PRODUCTION LINE MODELING: A SIMPLFIED APPROACH BASED

ON THEORY OF CONSTRAINTS

_______________

A Thesis

Presented to the

Faculty of

San Diego State University

_______________

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

in

Computer Science

_______________

by

John M. Stronks

Spring 2013

iii

Copyright © 2013

by

John M. Stronks

All Rights Reserved

iv

DEDICATION

I would like to dedicate this thesis to my wife for her patience and support, my older

brother for his model of perseverance under unrelenting circumstances, and my parents for

instilling in me the value of education.

v

Computers are like Old Testament Gods; lots of rules no mercy -Joseph Campbell

vi

ABSTRACT OF THE THESIS

Production Line Modeling: A Simplified Approach Based on Theory of Constraints

by John M. Stronks

Master of Science in Computer Science San Diego State University, 2013

Much academic energy has been invested in the study of optimizing assembly or production lines. The Assembly Line Balancing Problem design problem is an artifact of that work. Theory of Constraints purports that an assembly line that is purposely and strategically unbalanced provides superior performance in terms of predictability and throughput over the traditional balanced line. This study articulates a custom production line model based on Theory of Constraints and compares its performance to the traditional operations management paradigm, a balanced line. Results show that a purposely unbalanced line provides superior flow of material and greater throughput than the traditional balanced line configuration. Additionally the simplified model and approach may be more appealing with respect to the design, development, and computational costs than those required of the conventional line balancing methodologies.

vii

TABLE OF CONTENTS

PAGE

ABSTRACT ............................................................................................................................. vi

LIST OF TABLES ................................................................................................................... ix

LIST OF FIGURES ...................................................................................................................x

ACKNOWLEDGEMENTS ..................................................................................................... xi

CHAPTER

1 INTRODUCTION .........................................................................................................1 

Background ..............................................................................................................1 

Purpose of the Study ................................................................................................2 

Limitations of the Study...........................................................................................3 

2 BACKGROUND AND LITERATURE ........................................................................6 

Production Line Modeling .......................................................................................6 

Theory of Constraints Overview ............................................................................11 

3 METHODOLOGY ......................................................................................................15 

Introduction ............................................................................................................15 

LineSimulator Architecture ...................................................................................15 

Cells .................................................................................................................16 

Production Line ................................................................................................18 

Line Runner .....................................................................................................20 

Simulator ..........................................................................................................21 

Experimental Method.............................................................................................21 

Metrics .............................................................................................................22 

Balanced Line ..................................................................................................23 

Unbalanced Line ..............................................................................................25 

4 RESULTS ....................................................................................................................28 

Introduction ............................................................................................................28 

Balanced Line Results............................................................................................28 

viii

Unbalanced Line Results .......................................................................................33 

Comparison ............................................................................................................38 

5 CONCLUSION ............................................................................................................43 

6 FUTURE RECOMMENDATIONS ............................................................................45 

Introduction ............................................................................................................45 

Learning Classifier Systems ..................................................................................45 

Parallel Programming ............................................................................................47 

Wondering Bottleneck Management .....................................................................48 

Variant Line Models and Financial Measures .......................................................49 

REFERENCES ........................................................................................................................50

APPENDIX

A GLOSSARY ................................................................................................................51 

B LINE SIMULATOR UML ..........................................................................................53 

ix

LIST OF TABLES

PAGE

Table 1. Notional Classifier Chromosomal Representation ....................................................47 

x

LIST OF FIGURES

PAGE

Figure 1. Balanced line - throughput vs. WorkCell count. ......................................................24 

Figure 2. Balanced line - throughput variation. .......................................................................29 

Figure 3. Balanced line - throughput and inventory characterization. .....................................30 

Figure 4. Balanced line - throughput vs. variation with alternate buffer sizes. .......................31 

Figure 5. Balanced line - inventory vs. variation with alternate buffer sizes. .........................31 

Figure 6. Unbalanced line - inventory vs. cell output variation. ..............................................32 

Figure 7. Unbalanced line - throughout / inventory ratio vs. variation (Cp = 2.0). ..................35 

Figure 8. Unbalanced line - throughput vs. cell output variation (Cp 1.0-2.0). .......................35 

Figure 9. Unbalanced line - throughput / inventory vs. variation (Cp 1.0-2.0). .......................36 

Figure 10. Unbalanced line - inventory (Cp 1.0-2.0). ..............................................................36 

Figure 11. Comparison - throughput variation. .......................................................................38 

Figure 12. Unbalanced line - inventory surface. ......................................................................40 

Figure 13. Unbalanced line - throughput / inventory surface. .................................................42 

Figure 14. Line Simulator UML Diagram. ..............................................................................54 

xi

ACKNOWLEDGEMENTS

I would like to thank Dr. Joseph Lewis and Dr. Roger Whitney for their assistance

and guidance in the development of this work. I would also like to thank David Oakley for

introducing me to the Theory of Constraints, as well as, his mentorship during this study.

1

CHAPTER 1

INTRODUCTION

BACKGROUND

The industrialized world relies heavily on production line optimizing to efficiently

produce large volumes of products over extended periods of time. Boysen et al., define a

production line or assembly line as “a flow oriented production system where the productive

units performing the operations, referred to as stations, are aligned in a serial manner. The

workpieces visit stations successively as they are moved along the line by some kind of

transportation system, e.g. a conveyor belt.” [1]. Tambe notes “Historically assembly line is

designed for high volume production of a single item or family of items.” [2]. Similar

definitions can be found throughout published literature.

Key to the characteristics and definitions of an assembly line are the concepts of

automation and robotics, exact and extensive time studies, precedence structures, large

sustained volumes and little to no tolerance for variation. From a terminology perspective

production line or assembly line are generally used interchangeably.

The formal study and model of assembly lines can be traced back to Salveson in the

mid-1950s. From there, myriads of studies and formalizations have been evaluated. The

topic has been formalized and has its own acronym, Assembly Line Balancing (ALB) as well

as its own design problem category, the Assembly Line Balancing Problem (ALBP). Ample

variations of the problem exist, the General Assembly Line Balancing (GALB), and the

Single Assembly Line Balancing problem (SALB) all of which are considered NP-Hard.

Much study and computational energy has been devoted to solving this problem. The

question posed is “What do you do when you have a product that has relatively low volume

and high process variability?” It is at this point the ALB no longer applies. How many

products are produced like automobiles, not many? Many products are semi-custom designs,

with highly sophisticated processes and components, and limited volume. These products

2

rely on manual labor, operator and management developed heuristics, inherent with

embedded variabilities.

The intent of this study is to show that through the application of Theory of

Constrains (TOC), introduced by Eliyahu M. Goldratt in his book The Goal, that products

can be produced predictably and efficiently via flow balancing. An essential premise of the

study is that for low to medium volume products, in a high variability production

environment, balancing flow with capacity provides superior and more predictable

performance. A core tenant of TOC is that every system has a constraint, and if that

constraint is actively managed, the system can be optimized.

Here, the traditional Operation Management paradigm of a “balanced line” is

challenged. It can be shown that a “balanced line” with inherent variability will consistently

underperform relative to its expected output. It will be shown that strategically unbalancing

a line and managing a self-imposed constraint can produce superior performance relative to a

comparable balanced line configuration.

An alternative simplified assembly line balancing model is proposed. The model

incorporates production variability distributions seen in the real world. It will be shown that

through constraint management and proper definition and management of work station

capacities and variabilities this simplified approach provides superior results.

PURPOSE OF THE STUDY

The purpose of this study is to provide an alternate, simplified framework for a

production line model applicable to products with inherent process and task variability. The

goal is to demonstrate that predictable output can be maintained in the processing of custom

products with known, inherent process variabilities through a model based on TOC.

The traditional production line relies on precisely grouped tasks, precedence

structures, and fully optimized processes and controls. The traditional methods are

applicable in environments that can support extensive analysis and line development costs,

robotic or automated tasking, and large sustained volumes. While this might work in the

automotive, consumer electronic, or durable products industries, it is not an effective tool for

a sizable portion of the custom industrial market.

3

While traditional models focus on the intricacies of each individual task, this model

moves up one level of abstraction and encapsulates the individual tasks for each cell into a

simpler model that is defined by the cell capacity and variability. The model assumes the

sum of the individual tasks can be represented through the variability and capacity

parameters encapsulated in each cell.

The objective of this study is to provide a model of a synchronous production line

with managed constraints that provides a predictable output. A synchronous production line

is defined by Lueng as “an automatic production line consisting of a number of workstations

connected in series with synchronized part transfers between workstations. A single transfer

mechanism controls the entire line so that all workstations release their parts

simultaneously.” [3]. This model contends that with known capacities and variabilities, and

properly placed and managed constraints (or bottlenecks), flow management may be utilized

producing superior output.

Further the concept of the traditional “balanced line” model is challenged. It is

shown that the traditional notion of a “balanced” production line may not be the preferred

method for lower volume variable environments. The objective is to show that the traditional

model works under ideal conditions (low variability) and that a purposely “unbalanced line”

may be a better approach for the prescribed environment.

LIMITATIONS OF THE STUDY

Initially, one might present the simplicity in the representation of the model as a

limitation. As with any model, with increased fidelity comes increased complexity. The

intent of this study is to confirm the notion that a strategically unbalanced production line

with inherently variable processes can be designed to produced superior performance to that

of a similarly balanced line. Furthermore, that the simplified representation of a production

line is an effective analysis tool.

Additionally, the simplicity of this model could be challenged with respect to its

applicability to real life environments. The generalizations of the model are accurate,

however a more precise representation, pertinent to a specific problem domain, can be

4

developed. Recommendations and expansion of the representational model are discussed in

the Future Recommendations section.

Specifically, four items warrant discussion. First, one could argue that this study is

essentially not about line balancing. However this model provides a form of line balancing,

just not in the traditional sense of time studies and task identification requiring full

enumeration of possible solutions. This study looks at the advantages of balancing flow

versus the traditional notion of balancing a line to minimize total cycle time.

It is assumed that individual cells contain lower level tasks, with heuristic logic

applied to the grouping of the tasks to the cells. The attributes of the grouped tasks are

encapsulated in the capacity and variability parameters of the cell instead of the traditional

individual task duration and precedence models. The grouping of tasks could take the form

of a traditional line balancing exercise, or be informally defined based on a designer’s

heuristic knowledge of the product, the available resource base, or equipment and process

limitations. Or more likely, that highly customized products generally do not provide a

volume or resource base that supports a highly detailed, expansive optimal line balancing

analysis.

Secondly, typically these product types have medium term production cycles with

respect to time and volume. The shorter terms imply process variations. These variations

can be attributed to start up issues or general lack of optimization time which the traditional

models do not generally incorporate. A line is set up to run for a few months, maybe a year,

and then replaced by the next product. In this environment the idea of expending valuable

resources, defining tasks to an infinitesimal level, on a medium length production run does

not make sense. Which again bolsters the idea that the construct promoted in this model of

generalized task groupings into cells, with known capacity profiles and variabilities is a

viable and effective model.

Thirdly, mixed model lines provide an even greater challenge then the standard single

model line. This model provides an acceptable balance between complexity and

predictability. The mixed model line balancing frameworks are fraught with complexity.

Attempting to schedule and manage the arrival, rate, and tooling required for mixed model

lines is cumbersome to say the least. However, to develop cell profiles with this model one

5

could simply define the capacity required for each of the models, develop a standard tool set

across cells, and assign variability parameters or distributions to the cells based on the model

mix. The resulting representation being an effective, simple mixed model line, with

predictable output, at a reasonable planning and implementation cost.

Lastly, TOC theory incorporates financial implications. This model does not

incorporate the financial aspects of TOC. The intent of the study is to develop a simplified

production line model, not to model financial performance based on production line

execution. Extension of the model to incorporate financial measures is discussed in later

sections.

6

CHAPTER 2

BACKGROUND AND LITERATURE

PRODUCTION LINE MODELING

Production or assembly lines were pioneered into the industrial limelight by and are

synonymous with Henry Ford and the production of his Model T motor car. He is considered

the father of the modern assembly line which is now the core of production operations for

high volume industrial products. Variants and modifications to his original design are vast

and uncountable. Of course, with this came the drive to design and optimize production

lines, and predictably an entire category of academic study, the Assembly Line Balancing

Problem (ALBP).

Assembly lines are comprised of varying quantities of components depending on the

end product complexity and implementation. The line components can be broken down into

three categories; the physical features of the line, the line measures or attributes and

representations of the line. The ALBP attempts to represent the line in a model of some form

and measure the line performance with respect to an objective. Multiple models and

objectives exist; however typically, the main objective is to balance the work at each station

equally while minimizing the time it takes to produce the finished item.

The physical components of a line are the line itself, the workstations or cells, and the

workpieces. The line is comprised of cells ordered in some fashion. The cells are areas

where sets of appropriate operations are performed repeatedly. The workpieces are the items

on which the tasks are performed. The individual elementary operations performed in the

cells are defined as tasks.

Attributes of a line are cycle time, station time, idle time, and station load content or

capacity. The cycle time is the amount of time it takes for one item to traverse the line and

emerge in its final form. Station time is the amount of time required to perform the assigned

tasks at a station. When sum of the station times is less than the cycle time, that difference in

time is defined as idle time. The set of tasks assigned to the station is the station load or

7

content. The capacity of a station is the quantity of completed items a cell can produce for a

given period of time. Capacity and cycle time are generally considered inverses of each

other.

The representation of a line is typically presented in the form of a vector whose

elements describe the line, cell, and objective attributes. Production lines also maintain

graphical representations in the form of a precedence graph. The precedence graph is

essentially a directed graph that describes orientation of the cells and the flow of material

with respect to the cells.

Until 2001, the study of the ALBP paralleled the Wild West, anything goes. A

framework for describing and evaluating ALBPs was nonexistent. In 2006 Boysen and team

defined a uniform framework for the classification of ALBPs and their associated properties

and objectives. Their work resulted in a classification scheme for ALBPs. The scheme is

represented by a tuple [a|b|g] where a defines the precedence graph characteristics, b

identifies the station and line characteristics, and g the objectives.

The end result of the examination presented a potentially massive, complicated vector

representation of a production line. The precedence graph characteristics carried six

dimensions with 22 combinatorial options. The station and line characteristics element

allowed for six attributes with 19 available options. And the optimization objective element

provided the selection of multiple objectives out of a set of eight solution evaluations. Given

the number of dimensions and potential for high station counts, it is clear that the

computational resources could be massive for a single line, not to mention the comparison of

multiple lines and configurations.

Generally speaking, there are four measures of problem difficulty. Those measures

are order strength, flexibility ratio, west ratio, and time interval. Order strength and

flexibility ratio both view the difficulty of a problem with respect to the relative number of

precedence relationships in the graph. Order strength deems problems with higher values of

potential feasible solutions to be more difficult. Flexibility ratio, as the names implies, is the

converse of order strength or the flexibility within the precedence structure. West ratio

reflects the average number of tasks per station and is dependent on the optimum number of

stations in the solution. Task interval compares the range of task times with the cycle time.

8

The valuation of production line ”goodness” has been a point of controversy.

Driscoll and Thilakawardana sum it up by stating “Assembly line balancing is a classic ill-

structures problem where total enumeration is infeasible and optimal solutions uncertain for

industrial problems.” [4]. Driscoll and Thilakawardana tackle two prominent issues related

to the Simple Assembly Line Balancing Problem (SALBP). First is the measure of the

difficulty and second is the assessment of the solution.

Driscoll and Thilakawardana note that the existing measures of difficulty break down

into two measures related to precedence (time and method) and define a new compound

measure. They propose that identification of problem difficulty be a multi-step approach.

First, four measures of difficulty are calculated. These new measures are precedence

strength and bias and task time intensity and distribution. The precedence measures look at

the relative ordering constraints and assignment availability of a line during balancing. The

task time measures look at individual task times with respect to cycle time. One measure

looks at the average time while the other looks for shorter tasks that can be distributed

through the line. The equal combination of these measures then constitutes a metric of

problem difficulty.

Driscoll and Thilakawardana also propose the replacement of the traditional balance

assessment methods with two new measures. They recommend replacing the balance delay

and smoothness criteria with measures of line efficiency and balance efficiency.

An extensive survey of ALBP algorithms was promoted by Baybar in 1986 [5].

Baybar’s work focused strictly on deterministic models. He specifically left out models and

algorithms that were inexact, or heuristic or approximation based and stochastic models. His

survey categorized the ALBP into two basic types the SALBP-1 and SALBP-2. He also

provided a third distinction, the GALBP, but considered it a generalization of the SALBP.

Baybar distinguished between the two types of SALBP in the following manner. All

deterministic SALBP have all input parameters defined with certainty, and that all tasks be

identified with a single station (cannot be split between stations), processed in a specified

order and fully completed. SALBP-1 added the following conditions; that all stations be

capable of processing any one of the tasks and those tasks may be performed at any station

and their times be independent of the station where the task is performed. Additionally, no

9

feeder or parallel lines exist and a single model is produced within a defined and fixed cycle

time. SALBP-2 maintained the same criteria, the only difference being the fixed cycle time

is replaced with a fixed number of stations. Baybar’s also provided extensive mathematical

formulations and conventions to further define both types of SALBPs.

With this foundation Baybar identified four basic algorithm groupings; Integer

Programming (both general and specialized), Specialized Branch and Bound, Other Integer

Programming Methods, and Dynamic Programming algorithms.

The Integer Programming methods utilized integer programming theory and

techniques to systematically search the problem domain. Typical branch and bound search

methods such as newest node searching and depth first search or backtracking were

employed. Additionally, specialized search techniques were noted with their representations

and processes following integer programming constructs.

In the case of the Specialized Branch and Bound algorithms a tree representation

defined the problem space although integer programming techniques were not used. Various

tree search procedures such as dominance rules and branching and bounding heuristics were

identified. Variations to known heuristics such as first-fit decreasing and positional

weighting were identified with various update and bookkeeping methods applied.

The Other Integer programming methods employed integer programming

representations, but did not use tree representations or branch and bound methods of

searching. Methods engaged were subset definition and evaluation where precedence graphs

were traversed and analyzed for details such as shortest or critical paths.

The Dynamic Programming techniques involved generating all feasible solutions in

some defined manner. One method defined all feasible assignments for the first station, then

for the second and third, and so on. Logic was defined to eliminate inferior assignment sets

and then duplicate sets or subsets were eliminated. Various dynamic programming

techniques or recursive solution generations and evaluations were studied extensively.

Since the SALBP-2 is simply a variant of SALBP-1 there are few algorithms for type

two problems. Essentially, any SALBP-1 method can be used to solve SALBP-2 by

adjusting the cycle time until the defined station count is reached. Generally speaking, the

solution to an SALBP-2 instance is simply iteratively solving a series of SALBP-1 problems.

10

Predictably, with the rise in popularity of evolutionary computation came the

possibility of solving the ALBP with genetic algorithms (GA). The fit seemed natural as the

ALBP maintains a large search space and an optimal solution may not be mandatory, close is

good enough. Additionally, representation of a line in a chromosomal format is a natural

extension of some of the integer programming approaches use in previous works.

Chong et al note that “Since SALBP is classified as NP-hard, solving it optimally by

total enumeration is not practical with real world large-sized problems.” [6]. Falkenauer and

Delchambre also detected the applicability of the GA to the SALBP stating “As far as an

available algorithm for the LBP (Line Balancing Problem) is concerned, we are not aware of

any polynomial approximation similar to those known for BPP (Bin Packing Problem).” [7].

Employing a GA to solve the SALBP requires the definition of a representation, fitness

function (objective), and applicable genetic operators.

Chong et al showed that seeding the initial population of a GA provided slightly

better results that a randomly generated initial population. The chromosomal representation

of the SALBP took the form of feasible task sequences whose length is the number of tasks

based on the precedent diagram. In their study the population size was set to 100, with the

seeding being two individuals generated via ranked positional weight and largest candidate

rule heuristics.

Their GA employed the roulette wheel selection method with a 1% elitism population

replacement scheme. Modified two point crossover and a scrambled mutation operators were

used, both of which allowed only feasible solutions as offspring. For solution optimization

they used the traditional balanced delay measure and modified the line efficiency metric

defined by Driscoll and Thilakawardana.

Falkenauer and Delchambre found that the representations and genetic operators used

to solve the BPP were easily extended to the SALBP. They found that once they modified

the representation to account for the specifics of the SALBP they could use the same genetic

operators used to attack traditional grouping problems. They found that the fitness function

was also easily mapped from the BPP problem to the SALBP. The only demonstrative

modification required for the SALBP was to ensure that precedence requirements were

11

maintained in potential solutions. They found their results to be comparable to more

computationally intensive enumeration techniques.

THEORY OF CONSTRAINTS OVERVIEW

Theory of Constraints was developed by Elliot Goldratt in 1984. Goldratt defines a

constraint as “anything that limits a system from achieving higher performance versus its

goal” [8]. TOC does not limit its philosophy to production lines, but looks at the system as a

whole. TOC looks at and evaluates every facet of a system. A glossary of common TOC

terms is provided in Appendix A.

In broader terms TOC contends that every system must have a constraint. Without

some type of constraint performance or achievement would be limitless. The key is proper

identification and management of the constraint. TOC views a constraint as a process or

operation that limits throughput, internal or external factors that limit a system or

organization from achieving its goals, or factors that limit a system from improving.

Constraints can be physical entities, process deficiencies, resource limitations, or non-

tangibles such as culture or conventionally accepted constructs.

Adopting the core idea of a constraint, TOC asserts that once the proper constraint is

identified it must be managed. A widely known tenant of TOC is that “if you do not manage

the constraint, it will manage you”. This constraint, whether acknowledged or not, will

determine the output of the system. Additionally, as one constraint is mitigated, a new

constraint will certainly arise, and the process perpetuates indefinitely.

TOC provides a systematic approach for the management and maintenance of a

system constraint. The five focusing steps of TOC are:

1. Identify the constraint.

2. Decide to exploit the constraint.

3. Subordinate everything else to the decision.

4. Evaluate and elevate the constraint.

5. If the identified constraint is mitigated or moves, return to step one.

12

With the five focusing steps comes a warning. Keep up the momentum and do not let

inertia become the constraint. Continuous vigilance, maintenance and improvements are

required.

Briefly, the five steps call for the proper identification of the system constraint. Once

the constraint is identified, and consciously accepted and acknowledged, a decision must be

made on how to exploit the constraint. Exploitation can mean many things, most important

is a decision must be executed on how to optimize the constraint. Next, all other elements of

the system must be made subordinate to the constraint. If they are not, then the proper

constraint has not been identified or acknowledged. With this decision comes the proper

evaluation and elevation of the system constraint. Make the constraint the focal point and

monitor its performance and behavior. If through the evaluation and monitoring the

constraint begins to fail or migrate, start all over and identify the new constraint.

TOC is typically applied to a company or factory environment. In the case of a

factory there is a set of generally excepted fundamental measurements. These are

throughput, inventory and operating expenses. In TOC terminology, throughput is

considered the amount of money received from the customers minus the cost of the raw

materials. Inventory is denoted as the money invested in the system that has not yet

materialized as finished goods. While operating expenses are the funds the company invests

in transforming the inventory into throughput.

While rigorous TOC terminology or measurements are inherently financial,

applications employ these measurements in non-financial forms. Viewing these

measurements in non-financial terms is useful in factory of production floor settings. The

floor looks at what and how many of a given item was produced in a given period of time

and how much material and resources were required. Extending these ideas into financial

terms simply requires placing a monetary value on the quantity, material and resources.

Hence, it is quite simple to map the orthodox TOC measurements into useful factory metrics.

In terms of a synchronous production line, the constraint is viewed as the limiting cell

or operation in the production line, the one cell or process that limits the output of the entire

production process. Based on the focusing factors everything else in the line must become

subordinate to the constraint. Therefore, the inputs and outputs of the constraint must be

13

managed to fully support that constraint. In the TOC universe this means balancing the flow

of materials in and out of the constraint.

All processes have some level of variation and these variations imbedded in the

coupled events of a production environment cause a balanced line to act erratically. Due to

the statistics of dependent events the process or operation with the largest degree of

variability will dominate system performance. The principal concept is to manage the

capacity of and around this constraint. Managing the pre and post constraint activities

supports the constraint as TOC dictates, as well as forcing and maintaining the constraint as

“the constraint”. With the constraint controlled, management of entire system simplifies,

producing predictable and dependable output based on the output of the system constraint.

Essentially, consistent performance is realized by balancing the flow in and out of the

constraint.

TOC philosophy contends that with flow management, no time can be saved at a

bottleneck, or constraint, i.e. complete capacity utilization at the bottleneck is required.

Activities preceding and following the bottleneck should be capable of providing more than

the constraint can absorb or produce, hence, the notion of protective capacity. Surrounding

the constraint with protective capacity ensures full utilization of all of the constraint

resources enabling the constraint to dictates system performance. The final product is a

strategically unbalanced system or production line which interestingly is direct contrast to the

traditional operations management paradigms.

TOC also espouses continual improvement. Once a system is stable, additional

resources around the constraint will have “opportunity time”. While this “opportunity time”

may be frowned upon in financial circles, it is a necessary condition for an organization to

improve, train, and expand. There will be no wasted time if managed properly. The time

should be used constructively for process and operational improvements. If the time is not

used properly, and the system is not managed, inertia takes over and the system may collapse

into a declined state.

As a comparison, a look at the Just in Time (JIT) operational approach is worthwhile.

JIT relies on materials and resources to be systematically aligned, delivered, and utilized in a

carefully orchestrated chain of events. If any one of these events experiences variabilities

14

that violate the prescribed orchestration, the system cascades into disorder. For example, if

one supplier fails to deliver or a quality problem arises, everything down stream is starved,

while the upstream chokes on continued JIT delivered materials. This is the exact situation

that occurs in “balanced” systems, little to no tolerance for variance. In a balanced system,

every point in the system has the potential for failure which brings down the entire system.

Whereas in the TOC approach, the constraint is the focal point and meticulously

monitored for hints of misalignment or distress. This simplifies the system as there is one

central point of focus and potential failure. If upstream or downstream activities experience

variabilities, their protective capacity, the additional capacity in the non-constraint cells with

respect to the maximum constraint cell capacity, is readily available to absorb the bumps and

the constraint continues to be fed and the system continues to function. The unbalanced

approach allows the system to absorb inherent variabilities and provide predictable and

consistent behavior.

15

CHAPTER 3

METHODOLOGY

INTRODUCTION

The rationale behind the development of LineSimulator is twofold. Initially, this

study was intended to assess the Learning Classifier Systems (LCS) capability of monitoring

or classifying production line problems or optimize line configurations with respect to TOC.

However, as the development progressed, it became clear that an appropriate production line

model was necessary. Development and investigation of the model itself resulted in a sizable

enough task leaving the incorporation of the model into an LCS as an extended venture.

First, it was necessary to create a custom model of a synchronous production line

capable of conforming to both balanced and TOC endorsed line architectures. The

architecture and coding were developed by the author from production line simulations

observed in industry. Secondly, it is anticipated that future work on line optimization be

evaluated within the LCS framework where XCSJava is a known proven package for LCS

applications.

The LineSimulator package was created in Java in the jGrasp Integrated Development

Environment (IDE). The Java language was the obvious choice given that the XCSJava

framework is provided in Java. The jGrasp IDE was chosen due to the author’s familiarity

with the application. The Unified Modeling Language (UML) diagram, Appendix B, Figure

14 was produced using Eldean ESS-Model [9]. The line charts were created in Microsoft

Excel and the surface plots generated via GNUPlot [ 10].

LINESIMULATOR ARCHITECTURE

The LineSimulator package was written with flexibility and change dynamics in

mind. The goal was to develop an architecture that would allow a production line to be built

piece by piece, while at the same time provide for the line parameters to change dynamically.

The necessity of the dynamics comes from the notion that production lines are continually

16

influenced and react to their environment and a proper model must incorporate these

attributes. In an effort to manage these attributes and conform to best practices,

LineSimulator employs software design pattern practices. Specifically, the patterns utilized

are Strategy, Observer, Visitor, and Template Method.

Cells

The core component of the architecture is the Cell class. As noted earlier, production

lines are comprised of cells, each of which provides a specific component output of the

whole. A UML diagram of the dominant components is provided in Appendix B. The

basic idea behind the Cell class is that each cell contains the raw material required to perform

the tasks, a specified maximum output capacity, and a variable generating function to provide

some level of output.

The Cell class is essentially divided into two containers. One container houses the

inputs, or raw materials, and the other houses the output provided by the generating function

based on available raw materials. The transactions between the input and output containers

are handled by the Transactor class.

In order to provide runtime flexibility the OutputGenerator class utilizes the Strategy

pattern. The Strategy (or Policy) pattern is employed when classes require alternate

behaviors. For instance, one situation may call for the OutputGenerator to generate a

constant output stream while another calls for a variable output stream based on some known

distribution function. A specific output generation algorithm can be deployed to cells as

desired. As noted earlier, it is important that the cell output be easily customized for variable

output, as the impact of output variability is a key component of this work.

In this implementation three different OutputGenerator subclasses are utilized. The

first is the ConstantOutputGenerator. As the name implies this generator provides a constant

output based on the defined capacity. If the cell is designed to have an output capacity of

five, the generator will produce five. The actual output may be limited based on raw

materials and is formalized in the Transactor class discussion.

The RandomOutputGenerator provides for a uniform random output based on the

maximum output capacity of the cell. The typical application uses the cell capacity as the

17

maximum and one as the minimum. One could consider using zero as a minimum, implying

the cell provided no output. However using that approach does not materially change the

study or results. In the case of a cell capacity set to eight, the generating function will

randomly produce an output of between one and eight, each output independent of the last.

Of course the actual output may be limited by available material.

The Transactor class is responsible for the movement of materials within the cell. Its

primary responsibility is to monitor the output and move the required quantity from the input

container to the output container. Depending on the implementation, it ensures that a cell

cannot produce more output that it has raw materials. Or in other cases the transactor may do

nothing at all.

The Transactor class relies on the Template Method to define the logic of the

transaction method. The Template Method is used when the bulk of classes’ methods are

consistent across subtypes, but the algorithm of a specific method necessitates an alternate

algorithm. In this design the transactional characteristics of Transactor instances associated

with the SupplyCell, WorkCell, and ShipCell differ only in the algorithm of the transaction

method, or lack thereof.

For the purposes of this work three different Transactor classes are defined, one each

for the SupplyCell, WorkCell, and ShipCell. Each of these cells has a different material

movement requirement. The SupplyCell is considered the initial supply source for the entire

line and in this model has unlimited supply. Given unlimited supply, the SupplyCell

Transactor is not concerned with the typical raw material constraint and simply moves the

generated output to the output container.

It could be argued that unlimited supply is not a realistic assumption. However, the

rationale behind the policy is that raw materials from outside sources is a Supply Chain

function and beyond the scope of this evaluation. Additionally, in the case of a constrained

line, the output of the supply cell will be regulated by the associated constraint cell, which

inherently limits its output.

The ShipCell is simply a container for the finished goods produced by the line. In the

current architecture the ShipCell Transactor method does nothing. The finished goods are

simply deposited into the output container of the ShipCell and inventoried at the end of a

18

production run. However, an extension of the model could define a ShipCell that supplies

the SupplyCell or WorkCell of a downstream line. This would require the development of an

alternate Transactor which the architecture supports.

The WorkCellTransactor monitors both the raw material and the generated output.

The function of the WorkCellTransactor is to evaluate cell capacity, raw materials, and

generated output and transfer the proper quantity from the input container to the output

container. The WorkCellTransactor must ensure the output quantity is limited either by the

available raw materials or the cell output capacity. A cell cannot generate more output than

available raw material while also being limited by its maximum output capacity.

In the case of an unbalanced line configuration, a Cell can also be defined as a

constraint or regulator. A constraint Cell is a cell where the output capacity of the cell is

limited with respect to the other cells in the production line. The regulator cell is linked to

the constraint cell and has its output “regulated” or controlled by the constraint cell. The

constraint and regulated cells come in pairs, and are established within the ProductionLine

Class and associated Transactor.

Production Line

The ProductionLine model is formulated to articulate a synchronous production line,

through discrete events. The ProductionLine class is the architectural class of the model.

The ProductionLine class provides a representation of a production line by housing Cell class

instances. The standard, straight line configuration, implemented in this study, is comprised

of one SupplyCell, some quantity of WorkCells, and a ShipCell. The cells are maintained in

an ArrayList data structure. The ProductionLine class allows for the assembly of more novel

line configurations such as cascaded, parallel, and feeder line structures. Although these

configurations are beyond the scope of this study, the architecture provides for alternate line

configurations which provide ample opportunity for further study.

The construction of a line is fairly straightforward. The first element of the ArrayList

is the SupplyCell, the WorkCells occupy the next n elements, and the ShipCell is housed in

the last element. In the standard configuration, a production line of 10 WorkCells will

require a 12 element ArrayList. Each cell can be individually configured attribute by

19

attribute, however the standard test configuration begins with identical WorkCells. The

SupplyCell is essentially a WorkCell and is typically configured as such, except for its

Transactor.

The ShipCell is configured with zero initial inventories, its own empty Transactor and

OutputGenerator, and the same output capacity as the WorkCells. The flexibility of

framework allows for the ShipCell to be configured in such a way as to act as a Supply Cell

to another line or multiple lines if desired.

The LineSimulator model realizes the synchronous nature through two events that

represent a single production day. The first event is the generation of output from each cell.

Each cell, in succession, is called to generate its output via their defined output generating

function and Transactor attributes. The cells generate their respective outputs and the cell

input and output container inventories are allocated accordingly.

The second step is a call to a line visitor, the MaterialMover class, whose function is

to move the appropriate inventory from one cell to the next. Available inventory from a cells

output container is moved into the next cell’s input container. As the material is moved, the

container inventories are updated appropriately. New inventory is added to the existing

inventory of the input container and the output containers are reset to zero.

The MaterialMover and Inventorier classes both implement the Visitor pattern. The

visitor pattern provides the ability to perform additional operations on a class, without

altering the class itself. In the cases of both the MaterialMover and Inventorier, each cell in

the production line is visited and the appropriate action is taken based on the cell type. The

activities associated with the MaterialMover are described in the previous paragraph. The

Inventorier simply visits each cell and extracts inventory levels associated with the input and

output containers.

The ProductionLine class allows for both a single day production, as well as multiple

days of continuous production. A single day’s production may be used in a case where one

might want to add a single shift of overtime to an existing production cycle. The multi-day

functionality simply calls the single day activity the prescribed amount of times. Typical

implementation is a multi-day period of 20 cycles to represent a typical production month of

activity.

20

The above describes the normal activity associated with a balanced synchronous line.

The ProductionLine class must also provide the capability to model the unbalanced

constrained line architecture defined by TOC. The unbalanced architecture is realized by

defining a cell as the constraint cell and a second, precursor cell, as the regulator cell. The

addition, removal, and associated constraint and regulator cell attributes of a constraint and

its regulator objects can be activated at any time between single production days or periods.

The unbalanced architecture functions in the following manner. The constraint cell is

defined as a cell that limits or constrains the production of the entire line or system.

Ultimately, the constraint cell is a cell with less maximum output capacity than the rest of the

cells. In a typical application, the output of the constraint cell is used to manage the flow

through the system, as well as, the flow of new material into the system through the regulator

cell. In practical terms, if the constraint cell outputs quantity q, the maximum the regulator

cell can release is the same quantity q or less dependent on available raw materials. One

could utilize the constraint cell strictly as a capacity limiter, but without the regulator partner,

the idea of balancing the flow of the line is eliminated and nonsensical.

The Observer pattern is used to connect the constraint and regulator cells. The

Observer pattern is a one-to-many relationship between objects that allows for the automatic

notification to the dependent objects of a change in the primary object. In the case of the

production line, the standard model utilizes a one to one relationship between the constraint

and the regulator. The constraint cell can be any one of the WorkCells. By design the

default regulator cell is the SupplyCell.

An application where multiple regulator cells need be notified of a single constraint

cell change is a modest extension in a multi-line environment. The design incorporates the

ability to insert multiple constraints cells within a single line, as well as, the use of a

WorkCell or ShipCell as the regulator. The only limitation on the design is that the regulator

appears ahead of the constraint with respect to the production process.

Line Runner

The LineRunner class is used to define and instantiate a ProductionLine and define

the environment of the line. Environmental conditions associated with the production line

21

parameters are the number of days in a production period and the number of periods to be

run. The timing associated with the setting or resetting of line parameters is based on test

conditions. Additional environmental parameters of interest are the timing of constraint and

buffer attributes initiated while adding and removing constraints, the applicability of

executing additional shifts, and the varying of any production line parameters during runtime.

Simulator

The Simulator class is used to define the overall test conditions of an evaluation and

provide test results. The Simulator class uses the FileKeeper class to manage the test reports,

file types and locations.

EXPERIMENTAL METHOD

The experimental approach is to quantify and compare the performance of the

balanced and unbalanced line configurations. The first segment of testing requires

establishing baseline performance of a simple balanced line. Throughput and line inventory

will be monitored over varying parametric conditions. The variable parameters are the

number of WorkCells, buffer size and cell output variation. Various simulations will be run

manipulating one or more of the above parameters in an effort to establish baseline behavior

and performance.

WorkCell capacity will be held uniform across all cells through the baseline analysis.

For comparison purposes a uniform capacity model is required as a main tenant of the

unbalanced methodology is to manage flow through capacity manipulation.

Data set sizes were established through evaluation testing to identify the minimum

number of iterations required to provide valid results. To best mimic a typical production

line, a production period is defined as 20 days of continuous production, with each

production period considered a single iteration. At the beginning of each production period

the line is reset to its initial configuration. Meaning, the line inventory is cleared and the

input and output containers are reset to the initial line configuration values.

To establish the minimum test set size, tests of up to 100,000 production periods were

performed. Results showed that outputs were consistent from 5000 to 100,000 iterations.

22

Results were actually consistent under 5000 iterations. However, to provide adequate

sample size while limiting processing time, 10,000 iterations will be defined as the standard

test set size.

Once the baseline characteristics are established the unbalanced line will be evaluated

under the above conditions, with the addition of the utilization of protective capacity and

constraints placed at various points in the line. The unbalanced line will be tested with

varying levels of protective capacity while the constraint is moved through different positions

on the line. As in the case of the balanced line, throughput and line inventory will be

monitored.

Once the simulations are complete, the throughput and inventory values for the two

methods will be compared for the described tests. In the real world, the desired situation is

maximum throughput with minimum inventory. The architecture that provides the best

throughput to inventory ratio will be deemed superior. Notable or interesting behaviors will

also be reviewed as observed.

Metrics

Evaluation metrics of production line simulations are aligned with those of TOC. As

noted in the introduction, the basic metrics for TOC are throughput, inventory, and operating

expenses. Since financial analysis is beyond the scope this study operating expenses will not

be addressed. Throughput and inventory will be evaluated in quantitative, not financial

terms. A non-dimensional measure, the ratio of throughput over inventory (T/I) will be

added.

Throughput is the quantity of finished goods resident in the ShipCell at the end of the

defined production period. Inventory is the sum of available material in the input containers

of all the WorkCells at the end of a production period. T/I is simply that ratio of the two.

For each simulation cycle maximum, minimum, average, and standard deviation

characteristics of throughput and inventory will be collected. Additionally, that actual

throughput and inventory values for each production period throughout the entire simulation

cycle will be recorded.

23

Although T/I is not necessarily denoted a key TOC metric, it is a conventional metric

used to measure line effectivity. T/I is also known as inventory turns in the financial realm.

The T/I ratio provides an indication as to the healthiness of line flow. From the TOC view

point T/I is synonymous with velocity. It is a measure of how quickly material is moving

through the line, or a measure of flow, the higher the T/I ratio the higher the rate of

throughput for a given inventory.

Ideally, a line will produce its designed or expected throughput while consuming all if

its raw materials. However, due to line conditions all inventories cannot be consumed. Since

all inventories cannot be consumed the lower the level the better, which in turn raises T/I. Of

course higher throughput is also desired. Therefore, the desired state is increasing

throughput coupled with dwindling inventories resulting in an escalating T/I. The superior

line is one that provides the greatest T/I ratio.

Balanced Line

To properly evaluate the model and procedure, a baseline simulation analysis is

required. The baseline analysis will provide a standard for the model while providing a

comparison to the unbalanced approach. The baseline testing and analysis will incorporate

data generated from simulations that demonstrate the impacts of adjusting various parameters

of interest. Specifically, the parameters to be manipulated are the cell output variation,

buffer size, and cell count. This data will provide a roadmap for comparing performance

between balanced and unbalanced lines under various conditions.

Paramount to model definition is an evaluation of the impact of cell count on the line

metrics. The evaluation requires that the number of cells be varied while the capacity, buffer

size, and cell output variation are held constant. To ensure adequate sample size and cell

count, the average throughput for 10,000 production periods (20 days per period) is averaged

for WorkCell counts from two to 100 cells.

The maximum cell capacity is set to 10 with no buffer and cell output variation set to

50%. There is no specific rationale as to the selection of 50% for the cell output variation,

other than it being the nominal value of the range. The rationale for the selection of a cell

capacity of 10 is based on integer calculation limitations and is discussed in the next section.

24

Initial WorkCell inventories are set to 10 as the standard model provides for initial

inventories to be consistent with maximum daily capacity.

Line inventory for each production period was not evaluated with respect to

WorkCell count. The rationale behind this is that it is obvious that increasing the WorkCell

count will simply work as a multiplier on the total line inventory.

The basis for evaluation of work cell quantity is that the results set the WorkCell

count parameter for the remainder of the investigation. Figure 1 clearly illustrates the

negligible impact of WorkCell count on the throughput of a synchronous line. Other than

very low counts (2-4 cells) the throughput of a line is independent of the number of cells.

Based on the results the number of cells will be arbitrarily set to 10. This provides a

reasonable approximation of line for a simple product, as well as avoiding massive resources

with respect to simulation computations.

Figure 1. Balanced line - throughput vs. WorkCell count.

The standard line will consist of one SupplyCell, 10 WorkCells, and one ShipCell.

The maximum output capacity of each cell will be set to 10. The rationale behind a capacity

of 10 is that a real world line can only produce integer value outputs. Therefore, to test

different output variability values, a capacity of 10 allows for the variability to be tested in

10% increments from .10 to .90, or cell output variability from 10% to 90% of a cell’s

maximum capacity, resulting in integer outputs. The above parameters allow the line to

139

140

141

142

143

1 11 21 31 41 51 61 71 81 91

Throughput

Number of WorkCells

25

produce continuous integer outputs over the variability range without skipping to the next

highest or lowest integer.

With the WorkCell count defined and typical cell parameters set, next is to evaluate

the impact of the cell output variation, buffers, and capacity on throughput and inventory. To

provide a picture of how cell output variation impacts throughput and inventory, throughput

and inventory records for 10,000 production periods, with cell output variations from 10% to

90% was produced. Buffer sizes will be set to zero for the initial characterization. Analysis

of the metrics for the recorded data will provide a view into the typical performance under

standard conditions.

The next characterization reflects the impact of buffer size over the cell output

variation range. The same conditions as above were applied, while producing throughput

and inventory outputs with buffer sizes set to two and three times the maximum cell capacity.

It is expected that the buffers will provide additional throughput, but not necessarily produce

substantial changes in throughput. On the other hand, increased buffers should result in a

noticeable negative impact on line inventory levels.

Lastly, the inventory turn ratio was calculated from the above simulations. The

inventory turn ratio is a key measurement of performance. As noted earlier, the

configuration that produces greater throughput while requiring less line inventory is most

desirable. In conjunction with this, is an analysis of the stability and predictability of line

output.

Unbalanced Line

With the baseline performance of a balanced line characterized, the next task is to

characterize the unbalanced line in a similar manner augmented by the parameters associated

with the TOC line configuration. The test variations for the unbalanced characterization

include the impact of the location of a constraint and the effects associated with various

levels of protective capacity and time buffers.

Protective capacity is the amount of additional capacity placed in non-constrained

cells. The standard balanced model maintains a standard maximum output capacity across all

cells, while the unbalanced model allows for additional output capacity to be added to non-

26

constrained cells. The protective capacity ratio (Cp) is the capacity of a non-constrained

cells divided by the capacity of the constrained cell. For example, the non-constrained cells

may be set to a maximum output capacity of 15, with the constrained cell set to a maximum

capacity of 10, resulting in a Cp for the line of 1.5.

For the purposes of this study, and to best reflect practical real life limitations, the Cp

ratios were initially set to vary from .5 to 1.5. It is reasonable to assume that the addition of

10% to 25% capacity can be managed in the real world. Adding more than 25% capacity

generally becomes problematic. Initially, for demonstration purposes capacity was allowed

to vary up to an additional 50%. However, due to some noteworthy observations associated

with the Cp maximum limited to 1.5, it was decided that extending the range to 2.0 may

provide additional insights.

The unbalanced line will use time buffers as opposed to the traditional notion of

quantity buffers. Time buffers are essentially the same as traditional buffers, except they are

denoted in terms of production days instead of units. The quantity associated with a time

buffer is the maximum output capacity times the number of production days of buffer

desired. In the instance of a 2 day time buffer for a cell that has a capacity of 10, the

resulting buffer quantity is 20.

The first evaluation of the unbalanced line attempts to determine the optimal position

of the constraint in the line. Naturally, three positions will be evaluated, the front, middle,

and end of the line. For the initial tests, no protective capacity (Cp = 1.0) or time buffers will

be deployed. This test provides a side by side comparison to the balanced line as the only

change is the addition of a constraint as a regulator. Essentially, this configuration limits the

amount of inventory to be fed into the line, based on the output of the constraint.

Intuition leads one to believe that a constraint placed at the front or end of the line

will be less impactful than a constraint placed in the middle of a line. The assumption is that

the placement of the constraint at the front or end of the line will not materially change the

line behavior or structure of the line. However, placing a constraint in the middle of the line

provides the greatest structural change, as well as the potential for a material change in line

behavior.

27

Next, the unbalanced line configuration will be modified by deploying additional

capacity to the unconstrained cells with the constraint located in the optimal position. The Cp

ratio will be allowed to vary from 1.0 to 2.0 in 10% increments across the same cell output

variation used in the balanced line characterizations.

The same configuration will then be monitored with time buffers of two and three

days applied to the constraint cell. Finally, for comparison purposes, the T/I ratio of the

various results for the balanced and unbalanced lines will be compared and analyzed.

28

CHAPTER 4

RESULTS

INTRODUCTION

The results of the evaluations as defined in the Experimental Method section will be

examined. Examination will include analysis, interpretation and commentary on the findings

associated with both the balanced and unbalanced data individually and collectively.

Comparison of the individual results will be discussed followed by an assessment of the

results as they apply to the proposed hypothesizes.

BALANCED LINE RESULTS

Figure 2 provides the results of the throughput variation for the first 100 periods of

the 10,000 period evaluation cycle. For the legibility purposes only the first 100 production

periods for cell output variations of 10%, 50%, and 90% are displayed. As expected the

greater the cell output variation, the greater the variation in throughout. Throughput

variation with respect to the balance of the cell output variation values exhibited similar

performance in that the magnitude of the throughput variation followed the magnitude of the

cell output variation. Inventory variation exhibited similar characteristics and is not

displayed for clarity purposes.

Figure 2 also indicates the expected throughput for each of the cell output variable

values. Expected throughput is defined as the sum of all possible outputs divided by the

number of possible outputs per day, times the number of days in the production period. In

the case of the cell output variation at 50%, it is expected that the cell output be between six

and ten. The expected output quantity is calculated as (10 + 9 + 8 + 7 + 6) / 5, or 8 units per

cell per day. This results in an expected line output of 8 per cell per day over 20 production

days producing an expected throughout of 160 units per production period.

29

Figure 2. Balanced line - throughput variation.

Quite notable is that fact that none of the lines produced to their expected levels. As

anticipated, as the cell output variation decreases, as does the line throughput variation.

Additionally, the lower the cell output variation the closer the actual throughput gets to its

expected level. However, the expected throughput is never actually attained. This is due to

the dependent nature of the cells upon each other. One cell may potentially produce the

expected output, but if the previous cell does not provide enough raw materials on the

previous day, the current cell can only produce the limit of available raw materials. This is

compounded on the next day, as now the current cell has no raw materials and cannot

produce any output. This cascading dependency drives a balanced line to consistently under

perform with respect to expected throughput.

Figure 3 displays the maximum and minimum values of throughput and inventory for

each of the cell output variation values. As a reference point, it also contains the expected

line throughput for a cell output variability level of 100%.

Interestingly, the maximum throughput level for the 90% cell output variation barely

surpassed the expected output of the 100% variation line. Additionally, the minimum values

for the 60% thru 90% cell output variation lines, lower variability line configurations, do not

reach the expected throughput of a line with 100% variability. The fact that lowered

variability lines minimum throughput levels cannot meet the expected performance of higher

60

80

100

120

140

160

180

200Th

roughput

100 Production Periods

10% Variation 50% Variation 90% Variation

Expected Throughput at 90%

Expected Throughput at 50%

Expected Throughput at 10%

30

Figure 3. Balanced line - throughput and inventory characterization.

variability lines further demonstrates the susceptibility of the balanced line to

underperformance. Even by lowering the cell output variation, a line may not perform to the

level of a much higher variation line. This shows that even with improved methods or

processes that reduce variation, a balanced line is still susceptible to underperformance.

Figure 3 also demonstrates the inverse relationship of the maximum values of

throughput and inventory. This is expected as the throughput decreases with increased cell

output variation, available inventory is left on the line pushing the line inventory higher. On

the contrary, the minimum values of throughput and inventory follow the same decreasing

path, with the respective change, as cell output variation increases. The fact that the

inventory level exhibits a flatter response is not surprising and simply reflects the fact that

some minimum levels of inventory must be maintained regardless of the throughput

produced. Essentially, the line cannot be flushed of its inventory.

The differential magnitude between the maximum and minimum values for

throughput and inventory are evident in Figure 3. As the cell output variation increases, the

gap between throughput and inventory widens. Once the cell output variation hits 90% the

difference between the maximum and minimum values for the inventory is almost twice that

of the value of throughput. This shows that as the output variation increases, more and more

inventories are trapped in the line as throughput decreases. Essentially the entire line

becomes choked with excess inventory.

0

50

100

150

200

250

10% 20% 30% 40% 50% 60% 70% 80% 90%

Quan

tity

Cell Output Variation

Throughput Inventory Expected at 100% Variability

Maximum

Minimum

31

Figures 4 and 5 demonstrate the impact of adding buffer material to the line. Based

on the results, it seems that additional material as buffers does not improve performance.

Figure 4 shows that as with the standard line configuration, additional inventory as a buffer

does not lower the minimum throughput levels. What is interesting is that the maximum

throughput values do improve, but at a decreasing rate as the buffer is increased. The 2X

buffer provided some lift in throughput, but the 3X buffer did not provide a commensurate

level of lift with respect to 2X buffer. Extrapolating this idea out leads one to believe that

there is a point of diminishing returns where any additional of any amount of buffer

inventory will not improve throughput.

Figure 4. Balanced line - throughput vs. variation with alternate buffer sizes.

Figure 5. Balanced line - inventory vs. variation with alternate buffer sizes.

0

50

100

150

200

250

10% 20% 30% 40% 50% 60% 70% 80% 90%

Throughput

Cell Output Variation

3X Buffer (max) 2X Buffer (max) No Buffer Expected at 100% Variability

Minimums

Maximums

0

50

100

150

200

250

300

350

400

450

500

10% 20% 30% 40% 50% 60% 70% 80% 90%

Inventory

Cell Output Variation

3X Buffer (max) 2X Buffer (max) 3X Buffer (min)

No Buffer (max) 2X Buffer (min) No Buffer  (min)

32

Figure 6 shows the impact of buffer size on inventory. Not unexpectedly, increasing

buffer size simply increases inventory with marginal gains in throughput. This is evident

when Figures 5 and 6 are viewed in conjunction with one another. From Figure 5, the

throughput does not necessarily increase as additional buffers are added, and by the

conservation of energy, the material must reside somewhere, resulting in additional inventory

choking the line.

Figure 6. Unbalanced line - inventory vs. cell output variation.

Analysis of the balanced line data offers a few undeniable facts. First, increased

variability in the cell’s outputs inhibits performance and results in decreased throughput.

Secondly, any variability in a balanced line will force the line to underperform. Essentially

only a perfect line, with no variability whatsoever may be capable of meeting expected

performance levels.

Finally, attempting to add buffers to balanced line is detrimental. While a marginal

throughput improvement may be gained, it is more than offset by the amount of excess

inventory resident in the line. Simply speaking, more material will reside in the line than can

be pushed out, trapping an organization’s valuable financial resources that are better utilized

elsewhere.

0

20

40

60

80

100

120

140

160

180

200

10% 20% 30% 40% 50% 60% 70% 80% 90%

Inventory

Cell  Output Variability

Front of Line Middle of Line End of Line Balanced Line

33

UNBALANCED LINE RESULTS

The initial evaluations for the unbalanced line were designed to establish baseline

performance and the most appropriate point on a line to place a constraint. However, as

depicted in Figure 6, the results were somewhat inconclusive. The dashed lines represent the

maximum and minimum limits for the balanced line standard. The solid lines show the

minimum inventory levels for lines with the constraint placed at the front, middle and end of

the line. The maximum inventory levels overlay the balanced line standard and not shown

for clarity purposes.

A more definitive result was expected. Expectations were that a regulator would slow

the rate of inventory into a line, therefore reducing inventory levels. The fact that the

maximum inventory levels remained unchanged was mildly surprising. However given that

a maximum level is a limiting value and there exists a finite level of capacity, it is not

surprising that additional inventory did not materialize. By the same token it was expected

that the minimum inventory levels would drop in kind, not the case. It should also be noted

that the average inventory and throughput levels for the unbalanced line were the same as the

balanced line. Again, simply adding a regulator and making no other changes to the line

provides minimal impact.

The only material change appears with the addition of the constraint at the end of the

line, inventories rose. Interestingly the constraint at the front or middle of the line provided

minimal change. One would expect that insertion at the front of the line would have little

impact, as the line configuration is left essentially unchanged. A more noticeably change for

insertion at the middle was expected, however the change is minor. The change resulting

from insertion at the end of the line is most noticeable, however in a direction that decreases

line performance.

If one views the inventory with respect to pent up supply over time, the results begin

to make sense. With the constraint placed at the front or middle of the line, there is less time

for inventory to build up in the line. In effect the dependent nature of the coupled cells has

less time to impact the line inventory level. With the constraint placed at the end of the line,

the line sees the full impact of the coupled events between cells and the line builds more

inventories.

34

Given that the results of the first evaluation were somewhat inconclusive additional

analysis was required. The second stage of the evaluation was expanded to test the impact of

adding additional capacities to the non-constraint cells, on the front and middle constraint

configurations. For maximum effect, a Cp of 2.0 was arbitrarily chosen.

To better understand the impact of throughput and inventory simultaneously, the T/I

ratio will be put to use. There are two reasons for this. First, up to this point in the analysis,

the T/I ratio has provided no additional information. It should be noted that the T/I ratios for

the initial test segments were evaluated but provided no additional insights into the preferred

constraint position. Thus far in the study the T/I curves for the various evaluations were

essentially identical. Secondly, the incremental changes in the previous evaluations

systematically scaled with the varying parametric conditions making the T/I measurements

uninformative.

Figure 7 clearly shows that placing the constraint in the middle of the line offers

differential performance. Although not shown, the throughput results for the maximum,

minimum, and average levels tracked each other between the front and middle

configurations. The difference in inventory levels is what drives the noticeable difference in

T/I. The maximum and minimum inventory levels for the two configurations varied much

more than did the throughput, resulting in discernibly different T/I values. Based on the

above results, it is clear that the middle constraint location provides superior performance.

Therefore, the default constraint location for the balance of the testing is the middle of the

line.

The next test configuration called for an evaluation of the impact of protective

capacity (Cp). The initial methodology called for evaluation of the Cp from 1.0 to 1.5 over

the cell output variation range. Evaluation of the results showed what appeared to be

compression of T/I values as the Cp ratio approached 1.5. Naturally, the question arises of

“Does additional capacity become irrelevant at some point and if so, why?”.

The simulation was modified to allow the Cp to vary to 2.0. While the practicality of

doubling capacity is not realistic, the possibility of compression is interesting from an

academic perspective. The results of the extension of the Cp to 2.0 are shown in Figures 8, 9,

and 10.

35

Figure 7. Unbalanced line - throughout / inventory ratio vs. variation (Cp = 2.0).

Figure 8. Unbalanced line - throughput vs. cell output variation (Cp 1.0-2.0).

Figure 8 displays the average throughput of the line with the Cp incremented in .1

intervals. The lowest line on the chart depicts the performance of the balanced line standard.

Movement up the chart shows the respective performance change in throughput as the Cp is

increased by .1. The compression eluded to previously is clearly apparent. The top few lines

are the throughput for Cp values of 1.8, 1.9, and 2.0 respectively. It is clear that as the

protective capacity approaches 2.0 the effect of additional protective capacity diminishes.

0

0.5

1

1.5

2

2.5

10% 20% 30% 40% 50% 60% 70% 80% 90%

Throughput / Inventory

Cell Output Variation

Front Middle

90

110

130

150

170

190

10% 20% 30% 40% 50% 60% 70% 80% 90%

Throughput

Cell Output Variation

2

1.9

1.1

Cp=1 and Baseline Balanced"

36

Figure 9. Unbalanced line - throughput / inventory vs. variation (Cp 1.0-2.0).

Figure 10. Unbalanced line - inventory (Cp 1.0-2.0).

Extrapolating the results leads one the estimate that for both practical and performance

reasons, protective capacity above 2.0 is superfluous.

Figure 9 shows the impact of a varying Cp on T/I levels, as well as the baseline

balanced line performance. As in Figure 8, the baseline performance is the lowest line on the

chart. As with the throughput response, the same diminishing returns behavior is observed.

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

10% 20% 30% 40% 50% 60% 70% 80% 90%

T/I

Cell Output Variation

2

1.5

1.1

Cp = 1

80

90

100

110

120

130

140

10% 20% 30% 40% 50% 60% 70% 80% 90%

Inventory

Cell Output Variation

Cp = 1.0

1.5

2

37

The noticeable difference between the two responses is that the throughput displays a more

linear response than that of T/I. As Cp increases the T/I response begins to flatten out for

lower values of cell output variation. This shows that the increase in protective capacity does

provide benefits in preserving the T/I ratio over the lower range of cell output variation.

Essentially, the protective capacity and constraint allow the line to perform with more

stability over the cell output variability range.

Figure 10, inventory behavior, provides some insights into why the shape of the

throughput and T/I lines differs. The behavior of the inventory is inversely related to that of

the throughput, but also shows signs of diminishing returns. More noticeably, the inventory

levels minimize for different combinations of Cp and cell output variation. This indicates

that there is an optimum combination of protective capacity and cell output variation.

Following the T/I patterns exhibited in Figures 9 and 7, the insertion of a constraint in

the middle line coupled to the regulation of inventory into the line provides beneficial results.

Essentially, to provide stable performance with variable cell output capacity applying a

constraint that effectively pulls material into the line at a controlled rate provides improved

performance with respect to the T/I metric. Additionally, the performance is far superior to

that of a balanced line in a variable cell output environment. The last characterization of the

unbalanced line was to allow time buffers in the constraint cell. Two and three day time

buffers were established in the constraint cell.

Predictably, the time buffers raised the line inventory by the associated buffer

quantity, but the throughputs for all conditions remained unchanged. With increased

inventories and unchanged throughput the T/I values dropped accordingly. This was the case

for both the two and three day time buffer conditions. It seems that the addition of buffers

impedes performance with respect to T/I.

It was also noted that the standard deviation of both the throughput and inventory

increased slightly over the zero buffer configuration. This seems logical in that with raw

material buffers in the cell, the opportunity for shortages is eliminated, therefore there will

always be an output from the constraint cell into the rest of the line. This condition allows

for the downstream cells to have less of an opportunity for a shortage, resulting in a more

38

variability in output conditions. Effectively, the backend of the line has the opportunity to

use its entire output variability range, thus generating a higher line variability condition.

COMPARISON

The final stage of the analysis entails a comparison of performance differences

between the two line types. The comparison process will follow the methodology evaluation

sequence and examine the corresponding simulation results. Notable observations and

quantitative assessments of which configurations provides the best results will be reviewed.

Given that the buffered line configurations showed little change in performance to the non-

buffered condition, the non-buffered configuration will be used for the comparisons.

The first comparison is an examination of the throughput variation with respect to cell

output variation. Figure 11 mimics Figure 2 with the addition of the throughput performance

of the unbalanced line configuration given the same cell output variation but with additional

protective capacity. The horizontal dashed lines indicate the expected output for the different

line parameter configurations. The dotted lines show the throughput performance of the

balanced lines and the solid lines the performance of the unbalanced lines. The Cp values

associated with the lines are the minimum Cp values that allowed the lines to perform to

expectations. Lines configured with Cp values greater than those shown performed at the

same or higher throughput levels.

Figure 11. Comparison - throughput variation.

60708090

100110120130140150160170180190200210

Throughput

100 Production Periods

10% Variation, Cp = 1.0 50% Variation, Cp = 1.0 90% Variation, Cp = 1.0

10% Variation, Cp = 1.1 50% Variation, Cp = 1.3 90% Variation, Cp = 1.5

39

One item of note is the fact the performance of the line with the lowest variability,

10% and Cp = 1.1, is the only line that consistently outperforms expectations. This indicates

that with good line conditions (minimal variation) and little protective capacity that an

unbalanced line can consistently and predictably meet or beat expectations. Whereas the

balanced line has difficulty meeting expected performance.

The results show that through the insertion of a constraint and the addition of

protective capacity an unbalanced line is capable of meeting expected performance.

Whereas, the balanced line configuration in all cases was incapable of meeting expectations.

Based on this assessment, it is clear that the unbalanced configuration outperforms the

balanced configuration.

Results showed that maximum throughputs were reasonably consistent between the

two line configurations given the same parametric conditions. However, as the Cp was

increased the average throughputs of the unbalanced lines increased. The standard deviations

between the two line types remained consistent indicating that the cycle to cycle variability is

not impacted by the utilization of protective capacity.

However the comparison of inventory levels between the two lines differed

materially. Therefore, the real impact of the unbalanced line seems to come from its effect

on line inventory behavior. The addition of protective capacity around a constraint changes

the fundamental behavior of line inventory. On the throughput side the behavior was similar

as protective capacity was added, a shift up in value. But on the inventory side, the behavior

of the baseline (Figure 10, Cp=1.0) moved from a positive linear slope with increasing cell

output variability to a downward sloped curve, reaching a minimum and trending back up.

The change in the inventory behavior is quite dramatic. The properties of the

inventory behavior are best viewed as a surface. Figure 12 shows the inventory behavior as

the Cp and cell output variation change. Surprisingly, the surface contains a trough indicating

attractor locations (minimums) for specific combinations of Cp and cell output variation. The

solid line on the XY plane traces the intersection of the Cp and cell output variation

combinations that establish minimum inventory levels.

40

Fig

ure

12.

Un

bal

ance

d li

ne -

inve

ntor

y su

rfac

e.

41

Figure 13 illustrates the T/I behavior with varying Cp and cell output variation. The

solid line on the XY plane of Figure 13 is the same as in Figure 12. Conversely, the T/I

surface contains a ridge that defines the maximum T/I values. When viewed together the

surfaces shows the optimum level of protective capacity required for a given cell output

variation for the best line performance. Additionally, the data shows that the dominant factor

in line performance is the inventory behavior. Manipulating the line parameters shifts the

throughput performance, but the inventory is the dominant component in establishing

optimum performance.

It should be noted that edge defined by Cp = 1.0 defines the performance of the

baseline balanced line configuration. None of the points on this edge lie on the minimum

path indicating that the balanced line configuration is not an optimum arrangement.

42

Fig

ure

13.

Un

bal

ance

d li

ne

- th

rou

ghp

ut

/ in

ven

tory

su

rfac

e.

43

CHAPTER 5

CONCLUSION

The goal of this study was to evaluate the behavior of a synchronous production line

based on the TOC and compare its behavior to that of the traditional balanced production line

model. The study necessitated the development of LineSimulator, a custom software model

of a production line based on TOC. LineSimulator is based on teaching methods observed in

the industry, whose architecture, functionality, and attributes are described in this analysis.

Analysis of the traditional balanced production line provided some interesting

insights. Most significant is the fact that even under the best conditions, the traditional

model failed to meet expected production levels. The traditional model performs as expected

only under perfect conditions, no variability whatsoever. However, as soon as individual cell

output variabilities are introduced into the system, the traditional balanced models falls apart.

This calls into question the age old operations paradigm of a balanced production line.

With the balanced line behavior and performance as a baseline, the TOC model was

subjected to the same test criteria. Various parametric conditions associated with the

unbalanced model were analyzed and compared to the balanced line. The main functional

difference between the two lines is the addition of a constraint cell, a cell with less capacity

than all other the cells. The constraint cell is partnered with a regulator cell, placed at the

front of the line, which allows only the amount produced by the constraint cell to enter the

line. The analysis also determined that the optimal position for the constraint cell is the

middle of the line.

To assess the impact on performance of the constraint, the line was evaluated under

varying levels of protective capacity. The capacity levels of the non-constrained cells were

allowed to vary from one to two times the capacity of the constraint cell. Additionally, tests

were performed to test the influence of material buffers added to the constraint cell. The

results showed that the protective capacity played a large role in improving performance of

the TOC line. While for both configurations, balanced and unbalanced, the addition of

material buffers had little bearing on performance.

44

Based on the results of the simulations it is evident that in a production line

environment with variability, an unbalanced, constrained line provides superior performance.

The dominant impact of the constraint and protective capacity is felt on the inventory. The

addition of the two factors fundamentally changed the inventory behavior of the line. Line

throughput was also positively affected by the deployment of protective capacity and the

constraint, however nowhere near as significant as with inventory.

The most significant finding is that there exists a curve that defines the optimum

combination of protective capacity and cell output variation with respect to inventory

minimization. This same curve, when viewed with respect to throughput defines a

demarcation line where throughput either tails off on one side, or continually improves on the

other. The best perspective of these two findings comes through inspection of the T/I ratio

surface.

Analysis of the T/I metric of the unbalanced constrained line, with the protective

capacity and cell output variability manipulated simultaneously, shows that there exists a

“horizon of opportunity”. This horizon of opportunity is a line on the T/I surface that

separates improving and declining T/I performance. The minimum trough behavior of the

inventory coupled with the demarcation line behavior of the throughput work together to

produce this opportunity line. Essentially, depending on which side of the horizon line you

are on defines the behavior of the production line. Additionally, a balanced line

configuration does not lie on this curve, but in fact lies on the declining side of the horizon

line.

The results of this study show that for a production environment with even minor

levels of variability (>10%), the TOC model provides superior results. The data also shows

that the traditional notion of a balanced production line is not the best tool for variable

environments. Additionally, the results showed that as variabilities increase, the TOC

methodology actually helps stabilize performance over the traditional model.

45

CHAPTER 6

FUTURE RECOMMENDATIONS

INTRODUCTION

The successful implementation and testing of a line model based on TOC warrants

the question of how to utilize the model. A plethora of applications come to mind. This

section will discuss the considerable opportunities for future study. Among the topics

discussed are the insertion of the TOC model into an LCS, extension of the model to more

closely mimic its synchronous nature through parallel programming, and variant models and

line structures that may be explored.

The initial motivation for the development of the model was to develop an

environment for the evaluation and classification of a production line based on TOC. The

ultimate goal being the development of a system that provides early warning signals

associated with production line problems. A system that alerts a factory to potential line

shutdowns or bottlenecks is invaluable to any organization. The question becomes “What

does the line look like, and how can that model be classified based on past and current

properties?”. Secondarily, given a line model, what is the best method for optimizing a line

when inherent process variabilities exist and unlimited funds, time, or computing power are

not available.

The LCS provides the appropriate path. The LCS is a proven learning and classifier

technique. The use of the genetic algorithm by the LCS engine provides for the search of a

large space with relative simplicity. The use of genetic algorithms to provide a “close

enough” solution to NP hard problems has become common place.

LEARNING CLASSIFIER SYSTEMS

An LCS is a production system based construct that automatically generates its

resident rule set. The rule set could be an optimum line configuration or a set of line

conditions classified as a potentially bad situation. Rule sets are developed via interaction

between detectors and effectors within the environment. Through this feedback loop the

46

system learns (generates a rule set) based on the conditions of the environment. Detectors

and effectors might be items such as line conditions, constraint locations, and throughput and

inventory levels.

The core of the LCS construct consists of four primary components. These

components are the representation in the classifiers and message system, evaluation and

evolution mechanisms, and the GA. These components work symbiotically as the LCS

endeavors to generate potential solutions to the given problem domain. The classifier and

message systems are used to describe the domain and its interaction with the domain

environment. The key to the classier is its representation.

LCS systems can manage classifiers in either binary or real number forms.

Classifiers generally take a conditional predicate or “if-then” form. The “if” component of

the predicate is a representation of the problem domain. The classifier representation may

take the form of describing the individual cell attributes, the line conditions and

configuration, or a combination of both.

The “then” component is the action or outcome associated with that particular

condition. For the line model the outcome may take the form of adding or removing a

constraint, moving the location of a constraint, adjusting a cell’s capacity level, or adjusting

time buffers. Each of these may be used to test for optimization.

The message component houses the inputs from the environment. These messages

may be line efficiency metrics, trends in inventory or throughput values, or cell specific

attributes. The LCS looks to match classifiers to an environmental input from the message

system.

The third and fourth components of the LCS are the GA and components housed in

the GA. The GA utilizes a chromosomal representation of the solution. A notional

chromosomal representation of a classifier is provided in Table 1. The traditional classifier

condition-action representation is in a ternary form. The format is typically a string

consisting of 0, 1, and the # or “don’t care” symbol. The action element uses either a binary

string format composed of the above symbols or a simple 0 or 1 for classification purposes.

In the notional representation, the individual cells are defined by a 26 bit string. The

maximum capacity is denoted by a 4 bit integer, the input and output container quantities

denoted by a 10 bit integer, and the constraint and regulator designation defined by a single

47

Table 1. Notional Classifier Chromosomal Representation

Cell Representation

Maximum Capacity Input Container

Quantity

Output Container

Quantity Constraint Regulator

MMMM IIIIIIIIII OOOOOOOOOO C R

Action Representation

Add Additional

Capacity

Set to

Constraint Set To Regulator Add Buffer Days Add Shift

AAAA C R BBBB S

bit boolean. The line is then represented by a string composed of the concatenation of the

individual cell representations. The action segment is a 11 bit string where the amount of

additional capacity is identified with a 4 bit integer, the action to set or remove a constraint or

regulator is denoted by a single bit, the number of a buffers days is contained in a four bit

integer, and additional shifts are activated by a single bit string.

With the production line representation defined, the next task is to define the

environment of the LCS. To be defined within the environment are items such as the test

methodology, single or multi-step, fitness functions, selection methods, and applicable

genetic operators

PARALLEL PROGRAMMING

The synchronous nature of the proposed model naturally lends itself to a parallel

programming methodology. Simulations associated with the current algorithm carry with

them a computational complexity of O(n). A reasonable extension into a parallel architecture

could bring the complexity into constant time complexity levels. Realizing constant time

will of course depend on the number of cells and the capability of the machine used.

Assuming a thread count commensurate with the cell count, realizing O(1) for the

model simulation can be expected. In a structure where the processing of the cell functions is

housed in the threads, and the inter-thread activity is managed through shared memory, a

parallel architecture can be realized. Care must be taken in managing the inter-thread

communication in the constraint loaded configuration as timing issues will need to be

48

managed. However, ensuring that all threads complete before the inter-thread processing

begins will mitigate these timing issue.

In addition to adapting the line model, the LCS should also be migrated to a parallel

architecture. It is certainly possible to process the LCS in the sequential world and the

production line model in the parallel world. However, in a true parallel environment the

memory management between the two worlds has the potential of eliminating the gains

provided by the parallel enhancements. Additionally, the computations associated with the

GA lend themselves to a parallel environment. The real advantage comes when the model

and GA, both of which are well suited to the parallel world, are adapted into parallel

processing environment.

WONDERING BOTTLENECK MANAGEMENT

It is a well-known phenomenon that over time, as process improvements or material

factors change, the bottleneck of a line migrates, hence the “Wandering Bottleneck”. TOC

not only focuses in the proper configuration of line flow, but also on continued improvement

and management. Points mentioned in the LCS discussion spoke to discovery of optimal

configurations. Looking forward in time, the question of maintenance arises. What happens

as a line evolves due to environmental influences? An interesting study would consist of

investigating the signals associated with the wandering bottleneck.

Two lines of thought arise from the concept of the wandering bottleneck, those of

maintenance and evolution. Maintenance is associated with the active and continuous

evaluation of the line performance and adjustment of parameters in an effort to maintain

performance. The investigation would revolve around the study of the classification of line

parameters and the LCS’s ability to predict the next bottleneck.

Evolution of a line is associated with the drift of line parameters due to environmental

conditions. Events such as process improvements may manifest themselves in a change in

cell output variability. Or a required drop or shift in capacity might require a new

configuration of the line. Situations like these are easily modeled. The LCS is then set in

action to detect the change and provide adjustment to line parameters that reconfigure the

line, reestablishing line performance.

49

VARIANT LINE MODELS AND FINANCIAL MEASURES

The LineSimulator model was designed with flexibility and expansion in mind. The

ability to construct variant line model is embedded in the framework. Variant line structures

such as cascaded or a parallel feeder line structure should be modeled and evaluated.

Additionally, the development of new classes would allow financial measures to be attached

to the individual cell and line measurement parameters.

50

REFERENCES

[1] N. Boysen, M. Fliedner, and A. Scholl. Assembly line balancing: Which model to use when? Int. J. of Production Econ., 111(2):509-528, February 2008.

[2] P. Tambe. Balancing mixed-model assembly line to reduce work overload in a multi-level production system. Masters thesis, Louisiana State University and Agricultural and Mechanical College, Baton Rouge, LA, 2006.

[3] Y.T. Leung and M. Kamath. Performance analysis of synchronous production lines. IEEE Trans. Robot. Autom., 7:1-8, 1991.

[4] J. Dricsol and D. Thilakawardana. The definition of assembly line balancing difficulty and evaluation of balance solution quality. Robot. Comput. Integr. Manuf., 17:81-86, 2001.

[5] I. Baybars. A survey of exact algorithms for the simple assembly line balancing problem. Manage. Sci., 32:909, August 1986.

[6] K.E. Chong, M.K. Omar, and N.A. Bakar. Solving assembly line balancing problem using genetic algorithms with heuristics-treated initial population. Proc. World Congr. Eng., 2:1186-1192, 1992.

[7] E. Falkenauer and A. Delchambre. A genetic algorithm for bin packing and line balancing. Proceedings of the 1992 IEEE International Conference on Robotics and Automation, Nice, Frace, 1992. IEEE.

[8] E.M. Goldratt. What is this thing called Theory of Constraints and how should it be implemented. North River Press, Croton-on-Hudson, NY, 1990.

[9] Eldean ESS-Model 2.2. Sourceforge, n.d. http://essmodel.sourceforge.net/, accessed Mar. 2013.

[10] GNUplot 4.6. GNUPlot, 2012. http://www.gnuplot.info, accessed Mar. 2013.

51

APPENDIX A

GLOSSARY

52

GLOSSARY

Buffer: Amount of resident material in a cell above the maximum output capability.

Days Buffer: The quantity of excess material in a cell equivalent to a single days maximum output. Days Buffer may also be termed Time Buffer, as in the number of days buffer associated with a cell.

Capacity: The designed maximum output capability of a cell for a single day’s production.

Throughput: The total output of a line after the defined production period. The value of finished goods in the ShipCell output container at the end of the defined production cycle.

Inventory: The quantity of material in a cell’s input container.

Protective Capacity (Cp): The total capacity of a non-constraint cells divided by the capacity of the constrained cell. The additional capacity applied to non-constraint cells.

Constraint Cell: A cell that has less capacity than all other cells in the production line.

Bottleneck: A point in the system that limits the capacity of the entire system.

SupplyCell: The first Cell in a production line that acts to supply the line with its initial raw materials.

ShipCell: The final cell in a production line that houses the finished goods from the line.

WorkCell: Intermediate line cells, located between the Supply and ShipCells. These cells produce output, commensurate with their available raw material base that is then supplied to the next cell in the production line.

Production Line: A collection of ordered cells beginning with a SupplyCell, an associated number of WorkCells, and ending in a ShipCell.

53

APPENDIX B

LINE SIMULATOR UML

54

LIN

E S

IMU

LA

TO

R U

ML

Fig

ure

14.

Lin

e S

imu

lato

r U

ML

Dia

gram

.