour
1,846.1 bottles per hour x 92 % = 1,698.4 bottles per hour
Blowmolder number 3

4 bottles per 7.5 seconds = 0.53 bottles per second

0.53 bottles x 3,600 seconds = 1,920 bottles per hour
1,920 bottles per hour x 96 % = 1,843.2 bottles per hour
Blowmolder number 4

4 bottles per 7.4 seconds = 0.54 bottles per second

0.54 bottles x 3,600 seconds = 1,945.9 bottles per hour

1,945.9 bottles per hour x 93 % = 1,809.7 bottles per hour

Average total number of bottles produced per 5 hours;
(1,705.263 + 1,698.462 + 1,843.2 + 1,809.7297) x 5 = approximately 35,283

bottles.

For comparison, the results of 10, 5 hour long simulations are presented in
the following section. To ﬁnd the number of bottles produced, the TLI command
of “produced[X]” was introduced. The TLI command, “produced[19]” returned the
number of products produced in job 19.

Using the built-in analyzer in the “Experiments” sub-menu of the
“Simulate” menu, an average of 34,616 bottles per 5 hours was found between
34,5837 bottles and 34,6492 bottles with a conﬁdence interval of 95% (Figure

5).

48

    
   
  

Ito-.3 0'... A. 2" In‘!- _- n l'.) .‘u.-- “' '.._..

 

,1 . errment -'na :1; '

Confidence Intervals

   

34583 .75

   
 
   
 
    

produced[1 9]
Average : 34616.
Std. dev. 145.76

Precis. +1. : 0.09%
Correlation

 

 

95.00% confidence interval III observations 1

Figure 5. Experiment analysis of Model 1

To ﬁnd the average queue of products at element X, the “avgqueue[X]”
command was introduced. After 5 hours of running time, the average queue of
each element was measured. The results are shown in Figure 6. In Figure 6,
each of the blowmolding machines show 4 products in the queue and the cooling

tables and the trimmers also have adequate amounts of products.

49

 

lblowmolder lcooling table ntn‘mmer

 

 

a 17.16 17.38
18 16.12

16 _1 15.40

 

 

 

 

 

 

machine#1 machine#2 machine#3 nach'nerM

 

 

Figure 6. Average queue of each element in Model 1

After comparing the calculated results and simulated results, it was

concluded that this model behaved as intended.

2.5.2. Model 2 - Model of blowmolding station and wire conveyor l

Element numbers 4, 8, and 12 sent bottles to the conveyor numbers 21,
20, and 19 respectively. To describe this behavior, modiﬁcation of the
“bemoulli[X,Y,Z]” was required. In model 1 (Figure 4), all accepted bottles were
sent to the same buffer, but this time each machine was assigned to a different

conveyor. (Figure 7)

50

 

-_ |.wlnr II l3]

 

 

 

Figure 7. Model 2- blowmolding station and wire conveyor I

To describe the behavior of the line divider at the beginning of conveyor
25, User-deﬁned function and “Userevents” were introduced. Using “function
editor", four functions were deﬁned.

function open22 (open conveyor 22)

elsend[22]:=1

elsend[24]:=0

function open24 (open conveyor 24)

elsend[22]:=0

elsend[24]:=1

51

function close22 (close conveyor 22)

elsend[22]:=0

elsend[24]:=0

function close24 (close conveyor 24)

elsend[22]:=0

elsend[24]:=0
These functions executed the following:

The line divider was set to open for 15 seconds for the bottles from the
blowmolding machines numbers 1, 2 and 3 and closed for 4 seconds to clear the
path, followed by open for 4 seconds for bottles from blowmolding machine
number 4 and closed for 4 seconds to clear the pathway.

Using the “Userevents” sub-menu in the “Model” menu, each open and
close time was entered. The “Userevents” repeated every 27 seconds throughout
the entire run of a simulation.

Element number 26 represented the big buffer. All of the bottles from
blowmolding machines were sent to this element. The element does not exist in
the actual plant, however, for the purpose of veriﬁcation, a short job time with a
high capacity buffer was introduced.

The route listing is shown in Appendix C.

To verify the model, a visual check of the model in the screen was made
and ten, one hour long, simulation runs were executed. To verify the model
visually, the model was set to run in speed of 1, a full animation view and the

screen was refreshed at a rate of 1 unit (second). 80 the screen was updated

52

every second. Also the TLI command of “prodqueue[x,y] (element, product)” was
introduced. This command gives the current number of products with product
code y at element x. After one hour of run, the number of products was counted
at conveyor 25, immediately after the line divider, by TLI command
“prodqueue[x,y]”

prodqueue[25,1] = 244

prodqueue[25,2] = 236

prodqueue[25,3] = 258

prodqueue[25,4] = 254

The four products maintained the same ratio in the conveyor, after the line
divider. Therefore, it was concluded that the line divider used in the model acted

as intended.

2.5.3. Model 3 - Model of blowmolding station and wire conveyor l and Il

Elements 23 to 26 and 39 to 40 represent wire conveyor. After the ﬁrst line
divider, the bottles traveled through the wire conveyor and were divided at four
seconds each. At the end of conveyor 32, another line divider sent the bottles to
each ﬁlling machine at the same ratio of time, 4 seconds per machine. To
simulate this behavior, the stage parameter of “if time|8<4 then 33 else 34” was
used in the “send to” section.

To verify the model ﬁve one-hour long replications of the simulation were
executed. The results (Figure 9) show that the number of bottles supplied to

conveyor 36 and 39, were nearly identical.

53

mlaylnr II [I]

 

 

Figure 8. Model 3 - Model of blowmolding station and wire conveyor l and II

- 23'

 

Confidence Intervals

3231 .58 3242.02 producedlZ-W]

   
 

 

Jag? 3173i 0
bid dew 17 87
Precrz: 4!- ITI 70%
Correlation ‘ 0.16

3150.80 3195.20
Av

 

95.0096 conﬁdence Interval 5 observations

 

 

 

Figure 9. Experiment Analysis of Model 3

54

2.5.4. Model 4 - Model of blowmolding station and wire conveyor I, II and filling
machines
Model 4 included the rest of the machines; ﬁlling machines, casers,

stackers and cooling storage (Figure 10).

m1 Inylrll [11

TIT.—

 

 

 

Figure 10. Model 4 - Model of blowmolding station and wire conveyor I, II and

ﬁlling machines

A new product code was introduced in elements 40 and 46, casers, to

generate icons representing cases by using the “product[C]:=5” command. Also,

the batch size was changed from 4 to 1 so that 4 bottles become 1 case.

55

Again, a new product code was used in elements 42 and 48, stackers,
using the “product[C]:=6” command. Batch size was changed from 12 to 1 so that
12 cases became 1 batch. The sizes of products 5 and 6 were also deﬁned as

0.33 meters and 0.66 meters, respectively.

2.5.5. Model 5 - Further speciﬁcation
Up to this point, the model had been designed to ﬁt an unrealistic
situation, no machine downtime, no unwanted waiting time and no excessive
queue build up. To ﬁne tune the model, that is, to add stochastic behavior to the
elements, mean time between failure (MTBF) and mean time to repair (MTTR)
were deﬁned for all elements and the parameters for animation were introduced.
Also for visual presentation purposes, the icons representing milk bottles

were changed to new bottle-look-alike icons (Figure 11).

56

Simuldlrun control F-

 

 

 

Figure 11. Model 5 - Further speciﬁcation

57

CHAPTER 3

EXPERIMENTS AND DATA ANALYSIS

The plant starts production about seven o’clock in the morning and shuts
down after eleven o’clock in the evening. So, there is a natural event E that
speciﬁes the length of each run. Every night, bottles and milk are cleaned out so
that the end condition doesn’t affect the start condition of the plant or the model.
It can be concluded that the milk plant is a terminating system.

To analyze the simulation data, thirty replications of sixteen hour long
simulation runs were executed. A sixteen hour long simulation run took about 45
minutes using 200 MHz Intel Pentium CPU based personal computer. To
evaluate the system, the following parameters were measured; utilization, block
time, busy time, down time, average queue in the system, idle time, and total
number of ﬁlled one-gallon milk containers that were produced. Since Taylor II
can write the simulation output to a spreadsheet program, data was collected and
sorted using Microsoft Excel 97.

The total number of ﬁlled milk containers produced in a 16-hour run was
ranged between 97,513 and 100,246 with a reliability of 95%. The other outputs

of the 30 runs of simulation are shown in Appendix D.

3.1 Experiments

Based on the output of the simulation of the existing system and the

questions from plant personnel, the following experiments were devised;

58

1. Changing the length of conveyor

Changing the speed of conveyor

Adding accumulators

Changing the speed of casers and stackers

Adding the accumulators and changing the speed of casers and stackers

Increasing the efﬁciency of ﬁlling machines

>195»sz

Increasing the efﬁciency of casers

Increasing the efﬁciency of stackers

s05»

Increasing the efﬁciency of blowmolding machines

There could have been other experiments, such as adding a blowmolder
or replacing the current blowmolders. However, the current plant situation does
not allow for new equipment or overhauling equipment because of ﬁnancial and

space constraints.

3.1.1. Changing the length of conveyor (experiment 1)

The length of the conveyor from the blowmolding station to the ﬁlling
machines was 369.83 meters, which could hold up to 2,465 bottles, enough for
2,054 seconds of operation. During the simulation, the average number of bottles
in the conveyor was 506. So, 1,595 bottles could be accumulated in the case of
failure of ﬁlling machines. Also, from the Table DZ (average blocked time of
elements), there is almost no blocked time at the blowmolding stations. Therefore

it was concluded that the conveyors between the blowmolding station and ﬁlling

59

machines had enough capacity to hold the empty bottles. There was no need for

an experiment to change the length of conveyor.

3.1.2. Changing the speed of conveyor (experiment 2)
Two different speeds of conveyor were tested. The default speed of 1
meter per second was changed to 1.25 meters per second and 1.5 meters per

second.

3.1.3. Adding accumulators (experiment 3)

Four accumulators were added in front of the casers and the stackers,
respectively. The capacities of the accumulators were calculated based on the
average blocked time of casers and stackers.

The capacity for each accumulator was;

Accumulator number 1 (before caser number 1) - 380 bottles

Accumulator number 2 (before stacker number 1) — 180 bottles

Accumulator number 3 (before caser number 2) - 230 bottles

Accumulator number 4 (before stacker number 2) — 20 bottles

3.1.4. Changing the speed of casers and stackers (experiment 4)

In packaging lines, machines before and after the ﬁlling machine generally
have higher capacities than the ﬁlling machine to give a “pull out” effect. The
casers and stackers in the plant had the same speed as ﬁlling machines. To

simulate “pull out” effect the speed of casers and stackers were changed to 7.5

60

seconds and 33.3 seconds (10 percent and 20 percent increases in speed),

respectively.

3.1.5. Adding the accumulators and changing the speed of casers and stackers
(experiment 5)

Experiment 3 and 4 were applied in one experiment model.

3.1.6. Increasing the efﬁciency of ﬁlling machines (experiment 6)

There are several ways to increase the efﬁciency of the ﬁlling machines,
such as purchasing new equipment, overhauling old machines, or improving
maintenance. However, the current plant situation only allows faster reaction and
shorter repair time by maintenance department. So increasing machines speed
or minimizing downtime of the ﬁlling machines were not feasible solutions. To
increase the efﬁciency of the ﬁlling machines, the technique of minimizing the
repair time of the ﬁlling machines was used. Mean time to repair of ﬁlling
machine number 1 and 2 were changed to 802.8 and 827.37 (50 percent

decreases in time), respectively.

3.1.7. Increasing the efﬁciency of casers (experiment 7)
To increase the efﬁciency of casers, the technique of minimizing the repair
time of the casers was used. Mean time to repair of casers number 1 and 2 were

changed to 187 (50 percent decreases in time).

61

3.1.8. Increasing the efﬁciency of stackers (experiment 8)
To increase the efﬁciency of the stackers, the technique of minimizing the
repair time of the stackers was used. Mean time to repair of stackers number 1

and 2 were changed to 478 and 498 (50 percent decreases in time), respectively.

3.1.9. Increasing the efﬁciency of blowmolding machines (experiment 9)

From the basic equipment capacity study, it was concluded that the
blowmolding machines were a bottleneck in the existing system. The
blowmolding machines did not supply enough bottles for the rest of the line. Even
before performing the experiment it was obvious that increasing the efﬁciency of
the blowmolding stations would improve the production rate of the system.

To increase the efﬁciency of the blowmolding machines, the technique of
minimizing the repair time of the blowmolding machines was used. Mean time to
repair of blowmolding machine number 1, 2, 3 and 4 were changed to 1,617.4,

1,784.2, 1,092.1, and 1,550.4, respectively.

3.1 . 10. Experimental Method

All experiments were divided into three steps: adjusting experiment
conditions, carrying out the simulation, and registering results. Analysis of
variance (ANOVA) and multiple comparison, namely Fisher’s Least Signiﬁcant
Difference, performed by Minitab version 11 for Windows from Minitab lnc., were

employed to compare the proposed and original models.

62

3.2. Results and Discussion

The results of the experiments are shown in Table D1 to D8. The result of
the statistical analysis is presented in Table D9.

Figure 12 the ANOVA test, shows that the average number of ﬁlled milk
bottles from experiment 5, 3, 7, and 9 were different from the results of the
original model. Adding the accumulators and changing the speed of casers and
stackers, adding accumulators, increasing the efﬁciency of casers, and
increasing the efﬁciency of blowmolding machines can be recommended to
improve the production rate, respectively. The total number of ﬁlled milk
containers produced in 16 hours was found to be between 103,465 and 106,135
with a conﬁdence interval of 95 percent by reducing the repair time of
blowmolding stations to half of the current repair time. About 5.98 percent
improvement in production rate was obtained. Experiment 5, 3, and 7 show
improved production rate about 2.14 percent, 2.44 percent, and 3.04 percent,
respectively.

One additional experiment was performed, combining the experiments 7
and 9, reducing repair time of blowmolding machines and casers. The total
number of ﬁlled milk containers produced in this experiment was found to be
between 104,713 and 106,071 with a conﬁdence interval of 95%. The result of
statistical analysis is presented in Table 010 and it is not signiﬁcantly different
from that of experiment 9, increasing the efﬁciency of blowmolding machine.

Therefore it can be concluded that increasing the efﬁciency of

blowmolding machines by putting more time and effort to reduce the repair time

63

 

is the most suitable solution to improve the output of the current line considering

inadequate manpower, spatial, and ﬁnancial limitations in the plant.

104800
101888
100992 101296
99888
. 99344 99424 993.19 —1
98880 ,._ _
98144 —

em Original E106 Expz Exp4 Exp8 Exp5 Exp3 Em? Expo
Experiment

 

 

average produced bottles

§§§§§§§

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 12. Average number of produced bottles for each experiment

CHAPTER 4

CONCLUSION

The simulation program is a useful tool for packaging line design and
optimization. Packaging line variables including the efﬁciency of equipment,
downtime of equipment, and blocked time can be analyzed. Another advantage
is that even before actually building a simulation model, a simulation practitioner
can gain understanding of the line while collecting data and studying the system.

A simulation of a dairy plant packaging line was built to optimize the line
efﬁciency and to solve current problems on the packaging line. Data were
collected and analyzed to build simulation models.

From the simulation study, it was found that the blowmolding machines
were a bottleneck in the system. The blowmolding machines did not supply
enough bottles for the rest of the line.

Ten experimental models have been built and run to provide alternative
solutions to increase production rate and to answer ‘what if’ questions. From the
ten experimental models, increasing the efﬁciency of blowmolding machines by
reducing the repair time was the most beneﬁcial approach to improving the
output of the current line.

There has been no implementation of the simulation results to date.
However the simulation model predictions agreed very well with actual packaging
line results. The models provided a quick and inexpensive means to identify

bottlenecks and critical parameters to adjust. However, still it takes long time for

65

an average plant packaging engineer to learn the simulation software and
requires certain amount of programming skills and statistical knowledge to
analyze the input data and the output from simulation model runs.

The model can be utilized to evaluate the effectiveness of new equipment
to replace existing machines, in addition to being used to design new packaging
line for new plant. In this case, the modeler can readily evaluate numerous

equipment parameters to identify potential improvement and problems.

66

APPENDICES

67

APPENDIX A

MACHINE ELEMENT DATA

68

Table A1. Machine element data

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Element Speed Capacity Length ,
Blowmolder #1 7.6 seconds/4 bottles 4 bottles
Blowmolder #2 7.8 seconds/4 bottles 4 bottles
Blowmolder #3 7.5 seconds/4 bottles 4 bottles
Blowmolder #4 7.4 seconds/4 bottles 4 bottles
. 7.45
Stainless steel conveyor 1.9 meters/second 49 bottles meters
72.45
Conveyor from blowmolder #4 to 1 meters/second
ﬁrst line divider 482 bottles meters
Conveyor from stainless steel 1 meters/second 17.85
conveyor to ﬁrst line divider 119 bottles meters
Conveyor from the ﬁrst line 1 meters/second 1151 bottles 173.08
divider to the second line divider meters
Conveyor from the second line 1 meters/second 469 bottles 70.5
divider to the ﬁlling machine #1 meters
. 28.5
Conveyor from the second Ilne 1 meters/second
divider to the ﬁlling machine #2 189 ”was meters
Filling machine #1 0.833 seconds/bottle 26 bottles
Filling machine #2 0.833seconds/bottle 26 bottles
Caser #1 and #2 3.33 seconds/case 4 bottles
Stacker #1 and #2 40 seconds/load 12 cases
Chain conveyor from the stacker
#1 to the cooling storage 0.14 meters/second 13 loads 9 meters
Chain conveyor from the stacker 0.14 meters/second 34 I o a d s 23 meters
#2 to the coolan storage
2090loads
Cooling storage (about 25000
cases)

 

 

 

 

 

* Bottle - 15 centimeter x 15 centimeter (length x width)
* Plastic case - 33 centimeter x 33 centimeter (length x width)

69

APPENDIX 8

EXAMPLE OF RAW DATA OF TIME BETWEEN FAILURE AND TIME TO
REPAIR

70

Table B1. Raw data of time between failure and time to repair of blowmolding
machine #1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

No Time to Time between N 0 Time to Time between
Repalr Fallure ' Repalr Fallure
1 45 240 30 240 480
2 10 420 31 30 650
3 20 150 32 45 1120
4 20 405 33 60 150
5 45 355 34 60 10
6 85 50 35 35 350
7 10 300 36 10 90
8 45 10 37 45 810
9 165 450 38 15 65
10 45 240 39 360 165
11 10 60 40 10 665
12 180 90 41 30 245
13 10 30 42 45 30
14 120 60 43 10 420
15 50 120 44 10 60
16 30 90 45 90 360
17 100 30 46 30 30
18 150 350 47 10 120
19 12 60 48 20 840
20 10 540 49 10 355
21 10 570 50 10 270
22 100 100 51 45 1080
23 45 540 52 240 420
24 30 810 53 20 300
25 15 540 54 45 60
26 55 10 55 10 240
27 45 540 56 15 450
28 45 360 57 30 1130
29 30 25 58 10 295

 

 

 

 

 

 

 

 

* Unit: minute

71

 

 

Beta
W eibull
Gamma
Erlang

Normal
Logistic

Uniform

 

Distribution Par 1 Par2 Par3

Score

19453.45 0.60 1.50 5

19453.45 1. 20
19453.45 1. 20

194 4:3 45 1.00
19453. 45.7405. 43
19453. 45.7405. 43

Lognormal 1945345740543

- 1069364960053

PearsonTS 19453.45 3.20

 

T Gamma

 

Logistic Lognorma

l
I
I Distribution Fit Analysrs for 58 values. Best ﬁtzseta

Figure B1. Theoretical distribution of mean time between failure of blowmolding

machine #1

 

   

PearsonTS

 

 

Weibull
Logistic
Gamma
Negexp
Erlang

Uniform
Normal

 

Distribution Par 1 Par 2 Par 3
Lognormal 3234.83 4025.16
Beta 2

334.83 0.40 2.30
3234.83 0.90
3234.83 4025.16

3234 3 0.60

PearsonTS 3234. 83 2'50

-3736. 9610206. 61
3234.83 4025. 16

Score

58
62
62
64

 

\Iegexp Er‘ang Pearson

Distribution Fit Analysis for 58 values. Best ﬁt:LognormaI

 

h =Gamma
Uni rm Norma

 

Figure BZ. Theoretical distribution of mean time to repair blowmolding machine

#1

72

 

 

 

 

 

 

Distribution

  
 
 

Logbﬁc
Normal

Lognormal

Par 1 Par 2 Par 3

35129. 424 120 27
35129. 424120. 27
352 70. 70 0.90
35129.47 1. 40
35129.47

35129.47 2. 00
3561.29 47 2.107
8. 077690 U2
35129. 424120 2?
35129.47 4.10

Score

 

    

Er ang Gamma Uni

Distribution Fit Analysis for 57 values. Best ﬁt:Logistic

 

Figure B3. Theoretical distribution of mean time between failure of blowmolding

machine #2

 

Wei Li

  

rm Lognorma

PearsonTS

 

 

Distribution

Negexp
Erlang
Lognormal

PearsonTS
Logistic
Normal
Uniform

 

Par 1 Par2 Par3

35 68. 4
3568. 42 1.00
3568. 42 3712 88

8. 2.90
3568.42 3712.88
3568.42 3712.88
286247999931

Score

15
15
23
25

2
2
3
44

48
54

\ICOV

 

Lo norma

 

Wei PearsonTS Logistic

Distribution Fit Analysis for 5.? values. Best ﬁt:Negexp

 

Figure B4. Theoretical distribution of mean time to repair blowmolding machine

#2

73

 

 

 

 

 

 
  

 

    

     
 
  
  
 

 

 

 

 

 

 

Distribution Par 1 Par 2 Par 3 Score
Gamma 33438. 9 0.90 12
Negexp 334' 8.’ 9 15
Er ang 334 8. 9 1.00 15
Weibull 334 8.’ 9 1.00 15
334’ 8.’ 90.40 1.20 24
Lognormal 334‘ R '- Q50 m 86 34
Normal 334. 8 195920 86 57
Logistic 334 Fl ”-9140 in en 63
Uniform 2877839565514 64
PearsonTS 33438.39 2.90 .73

 

 

      

_ognorma Norma Logistic PearsonTS

Distribution Fit Analysis for 62 values. Best ﬁtGamma

 

 

Figure B5. Theoretical distribution of mean time between failure of blowmolding
machine #3

 

 

Distribution Par 1 Par 2 Par 3 Score
Lognormal 2184.19 3364.75 72
Weibull 2184.19 0.60 85
Negexp 2184.19 103
Gamma 2184.19 0.40 104
PearsonTS 2184.19 2.40 121
eta 2184.19 0.3I 2 70 123
Normal 2184.19 3364.75 3
Logistic 2184.19 3364.75 222
Uniform 36437230121 1 253

 

 

 

ii

  

I .
.

PeaSnTS

 

-oinormal Wei u h Gamma

Beta Norma Logistic

 

Distribution Fit analysis for 62 values. Best ﬁt:Lognormal

 

 

Figure BB. Theoretical distribution of mean time to repair blowmolding machine
#3

74

 

 

Distribution Par 1 Par 2 Par 3 Score
Weibull 35475.00 0.70 5
Negexp 475.00

Erlang 35475.00 1 00 9
Gamma 5475.00 0 6 11
Beta 35475. 00 0. 30 1.50 15
Lognormal 35475. 005691. 45 23
Logistic 35475. 085691. 45 24
Normal 35475. 005691. 45 4B
PearsonTS 3754 5. 020 49
Uniform -43664. 9114614. 9 51

 

 

 

   

_ognorma Logistic Norma P90arsr15

Distribution Fit Analysis for 44 values. Best ﬁt:Weibull

 

 

 

 

Figure B7. Theoretical distribution of mean time between failure of blowmolding
machine #4

 

   
 
 
 
 
 
 
 
 
 
  

Distribution Par 1 Par2 Pai 3 Score

3 Lognormal 3100. 91 3794 6.0 18

g Wéibull 3100.91 0. 90 24

t PearsonT5 3100.91 2 70 27

{ Gamma 3100.91 0. 70 27

; Nege 0 3100.91 43 l
Erlang 3100.91 1. 00 43 l
=. Beta 3100. 91 0. 40 1.90 48

. I lniform 8471. 53673. 34 65 l
9‘ Logistic 3100. 913 794 no 65 i;
i P-lijil'i ial 3100.91 3794.60 72 ‘ '

 

Erang ' ' "7 7 Uniform

Distribution Fit Analysis liar 44 values. Best ﬁtchigi‘lormal

 

Figure B8. Theoretical distribution of mean time to repair blowmolding machine

75

 

 

   
  
 
 
 
 
  
  
    
   

 

Distribution Par 1 Par 2 Par 3 Score
Beta 53240.87 0.60 1 70 1
Normal 5324085100329 1
Logistic 53240815100329 1
Negexo 53240.87 2
Erlang 53240.87 1 00 2
Weibull 23240. 87 1.10 2
Gamma 53240 87110 2
Lognormal 53240. 851003. 29 5

I Inifor rm 35099. 414 1581. 1 8
PearsoriTS 53240. 873.10 15

 

 

    

Wei Gamma PearsonT5

Distribution Fit Analysis for 23 values. Best ﬁt:Beta

 

Figure B9. Theoretical distribution of mean time between failure of conveyor

 

          

   

     

Distribution Par 1 Par 2 Par 3 Score
Lognormal 0190 43 1153 7-9 1
P9arsonT5 1090.43 2 90 3
Negexo 1090.43 4
Erlang 1090.43 1.00 4
Weibull 1090.43 1.00 4
Gamma 1090.43 0.90 8
Beta 1090.43 0.50 2.00 11
Logistic 1090.43 1153.79 12
Uniform 907. 99 3088. 86 17
Normal 1090. 43 1153 79 17

 

 

PearsonTS

   

Gamma Beta Logistic

 

. Distribution Fit Analyse for 7’3 values. Best ﬁt: Li: igrii :irmal

Figure B10. Theoretical distribution of mean time to repair conveyor

 

 

Distribution Par 1 Par 2 Par 3 Score
Weibull 75868.97 1.10 1
Negexp 868.97 1
Erlang 7586897 1.00 1
Gamma 7586897 1.00 1
Beta 75868.97 0.60 2.20 3
Logistic 7586897406689 3
Lognormal 7586897406689 4
Normal 7586897406689 8
PearsonT5 75868.97 3.00 12
Uniform 5241862041565 13

 

 

   

PearsonT5

_ogistic -__

 

Distribution Fit Analysis for 29 values. Best ﬁt:Weibull

 

 

Figure B11. Theoretical distribution of mean time between failure of ﬁlling
machine #1

 

 

 
   
 
  
 

Distribution Par 1 Par 2 Par 3 Score
Lognormal 1605.52 2416.21 6
PearsonTS 1605.52 2.40 30
Normal 160552241621 32
Negex 605. 32
Weibul 1605.52 0.60 33
Gamma 1605.52 0.40 33
Logistic 1605.52 2416.21 46
Beta 1605.52 0.20 1.10 46
Uniform 257949579852 59

 

 

 

Samma

Distribution Fit Analysis for 29 values. Best ﬁt:L0gnormal

 

 

Figure 812. Theoretical distribution of mean time to repair ﬁlling machine #1

77

Distribution Par 1 Par2 Par3 Score

Beta 30356.84 0. 50 1.20 6
Gamma 30356.84 1.10 7

Erlang 30356.84 1. 00 11
Weibull 30356.84 1. 00 11
Uniform -18894.‘:T."960821 13
Lognormal 30356842843529 23
Normal 30356. 8428435. 29 32
Logistic 30356. 8428435. 29 38

PearsonTS 303568 4.3 10 47
3eta G_WIWIB

Neiexi ____2
Jnigrm Lognorma Norma

§ Distribution Fit Analysis for 38 values. Best ﬁt:Beta

 

 

 

       

Logistic PearsonTS

 

 

Figure B13. Theoretical distribution of mean time between failure of ﬁlling
machine #2

 

a Distribution Par 1 Par 2 Par 3 Score 1
E Gamma 1654.74 0.90 5 l
5 Negexo 1654.74 7 .
; Eila‘ng 1654.74 1. 00 7 l
IWeibull 1654.74 1. 00 7

E Lognormal 1654. 74 178 1. 45 7 l
f Beta 1554 74 0. 50 2.20 15

'; PearsonTS 1654.74 2.90 18 i
, Normal 1654.74 1781.45 24

. Logistic 1654. 74 1781. 45 27

a Uniform 1430934741 30 42 l .

 

Wei u L0 norma

    

      

Milli ma

PearsonTSW

Logistic

Uniform

Distributior‘i Fit Analvsis for 38 values. Best ﬁt:Gamma

 

Figure B14. Theoretical distribution of mean time to repair ﬁlling machine #2

78

 

Distribution

Weibull
Negexp
Lognormal
Logistic
Uniform
Normal
PearsonT5

 

Par 1 Par 2 Par 3 Score

19546.71 0.50 58
19546.71 376
1954673834495 386
1954673834495 841
46868685962. 10 926
1954673834495 1031
19546.71 2.30 1283

 

 

   

Distribution Fit Analysis for 167 values. Best ﬁt2Weibull

 

 

  

Lognorma

_ogistic Uni rm Norma PearsonT5

Figure B15. Theoretical distribution of mean time between failure of caser

 

 

Distribution

Weibull
Logistic
Uniform
Gamma
Normal
Negexp
Erlang
Lognormal

PearsonT5

 

Par 1 Par 2 Par 3 Score
374.37 0.90 510
374.37 463.88 510
-429.09 1177.84 511
374.37 0.70 512
374.37 463.88 512
374.37 512
374.37 1.00 512
374.37 463.88 517
3 4.37 0.50 6.70 520
374.37 2.70 520

 

 

Wei ull

 

\legexp Er ang Lonormal

Distribution Fit Analysis for 167 values. Best ﬁtz‘Neibull

 

 

PearsonT5

 

Figure B16. Theoretical distribution of mean time to repair caser

79

 

 

 

 

Distribution Par 1 Par 2 Par 3 Score

Lognormal 2848808339304 2
Weibull 28488.00 0.60 3
Negexo 28488.00 5
Gamma 2848800 0.40 7
Beta 2848800 0.20 1.10 14
PearsonT5 28488 00 2. 40 17
Uniform -46670. 9103646. 9 28
Normal 28488 083393. 04 28
Logistic 2848808339304 32

 

 

 

-0 norma Gamma Beta

      

Norma

DearsonTS Uni rm

Logistic

Distribution Fit Analysrs for 25 values. Best ﬁt: Lognormal

 

Figure B17. Theoretical distribution of mean time between failure of stacker #1

 

   
 
  
  
 
  
 
  

 

Distribution Par 1 Par 2 Par 3 Score
Lognormal 955. 20 102408 2
Gamma 955. 20 3
Negexp 955.20

Erlang 955.20 1.00 4
Weibull 955.2 1.00

PearsonT5 955.20 2.90 12
Beta 955. 20 0. 40 1.10 16
Uniform 819. 86 2730. 26 33
Normal 955.20 10: )4. 83 33
Logistic 955. 20 1024. 83 33

 

 

-0 norma

      

Logbﬂc

39arsonT5 Beta

Distribution Fit Analysis for 25 values. Best ﬁt:Lognormal

 

Figure B18. Theoretical distribution of mean time to repair stacker #1

80

 

 

Distribution Par 1 Par 2 Par 3 Score
Gamma 45484.29 0.40 4
Weibull 45484.29 0.60 6
Beta 45484.29 0.20 1.10 11
Negexb 45484.29 2
Lognormal 4548429236498 13
Normal 4548429236498 25
Logistic 4548429236498 29
PearsonT5 45484.29 2.40 29
Uniform 398555120824. 1 32

 

 

 

 

    

i Lognorma

   

Uni rm

f: \lorma Logistic PearsonT5

! Distribution Fit Analysis for 28 values. Best ﬁt:Gamma

 

Figure B19. Theoretical distribution of mean time between failure of stacker #2

   

 

Distribution Par 1 Par2 Par3 Score

Logistic 996.43 513.90 3 l
. Weibull 996.43 2.10 3 I
; Lognormal 996.43 513.90 5
1 Normal 996.43 513.90 5
g Erlang 996.43 4.00 5
; PearsonT5 996.43 5.80 5
.‘- Beta 996.43 1.50 1.70 7' ,
Gamma 996.43 3.80 7 i
i Uniform 106.33 1886.52 9 .
i Negexp 996.43 10 l
‘ .
l

 

L0 norma

"
_‘

   

DearsonTS Beta Gamma

,1 Distribution Fit Arial'srsrs for 28 values. Best ﬁt:Logistic

 

Figure B20. Theoretical distribution of mean time to repair stacker #2

 

 

l Distribution Par 1 Par 2 Par 3 Score

1 Logistic 1317935418890 2

i Beta 1317935 0.40 1.10 2

3 Negexp 1317935 2

; Erlang 1317935 1.00 2

; Weibull 1317935 1.00 2
Gamma 31793.5 0.90 2
Normal 1317935418890 5
Lognormal 1317935418890 7
PearsonT5 1317935 2.90 15
Uniform 4139653775525 18

 

 

 

     

-oiistic _ Beta

Gamma Norma Lognorma

   

PearsonT5

 

i Distribution Fit Analyse for 24 values. Best ﬁtzLogistic

Figure B21. Theoretical distribution of mean time between failure of cooling
storage

 

 

 

 

Distribution Par 1 Par 2 Par 3 Score i
Negexp 2110.00 5 i .
Erlang 2110.00 1.00 5 l
Lognormal 2 1 10.00 2122.55 5 l
Weibull 2110.00 0.90 5 l'
Gamma 2110.00 1.00 5 i"
PearsonT5 2110.00 3.00 9 .
Logistic 21 10.00 2 122.55 10 l
Beta 2110.00 0.50 1.40 12 i

; Normal 2 1 10.00 2122.55 14 i ‘

Uniform -1566.3$786.36 21 l ,

= \leiexi Eran Lo norma Wei u Gamma

3earsonTS Logistic _ Beta Norma Uni rm
l .
7 Distribution Fit Analysis tor 24 values. Best ﬁt:l'-iege>:r:i

 

Figure 822. Theoretical distribution of mean time to repair cooling storage

82

APPENDIX C

DOCUMENTATION OF MODELS

83

Documentation of Model 1

GENERAL REMARKS

1.SIM consists of 20 elements, 20 jobs and 20 stages.

Time representation is as follows: 60 units make 1 minute,

60 minutes make 1 hour, 8 hours make 1 day.

At request usertli will be executed.

TABLE 1: Element parameters

 

 

 

ELEM NAME T CAP EXIT

NR COND

1 Inou_1 I 2

2 machine M 4

3 Buff_3 B 20 *

4 Mach_4 M 12 *

5 Inou_S I 2

6 Mach_6 M 4

7 Buff_7 B 20

8 Mach_8 M 12

9 Inou_9 I 2

10 Mach_lO M 4

11 Buff_ll B 20

12 Mach_12 M 12

13 Inou_13 I 2

14 Mach_14 M 4

15 Buff_lS B 20

16 Mach_16 M 12

17 Regrinder B 100

18 Inou_18 I 2

l9 Buff_19 B 30000

20 Inou_20 I 2

TABLE 3: Job parameters

JOB NAME ELEM JOBTIME BATCH IN OUTBATCH
NR parl dis par2 parl dis par2 parl dis par2
1 E1:J1 1 1.00 1.00 "—
2 E2:J1 2 7.60 4.00 4.00

 

.00
.00
.OO
.00
.00
.OO
.00
.OO
.00
.00
.OO
.00
.OO
.00
.00
.00
.00
.OO

 

3 E3:J1 3 7.60 4.00 4
4 E4:J1 4 1.90 1.00 1
5 E5:J1 5 1.00 1
6 E6:Jl 6 7.80 4.00 4
7 E7:Jl 7 7.80 4.00 4
8 E8:J1 8 2.00 1.00 1
9 E9:J1 9 1.00 1
10 E10:J1 10 7.50 4.00 4
11 E11:J1 11 7.50 4.00 4
12 E12:Jl 12 1.90 1.00 l
13 E13:J1 13 1.00 1
14 E14:J1 14 7.40 4.00 4
15 E15:J1 15 7.40 4.00 4
16 E16:J1 16 1.90 1.00 1
l7 E17:J1 17 5.00 1.00 l
18 E18:Jl 18 1.00 1
19 E19:J1 19 1.00 1
20 E20:Jl 20 1.00 1
ROUTE LISTING

ROUTE STAGE NAME USES SEND

NR NR JOBNR TO

1 l Rlzl 1 2

1 2 Rl:2 2 3

l 3 R1:3 3 4

1 4 Rl:4 4 bernoulli[90,l9,l7]

1 5 R1:5 S 6

1 6 R1:6 6 7

l 7 R1:7 7 8

1 8 R1:8 8 bernoulli[92,19,17]

1 9 R1:9 9 10

1 10 Rlle 10 11

1 11 R1:11 ll 12

1 12 R1:12 12 bernoulli[96,19,17]

1 13 R1:13 13 14

1 14 R1:14 14 15

1 15 R1:15 15 16

1 16 R1:16 16 bernoulli[93,19,17]

1 l7 R1:17 17 18

1 18 R1:18 18 O

1 19 R1:19 19 20

1 20 R1:20 20 0

PRODUCT PARAMETERS

prod 1 size= 0.15 icon= 10

prod 2 size= 0.15 icon= ll

prod 3 size= 0.15 icon= 12

prod 4 size= 0.15 icon= 13

All other products default (size=1 and weight=l).

85

STOCK LISTING

(1)
(5)
(9)
(13)

(R1:
(R1:
(R1:
(R1:

1) -->
5) -->
9) -—>
13) —->

TLI SYNTAX LISTING

(3)
(4)
(7)
(8)
(11)
(12)
(15)
(16)
(2)
(2)
(4)
(8)
(12)
(16)

Exit
Exit
Exit
Exit
Exit
Exit
Exit
Exit
MTBF
MTTR
Send
Send
Send
Send

condition
condition
condition
condition
condition
condition
condition
condition

to
to
to
to

l—‘li-Jt—‘l—l

product (code=1)

product (code=2)
product (code=3)
product (code=4)

elqueue[3]>16
elqueue[4]>8
elqueue[7]>16
elqueue[8]>8
elqueue[11]>16
elqueue[12]>8
elqueue[15]>16
elqueue[l6]>8

bernoulli[90,l9,l7]
bernoulli[92,19,17]
bernoulli[96,19,17]
bernoulli[93,19,17]

EXECUTE FUNCTION AT REQUEST: usertli

End of document

86

 

Documentation of Model 2

GENERAL REMARKS

2.81M consists of 27 elements,

Time representation is as follows: 60

60 minutes make 1 hour,

27 jobs and 27 stages.

units make 1 minute,

8 hours make 1 day.

The systemsize has been changed to 10000.
At request usertli will be executed.

 

 

--> CONVEYOR/WAREHOUSE/RESERVOIR

 

 

 

TABLE 1: Element parameters

ELEM NAME T CAP EXIT QUEU
NR COND DISC
1 Inou_1 I 2000 Fifo
2 Mach_2 M 4 Fifo
3 Buff_3 B 20 * Fifo
4 Mach_4 M 12 * Fifo
5 Inou_5 I 2 Fifo
6 Mach_6 M 4 Fifo
7 Buff_7 B 20 * Fifo
8 Mach_8 M 12 * Fifo
9 Inou_9 I 2 Fifo
10 Mach_lO M 4 Fifo
ll Buff_ll B 20 * Fifo
12 Mach_12 M 12 * Fifo
13 Inou_13 I 2 Fifo
14 Mach_l4 M 4 Fifo
15 Buff_lS B 20 * Fifo
16 Mach_16 M 12 * Fifo
17 Buff_17 B 100 Fifo
18 Inou_18 I 2 Fifo
19 Conv_l9 C 11 Location
20 Conv_20 C 13 Location
21 Conv_21 C 25 Location
22 Conv_22 C 119 Location
23 Conv_23 C 221 Location
24 Conv_24 C 261 Location
25 Conv_25 C 3333 Location
26 Buff_26 B 900000 Fifo
27 Inou_27 I 2 Fifo
TABLE 2: Element parameters (various)
ELEM NAME T CAP PROD ACM SPEED
NR SPAC

19 Conv_19 C 11 Y 1.90

87

 

 

 

20 Conv_20 C 13 Y 1.90 2.00

21 Conv_21 C 25 Y 1.90 3.80

22 Conv_22 C 119 Y 1.00 17.85

23 Conv_23 C 221 Y 1.00 33.22

24 Conv_24 C 261 Y 1.00 39.23

25 Conv_25 C 3333 Y 1.00 500.00

TABLE 3: Job parameters

JOB NAME ELEM JOBTIME BATCH IN OUTBATCH
NR parl dis par2 parl dis par2 parl dis par2
1 E1:J1 1 1.00 1.00
2 E2:J1 2 7.60 4.00 4.00
3 E3:Jl 3 7.60 4.00 4.00
4 E4:J1 4 1.90 1.00 1.00
5 E5:Jl 5 1.00 1.00
6 E6:J1 6 7.80 4.00 4.00
7 E7:J1 7 7.80 4.00 4.00
8 E8:J1 8 1.95 1.00 1.00
9 E9:Jl 9 1.00 1.00
10 E10:J1 10 7.50 4.00 4.00
11 E11:J1 11 7.50 4.00 4.00
12 E12:J1 12 1.88 1.00 1.00
13 E13:J1 13 1.00 1.00
14 E14:Jl 14 7.40 4.00 4.00
15 E15:J1 15 7.40 4.00 4.00
16 E16:J1 16 1.85 1.00 1.00
17 E17:J1 17 5.00 1.00 1.00
18 E18:Jl 18 1.00 1.00
19 E19:J1 19 1.00 1.00
20 E20:J1 20 1.00 1.00
21 E21:Jl 21 1.00 1.00
22 E22:Jl 22 1.00 1.00
23 E23:J1 23 1.00 1.00
24 E24:Jl 24 1.00 1.00
25 E25:J1 25 1.00 1.00
26 E26:J1 26 0.10 1.00 1.00
27 E27:J1 27 1.00 1.00
ROUTE LISTING

ROUTE STAGE NAME USES SEND

NR NR JOBNR TO

1 1 R1:1 1 2

1 2 R1:2 2 3

1 3 R1:3 3 4

1 4 R1:4 4 bernoulli[90,21,17]

1 5 R1:5 5 6

1 6 R1:6 6 7

1 7 R1:7 7 8

88

1 8 R1:
1 9 R1:
1 10 R1:
1 11 R1:
1 12 R1:
1 13 R1:
1 14 R1:
1 15 R1:
1 16 R1
1 17 R1:
1 18 R1:
1 19 R1:
1 20 R1:
1 21 R1
1 22 R1:
1 23 R1
1 24 R1
1 25 R1:
1 26 R1
1 27 R1:
EVENT LIST

1. Time= 0.00

8

9

10
11
12
13
14
15

:16

17
18
19
20

:21

22

:23
:24

25

:26

27

8 bernoulli[92,20,l7]

bernoulli[96,19,l7]

16 bernoulli[93,23,17]

9 10
10 11
11 12
12
13 14
14 15
15 16
17 18
18 19
19 20
20 21
21 22
22 25
23 24
24 25
25 26
26 27
27 O

(repeated every 27.00 units)

15.00 (repeated every 27.00 units)

19.00 (repeated every

Tli = open22
2. Time=

Tli = close22
3. Time=

Tli = open24
4. Time= 23.00

Tli = close24

PRODUCT PARAMETERS

prod 1
prod 2
prod 3
prod 4

size= 0.
size=
size= 0.
size=

0.

0.

All other products

STOCK LISTING

(1)
(5)
(9)
(13)

(R1:
(R1:
(R1:
(R1:

1)
5)
9)
13)

15 icon= 10
15 icon= 11
15 icon= 12
15 icon= 13
default (size=1
1 product
1 product
1 product
1 product

(repeated every

27.00 units)

27.00 units)

and weight=l).

(code=1)
(code=2)
(code=3)
(code=4)

89

TLI SYNTAX LISTING

(3) Exit condition = elqueue[3]>16
(4) Exit condition = elqueue[4]>8
(7) Exit condition = elqueue[7]>16

(8) Exit condition
(11) Exit condition
(12) Exit condition
(15) Exit condition
(16) Exit condition

elqueue[8]>8
elqueue[11]>16
elqueue[12]>8
elqueue[15]>16
elqueue[16]>8

R375
3::
are
air
win
n u

(4) Send to bernoulli[90,21,l7]
(8) Send to bernoulli[92,20,17]
(12) Send to = bernoulli[96,19,l7]
(16) Send to = bernoulli[93,23,17]
EXECUTE FUNCTION AT REQUEST: usertli

TLI FUNCTIONS

function open22
elsend[22]:=1
elsend[24]:=0
function open24
elsend[22]:=0
elsend[24]:=1
function close22
elsend[22]:=0
elsend[24]:=0
function close24

elsend[22]:=0
elsend[24]:=0

End of document

90

Documentation of Model 3

GENERAL REMARKS

3.SIM consists of 41 elements, 41 jobs and 41 stages.

Time representation is as follows: 60 units make 1 minute,
60 minutes make 1 hour, 8 hours make 1 day.

The systemsize has been changed to 10000.

At request usertli will be executed.

TABLE 1: Element parameters

 

 

ELEM NAME T CAP EXIT QUEU
NR COND DISC
1 Inou_1 I 2000 Fifo
2 Mach_2 M 4 Fifo
3 Buff_3 B 20 * Fifo
4 Mach_4 M 12 * Fifo
5 Inou_5 I 2 Fifo
6 Mach_6 M 4 Fifo
7 Buff_7 B 20 * Fifo
8 Mach_8 M 12 * Fifo
9 Inou_9 I 2 Fifo
10 Mach_10 M 4 Fifo
11 Buff_11 B 20 * Fifo
12 Mach_12 M 12 * Fifo
13 Inou_13 I 2 Fifo
14 Mach_14 M 4 Fifo
15 Buff_15 B 20 * Fifo
16 Mach_16 M 12 * Fifo
17 Buff_l7 B 100 Fifo
18 Inou_18 I 2 Fifo
19 Conv_19 C 11 Location
20 Conv_20 C 13 Location
21 Conv_21 C 25 Location
22 Conv_22 C 119 Location
23 Conv_23 C 221 Location
24 Conv_24 C 261 Location
25 Conv_25 C 228 Location
26 Conv_26 C 229 Location
27 Conv_27 C 46 Location
28 Conv_28 C 186 Location
29 Conv_29 C 163 Location
30 Conv_30 C 66 Location
31 Conv_31 C 120 Location
32 Conv_32 C 113 Location
33 Conv_33 C 403 Location
34 Conv_34 C 63 Location
35 Conv_35 C 63 Location
36 Conv_36 C 63 Location

91

37 Buff_37 B 1000 Fifo

 

 

 

38 Inou_38 I 2 Fifo

39 Conv_39 C 66 Location

40 Buff_40 B 1000 Fifo

41 Inou_41 I 2 Fifo

TABLE 2: Element parameters (various) --> CONVEYOR/WAREHOUSE/RESERVOIR
ELEM NAME T CAP PROD ACM SPEED LNGTH

NR S PAC

19 Conv_19 C 11 Y 1.90 1.65

20 Conv_20 C 13 Y 1.90 2.00

21 Conv_21 C 25 Y 1.90 3.80

22 Conv_22 C 119 Y 1.00 17.85

23 Conv_23 C 221 Y 1.00 33.22

24 Conv_24 C 261 Y 1.00 39.23

25 Conv_25 C 228 Y 1.00 34.29

26 Conv_26 C 229 Y 1.00 34.29

27 Conv_27 C 46 Y 1.00 7.00

28 Conv_28 C 186 Y 1.00 28.00

29 Conv_29 C 163 Y 1.00 24.50

30 Conv_30 C 66 Y 1.00 10.00

31 Conv_31 C 120 Y 1.00 18.00

32 Conv_32 C 113 Y 1.00 17.00

33 Conv_33 C 403 Y 1.00 60.50

34 Conv_34 C 63 Y 1.00 9.50

35 Conv_35 C 63 Y 1.00 9.50

36 Conv_36 C 63 Y 1.00 9.50

39 Conv_39 C 66 Y 1.00 10.00

TABLE 3: Job parameters

JOB NAME ELEM JOBTIME BATCH IN OUTBATCH
NR parl dis par2 parl dis par2 parl dis par2
1 E1:J1 1 1.00 1.00
2 E2:Jl 2 7.60 4.00 4.00
3 E3:J1 3 7.60 4.00 4.00
4 E4:J1 4 1.90 1.00 1.00
5 E5:J1 5 1.00 1.00
6 E6:J1 6 7.80 4.00 4.00
7 E7:J1 7 7.80 4.00 4.00
8 E8:J1 8 1.95 1.00 1.00
9 E9:J1 9 1.00 1.00
10 E10:J1 10 7.50 4.00 4.00
11 E11:J1 11 7.50 4.00 4.00
12 E12:J1 12 1.88 1.00 1.00
13 E13:Jl 13 1.00 1.00
14 E14:J1 14 7.40 4.00 4.00

 

15 E15:J1 15 7.40 4.00 4.00
16 E16:J1 16 1.85 1.00 1.00
17 E17:J1 17 5.00 1.00 1.00
18 E18:J1 18 1.00 1.00
19 E19:J1 19 1.00 1.00
20 E20:J1 20 1.00 1.00
21 E21:J1 21 1.00 1.00
22 E22:J1 22 1.00 1.00
23 E23:J1 23 1.00 1.00
24 E24:J1 24 1.00 1.00
25 E25:J1 25 1.00 1.00
26 E26:J1 26 1.00 1.00
27 E27:J1 27 1.00 1.00
28 E28:J1 28 1.00 1.00
29 E29:J1 29 1.00 1.00
30 E30:J1 30 1.00 1.00
31 E31:J1 31 1.00 1.00
32 E32:J1 32 1.00 1.00
33 E33:J1 33 1.00 1.00
34 E34:J1 34 1.00 1.00
35 E35:J1 35 1.00 1.00
36 E36:J1 36 1.00 1.00
37 E37:J1 37 1.00 1.00 1.00
38 E38:J1 38 1.00 1.00
39 E39:J1 39 1.00 1.00
40 E40:J1 40 1.00 1.00 1.00
41 E41:J1 41 1.00 1.00
ROUTE LISTING

ROUTE STAGE NAME USES SEND

NR NR JOBNR TO

1 1 R1:1 1 2

1 2 R1:2 2 3

1 3 R1:3 3 4

1 4 R1:4 4 bernoulli[90,21,l7]

1 5 R1:5 5 6

1 6 R1:6 6 7

1 7 Rl:7 7 8

1 8 R1:8 8 bernoulli[92,20,17]

1 9 R1:9 9 10

1 10 R1:10 10 11

1 11 R1:1l 11 12

1 12 R1:12 12 bernoulli[96,19,l7]

1 13 R1:13 13 14

1 14 R1:14 14 15

1 15 R1:15 15 16

1 16 R1:16 l6 bernoulli[93,23,17]

1 17 R1:17 17 18

1 18 R1:18 18 19

1 19 R1:19 19 20

1 20 R1:20 20 21

1 21 R1:21 21 22

93

1 22 R1:22 22 25
1 23 R1:23 23 24
1 24 R1:24 24 25
1 25 R1:25 25 26
1 26 R1:26 26 27
1 27 R1:27 27 28
1 28 R1:28 28 29
1 29 R1:29 29 30
1 30 R1:30 30 31
1 31 R1:31 31 32
1 32 R1:32 32 if time|8<4 then 33 else 34
l 33 R1:33 33 39
1 34 R1:34 34 35
l 35 R1:35 35 36
1 36 R1:36 36 37
1 37 R1:37 37 38
1 38 R1:38 38 0
1 39 R1:39 39 40
1 40 R1:40 40 41
1 41 R1:4l 41 0
EVENT LIST

1. Time= 0.00 (repeated every 27.00 units)
Tli = open22

2. Time= 15.00 (repeated every 27.00 units)
Tli = close22
3. Time= 19.00 (repeated every 27.00 units)

Tli = open24
4. Time= 23.00 (repeated every 27.00 units)
Tli = close24

PRODUCT PARAMETERS

prod 1 size= 0.15 icon= 10
prod 2 size= 0.15 icon= 11
prod 3 size= 0.15 icon= 12
prod 4 size= 0.15 icon= 13

All other products default (size=1 and weight=l).

STOCK LISTING

(1) (Rlzl) —-> 1 product (code=1)
(5) (R1:5) -—> 1 product (code=2)
(9) (R1:9) —-> 1 product (code=3)
(13) (R1:13) --> 1 product (code=4)

94

SYNTAX LISTING

(3) Exit condition

(4) Exit condition =
(7) Exit condition =
(8) Exit condition =
(11) Exit condition =
(12) Exit condition =
(15) Exit condition =
(16) Exit condition =
(2) MTBF =
(2) MTTR =
(4) Send to

(8) Send to =
(12) Send to =
(16) Send to =
(32) Send to =

EXECUTE FUNCTION AT REQUEST:

TLI FUNCTIONS

function open22
elsend[22]:=1
elsend[24]:-

function open24
elsend[22]:=0
elsend[24]:=1

function close22

elsend[22]:=0
elsend[24]:=0

function close24

elsend[22]:=0
elsend[24]:=0

End of document

= elqueue[3]>16

elqueue[4]>8
elqueue[7]>16
elqueue[8]>8
elqueue[11]>16
elqueue[12]>8
elqueue[15]>16
e1queue[16]>8

= bernoulli[90,21,17]

bernoulli[92,20,17]
bernoulli[96,19,l7]
bernoulli[93,23,17]

if time|8<4 then 33 else 34
usertli

95

Documentation of Model 4

GENERAL REMARKS

4.81M consists of 51 elements, 51 jobs and 51 stages.

Time representation is as follows: 60 units make 1 minute,
60 minutes make 1 hour, 8 hours make 1 day.

The systemsize has been changed to 10000.

At request usertli will be executed.

TABLE 1: Element parameters

 

 

ELEM NAME T CAP EXIT QUEU
NR COND DISC
1 Inou_1 I 2000 Fifo
2 Mach_2 M 4 Fifo
3 Buff_3 B 20 * Fifo
4 Mach_4 M 12 * Fifo
5 Inou_S I 2 Fifo
6 Mach_6 M 4 Fifo
7 Buff_7 B 20 * Fifo
8 Mach_8 M 12 * Fifo
9 Inou_9 I 2 Fifo
10 Mach_10 M 4 Fifo
11 Buff_ll B 20 * Fifo
12 Machm12 M 12 * Fifo
13 Inou_13 I 2 Fifo
14 Mach_14 M 4 Fifo
15 Buff_15 B 20 * Fifo
16 Mach_16 M 12 * Fifo
17 Buff_17 B 100 Fifo
18 Inou_18 I 2 Fifo
19 Conv_19 C 11 Location
20 Conv_20 C 13 Location
21 Conv_21 C 25 Location
22 Conv_22 C 119 Location
23 Conv_23 C 221 Location
24 Conv_24 C 261 Location
25 Conv_25 C 228 Location
26 Conv_26 C 229 Location
27 Conv_27 C 46 Location
28 Conv_28 C 186 Location
29 Conv_29 C 163 Location
30 Conv_30 C 66 Location
31 Conv_31 C 120 Location
32 Conv_32 C 113 Location
33 Conv_33 C 403 Location
34 Conv_34 C 63 Location
35 Conv_35 C 63 Location

96

36 Conv_36 C 63 Location
37 Conv_37 C 66 Location
38 Mach_38 M 26 Fifo
39 Buff_39 B 48 Fifo
40 Mach_40 M 4 Fifo
41 Buff_41 B 5 Fifo
42 Mach_42 M 12 Fifo
43 Conv_43 C 34 Location
44 Mach_44 M 26 Fifo
45 Buff_45 B 48 Fifo
46 Mach_46 M 4 Fifo
47 Buff_47 B 5 Fifo
48 Mach_48 M 12 Fifo
49 Conv_49 C 13 Location
50 Buff_50 B 2090 Fifo
51 Inou_51 I 2 Fifo

TABLE 2: Element parameters (various) -—> CONVEYOR/WAREHOUSE/RESERVOIR

ELEM NAME T CAP PROD ACM SPEED LNGTH

 

 

 

 

 

NR SPAC

19 Conv_19 E 11 y 1.90 1.65

20 Conv_20 C 13 Y 1.90 2.00

21 Conv_21 C 25 Y 1.90 3.80

22 Conv_22 C 119 Y 1.00 17.85

23 Conv_23 C 221 Y 1.00 33.22

24 Conv_24 C 261 Y 1.00 39.23

25 Conv_25 C 228 Y 1.00 34.29

26 Conv_26 C 229 Y 1.00 34.29

27 Conv_27 C 46 Y 1.00 7.00

28 Conv_28 C 186 Y 1.00 28.00

29 Conv_29 C 163 Y 1.00 24.50

30 Conv_30 C 66 Y 1.00 10.00

31 Conv_31 C 120 Y 1.00 18.00

32 Conv_32 C 113 Y 1.00 17.00

33 Conv_33 C 403 Y 1.00 60.50

34 Conv_34 C 63 Y 1.00 9.50

35 Conv_35 C 63 Y 1.00 9.50

36 Conv_36 C 63 Y 1.00 9.50

37 Conv_37 C 66 Y 1.00 10.00

43 Conv_43 C 34 Y 0.14 23.00

49 Conv_49 C 13 Y 0.14 9.00

TABLE 3: Job parameters

JOB NAME ELEM JOBTIME BATCH IN OUTBATCH TRIG
NR parl dis par2 parl dis par2 parl dis par2 ENTR
1 E1:J1 1 1.00 ___ 1.00
2 E2:J1 2 7.60 4.00 4.00

97

CDQONUWDUJ

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23
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29
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31
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33
34
35
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39
40
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42
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98

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t—‘Ht—‘t—‘F—‘F—JHHi—‘HI—Jt—‘l—‘t—‘Hi—‘Hi—‘t—‘t—‘l—‘b—‘F—‘l—JI—JHHHHHHHHHHbeHHbAHH-ﬁth—‘b

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$14-$4-

sari-xi-

ROUTE LISTING

ROUTE STAGE NAME USES SEND

 

NR NR JOBNR TO
1 1 R1:1 1 2
1 2 R1:2 2 3
1 3 R1:3 3 4
1 4 R1:4 4 bernoulli[90,21,17]
1 5 R1:5 5 6
1 6 R1:6 6 7
1 7 R1:7 7 8
1 8 R1:8 8 bernoulli[92,20,17]
l 9 R1:9 9 10
1 10 R1:10 10 11
1 11 R1:11 11 12
1 12 R1:12 12 bernoulli[96,19,l7]
1 13 R1:13 13 14
1 14 R1:14 14 15
l 15 R1:15 15 16
1 l6 R1:16 16 bernoulli[93,23,17]
1 l7 R1:17 17 18
1 18 R1:18 18 0
1 19 R1:19 19 20
1 20 R1:20 20 21
1 21 R1:21 21 22
1 22 R1:22 22 25
1 23 R1:23 23 24
1 24 R1:24 24 25
1 25 R1:25 25 26
1 26 R1:26 26 27
1 27 R1:27 27 28
1 28 R1:28 28 29
1 29 R1:29 29 30
1 30 R1:30 30 31
1 31 R1:31 31 32
1 32 R1:32 32 if time|8<4 then 33 else 34
1 33 R1:33 33 37
1 34 R1:34 34 35
1 35 R1:35 35 36
1 36 R1:36 36 38
l 37 R1:37 37 44
1 38 R1:38 38 39
l 39 R1:39 39 40
1 40 R1:40 40 41
1 41 R1:41 41 42
1 42 R1:42 42 43
1 43 R1:43 43 50
1 44 R1:44 44 45
1 45 R1:45 45 46
1 46 R1:46 46 47
1 47 R1:47 47 48
1 48 R1:48 48 49
1 49 R1:49 49 50
l 50 R1:50 50 51
l 51 R1:51 51 0

99

EVENT LIST

1. Time=
Tli =
2. Time=
Tli =
3. Time=
Tli =
4. Time=
Tli =

0.00
open22
15.00
close22
19.00
open24
23.00
close24

PRODUCT PARAMETERS

size=
size=
size=
size=
size=
prod size=
prod 7 size=
All other products

prod
prod
prod
prod
prod

030115me

STOCK LISTING

condition
condition
condition
condition
condition
condition
condition
condition

) Exit
) Exit
) Exit
) Exit
Exit
Exit
Exit
Exit
MTBF
MTTR
Trig. on Entry
Jobtime

Trig. on Entry

.15
.15
.15
.15
.33
.66
.00
default

F’H’P‘H

(repeated every

(repeated every

ll

(repeated every 27.00 units)
(repeated every 27.00 units)
27.00 units)

27.00 units)

43
44
45
46
41

icon=
icon=
icon=
icon=
icon=
icon= 23
icon= 2

(size=1 and weight=l).

product
product (
product
product (

elqueue[3]>16
elqueue[4]>8
elqueue[7]>16
elqueue[8]>8
elqueue[11]>16
elqueue[12]>8
elqueue[15]>16
elqueue[16]>8

attl[C]:=time+8
attl[E,1]-time
product[C]:=5

100

(41)
(41)
(42)
(45)
(45)
(46)
(47)
(47)
(48)
(50)
(4)

(8)

(12)
(16)
(32)

EXECUTE FUNCTION AT REQ EST:

Trig. on
Jobtime
Trig. on
Trig. on
Jobtime
Trig. on
Trig. on
Jobtime
Trig. on
Trig. on
Send to
Send to
Send to
Send to
Send to

TLI FUNCTIONS

Entry

Entry
Entry

Entry
Entry

Entry
Entry

function open22

elsend[22]:=1

elsend[24]:-

function open24

elsend[22]:—

elsend[24]:=1

function close22

elsend[22]:=0
elsend[24]:=0

function close24

elsend[22]:=0
elsend[24]:=0

End of document

I)

—
_—

attl[C]:=time+8
attl[E,1J-time
product[C]:=6
attl[C]:=time+8
attl[E,1]-time
product[C]:=5
attl[C]:=time+8
attl[E,1]-time
product[C]:=6
product[C]:=7
bernoulli[90,21,17]
bernoulli[92,20,17]
bernoulli[96,19,l7]
bernoulli[93,23,17]
if timel8<4 then 33 else 34
usertli

101

Documentation of Model 5

GENERAL REMARKS

5.81M consists of 51 elements, 52 jobs and 52 stages.

Time representation is as follows: 60 units make 1 minute,

60 minutes make 1 hour, 24 hours make 1 day.

The systemsize has been changed to 10000, and the number of attributes
is 2

At request usertli will be executed.

TABLE 1: Element parameters

 

 

 

ELEM NAME T CAP EXIT QUEU MTBF MTTR

NR COND DISC parl dis par2 parl dis par2

1 Inou_1 I 2000 Fifo

2 Mach_2 M 4 Fifo TLI 3234.60 Log 4025.16
3 Buff_3 B 20 Fifo

4 Mach_4 M 12 Fifo

5 Inou_S I 2 Fifo

6 Mach_6 M 4 Fifo 100458.40 Log 145152.20 TLI

7 Buff_7 B 20 Fifo

8 Mach_8 M 12 Fifo

9 Inou_9 I 2 Fifo

10 Mach_10 M 4 Fifo TLI 2184.00 Log 3364.80
11 Buff_11 B 20 Fifo

12 Mach_12 M 12 Fifo

13 Inou_13 I 2 Fifo

14 Mach_14 M 4 Fifo TLI 3100.80 Log 3794.40
15 Buff_15 B 20 Fifo

16 Mach_16 M 12 Fifo

17 Buff_17 B 100 Fifo

18 Inou_18 I 2 Fifo

19 Conv_19 C 11 Location

20 Conv_20 C 13 Location

21 Conv_21 C 25 Location

22 Conv_22 C 119 Location

23 Conv_23 C 221 Location

24 Conv_24 C 261 Location

25 Conv_25 C 228 Location

26 Conv_26 C 229 Location

27 Conv_27 C 46 Location

28 Conv_28 C 186 Location

29 Conv_29 C 163 Location 148552.20 Neg 1090.20 Log 1153.80
30 Conv_30 C 66 Location

31 Conv_31 C 120 Location

32 Conv_32 C 113 Location TLI TLI
33 Conv_33 C 403 Location

34 Conv_34 C 63 Location

102

2: Element parameters

 

35 Conv_35
36 Conv_36
37 Conv_37
38 Mach_38
39 Buff_39
40 Mach_40
41 Buff_41
42 Mach_42
43 Conv_43
44 Mach_44
45 Buff_45
46 Mach_46
47 Buff_47
48 Mach_48
49 Conv_49
50 Buff_SO
51 Inou_51
TABLE

ELEM NAME

NR

19 Conv_19
20 Conv_20
21 Conv_21
22 Conv_22
23 Conv_23
24 Conv_24
25 Conv_25
26 Conv_26
27 Conv_27
28 Conv_28
29 Conv_29
30 Conv_30
31 Conv_31
32 Conv_32
33 Conv_33
34 Conv_34
35 Conv_35
36 Conv_36
37 Conv_37
43 Conv_43
49 Conv_49

wmozmzwzozmzwzoon

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CAP PROD ACM SPEED

 

SPAC

Location
Location
Location
Fifo
Fifo
Fifo
Fifo
Fifo
Location
Fifo
Fifo
Fifo
Fifo
Fifo
Location
Fifo
Fifo

(variou

131793.60 Neg

5)

80766.00 Neg

43510.00 Neg

TLI

TLI

TLI

TLI

TLI
TLI
TLI
1605.60 Log 2416.20
TLI
TLI

2110.20 Log 2122.80

--> CONVEYOR/WAREHOUSE/RESERVOIR

LNGTH

 

P<F<*<*<*<*<*<P<*<t-<*<*<*<F<F<*<*<r<t-<F<r<|
O<DF4F4P‘F‘P'HtAPAFJFJFJH‘HIAFAFJFJH’H

.90
.90
.90
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.14
.14

34
34

28
24

10.
18.
17.
60.
.50
.50
.50
10.
23.
.00

103

.65
.00
.80
17.
33.
39.
.29
.29
.00
.00
.50

85
22
23

00
00
00
50

00
00

‘f— _

 

TABLE 3:

Job parameters

JOBTIME

parl dis par2

 

JOB NAME ELEM

NR

1 E1:J1 1

2 E2:J1 2 7.60
3 E3:J1 3 7.60
4 E4:J1 4 1.90
5 E5:J1 5

6 E6:J1 6 7.80
7 E7:J1 7 7.80
8 E8:J1 8 1.95
9 E9:J1 9

10 E10:J1 10 7.50
11 E11:J1 11 7.50
12 E12:J1 12 1.88
13 E13:J1 13

14 E14:Jl 14 7.40
15 E15:J1 15 7.40
16 E16:J1 16 1.85
17 E17:J1 17 5.00
18 E18:J1 18

19 E19:Jl 19

20 E20:J1 20

21 E21:J1 21

22 E22:J1 22

23 E23:J1 23

24 E24:J1 24

25 E25:J1 25

26 E26:J1 26

27 E27:J1 27

28 E28:J1 28

29 E29:J1 29

30 E30:J1 30

31 E31:J1 31

32 E32:J1 32

33 E33:J1 33

34 E34:J1 34

35 E35:J1 35

36 E36:J1 36

37 E37:Jl 37

38 E38:J1 38 0.83
39 E39:J1 39

40 E40:J1 40 0.83
41 E41:J1 41

42 E42:J1 42 3.33
43 E43:J1 43

44 E44:J1 44 0.83
45 E45:J1 45

46 E46:J1 46 0.83
47 E47:J1 47

48 E48:J1 48 3.33
49 E49:J1 49

50 E50:J1 50 10.00
51 E51:J1 51 0.50

TLI

TLI

TLI

TLI

BATCH IN
parl dis par2

'._.i

l—‘
F—‘i—‘t—‘Nl—‘bl—‘Hl—‘ND—‘bl—‘i—‘l—‘l—‘l—‘Hl—‘Ht—‘t—‘Ht—‘i—JHHHF—‘I—‘t—Jt—‘l—‘t—‘HHbel—Jbbt—‘l—‘AAHHDAl--'
O
O

104

OUTBATCH TRIG
parl dis par2 ENTR

O
O
##1##

l—‘l—‘Hl—‘F—‘l—‘i—‘l—‘Ht—Jb—‘t-‘Hl—‘l—‘t—‘t—‘Hl—‘t—‘t—‘t—‘l—‘t—‘r—‘t—‘i—‘HHHHi—‘HHt—‘beHbel—‘HDDHHDAH
0.0... O O I O O. .0. O. D
O O
O O
4+4:-

 

 

1.

 

52 E44:J2 44 0.83 1.
ROUTE LISTING

ROUTE STAGE NAME USES SEND

NR NR JOBNR TO

1 l R1:1 1 2

1 2 R1:2 2 3

1 3 R1:3 3 4

1 4 R1:4 4 bernoulli[90,21,17]
1 5 R1:5 5 6

1 6 R1:6 6 7

1 7 R1:7 7 8

1 8 R1:8 8 bernoulli[92,20,17]
1 9 R1:9 9 10

1 10 R1:10 10 11

l 11 R1:11 11 12

1 12 R1:12 12 bernoulli[96,19,l7]
l 13 R1:13 13 14

1 14 R1:14 14 15

1 15 R1:15 15 16

1 16 R1:16 16 bernoulli[93,23,17]
1 17 R1:17 17 18

1 18 R1:18 18 0

1 l9 R1:19 19 20

1 20 R1:20 20 21

1 21 R1:21 21 22

1 22 R1:22 22 25

1 23 R1:23 23 24

1 24 R1:24 24 25

1 25 R1:25 25 26

1 26 R1:26 26 27

1 27 R1:27 27 28

1 28 R1:28 28 29

l 29 R1:29 29 30

1 30 R1:30 30 31

1 31 R1:3l 31 32

1 32 R1:32 32 if timel8<4 then 33 else 34
l 33 R1:33 33 37

1 34 R1:34 34 35

1 35 R1:35 35 36

1 36 R1:36 36 38

1 37 R1:37 37 44

1 38 R1:38 38 39

1 39 R1:39 39 40

1 40 R1:40 40 41

1 41 R1:41 41 42

1 42 R1:42 42 43

1 43 R1:43 43 50

1 44 R1:44 44 45

1 45 R1:45 45 46

1 46 R1:46 46 47

105

00

1 47 R1:47 47 48
l 48 R1:48 48 49
1 49 R1:49 49 50
1 50 R1:50 50 51
l 51 R1:51 51 0
1 52 R1:52 52 45
EVENT LIST

1. Time= 0.00 (repeated every 27.00 units)
Tli = open22

2. Time= 15.00 (repeated every 27.00 units)
Tli = close22

3. Time= 19.00 (repeated every 27.00 units)
Tli = open24

4. Time= 23.00 (repeated every 27.00 units)
Tli = close24

 

PRODUCT PARAMETERS

prod 1 size= 0.15 icon= 43

prod 2 size= 0.15 icon= 44

prod 3 size= 0.15 icon= 45

prod 4 size= 0.15 icon= 46

prod 5 size= 0.33 icon= 41

prod 6 size= 0.66 icon= 23

prod 7 size= 1.00 icon= 2

All other products default (size=1 and weight=l).

STOCK LISTING

(1) (R1:1) --> 1 product (code=1)
(5) (R1:5) --> 1 product (code=2)
(9) (R1:9) --> 1 product (code=3)
(13) (R1:13) --> 1 product (code=4)
TLI SYNTAX LISTING

(3) Exit condition = elqueue[3]>16

(4) Exit condition = elqueue[4]>8

(7) Exit condition = elqueue[7]>16

(8) Exit condition = elqueue[8]>8

(11) Exit condition = elqueue[11]>16

106

(12)
(15)
(16)
(2)

(10)
(14)
(32)
(38)
(40)
(44)
(46)
(6)

(32)
(38)
(40)
(42)
(46)
(48)
(39)
(39)
(40)
(41)
(41)
(42)
(45)
(45)
(46)
(47)
(47)
(48)
(52)
(4)

(8)

(12)
(16)
(32)

Exit condition
Exit condition
Exit condition

Trigger on Entry

MTBF
MTBF
MTBF
MTBF
MTBF
MTBF
MTBF
MTBF
MTTR
MTTR
MTTR
MTTR
MTTR
MTTR
MTTR
Trig. on
Jobtime
Trig. on
Trig. on
Jobtime
Trig. on
Trig. on
Jobtime
Trig. on
Trig. on
Jobtime
Trig. on
Send to
Send to
Send to
Send to
Send to

Entry

Entry
Entry

Entry
Entry

Entry
Entry

Entry

ll

ll

elqueue[12]>8
elqueue[15]>16
elqueue[16]>8
weibull[49364.4,0.6]
weibull[41090.4,0.8]
weibull[57736.8,0.7]

beta[105343.4,0.4,1.1]
weibull[l9546.8,0.5]
gamma[110611.2,0.8]
weibull[19546.8,0.5]
pearson5[3803.08,2.7]

pearson5[1467,2.7]
weibull[374.4,0.9]
beta[1014,2.6,2]
weibull[374.4,0.9]
beta[900,0.1,0.3]
attl[C]:=time+8
attl[E,l]—time
product[C]:=5
attl[C]:=time+8
attl[E,l]-time
product[C]:=6
attl[C]:=time+8
attl[E,1]-time
product[C]:=5
attl[C]:=time+8
attl[E,1]-time
product[C]:=6
att3[C]:=time - att3[C]
bernoulli[90,21,17]
bernoulli[92,20,17]
bernoulli[96,19,l7]
bernoulli[93,23,17]
if timel8<4 then 33 else 34

EXECUTE FUNCTION AT REQ EST: usertli

TLI FUNCTIONS

function open22

elsend[22]:=1
elsend[24]:=0

function open24

elsend[22]:=0
elsend[24]:=1

function close22

107

l

elsend[22]:=0
elsend[24]:=0

function close24

elsend[22]:=0
elsend[24]:=0

End of document

108

 

Es

APPENDIX D

OUTPUT OF SIMULATION RUNS AND ANALYSES

109

Table D1. Utilization of element

95 % Confidence interval

AVG STDEV

Element

Blowmolder #1

85.1 i 3.8
84.6 i 3.8
84.2 i 3.8

10.5
10.5

85

84
84

5

10.

Blowmolder #2

94.3 i 2.0
93.7 i 2.0
93.3 i 2.0

.6
.6
.6

94

93

93

Blowmolder #3

92.1 i 3.5
91.5 i 3.5
91.3 i 3.5

.9
.8
.9

92

10

91.

11

91

12

13

Blowmolder #4

91.2 i 3.0
90.7 i 3.0
90.3 i 3.0
68.0 i 1.2

.3
.3
.3
.3

91

14
15
16
17

8
8

90

90

68

Regrinder

18
19
20
21

4.2 i 0.2

.5

Conveyor 1

i 0.2

23.9 i 0.3
73.0 i 0.3
88.6 i 2.9
46.2 i 1.4
98.7 i 0.4
98.1 i 0.6
75.2 i 1.2
96.6 i 1.2
95.4 i 1.9
84.7 i 2.2
92.9 i 2.8
91.4 i 3.3
82.5 i 6.0
50.7 i 2.4
49.0 i 2.7
46.5 i 3.1
44.6 i 3.9
71.8 i 1.2
91.0 i 1.8
17.9 i 0.3
90.4 i 1.8
5.9 i 0.1
29.3 i 0.5
72.2 i 1.1
88.9 i 2.2
18.0 i 0.3

9.7

.0
.8
.1
.0
.0
.7
.4
.5
.3
.2
.9
.2

23

73
88
46

22

8

23

24
25

1
1

98
98

Conveyor 2

26
27

75
96
95

3
5
6
7

28

29
30
31

84
92

9

91

32

16.7

82

33

Conveyor to Filler #2

.6
.6
.7

6

50
49

34
35
36
37
38
39
40
41

46
44

Conveyor to Filler #1

.0

.2
.1
.8
.0
.3
.4
.1
.2
.8
.5
.3
.5
.4

11

71

Filler #2

5

91

17.

caser #2

90

42
43

stacker #2

29

72
88.

44
45

Filler #1

18
88

46

caser #1

2.0
5.9 i 0.1
11.5 i 0.2
35.7 i 0.5

88.3

5

47
48

stacker # 1

11

49
50

cooling storage

35

110

Table D2. Average blocked time of elements

Element AVG STDEV 95% Confidence Interval
Blowmolder #1 1 57600.0 0.0
2 0.0 0.0
3 0.0 0 0
4 1.0 0.3 1.0 i 0 1
Blowmolder #2 5 57600.0 0.0
6 13.1 71.7 13.1 i 25.6
7 15.7 85.9 15.7 i 30.7
8 17.6 89.3 17.6 i 32.0
Blowmolder #3 9 57600.0 0.0
10 24.3 45.3 24.3 i 16.2
11 105.8 45.7 105.8 1 16.3
12 7.6 41.4 7.6 i 14.8
Blowmolder #4 13 57600.0 0.0
14 0.0 0.0
15 0.0 0.0
16 0.0 0.0
Regrinder 17 0.0 0.0
18 0.0 0.0
Conveyor 1 19 15.7 86.0\ 15.7 i 30.8
20 20.2 110.5 20.2 i 39.6
21 38.6 158 3 38.6 i 56.7
22 58.0 315.4 58.0 1 112.9
23 0 0 0 O
24 57.6 315 5 57.6 1 112.9
Conveyor 2 25 184.1 584.2 184.1 1 209.0
26 501.2 1004.1 501.2 i 359.3
27 594.5 1114.0 594.5 i 398.6
28 1328.8 2001 7 1328.8 1 716.3
29 1378.8 2962 5 1378.8 i 1060.1
30 1651.6 3435.5 1651.6 i 1229.3
31 2284.6 4347.2 2284.6 i 1555.6
32 2890.0 5097.3 2890.0 i 1824.0
Conveyor to Filler #2 33 7877.2 8192.0 7877.2 1 2931.4
34 4027.9 5506.9 4027.9 1 1970.6
35 5828.4 6624.2 5828.4 i 2370.4
Conveyor to Filler #1 36 8424.9 8046 8 8424.9 i 2879.5
37 11036.9 9356.3 11036.9 1 3348.0
Filler #2 38 479.4 723.9 479.4 i 259.1
39 1783.3 1403.5 1783.3 i 502.2
caser #2 40 252.2 251.7 252.2 i 90.1
41 131.7 252.4 131.7 i 90.3
stacker #2 42 0.0 0.0
43 0.0 0.0
Filler #1 44 1056.7 1569.8 1056.7 i 561.7
45 2998.7 2723.6 2998.7 i 974.6
caser #1 46 1420.7 1619.7 1420.7 1 579.6
47 1408.1 1582.9 1408.1 1 566.4
stacker # 1 48 0.0 0.0
49 0.0 0.0
cooling storage 50 0.0 0.0

111

Table D3. Average busy time of elements

Element AVG
Blowmolder #1 1 49023.6
2 48723.5
3 48514.2
4 0
Blowmolder #2 5 54290.5
6 53982.6
7 53767.6
8 0
Blowmolder #3 9 53025.5
10 52690.6
11 52608.7
12 0
Blowmolder #4 13 52509.5
14 52215.4
15 52011.9
16 39146.3
Regrinder 17 0
18 2416.3
Conveyor 1 19 5600.5
20 13765.3
21 42057.1
22 51039.4
23 26587.8
24 56864.1
Conveyor 2 25 56512.9
26 43340.5
27 55638.8
28 54978.7
29 48811.9
30 53529.1
31 52661.9
32 47522.1
Conveyor to Filler #2 33 29200.3
34 28211.3
35 26762.7
Conveyor to Filler #1 36 25685.3
37 41342.1
Filler #2 38 52388.7
39 10288.1
caser #2 40 52074.5
41 3422.4
stacker #2 42 16871.8
43 41608.5
Filler #1 44 51216.0
45 10354.0
caser #1 46 50848.7
47 3399.9
stacker #1 48 6650.6
49 20550.9
cooling storage 50 0

112

STDEV 95 % Confidence
.6
48723.
.2

6046.3
6045.4
6045.4
0
3224.6
3224.7
3224.6
0
5689.
5672.
5687.
O
4758.
4757.
4757.
1902.
0
262.6
313.9
551.3
481.9
4660.3
2330.5
582.8
1001.
1936.
2000.
3078.
3579.
4552.
5293.
9611.
3782.
4354.
5003.
6354.
1871.
2939.
469.6
2874.1
158.1
779.4
1805.0
3593.3
455.6
3148.9
149.0
289.8
811.0
0

NQN

mmxow

mmqmmmbmmmomwxo

49023

48514

54290.
S3982.
53767.

53025.
52690.
52608.

52509.
52215.
52011.
39146.

2416.

5600.
13765.
42057.
51039.
26587.
56864.
56512.
43340.
55638.
54978.
48811.
53529.
52661.
47522.
29200.
28211.
26762.
25685.
41342.
52388.
10288.
52074.

3422.
16871.
41608.
51216.
10354.
50848.

3399.

6650.
20550.

5

qmm mmm
H-Hl+ H-Hl+

WWIbU'I
H'H'H'H-

\ommqoommlbmr-IqpqumeqummmHmna-mew

t
i
i

H-Hl+++H—Hl+l+H-HI+++H—Hl+l+H—Hl+l+H-HI+++H-HI+++H—Hl+l+

2163.6
2163.3
2163.3

1153.9
1153.
1153.9

\0

2035.8
2029.9
2035.1

1702.7
1702.6
1702.6
680.9

94.0
112.3
197.3
172.4
1667.6
833.9
208.5
358.5
692.9
715.9
1101.
1281.
1629.
1894.
3439.
1353.
1558.
1790.
2274.
669.8
1051.9
168.0
1028.4
56.6
278.9
645.9
1285.8
163.0
1126.8
53.3
103.7
290.2

ObﬁQWbNOh

Interval

Table D4. Average down time of elements

Element AVG STDEV 95% Confidence Interval

0.0
.4 6046.3 8576.4 i 2163.6
0.0
0.0

Blowmolder #1

q o

m
OOOOOOOOOOOOOOOOOOOOOOGOOOQO

Blowmolder #2

0
w .
O

OrbOrb-COOOOOOOOOOOOOOOOOOOOOOCDOOOOOOOC

.6 3296.4 i 1156.0

U
\o o
b
N

\qummnﬁUNH
OU'IOU'IOU'ICNOkOOOOOOOOOOOOOOOOOOOOOOOO\IOOOMOOON

Blowmolder #3

\O o

.7 4550.2 i 2036.4

é»
U1 0

OWOIﬁOWOHCabot-‘00OOOOOOWOOOOOOOOOOOOOOOOOOUTOOONOOOUIO
N
01

10

12
Blowmolder #4 13
14
15
16
Regrinder 17
18
Conveyor 1 19
20
21
22
23
24
Conveyor 2 25
26
27
28
29
30
31
32
Conveyor to Filler #2 33
34
35
Conveyor to Filler #1 36
37
Filler #2 38
39
Caser #2 40
41
Stacker #2 42
43
Filler #1 44
45
Caser #1 46
47
Stacker # 1 48 1685.4 1962.9 i 603.1
49 0.0
Cooling Storage 50 618.2 1049.8 618.2 i 375.7

U1 0

.3 5090.5 1 1702.7

U1
go .
U1
uh

.0 535.7 i 382.9

U1
U1
‘1
H
q .

2106.1 1 1057.3

0'
OWCmCCOOOOOO'

H

N

U].

(D

N

1473.0 i 438.1

H
q.
C
H
N-
U

114.9 1 127.3

H
lb
\0
6:
Ln
m

1393.4 1 919.1

‘00

h

N

m.
ONomo-

U1

H
\O
ONOWCWQ.
H
H

1493.1 i 541.4

H
H .
\O

H
m a
\O

113

Table D5. Average queue of elements

Element AVG STDEV 95% Confidence Interval

Blowmolder #1 1 1.0 0.0

2 4.0 0.0

3 15.9 0.0

4 9.2 0.2 9.2 i 0.058
Blowmolder #2 5 1.0 0.0

6 4.0 0.0

7 15.9 0.3 15.9 i 0.108

8 9.3 0.2 9.3 i 0.068
Blowmolder #3 9 1.0 0.0

10 4.0 0.0

11 17 3 0.7 17.3 i 0.260

12 10 1 0.3 10.1 i 0.097
Blowmolder #4 13 1.0 0.0

14 4.0 0.0

15 15.9 0.1 15.9 i 0.026

16 9.3 0.1 9.3 i 0.049
Regrinder 17 1.5 0.2 1.5 i 0.083

18 0.0 0.0
Conveyor 1 19 0.0 0.0

20 0.1 0.0

21 0.3 0.1 0.3 i 0.021

22 2.8 0.5 2.8 i 0.189

23 1.5 0.1 1.5 i 0.052

24 2.3 0.4 2.3 i 0.127
Conveyor 2 25 6.4 1.7 6.4 i 0.620

26 7.2 3.1 7.2 i 1.109

27 1.7 0.9 1.7 i 0.305

28 7.8 4.8 7.8 i 1.717

29 7.4 6.9 7.4 i 2.462

30 3.5 3.7 3.5 i 1.319

31 7.3 8.2 7.3 i 2.918

32 8.1 9.4 8.1 i 3.348
Conveyor to Filler #2 33 33.2 40.1 33.2 i 14.350

34 4.4 5.5 4.4 i 1.967

35 6.2 6.6 6.2 i 2.365
Conveyor to Filler #1 36 8.6 8.0 8.6 i 2.858

37 11.6 10.1 11.6 i 3.622
Filler #2 38 5.4 3.6 5.4 i 1.278

39 7.7 0.8 7.7 i 0.284
Caser #2 40 2.3 0.1 2.3 i 0.033

41 1.7 0.1 1.7 i 0.029
Stacker #2 42 6.2 0.2 6.2 i 0.060

43 0.3 0.0
Filler #1 44 6.6 4.1 6.6 i 1.472

45 8.4 1.7 8.4 i 0.614
Caser #1 46 2.3 0.1 2.3 i 0.040

47 1.8 0.2 1.8 i 0.054
Stacker #1 48 6.2 0.2 6.2 i 0.080

49 0.1 0.0 0.1 i 0.002
Cooling Storage 50 0.4 0.2 0.4 i 0.062

114

Table D6. Average idle time of elements

Blowmolder #1

Blowmolder #2

Blowmolder #3

Blowmolder #4

Regrinder

Conveyor 1

Conveyor 2

Conveyor to Filler #2

Conveyor to Filler #1
Filler #2

Caser #2

Stacker #2

Filler #1

Caser #1

Stacker #1

Cooling Storage

Element

WWQO‘U'IQWNH

m p p n b A 9 ¢ h o p w w w w w w u u w w M N M N w w M N w w H H H H H H H H H H
o m m 4 m m b w M H o m m q m m b u N H o m m q m m A u N H o m m 4 m m a u N H 0

AVG

0.0
0.0
8876.5
9084.8
0.0
0.0
3601.7
3814.7
0.0
0.0
4803.6
4983.8
0.0
0.0
5384.
5588.
18453.
57600.
55168.
51979.
43796.
15484.
6560.
30954.
551.8
585.9
13665.0
632.4
706.8
7136.
1786.
2048.
2200.
24371.
23560.
22412.
20877.
13672.
3428.
45586.
5393.
54062.
40728.
13541.
3385.
44332.
5343.
52237.
50949.
36430.

mmml-‘WOO‘JI-‘m

mhwuwwbwqmqolbmhwquwm

115

STDEV

0.0
0.0
6045.4
6045.5
0.0
0.0
3232.1
3232.4
0.0
0.0
5685.1
5679.1
0.0
0.0
4757.
4757.
1902.8
0.0
259.8
315.3
555.5
397.5
4660.3
2366.1
14.2
14.4
1628.3
18.8
46.3
1584.
1108.
1127.
1928.
2228.
2661.
3351.
3496.
2665.
2888.
1366.
2927.
381.7
779.4
2710.
2790.
2509.
2799.
1646.
289.8
1007.9

\OW

UbONQONWIﬁQQQ

\DNU‘IO‘G)

95%

8876.
9084.

3601.
3814.

4803.
4983.

5384.
5588.
18453.

55168.
51979.
43796.
15484.
6560.
30954.
551.
585.
13665.
632.
706.
7136.
1786.
2048.
2200.
24371.
23560.
22412.
20877.
13672.
3428.
45586.
5393.
54062.
40728.
13541.
3385.
44332.
5343.
52237.
50949.
36430.

01

HQ

4
H-

\olhtowwwbtoqwuoomhwquwmmbommmmmeo
H H H H H H H H H H H H H H H H H H»H H H H H H'H H H'H H H H’H

H-I+

Confidence Interval

2163.3
2163.3

1156.6
1156.7

2034.3
2032.2

1702.6
1702.6
680.9

93.0
112.8
198.8
142.2
1667.6
846.7
5.1
5.2
582.7
6.7
16.6
567.
396.
403.
690.
797.
952.
1199.1
1251.3
953.7
1033.4
489.0
1047.5
136.
278.
970.
998.
898.
1001.6
589.3
103.7
360.7

w b H m 4 H

omomm

Table D7. Total number of produced of each element

Element AVG STDEV 95% Confidence Interval
Blowmolder #1 1 2685.7 243.9 2685.7 i 87.3
2 2681.7 243.9 2681.7 i 87.3
3 2665.6 243.9 2665.6 i 87.3
4 2656.1 243.6 2656.1 1 87.2
Blowmolder #2 5 2771.3 179.4 2771.3 i 64.2
6 2767.3 179.4 2767.3 i 64.2
7 2751.2 179.6 2751.2 i 64.3
8 2741.5 179.6 2741.5 i 64.3
Blowmolder #3 9 2788.5 305.1 2788.5 i 109.2
10 2784.5 305.1 2784.5 1 109.2
11 2767.2 304.5 2767.2 i 109.0
12 2757.0 304.4 2757.0 i 108.9
Blowmolder #4 13 2856.5 236.8 2856.5 i 84.7
14 2852.5 236.8 2852.5 1 84.7
15 2836.5 236.8 2836.5 1 84.7
16 2827.5 236.3 2827.5 i 84.6
Regrinder 17 783.8 35.5 783.8 1 12.7
18 0.0 0.0
Conveyor 1 19 2645.8 293.4 2645.8 i 105.0
20 5168.4 327.9 5168.4 i 117.3
21 7564.5 356.7 7564.5 i 127.6
22 7562.0 356.7 7562.0 i 127.6
23 2630.2 218.7 2630.2 i 78.3
24 2627.6 218.7 2627.6 i 78.2
Conveyor 2 25 10181.6 392.3 10181.6 i 140.4
26 10167.3 403.0 10167.3 1 144.2
27 10164.8 405.7 10164.8 i 145.2
28 10154.1 418.1 10154.1 i 149.6
29 10144.3 430.5 10144.3 1 154.0
30 10140.6 435.9 10140.6 1 156.0
31 10133.2 446.5 10133.2 1 159.8
32 10126.1 457.1 10126.1 i 163.6
Conveyor to Filler #2 33 5069.8 303.0 5069.8 i 108.4
34 5009.4 251.2 5009.4 i 89.9
35 5001.6 251.3 5001.6 1 89.9
Conveyor to Filler #1 36 4989.1 254.1 4989.1 i 90.9
37 5051.6 308.3 5051.6 i 110.3
Filler #2 38 4979.9 255.5 4979.9 1 91.4
39 4972.7 255.8 4972.7 i 91.5
Caser #2 40 1242.8 63.8 1242.8 i 22.8
41 1240.9 64.0 1240.9 1 22.9
Stacker #2 42 102.8 5.3 102.8 i 1.9
43 102.6 5.3 102.6 i 1.9
Filler #1 44 5041.7 311.5 5041.7 i 111.4
45 5032.0 313.4 5032.0 i 112.1
Caser #1 46 1257.4 78.4 1257.4 i 28 1
47 1255.4 78.8 1255.4 i 28.2
Stacker #1 48 104.1 6.6 104.1 1 2.4
49 104.0 6.6 104.0 1 2.3
Cooling Storage 50 206.1 10.9 206.1 i 3.9

116

Table D8. Average number of produced bottles

 

 

 

 

 

 

 

 

 

 

 

 

, standard
Expenment average confidence Interval
deviation

Original Model 98880 3819 98880 1 1366.7
Conveyor speed 1 98144 4636 98144 :t 1659
Conveyor speed 2 99424 4770 99424 i 1706.9
Adding

101296 2834 100704 at 1014
accumulators
Speeding up

99819 3468 99592 :l: 1241
stackers and casers
Adding
accumulators and

_ 100992 3841 100992 1 1374.5

speeding up
stackers and casers
Reducing repair
time of ﬁlling 99344 4174 99424 3: 1493.6
machines
Reducing repair
. 101888 2937 100912 i 1051
time of casers
Reducing repair

99888 4982 99888 1 1782.9
time of stackers
Reducing repair

104800 3731.6 104800 i 1335.3

time of blowmolders

 

 

 

 

117

 

Table D9. Output of ANOVA test

One-Way Analysis of Variance

Analysis of Variance for C2

Source DF SS
C1 10 1.650E+O9
Error 319 4.700E+O9
Total 329 6.349E+09
Level N Mean
Expl 30 98144
Original 30 98880
Exp6 30 99344
Epo 30 99424
Exp4 30 99819
Exp8 30 99888
ExpS 30 100992
Exp3 30 101296
Exp7 30 101888
Exp9 30 104800
Pooled StDev = 3838

MS
164990280
14731993

Fisher's pairwise comparisons

Family error rate =
Individual error rate

Critical value = 1.967

0.672
0.0500

Intervals for (column level mean)

Expl

Original -2685
1213

Exp6 -3149
749

Epo -3230
669

Exp4 -3624
274

Exp8 -3693
205

Exp5 -4797
-899

Original

-2413
1485

-2494
1405

-2888
1010

-2957
941

-4061
-163

F

11.20

Exp6

-203O
1869

-2424
1474

-2493
1405

-3597
301

118

P
0.000

(row level mean)

Epo

-2344
1555

-2413
1486

-3517
382

Individual 95% CIs For Mean
Based on Pooled StDev

-------- +----—----+---------+-------—
(---*--~-)
(----*—-->
(---*---->
(---*----)
(----*--—)
(-—-—*—-—-)
<----*--->
(----*---)
<——--*--->
<--—*----)
-------- +---------+---—---—-+-—--—---
99000 102000 105000

Exp4

-2018
1880

-3122
776

Exp8

-3053
845

Table D9. Output of ANOVA test

One-Way Analysis of Variance

Analysis of Variance for C2

Source DF SS
C1 10 1.650E+O9
Error 319 4.700E+09
Total 329 6.349E+09
Level N Mean
Expl 30 98144
Original 30 98880
Exp6 30 99344
Epo 30 99424
Exp4 30 99819
Exp8 30 99888
ExpS 30 100992
Exp3 30 101296
Exp7 30 101888
Exp9 30 104800
Pooled StDev = 3838

MS
164990280
14731993

Fisher‘s pairwise comparisons

Family error rate =
Individual error rate =

Critical value = 1.967

0.672
0.0500

Intervals for (column level mean)

Expl

Original -2685
1213

Exp6 -3149
749

Exp2 -3230
669

Exp4 -3624
274

Exp8 -3693
205

ExpS -4797
-899

Original

-2413
1485

-2494
1405

-2888
1010

-2957
941

-4061
-l63

F P
11.20 0.000

Individual 95% CIs For Mean
Based on Pooled StDev

99000 102000 105000

(row level mean)

Exp6 Exp2 Bxp4 Exp8
-2030
1869
-2424 -2344
1474 1555
-2493 -2413 ~2018
1405 1486 1880
-3597 ~3517 -3122 -3053
301 382 776 845

118

(Continued)

Exp3 -5101 -4365 -3901 -3821 -3426 -3357
—1203 —467 -3 78 472 541

Exp7 —5693 -4957 —4493 -4413 -4018 -949
-1795 -1059 -595 -514 -120 -51

Exp9 -8605 -7869 -7405 -7325 -6930 -6861
-4707 -3971 -3507 -3426 -3032 —2963
ExpS Exp3 Exp7

Exp3 -2253
1645

Exp? -2845 -2541
1053 1357

Exp9 -5757 -5453 -4861
-1859 -1555 ~963

Note:

1. Expl: Changing the speed of conveyor 1

2. Epo: Changing the speed of conveyor 2

3. Exp3: Adding accumulators

4. Exp4: Changing the speed of casers and stackers

5. Exp5: Adding the accumulators and changing the speed of casers and

stackers

6. Exp6: Increasing the efficiency of filling machines

7. Exp7: Increasing the efficiency of casers

8. ExpB: Increasing the efficiency of stackers

9. Exp9: Increasing the efficiency of blowmolding machines

119

Table D10. Output of ANOVA test

One-Way Analysis of Variance

Analysis of Variance for C2

Source DF SS MS F P
C1 10 1.650E+O9 164990280 11.20 0.000
Error 319 4.7OOE+09 14731993

Total 329 6.349E+09

Individual 95% CIs For Mean
Based on Pooled StDev

Level N Mean StDev -------- + --------- + --------- + ________

EXpl 30 98144 4636 (---*—---)

Original 30 98880 3819 (----*--—)

Exp6 30 99344 4174 (---*-—--)

EXPZ 30 99424 4770 (-__.____)

Exp4 30 99819 3468 (----*---)

Exp8 30 99888 4982 (----*----)

Exp5 30 100992 3841 (----*---)

Exp3 30 101296 2834 (----*---l

Exp7 30 101888 2937 (--—-*——-)

Exp9 30 104800 3732 (~--*----)

ExplO 30 105392 1898 (~--*----)
-------- +---------+---------+--------

Pooled StDev = 3838 99000 102000 105000

Fisher's pairwise comparisons

Family error rate = 0.672

Individual error rate = 0.0500
Critical value = 1.967
Intervals for (column level mean) - (row level mean)
Expl Original Exp6 Exp2 Exp4 Exp8
Original -2685
1213
Exp6 -3149 -2413
749 1485
Epo -3230 —2494 -2030
669 1405 1869
Exp4 -3624 -2888 -2424 -2344
274 1010 1474 1555
Exp8 -3693 -2957 -2493 -2413 -2018
205 941 1405 1486 1880
Exp5 -4797 -4061 -3597 -3517 -3122 -3053
-899 -163 301 382 776 845

120

(Continued)

Exp3 -5101 -4365 -3901 -3821 -3426 -3357
-1203 -467 -3 78 472 541
Exp? -5693 —4957 -4493 -4413 —4018 ~949
-1795 -1059 -595 -514 -120 -51
Exp9 -8605 -7869 -7405 —7325 -6930 -6861
-4707 -3971 -3507 -3426 -3032 —2963
Exp5 Exp3 Exp7 Exp9
Exp3 -2253
1645
Exp7 -2845 -2541
1053 1357
Exp9 -5757 -5453 -4861
-1859 -1555 -963
ExplO -6349 -6045 -5453 ~2541
-2451 -2147 -1555 1357
Note:

1. Expl: Changing the speed of conveyor 1

2. Epo: Changing the speed of conveyor 2

3. Exp3: Adding accumulators

4. Exp4: Changing the speed of casers and stackers

5. ExpS: Adding the accumulators and changing the speed of casers and
stackers

6. Exp6: Increasing the efficiency of filling machines

7. Exp7: Increasing the efficiency of casers

8. Exp8: Increasing the efficiency of stackers

9. Exp9: Increasing the efficiency of blowmolding machines

10.Exp10: Increasing the efficiency of blowmolding machines and casers

121

BIBLIOGRAPHY

122

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