examination of the effects of bottlenecks and …

EXAMINATION OF THE EFFECTS OF BOTTLENECKS AND PRODUCTIONCONTROL RULES AT ASSEMBLY STATIONS

By

TIMOTHY M. ELFTMAN

A THESIS PRESENTED TO THE GRADUATE SCHOOLOF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCE

UNIVERSITY OF FLORIDA

1999

Copyright 1999

by

Timothy M. Elftman

iii

ACKNOWLEDGMENTS

During the last few years, I have received an incredible amount of opportunities

and was given many chances to broaden my experiences. I do not believe I could

acknowledge everyone who has helped me during this time. But I will highlight specific

people whom I believe deserve more than this simple recognition.

First and foremost, I would like to thank Sam and Charlene Scaggs for their

emotional support over the last few years. I would also like to thank June Cheng for her

support and understanding. I know it has been difficult. Finally, I thank Dr Tufekci for

his insight and support in this paper’s development.

iv

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS .............................................................................................. iii

LIST OF TABLES ......................................................................................................... vi

LIST OF FIGURES....................................................................................................... vii

ACRONYMS ................................................................................................................. ix

ABSTRACT....................................................................................................................x

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

1.1 Motivation.................................................................................................................11.2 Fundamentals of Manufacturing Control Systems.......................................................81.3 Manufacturing Systems Philosophies........................................................................111.4 Manufacturing System Control Methodologies.........................................................12

1.4.1 MRP and MRPII Systems ...............................................................................121.4.2 DBR System ...................................................................................................151.4.3 Kanban System................................................................................................161.4.4 CONWIP ........................................................................................................181.4.5 Pull-Push Systems ...........................................................................................191.4.6 Comparison of Production Methodologies.......................................................21

MRP / MRPII and DBR .....................................................................................21MRP / MRPII and Kanban .................................................................................22Kanban and CONWIP ........................................................................................22CONWIP and Push ............................................................................................23JIT and TOC......................................................................................................23

1.4.7 Comparison Summary .....................................................................................241.5 Preliminaries of Queuing Theory..............................................................................241.6 Statistical Hypothesis ...............................................................................................25

2 SIMULATION MODELING AND THE ASSEMBLE SYSTEM MODEL................29

2.1 Simulation Modeling................................................................................................292.1.1 Emulated Flexible Manufacturing Laboratory Software ...................................29

Factory Setup Object..........................................................................................30Machine Object ..................................................................................................31

v

Dispatch and Raw Material Object .....................................................................322.1.2 Comparison of EFML to Traditional Simulation Programs ..............................32

2.2 Simulation Model.....................................................................................................332.2.1 Experimental Conditions .................................................................................362.2.2 Calculations ....................................................................................................37

Cycle Time.........................................................................................................37Final Inventory Status ........................................................................................37

3 FEEDER LINE ANALYSIS.......................................................................................38

3.1 MRP Feeder Lines ...................................................................................................383.2 Kanban Feeder Lines................................................................................................443.3 CONWIP Feeder Line..............................................................................................503.4 Feeder Line Production Control Systems Summary and Conclusions of

Findings ...................................................................................................................55

4 ASSEMBLY SYSTEM ANALYSIS ..........................................................................58

4.1 Pure Push Assembly Systems Using a Synchronization Process ................................604.2 Pure Push Assembly Systems with No Synchronization Process ...............................63

4.2.1 Process Analysis of Unmatched Feeder Line Inventory ....................................684.2.2 Verification of Analysis ...................................................................................69

4.3 Pull-Push Assembly Systems ....................................................................................704.4 Hybrid Pull/Push-Push Assembly Systems ................................................................744.5 Assembly System Summary and Conclusions of Findings .........................................79

5 ASSEMBLY SYSTEM COMPARISON ANALYSIS ................................................82

5.1 Push and Pull-Push Assembly Systems .....................................................................845.2 Push and Hybrid Pull/Push-Push Assembly Systems .................................................855.3 Hybrid and Pull-Push Assembly Systems ..................................................................855.4 Assembly System Comparison Summary of Findings ................................................86

6 CONCLUSIONS........................................................................................................88

GLOSSARY OF TERMS..............................................................................................92

LIST OF REFERENCES...............................................................................................94

BIOGRAPHICAL SKETCH .........................................................................................96

vi

LIST OF TABLES

Table page

1.1: Hypothesis Test on Variance...................................................................................261.2: Hypothesis Test on Means of Large Samples ..........................................................261.3: Hypothesis Test on Means of Small Samples...........................................................274.1: Assembly System Types..........................................................................................594.2: Series Comparison of Actual Feeder Line Inventory to the Predicted Value.............70

vii

LIST OF FIGURES

Figure page

1.1: Generalized Assembly Process ..................................................................................51.2: Synchronization Process ...........................................................................................61.3: General Push System ................................................................................................91.4: General Pull System................................................................................................101.5: MRP Process ..........................................................................................................141.6: Single Card Kanban Process....................................................................................171.7: CONWIP Process ...................................................................................................191.8: Pull – Push Process.................................................................................................202.1: Feeder Line Production Process..............................................................................332.2: Assembly System Production Process.....................................................................342.3: Modified Simulation Model Configuration ..............................................................352.4: EFML Simulation Model ........................................................................................363.1: Analyst Procedure...................................................................................................393.2: Throughput Analysis of 3 Machine MRP Lines– Interarrival Time Constant ............393.3: Throughput Analysis of 3 Machine MRP Lines– Bottleneck Position Constant........403.4: WIP Analysis of 3 Machine MRP Lines – Interarrival Time Constant ......................413.5: WIP Analysis of 3 Machine MRP Lines– Bottleneck Position Constant ...................423.6: Cycle Time Analysis of 3 Machine MRP Lines– Interarrival Time Constant.............433.7: Cycle Time Analysis of 3 Machine MRP Lines– Bottleneck Position Constant ........443.8: Throughput Analysis of 3 Machine Kanban Lines– Card Allocation Constant ..........453.9: Throughput Analysis of 3 Machine Kanban Lines– Bottleneck Position Constant ....463.10: WIP Analysis of 3 Machine Kanban Lines– Card Allocation Constant ...................473.11: WIP Analysis of 3 Machine Kanban Lines– Bottleneck Position Constant .............483.12: Cycle Time Analysis of 3 Machine Kanban Lines– Card Allocation Constant.........493.13: Cycle Time Analysis of 3 Machine Kanban Lines– Bottleneck Position Constant ...503.14: Throughput Analysis of 3 Machine CONWIP Lines– Cards Allocated Constant ....513.15: Throughput Analysis of 3 Machine CONWIP Lines– Bottleneck Position Constant523.16: Cycle Time Analysis of 3 Machine CONWIP Lines– Cards Allocated Constant .....543.17: Cycle Time Analysis of 3 Machine CONWIP Lines– Bottleneck Position Constant554.1: Throughput Analysis of Base Push Assembly System..............................................604.2: WIP Analysis of Base Push Assembly System.........................................................614.3: Cycle Time Analysis of Base Push Assembly System...............................................634.4: Unmatched Inventory after 4000 Batches - Bottleneck Feeder Line.........................654.5: Unmatched Inventory after 4000 Batches - Dual Nonbottleneck Feeder Lines.........654.6: Unmatched Inventory after 4000 Batches - Assembly Systems with One Bottleneck

Feeder Line............................................................................................................66

viii

4.7: Unmatched Inventory after 4000 Batches - Dual Bottleneck Feeder Lines ...............664.8: Unmatched Inventory after 4000 Batches - Nonbottleneck Feeder Line...................674.9: Unmatched Inventory after 4000 Batches - Assembly Systems with Two Bottleneck

Feeder Lines ..........................................................................................................674.10: Assembly Station Raw Material Combination........................................................694.11: Throughput Analysis of Pull-Push Assembly System .............................................714.12: WIP Analysis of Pull-Push Assembly System.........................................................724.13: Cycle Time Analysis of Pull-Push Assembly System..............................................734.14: Throughput Analysis of Hybrid Pull/Push-Push System.........................................754.15: WIP Analysis of Hybrid Pull/Push-Push System ....................................................774.16: Cycle Time Analysis of Hybrid Pull/Push-Push System..........................................785.1: Throughput Comparison Analysis of Assembly Systems..........................................835.2: WIP Comparison Analysis of Assembly Systems .....................................................835.3: Cycle Time Comparison Analysis of Assembly Systems...........................................83

ix

ACRONYMS

This thesis uses a variety of acronyms that the reader may not be aware of or that

differ from literature source to literature source. These acronyms are defined when first

used, but are supplied here to aid the reader.

Acronym DefinitionBOM Bill of MaterialsCONWIP Constant Work in ProcessCT Cycle TimeDBR Drum Buffer RopeEFML Emulated Flexible Manufacturing LaboratoryMPS Master Production ScheduleMRP Material Requirement PlanningMRPII Manufacturing Resource PlanningTOC Theory of ConstraintsTH ThroughputWIP Work in Process

x

Abstract of Thesis Presented to the Graduate Schoolof the University of Florida in Partial Fulfillment of the

Requirements for the Degree of Master of Science

EXAMINATION OF THE EFFECTS OF BOTTLENECKS AND PRODUCTIONCONTROL RULES AT ASSEMBLY STATIONS

By

Timothy M. Elftman

May 1999

Chairman: Dr. Suleyman TufekciMajor Department: Industrial and Systems Engineering

In manufacturing centers products manufactured at different locations are often

joined together at assembly stations. If not managed properly this common event can lead

to orphaned products, lost throughput, and increased WIP. All of which will result in lost

capital for the manufacturing center.

This study analyzes an assembly line, which is fed by three parallel independent

feeder lines, to determine characteristics unique to assembly systems. The assembly

systems are managed by MRP / MRPII, Pull-Push, and Pull/Push-Push Hybrid production

control methods. The study focuses on the effects of bottlenecks, batch synchronization,

and production control methods on the assembly systems’ throughputs, WIPs, and cycle

times.

The study will show that assembly systems have several unique characteristics.

The first characteristic occurs in assembly systems that use push control techniques to

xi

manage the assembly station. In these systems if the bottleneck feeder lines are not

synchronized with the nonbottleneck feeder lines, instability results. This instability is the

accumulation of the nonbottleneck feeder lines’ product at the assembly station. If the

assembly system is left unchanged the orphaned products can grow infinite in number.

The second characteristic occurs in assembly systems with two bottleneck feeder lines. In

these systems the probability of both bottleneck feeder lines finishing a product

simultaneously is zero. The result is a delay in processing at the assembly station that can

decrease the system’s throughput. Although all of the assembly systems with two

bottleneck feeder lines experience this delay only the systems that manage the bottleneck

feeder lines with pull techniques show a significant reduction in throughput. The third

characteristic concerns assembly systems that are controlled entirely by push techniques.

In these systems if the nonbottleneck feeder lines are controlled by pull techniques, the

assembly system will experience decreased WIP with no change in throughput. The fourth

and final characteristic is that assembly systems, which manage the bottleneck feeder lines

with pull techniques, can outperform systems that manage the bottleneck feeder lines with

push techniques.

1

CHAPTER 1

INTRODUCTION

1.1 Motivation

Manufacturing centers are a conglomerate of workstations, assembly stations,

bottleneck stations, dispatch stations, buffers, inventories, forklifts, hand trucks, and

personnel. The center’s dependence on the conglomerate’s performance is similar to a

human’s dependence on his muscles, tissues, eyes, hands, legs, organs, skin, and brain. As

we are more than the sum of our parts so are manufacturing centers.

As succinctly put by Eliyahu Goldratt [7] the primary goal of manufacturing is to

make profit in the present and in the future. Accomplishing this goal has been a daunting

challenge for manufacturing managers since the dawn of time. There are many obstacles

in a manufacturing enterprise that prevents management from accomplishing this goal.

Goldratt calls these obstacles constraints or bottlenecks. The Theory of Constraints

(TOC) is a management philosophy proposed by Goldratt that deals with managing system

constraints or bottlenecks. The five-step methodology focuses on identifying the system

constraints, exploiting the constraint, subordinating the rest of the system to the needs of

the constraint, improving the constraint, and repeating the process continually.

In a factory the bottlenecks are usually those machines or processes which control

the throughput of the system. Managing the bottlenecks effectively and efficiently yields

higher system throughput. Many production control systems have been proposed to

2

improve throughput in the past. Among them are the Materials Requirement Planning

(MRP), Just-in-Time (JIT), Kanban, Constant Work in Process (CONWIP), and Drum-

Buffer-Rope (DBR) systems. In this thesis an analysis of bottlenecks and their impact on

throughput, work-in-process (WIP), and cycle time in manufacturing systems where three

parallel production lines feed components into an assembly line is carried out.

Successful manufacturing centers are required to identify and manage their

system’s throughput, WIP, and cycle time. Here, throughput is the number of final

products produced per unit time by the system, WIP is the material within the system

undergoing transformation into a final product, and cycle time is the average amount of

time required for raw material to be transformed into a final product. Insufficient

throughput leads to unmet demand. Excessive WIP requires tying up excessive capital.

Excessive cycle time leads to the loss of customer orders. In short, if any of these

parameters are not managed properly, then the manufacturing center loses money. These

parameters are influenced by process variability, process time, process reliability, system

bottlenecks, and the production control system used.

Recent work has investigated how bottlenecks affect a system’s throughput, WIP,

and cycle time in relation to different control methodologies. The goal of these works is

to determine optimal settings of control parameters within the production control systems,

and selecting the appropriate production control systems for different manufacturing

environments. The current manufacturing control systems may be classified into three

categories. The first is MRP and its successor Manufacturing Resource Planning

(MRPII). These control systems push materials into the production facility based on

forecasted demand, and are thus known as push systems. In the second category of

3

control systems, known as pull systems, the material is released into the production facility

only when the demand for the end product triggers it. Since the material is released into

the system only when it is needed, these control system are also called JIT systems. The

two popular implementations of JIT control systems are Kanban (card) control systems

and CONWIP control systems. In all JIT systems the WIP is controlled by the number of

authorization cards assigned to the individual workstations or system of stations. The

third category of control systems is mixed control systems. In these systems, the pull and

push control systems are used to manage certain segments of the production line.

Examples of mixed control systems are DBR, pull-push and push-pull control systems.

These systems will be further defined later in this section.

There is a great amount of literature evaluating the performance of these systems.

Cook demonstrates that serial production systems using DBR results in greater average

throughput and lower levels of WIP variance than when the same system is managed by

kanban [4]. Guide in the analysis of a re-manufacturing facility proves that DBR results in

a reduction in WIP and throughput variance compared to MRP [8]. Bonvik et al. in the

analysis of CONWIP, kanban, and pull-push production control systems demonstrates that

the pull-push systems carries the lowest WIP at any particular throughput level with the

kanban system generally carrying the highest WIP [3]. Altug also demonstrates the

superiority of the pull-push control system over pure MRP, kanban, and CONWIP [1].

The above analyses were mainly conducted with serial systems, or flow lines, as the case

of most manufacturing studies, but serial systems only represent a portion of production

systems in manufacturing.

4

The main work done with assembly systems (systems containing parallel

production lines feeding an assembly line) is modeled as a fork-join with blocking type of

queuing system. The fork operation is when a product is decomposed into smaller units

with each unit following a separate production process. The join operation, which occurs

at the assembly station, is the synchronization of operations over a set of units. In other

words, multiple parallel production lines or workstations feed an assembly station different

components. The assembly station then joins the components. Blocking is the limiting

factor of the number of units in the model. All fork-join articles provide description of

how mathematical modeling techniques can be applied to manufacturing control

methodologies, and assembly systems. Yves Dallery et al. derived methods of modeling

kanban and assembly operations in production facilities [5]. Rao et al. reviews the use of

queuing theory in flexible manufacturing systems, computer-integrated manufacturing, and

kanban systems [13]. Agnetis et al. studies the effects that push, pull, and synchronization

procedures have on assembly stations by using simulation [2]. His results indicate that

push systems lead to increased WIP compared to pull. Furthermore, the results show that

pull systems have increased throughput compared to synchronized push systems.

The assembly system of Agnetis’ study consists of a main production line with

assembly stations located within it. The assembly stations are fed from the main line and

other feeder lines. In the assembly system it is detrimental for the main line to be balked.

By balking the main line the throughput of the system is reduced. If the feeder line’s

product is late in arriving to the assembly station, or tardy, the productivity suffers.

Therefore Agnetis’ study used the system’s throughput and WIP as well as the number of

tardy jobs as performance indicators.

5

In this study the performance indicators are system throughput, cycle time, and

WIP. The assembly system, as indicated in figure 1.1, will be studied to determine general

characteristics of the push, pull, and synchronization strategies at the assembly station.

Figure 1.1: Generalized Assembly Process

In literature, assembly stations are stations where the act of joining components is

carried out. The components to be joined are not necessarily produced in that production

system. By evaluating a process where the synchronization of sub-components is of

valued importance the use of the assembly station term holds special significance. The

assembly station is the station which two or more workstations feed with different

products. The assembly station combines these items into its own unique product. A

workstation is a station that does not combine products from two or more workstations.

A workstation has one input and one output per product type. A sequential series of

workstations is referred to as a serial production line or flow line. Parallel production

lines feeding an assembly station are feeder lines. An assembly station followed by a

Line 4 Machine 10 Machine 12Machine 11




6

sequential series of workstations is an assembly line. A system of two or more production

lines feeding an assembly line is an assembly system. The feeder lines that have the lowest

average throughput are the bottleneck feeder lines, and the other feeder lines are the

nonbottleneck feeder lines.

Figure 1.2: Synchronization Process

A synchronization process occurs when each of the components used in the

assembly station’s product is introduced into the assembly system simultaneously to

specifically combine with one another. For example the product C1, in figure 1.2, is

manufactured from items that were introduced to the assembly system simultaneously. If

product A1 is present at the assembly station and product B1 is not present, then A1 is

regarded as unmatched. A consequence of this synchronization process is that the

maximum amount of unmatched product A1 waiting at the assembly station is the total

sum of unprocessed and processing B0 items.

The primary purpose of this work is to study the effects of bottlenecks on an

assembly system under different production rules. In particular the location of the

A0 is transformed to A1

A1 and B1 are combined into C1

Raw Material A0

Raw Material B0

B0 is transformed to B1

7

bottlenecks relative to the assembly station and the resulting effects on selected

performance indicators of throughput, WIP, and cycle time will be studied. The goal of

this thesis will be achieved in the following manner.

1. Decompose the manufacturing system into its component production lines.

2. Analyze these subsystems with one and two bottlenecks at differing locations,

following differing production rules, and using differing control parameters.

3. Use the information generated in Step 2, to design a push system with a

synchronization procedure, a push system without a synchronization

procedure, a pull-push system, and a hybrid pull/push-push system.

4. Analyze these systems with two bottlenecks in a single feeder line.

5. Analyze these systems with one bottleneck in a feeder line, and one bottleneck

in the assembly line.

6. Analyze these systems with the bottlenecks in two separate feeder lines.

7. Compare all control systems in regard to throughput, WIP, and cycle time.

All statistical analyses will be conducted using hypothesis tests at an α level of

0.05. The throughputs and the WIPs will be compared by using t-statistics, and the cycle

times will be compared using by z-statistics to determine the relation the parameters have

to one another. The experimental data samples were generated from the following two

simulation software programs: Emulated Flexible Manufacturing Laboratory (EFML), and

Arena.

The remainder of the paper is organized in the following manner. The latter part

of this chapter will provide background information in regard to manufacturing control

8

systems, statistical hypothesis testing, and queuing theory. Chapter 2 provides

information on the EFML software and the simulation model. Chapter 3 is the in-depth

analysis of the feeder lines under MRP, kanban, and CONWIP production rules. Chapter

4 is the in-depth analysis of the four assembly system types. Chapter 5 is the comparison

of the assembly systems. Chapter 6 is the summary of the results and recommendations.

1.2 Fundamentals of Manufacturing Control Systems

There are two primary manufacturing control systems: push and pull. All other

control systems are either combinations or derivatives of these two systems. This section

will describe the theories and philosophies associated with manufacturing production

control and the following sections will be used to define different techniques that have

been developed to implement these philosophies.

Many theories have been proposed in managing manufacturing. In a flow shop

environment each product follows a fixed routing. In a job shop environment the routing

depends on the shop and the job being processed. At each station, buffers or finite storage

spaces exist for receiving incoming material and storing completed units. The buffers act

as a safety net to guard against line starvation and blockage caused by random events.

Manufacturing control systems manage how products are passed on, how buffers are

utilized, and when raw material enters the system.

“Push” control systems utilize forecasted demand to determine a production

schedule. The production schedule sets when raw material is delivered to the appropriate

workstations. Each workstation provides the necessary processing to the units waiting in

its buffer prior to releasing it to be transferred to the next downstream station. This cycle

9

of receiving, processing and releasing of material is carried out until the end product is

complete. In a push control system shipping of goods downstream is independent of the

downstream stations’ condition. This independence can cause problems if the downstream

station is offline. If the downstream station is offline, the WIP in the system escalates until

the station is online again. The WIP may or may not decrease at this time.

A push system is represented in figure 1.3. The arrows in the diagram refer to the

movement of the product through the system. Since the production schedule represents

demand information, the quantity of moving products represents the movement of

information in the system.

Figure 1.3: General Push System

“Pull” systems rely on the status of the system to determine production. In this

type of system, inventory is controlled through a system of cards. The number of cards

available determines the maximum allowable inventory for a particular workstation or

system of workstations. In such a system the production rate is determined by how the

finished goods of the final workstation is demanded by the customer. When the finished

goods are removed from the system the cards associated with these units are released.

Process 1 Process 3 Process 4Process 2

Raw Material

End Product

10

The released cards enable the final station to procure additional material from the

upstream station to process. Upon procurement of raw material from the upstream station

and release of the associated cards, the upstream station is able to obtain its own raw

material from its upstream station. This process of card release and material procurement

is repeated throughout the system until the raw material of the first station is obtained.

Since product movement is dependent on the condition of the next station, the entire

production line may stop due to the breakdown of an upstream station.

A pull system is represented in figure 1.4. The solid and dashed arrows in the

diagram respectively refer to the movement of the products and information. Since the

cards represent demand information, the movement of cards represents the movement of

information in the system. Unlike the push system, demand information originates in the

final station and proceeds to the initial station.

Figure 1.4: General Pull System


Raw Material

End Product

The solid line is product being pulled to the next station.The dashed line is the release of cards or informationtransfer.

11

MRP and its successor MRPII are push systems; kanban and CONWIP are pull

systems. Pull systems follow the Just-In-Time (JIT) philosophy, and DBR and some pull-

push systems follow the Theory of Constraints (TOC) philosophy.

1.3 Manufacturing Systems Philosophies

Philosophies in manufacturing systems define goals to be accomplished by control

techniques. The JIT philosophy’s goal is to have raw material of a process delivered just-

in-time for processing. The TOC philosophy’s goal is to maximize profit. Both of these

philosophies ascribe to process improvement. The improvement reduces variabili ty caused

by breakdowns and raw material shortages.

JIT focuses on minimizing the waste in a system by striving for no buffers, no

defects, and no variation. This is accomplished by:

• designing products for optimal quality, cost, and manufacturing ease,

• minimizing the amount of resources used to design and produce the product,

• designing the product to meet the customer’s needs,

• obtaining and maintaining good relationships with suppliers and vendors,

• and, developing a commitment to improving the manufacturing system [12].

When JIT is implemented, its purpose is to set a production rhythm that exploits

the available capacity of the system to fully meet the customer’s demand. Since JIT is a

pull-oriented system, the demand of the customer directly sets the production rhythm.

TOC focuses on maximizing profit now and in the future by maximizing the flow in

a system. This is accomplished by:

12

• identifying the bottleneck in the system,

• scheduling jobs and operations to ensure the complete utilization of the

bottleneck,

• determining the appropriate bottleneck buffer size to guard against upstream

station variability,

• improving bottleneck performance,

• and, then repeating the process [7, 8].

TOC is a profit oriented manufacturing control system. When using the TOC

system throughput is defined as the rate at which money is generate from sales, and

inventory is defined as the amount of money captured in the system [7]. By defining

manufacturing in this manner a bottleneck may be located off the production floor, such as

poor product sales. When TOC is implemented, its purpose is to set a production rhythm

that exploits the bottleneck of the system. The bottleneck is the constraint that hinders

greater throughput. By scheduling the bottleneck of the system, the WIP is reduced while

maintaining high throughput. Since the bottleneck determines the capacity of the system

by improving bottleneck performance, the system’s capacity is improved. [7, 8]

1.4 Manufacturing System Control Methodologies

1.4.1 MRP and MRPII Systems

MRP is the oldest push-type manufacturing control system. Its major components

are the bill of materials (BOM), the master production schedule (MPS), and the materials

requirement planning system. The BOM is a chart that shows the required components at

13

each stage of production starting from the final product, preceding with the intermediate

products, and then ending with the raw material for the initial processes. Each stage of

the BOM lists the quantities and the types of components required in producing that

stage’s product. The MPS contains information such as the time required at each stage of

production, the outstanding order status, the inventory status, and the demand for the final

product. The production time at each stage is regarded as fixed and the demand is

forecasted. The MRP system, as shown below, determines the production schedule.

1. Determine net requirements by subtracting on-hand inventory and scheduled

receipts from demanded requirements.

2. Determine the job lot sizes.

3. Offset the due dates of the individual jobs with the production times of the

product to arrive at the start times.

4. Using the start times, the lot sizes, and the BOM determine the demanded

requirements for the material used in the production of that stages’ product.

5. Starting with the final product repeat this process until all production stages

have been processed.

MRPII adds capacity analysis to MRP by incorporating information such as setup

time, resource requirements, and labor requirements into the MRP system. Through the

use of this information the MRP system provides a more realistic production schedule.

Figure 1.5 demonstrates how the MRP system generates planned order releases or a

production schedule for the manufacturing facility.

14

Figure 1.5: MRP Process

Although extensively used in the United States, MRP and its successor MRPII

have many shortcomings. Some of them are listed below.

• The MRP / MRPII systems do not consider fluctuations in production time due

to worker illness, machine breakdown, demand change, and availability of raw

material. To accommodate for these uncertainties safety stocks and safety lead

times are often used, but the inclusion of the safety stocks and safety lead times

increases inventory levels and production cycle times.

• MRP systems assume fixed cycle times or lead times regardless of the

inventory level. A consequence of this assumption coupled with a large WIP

leads to a large throughput. Regretfully throughput is limited by the

production rate of the bottleneck station. Once the throughput is maximized,

any additional inventory in the system results only in increased cycle time [14].

MPS

Production SchedulePurchase Orders

InventoryBOM

MRP ProcessNet RequirementsJob Lot SizesOffsettingExplosion

15

• The purpose of MRP systems is to meet the projected demand as provided by

the MPS. No effort is specifically expended to improve production.

1.4.2 DBR System

DBR is a newer system of production control that follows the TOC philosophy. In

doing so, it concentrates on managing the flow of products to meet the bottleneck

constraint’s needs. Since the bottleneck acts as a valve controlli ng the system’s

throughput, managing the bottleneck’s throughput manages the system’s throughput. To

maximize the system’s throughput, the bottleneck must utili ze all of its available capacity.

Similar to the MRP / MRPII systems, the DBR system uses a scheduled release of

products to control the production rate, and a safety stock or buffer at the bottleneck to

guard against stoppages from the upstream workstations [8].

Although the DBR control system provides improvement over the MRP / MRPII

systems, it is not immune from shortcomings. Some of them are listed below.

• Failure to locate the bottleneck of the system will result in lost throughput, or

increased WIP and cycle time depending on the false bottlenecks’ location

relative to the real bottleneck.

• The use of fixed lead times to schedule the bottleneck can lead to increased

WIP much as in MRP / MRPII systems.

• Incorrect bottleneck buffer size can result in bottleneck starvation; thus system

throughput is lost [15].

16

1.4.3 Kanban System

The kanban system was developed by Japanese manufacturers to implement the

JIT philosophy. In this system the kanban acts as an inventory control mechanism and

information relay device. It controls the inventory by requiring every batch in production

to be assigned to a kanban. The number of kanbans in the system thus determines the

maximum inventory possible. The kanbans transmit demand information from the

downstream stations to the upstream stations through the number of kanbans available and

how often the kanbans become available.

The single card kanban system, figure 1.6, allocates a set amount of kanban cards

to each workstation in the system. A kanban card is initially attached to a batch to be

processed by that workstation. The kanban card stays attached to the batch until a

downstream workstation has a kanban card available. When this occurs the attached

kanban card is freed from the workstation’s product and the previously freed kanban card

from the upstream workstation becomes assigned to that batch. Thus a free kanban card

allows a workstation to obtain material from the previous station when the material is

available [14].

17

Figure 1.6: Single Card Kanban Process

Successful implementation of the kanban system requires large production runs,

minimal defects, steady demand, reliable workstations, few product types, and reliable

vendors. Determining the number of kanban cards to allocate to each workstation is of

significant importance. One manner of determining the initial amount of kanban cards

uses the formulation below.

N > D * L (1 + α) / a

Here, N equals the number of kanban cards allocated to the workstation, D is the

demanded throughput, L is the cycle time, α is the safety factor, and “a” is the batch size.

N is first estimated by choosing a high α value in the range [0, 1]. Once the number of

kanban cards is determined the system is operated for a set length of time. Depending on

the production system dynamics, N is then adjusted on each separate workstation in an

effort to reduce WIP but maintain throughput [3].


Raw Material

End Product

The solid line is product being pulled to the next station.The dashed line is the release of cards or information transfer.

18

For all of kanban’s improvements to the production system, it also has its

shortcomings. Some of them are listed below.

• Kanban systems are not suited for manufacturing environments with short

production runs, highly variable product demand, poor quality products, and a

multitude of product types [11].

• A breakdown in the kanban system can result in the entire line shutting down.

• The throughput of a kanban system is not managed but is instead a result of

controlled WIP and known cycle times.

1.4.4 CONWIP

The CONWIP system is a generalized form of the kanban system. Like kanban,

CONWIP uses cards to limit the WIP of a system; unlike kanban the cards are allocated to

a system of workstations instead of just one. This difference allows CONWIP to be

applied in production environments that are detrimental to the kanban system [10].

In a CONWIP system the cards get attached to batches only at the first station.

The card remains affixed to the batch until the batch has finished processing on the final

workstation of the CONWIP system and the batch is used to satisfy a customer’s demand.

The released card is then returned to the initial workstation of the CONWIP line and to

authorize the entry of a new batch into the system.

Under a CONWIP system enough cards should be allocated to ensure the

bottleneck is fully utili zed. If the number of cards is insufficient the bottleneck starves and

thereby reduces the system’s throughput. Figure 1.7 shows the CONWIP process.

19

Figure 1.7: CONWIP Process

Even though CONWIP generally provides improvement over kanban and MRP /

MRPII, it does have its share of shortcomings. Some of them are listed below.

• Kanban systems can achieve higher throughput with lower WIP in some

situations over CONWIP systems.

• CONWIP systems cannot be successfully implemented in a job shop

environment.

• Incorrect card determination can lead to increased WIP or lost throughput for

the system.

• Machine breakdown can bring the entire CONWIP system to a halt.

1.4.5 Pull-Push Systems

Spearman et al. proposed a generalization of DBR that is modeled by using

CONWIP and a push system on a flow line [14]. By using a CONWIP system that

encapsulates all stations between and including the initial and the bottleneck stations, and

using a push system following the bottleneck station, the DBR system is approximated.


Raw Material

End Product

The solid line is product being pushed to the next station.The dashed line is the release of cards or information transfer.The double line is product being pulled into the system.

20

The DBR system determines a production schedule to ensure bottleneck of the system is

completely utilized. In the DBR system, the bottleneck is protected against variation from

the upstream stations via a buffer prior to the bottleneck. In the pull-push system enough

cards are allocated to the CONWIP segment to ensure the bottleneck is completely

utilized. Prior to the bottleneck a buffer will naturally develop and will be limited in

quantity by the CONWIP cards. Following the bottleneck in both systems the batches are

pushed through as fast as possible. The pull-push process is represented in figure 1.8,

where process 4 is the bottleneck process.

Figure 1.8: Pull – Push Process


Raw Material

End Product


The solid line is product being pushed to the next station.The dashed line is the release of cards or information transfer.The double line is product being pulled into the system.Process 4 is the bottleneck.

21

Although the pull-push system provides improvements to pull systems and DBR it

still has some shortcomings. Some of them are listed below.

• Failure to locate the bottleneck of the system will result in lost throughput, or

increased WIP and cycle time depending on the false bottlenecks’ location

relative to the real bottleneck.

• Incorrect card determination can lead to increased WIP or lost throughput for

the system.

• Machine breakdown can bring the entire pull-push system to a halt.

• Increased complexity over pure systems.

1.4.6 Comparison of Production Methodologies

There is extensive literature proving that pull systems tend to have lower WIP and

cycle time mean and variance compared to push systems. Pull systems are also easy to

control since WIP can be controlled directly whereas push systems manage throughput.

On the other hand, push systems can be implemented in many environments [4, 9, 14].

MRP / MRPII and DBR

MRP / MRPII and DBR are very similar systems, the diff erence lies in the focus of

production and the manner in which it is carried out. MRP / MRPII focuses on

maximizing the capacity of the production system. DBR focuses on maximizing the flow

of the production system. As a result DBR experiences reduced WIP levels and are more

capable of adjusting to fluctuations in the production environment [4].

22

MRP / MRPII and Kanban

MRP / MRPII and kanban systems differ in philosophies, environmental settings,

and control methods. MRP / MRPII systems operate under the philosophy of maximizing

throughput, can be applied in most manufacturing environments, and place production

control in the production schedule. Kanban systems use a philosophy of improvement,

require stable environments with large production runs, small setup times, minimal defects,

consistent demand, and places production control on the factory floor. Once the

production environment is achieved, the kanban system can achieve high throughput with

lower amounts of WIP compared to the MRP / MRPII systems [4, 11].

Kanban and CONWIP

Kanban and CONWIP systems only differ in that kanban fixes the inventory on a

per station basis, whereas CONWIP fixes the inventory on a per system basis. This

difference in implementation results in the following performance differences [9, 14].

• CONWIP can be implemented in production environments that have variable

demand and have a multitude of products, whereas kanban requires stable

environments and few product types.

• CONWIP does not attempt to control the location of the WIP in the

production system.

• CONWIP generally results in lower WIP levels than kanban given the same

throughput levels. Kanban in some situations can outperform CONWIP by

optimally placing cards in some systems [6].

23

CONWIP and Push

CONWIP is superior to push systems when the production systems run under the

highest possible throughput rate. In this situation at equivalent throughput rates, the push

system experience higher WIP and cycle time compared to the CONWIP system

[4, 9, 14].

JIT and TOC

TOC and JIT, through different approaches in managing a production

environment, achieve similar results.

• Both systems strive to improve and reduce variation in the production system.

TOC concentrates on improving the bottleneck station, and JIT improves each

station in the system.

• Both systems experience a reduction in WIP compared to MRP / MRPII

systems at equivalent throughputs. TOC accomplishes this by scheduling the

bottleneck to its fullest, and JIT does this by allocating kanban cards to keep

the bottleneck working.

• These systems differ in that TOC generally provides better throughput than JIT

with only slightly higher levels of WIP and greater cycle time [4].

24

1.4.7 Comparison Summary

From the previous descriptions of the above production systems the following can

be inferred.

• Scheduled releases of raw material can lead to increased system WIP,

depending on the variability of the system.

• Complete utilization of bottleneck maximizes system throughput.

• If the system conditions determine the release of raw material, the WIP of the

system is controlled.

• Pull systems are much more susceptible to system variation than push systems.

• Improving the production system can decrease system variability.

1.5 Preliminaries of Queuing Theory

Queuing theory studies how people, messages, and items flow through a system.

Practically all models and formulas developed in queuing theory are for systems in steady

state or equilibrium conditions. For a queuing system to be in steady-state the average

capacity of the system (C) must always be greater than the average arrival of entities to

the system (R). The above statement, C > R, is true for a single server system as well as

for networks of queues, as captured by Little’s Law.

In a steady state queuing system the following fundamental relationship N = λT

always holds true.

Little’s Law states that the average number of customers in a queuingsystem (N) is equal to the average arrival rate of customers to that system(λ), times the average time spent in that system (T). Furthermore, it does

25

not depend upon any specific assumptions regarding the arrival rate or theservice time distribution; nor does it depend on the particular queuingdiscipline within the system. [10, page 17]

In manufacturing, production lines can be viewed as queuing networks. Ergo, the

above law may be adapted as follows: Work-In-Process (WIP) is equal to throughput

(TH) times cycle time (CT).

WIP = TH* CT

1.6 Statistical Hypothesis

A statistical hypothesis is a formal statement concerning the parameters of a

probabili stic distribution. In order to check a parameter’s relationship to a specific value

hypothesis testing procedures are used. In testing a hypothesis a random sample is

obtained from the population under study and used to generate a test statistic. The value

of the test statistic determines whether to reject or fail to reject the null hypothesis, Ho.

The results obtained from the simulation programs often yielded similar results. In

order to test if a difference existed or if one parameter was greater than the other

statistical hypothesis tests were used. Based on the number of runs carried out, different

test statistics were used to validate the null hypothesis. The test results are available in

chapters 3, 4, and 5. Tables 1.1, 1.2, and 1.3 illustrate the types of tests used in the

analysis of the simulation results.

26

Table 1.1: Hypothesis Test on Variance

Hypothesis Test Statistic Criteria for Rejection

Table 1.2: Hypothesis Test on Means of Large Samples


22

210 : σσ =H

22

211 : σσ ≠H

22

21

0S

SF =

1,1, 212

0 −−> nnFF α

1,1, 21210 −−<

−nnFF α

22

21

0S

SF = 1,1, 210 −−> nnFF α

22

210 : σσ =H

22

211 : σσ >H

22

210 : σσ =H

22

211 : σσ <H

1,1, 1210 −−< − nnFF α22

21

0S

SF =

210 : µµ =H

211 : µµ >H2

22

1

21

210

n

S

n

S

xxZ

+

−=

αZZ >0

210 : µµ =H

211 : µµ ≠H2

22

1

21

210

n

S

n

S

xxZ

+

−=

20 αZZ >

210 : µµ =H

211 : µµ <H2

22

1

21

210

n

S

n

S

xxZ

+

−=

αZZ −<0

27

Table 1.3: Hypothesis Test on Means of Small Samples


The use of hypothesis tests requires a certain degree of normality for the sample

data. The central limit theorem (CLT) ensures this for the larger samples. The CLT

implies that the sum of n independently distributed random variables regardless of

2

*)1(*)1(

21

222

2112

−+−+−

=nn

SnSnS p

221 −+= nnv

22

21 σσ =

21

210

11

nnS

xxt

p +

−=

210 : µµ =H

211 : µµ ≠Hv

tt,2

0 α>

210 : µµ =H

211 : µµ <Hvtt ,0 α−<

210 : µµ =H

211 : µµ >Hvtt ,0 α>

2

11 2

2

2

22

1

2

1

21

2

2

22

1

21

−

+

++

+

=

n

n

S

n

n

S

n

S

n

S

v

22

21 σσ ≠

2

22

1

21

210

n

S

n

S

xxt

+

−=

210 : µµ =H

211 : µµ ≠Hv

tt,2

0 α>

210 : µµ =H

211 : µµ <Hvtt ,0 α−<

210 : µµ =H

211 : µµ >Hvtt ,0 α>

28

distribution followed is approximately normal. For the smaller samples normality is

assumed.

29

CHAPTER 2

SIMULATION MODELING AND THE ASSEMBLE SYSTEM MODEL

2.1 Simulation Modeling

Simulation is a tool that allows actual or hypothetical facilities or processes to be

studied. Similar to other methods of analysis an accurate model is essential for the

analysis to be meaningful. The simulation models’ advantage over mathematical models is

that it can be used to study large and complex systems quickly. The simulation program’s

speed and its ability to collect system data enables the analyst to study alterations to the

system easily. But unlike mathematical models, simulation cannot place theoretical limits

on a system and it cannot prove innate characteristics of the system.

2.1.1 Emulated Flexible Manufacturing Laboratory Software

The Emulated Flexible Manufacturing Laboratory (EFML) Software is a real-time

simulation program developed in the Industrial and Systems Engineering Department at

the University of Florida. It has been designed using Borland’s Delphi 4.0 and runs on

the Windows NT, 95, and 98 platforms with TCP/IP network communication protocol.

The software creates an interactive environment that allows users to experience the basics

in operation management, and production control systems.

30

EFML is written in an object oriented programming language. Each object in

EFML emulates an actual object in a manufacturing plant and is represented in an object

window. The main objects are factory setup, machine, dispatch and raw material,

transport, repair, and finished goods. These objects communicate with each other using a

message passing protocol over the internet thus allowing large facility and supply chain

management emulation. A small percentage of the software’s capabilities were utilized

during this study. Of all the available objects only the factory setup, machine, and the

dispatch and raw material objects were used.

Factory Setup Object

The factory setup object is the main object of EFML. It controls the factory setup,

the emulation model loading, the starting and stopping of the emulation, and the gathering

of the emulation statistics into a usable report. Additionally this window allows the user

to view and adjust remote system components and parameters.

Once EFML is started, a preset factory can be loaded by selecting “Autoload”

from the “Global” menu, or a factory can be built with the objects available to the user. If

a preset factory is loaded, selecting objects and changing their parameters can alter the

factory. If the user desires to save this change for future factory runs, it can be

accomplished using the “Save” option from the “File” menu.

When the setup is accomplished manually, the user chooses the needed objects

from the “Components” bar and places them in the active setup window. The setup

window serves as a background and moderator for the other objects (windows). The

overall control of the emulation resides in the setup object. In this object, the user adjusts

31

the speed of the emulation, the stop condition, where the report file is saved, and can

manually start and stop the emulation.

Machine Object

The machine object serves a dual purpose. It can be used to represent a process

center or it can emulate an assembly station. During emulation each machine is in one of

four states: idle, running, setup, and breakdown. In the running mode the machine follows

MRP, CONWIP, or kanban production rules. Each of these states and modes of the

machine object are color coded for ease of viewing. The color codes and states are listed

below.

• Idle status and any production process is white.

• Running status and MRP is blue.

• Running status and CONWIP is green.

• Running status and kanban is red.

• Setup status and setup is the color of the production process (green, blue, or

red).

• Breakdown status and any production process is yellow.

When setting up a machine object, the user is asked to specify the incoming and

outgoing batch names and sizes, the production rule to follow, the process distribution and

parameters, as well as the failure rate of the machine. While running, the machine objects

compute the statistics on the mean and variance of the machine’s processing time, the

mean and variance of the machine’s cycle time, the machine’s throughput, the batch’s start

and end times, and the number of batches processed.

32

Batches move through the system as directed by the machine and dispatch objects

and follow the implemented production control system. While at a machine the batch is in

one of three states: waiting in the in-queue buffer, being processed, or waiting in the out-

queue buffer. Following processing the batches are transported to the next machine object

or to the finished goods object.

Dispatch and Raw Material Object

The functions of the dispatch and raw material object include the storage of the

generated BOM, storage of the product routing, managing raw material inventory, and

dispatching of inventory to the appropriate workstations. The dispatching can either be

performed automatically or manually. In addition this object may be used to track

inventory cost and record transaction data.

2.1.2 Comparison of EFML to Traditional Simulation Programs

In traditional simulation programs, model events are determined to occur at a

specific time. The simulation program finds the earliest occurring event, sets its simulation

clock to that time, carries out any required functions, and then looks for the next event to

repeat this process. EFML, unlike the traditional simulation programs, advances through

time and at each clock tick determines if an event has occurred. If an event occurred,

EFML carries out any required functions before advancing to the next clock tick to repeat

the process. In this manner EFML runs in real time and allows individuals to see virtual

processes being accomplished.

33

2.2 Simulation Model

The primary system under analysis is an assembly system composed of three feeder

lines, and a three-station assembly line. The three-workstation feeder lines’ products are

the raw material for the assembly line. The assembly system is depicted in figure 2.1.

Using throughput, WIP, and cycle time as performance indicators, the goal of this

study is to ascertain general effects of push systems with and without batch

synchronization procedures implemented, pull-push systems, and hybrid pull/push-push

systems, in the presence of bottlenecks. In particular the location of the bottlenecks

relative the assembly station and the resulting effects on the performance indicators of the

assembly systems will be studied. The feeder lines, figure 2.4, were studied using one and

two bottlenecks under differing bottleneck locations, differing production rules, and

differing control settings. Following the feeder line study the full assembly system is

studied extensively. In all our experiments the processing times are assumed to be

independently and identically distributed random variables.

Figure 2.1: Feeder Line Production Process

Single LineMachine 1 Machine 3Machine 2

34

The assembly system in this study is assumed to contain two separate bottlenecks

with at least one of the bottlenecks located prior to the assembly station. A description of

the four assembly systems follows. The base push system is a pure push system using a

batch synchronization procedure. Batch synchronization is accomplished by releasing the

raw material to all the feeder lines simultaneously. The pure push systems without a batch

synchronization procedure use different interarrival times for the raw material of the

bottleneck and nonbottleneck feeder lines. The pull-push system uses CONWIP control

rules to manage all of the feeder lines. The assembly line is managed by a push system.

The hybrid pull/push-push system uses a pull process to manage the nonbottleneck feeder

lines and a push process elsewhere. The entire manufacturing assembly system studied in

this paper is shown in figure 2.2.

Figure 2.2: Assembly System Production Process





35

EFML though a very dynamic and powerful software package was not originally

designed to handle feeder lines / assembly stations models for all control systems. In order

to create the experiments a dummy workstation with a constant zero processing time is

used to match the required batches in front of the assembly line. Figure 2.3 is the new

simulation model configuration and figure 2.4 is the modified assembly system with the

dummy or matching station noted.

Figure 2.3: Modified Simulation Model Configuration





Dummy MatchingStation

36

Figure 2.4: EFML Simulation Model

2.2.1 Experimental Conditions

The following control parameter settings were used throughout the experiments.

• The processing times on each nonbottleneck machine follows an exponential

distribution with a mean of 25 seconds per item.

• The processing times on each bottleneck machine follows an exponential

distribution with a mean of 30 seconds per item.

• The batch size is 10 items.

• In order to reach equilibrium conditions, each experiment was run until 4000

batches were produced.

Machine Object

Matching Station

Dispatch Object

Setup Object

37

• There is an infinite amount of demand.

• There is an infinite supply of raw materials.

• Setup times are assumed to be zero for all batches and operations.

• Transportation time of a batch between two stations is instantaneous.

• The system components are 100% reliable with no breakdowns.

2.2.2 Calculations

Cycle Time

Cycle Time of Line 1 = Σ(cycle times of machines 1, 2, 3)

Cycle Time of Line 2 = Σ (cycle times of machines 4, 5, 6)



System Cycle time* = maximum (Feeder Line Cycle Times) + Cycle Time of

Line 4

*If line 2 and / or 3 follow the pull style production rules, the line’s cycle times are

not included in the formulation.

Final Inventory Status

This calculation serves the purpose of monitoring how many batches from a feeder

line are left unmatched at the dummy station after 4000 batches are produced by the

system. Here Nj is the number of items produced by Line j.

Unmatched Inventory at Line j = Nj – minimum (N1, N2, N3)

}3,2,1{∈j

38

CHAPTER 3

FEEDER LINE ANALYSIS

Hypothesis tests, with an α level of 0.05, were carried out on all of the feeder line

systems to determine the relationship of the samples’ parameters mean and variance with

each other. The parameters under consideration are throughput, WIP, and cycle time.

The throughput and WIP values represent the average throughput and WIP of sixteen

trials where each trial produced 4000 batches. The cycle time is the average cycle time of

4000 batches.

Administration of the hypothesis tests followed the procedure in figure 3.1.

3.1 MRP Feeder Lines

The MRP feeder lines contain three variables that affect the performance

indicators: the amount and location of the bottlenecks, and the interarrival time of raw

material to the feeder line. To identify the effects of the bottleneck and the interarrival

time, two separate analyses were carried out for each parameter. In the first section the

interarrival time of the raw material is held constant while the bottleneck locations are

varied, and in the second section the bottleneck location is held constant while the

interarrival times of the raw material is varied.

39

Figure 3.1: Analyst Procedure

Throughput Analysis of 3 Machine Lines

0.194

0.195

0.196

0.197

0.198

0.199

1 2 3 1, 2 1, 3 2, 3

Bottleneck Location

Ob

serv

ed T

hro

ug

hp

ut

(Bat

ches

/M

inu

te)

300

301

302

303

304

305

306

307

Figure 3.2: Throughput Analysis of 3 Machine MRP Lines– Interarrival Time Constant

Test if variances areequal between sample’sparameters

Variances arenot equal

Variances areequalIf sample size is

greater than 30 useZ statistic

If sample size is less than 30 use Tstatistic with unequal variances anddetermine appropriate degrees offreedom

If sample size is less than 30 use Tstatistic with equal variances anddetermine appropriate degrees offreedom

Analyze grouped data, check forpatterns in acceptance andrejection of null hypothesis

40

Figure 3.2 provides the observed throughput for feeder lines managed under a

MRP system with constant interarrival times. The following experimental results were

obtained using an α level of 0.05.

• The throughput variances are equal within any MRP system regardless of the

number or position of the bottlenecks, given that interarrival times are 300,

301 or 302.

• In 80 out of 90 statistical comparisons, the throughput means and variances in

any single bottleneck or dual bottleneck systems are equal regardless of the

bottleneck location, given interarrival times of 300 to 305.

• As the number of bottlenecks increase, the throughput decreases.

Figure 3.3: Throughput Analysis of 3 Machine MRP Lines– Bottleneck Position Constant


0.192

0.193

0.194

0.195

0.196

0.197

0.198

0.199

300 301 302 303 304 305 306 307

Inter Arrival Time (Seconds/Batch)

Ob

serv

ed T

hro

ug

hp

ut

(Bat

ches

/ M

inu

te)

1

2

3

1, 2

1, 3

2, 3

41


MRP system with constant bottleneck locations. The following experimental results were


• The throughput variances of MRP systems are equal at interarrival times of

300, 301, and 302, given identical bottleneck positions.

• The throughput means of MRP systems either remains unchanged or decreases

as interarrival times increase.

WIP Analysis of 3 Machine Lines

4

6

8

10

12

14

16

18

20

1 2 3 1, 2 1, 3 2, 3

Bottleneck Location

Ob

serv

ed W

IP (

Bat

ches

)

300

301

302

303

304

305

306

307

Figure 3.4: WIP Analysis of 3 Machine MRP Lines – Interarrival Time Constant

Figure 3.4 provides the observed WIP for feeder lines managed under a MRP

system with constant interarrival times. The following experimental results were obtained

using an α level of 0.05.

• The WIP variances are equal within any MRP system regardless of the number

or position of the bottlenecks, given that interarrival times are 300, 301 or 302.

42

• In 75 out of 90 statistical comparisons, the WIP means and variances in any

single bottleneck or dual bottleneck systems are equal regardless of the

bottleneck location, given interarrival times of 300 to 305.

• As the number of bottlenecks increase, the WIP increases.


4

6

8

10

12

14

16

18

20

300 301 302 303 304 305 306 307

Raw Material Arrival Time (Seconds/Batch)

Ob

serv

ed W

IP (

Bat

ches

)

1

2

3

1, 2

1, 3

2, 3

Figure 3.5: WIP Analysis of 3 Machine MRP Lines– Bottleneck Position Constant

Figure 3.5 provides the observed WIP for feeder lines managed under a MRP

system with constant bottleneck locations. The following experimental results were


• The WIP variances of MRP systems are equal at interarrival times of 300, 301,

and 302, given identical bottleneck positions.

• The WIP means of MRP systems either remains unchanged or decreases as the

interarrival times increase.

43

Cycle Time Analysis of 3 Machine Lines

0

2000

4000

6000

8000

10000

12000

1 2 3 1, 2 1, 3 2, 3Bottleneck Location

Cyc

le T

ime

(S

eco

nd

s/B

atch

)

300

301

302

303

304

305

306

307

Figure 3.6: Cycle Time Analysis of 3 Machine MRP Lines– Interarrival Time Constant

Figure 3.6 provides the observed cycle time for feeder lines managed under a MRP

system with constant interarrival times. The interarrival time of 300, as shown in figures

3.4a and 3.4b does exhibit anomalous behavior. The following experimental results were


• In 68 out of 72 statistical comparisons, increasing the number of bottlenecks

increases the cycle time mean.

• There is no discernible statistical pattern indicating that the position of the

bottleneck influences the cycle time mean of the MRP system.

44


0

2000

4000

6000

8000

10000

12000

300 301 302 303 304 305 306 307

Interarrival Time

Cyc

le T

ime

(S

eco

nd

s /

Ba

tch

)

1

2

3

1, 2

1, 3

2, 3

Figure 3.7: Cycle Time Analysis of 3 Machine MRP Lines– Bottleneck Position Constant

Figure 3.7 provides the observed cycle time for feeder lines managed under a MRP

system with constant bottleneck locations. The interarrival time of 300, as shown in

figures 3.4a and 3.4b does exhibit anomalous behavior. The following experimental result

was obtained using an α level of 0.05. In 111 out of 126 statistical comparisons,

increasing the interarrival times of raw material reduce or maintain the cycle time mean.

3.2 Kanban Feeder Lines

The kanban feeder lines contain five variables that affect the performance

indicators: the number and locations of the bottlenecks, and the number of cards allocated

to each workstation. Each workstation has either one or two kanban cards allocated. To

identify the effects of the bottleneck and the card allocation, two separate analyses were

carried out for each parameter. In the first section the card allocation is held constant

45

while the bottleneck locations are varied, and in the second section the bottleneck location

is held constant while kanban card allocation is varied.


0.160

0.165

0.170

0.175

0.180

0.185

0.190

0.195

0.200

1 2 3 1, 2 1, 3 2, 3

Bottleneck Location

Ob

serv

ed T

hro

ug

hp

ut

(B

atch

es /

Min

ute

)

1-1-1

1-1-2

1-2-1

2-1-1

1-2-2

2-1-2

2-2-1

2-2-2

Figure 3.8: Throughput Analysis of 3 Machine Kanban Lines– Card Allocation Constant


kanban system with constant card allocations. The following experimental results were


• In 114 out of 120 statistical comparisons, the throughput variances of the

kanban systems are equal regardless of bottleneck position, given identical card

allocations.

• As the number of bottlenecks increase the throughput means decrease, given

identical card allocations.

46

• The throughput means increase for single bottleneck kanban systems in the

following cases: if an extra card is associated with the bottleneck station; if an

extra card is associated with the workstation prior to the bottleneck station; or

if the bottleneck is located at the initial workstation.

Figure 3.9: Throughput Analysis of 3 Machine Kanban Lines– Bottleneck PositionConstant


kanban system with constant bottleneck locations. The following experimental result was

obtained using an α level of 0.05. As additional cards are allocated to the system, the

throughput means increase or remain constant, given identical bottleneck locations.


0.160

0.165

0.170

0.175

0.180

0.185

0.190

0.195

0.200

1-1-1 1-1-2 1-2-1 2-1-1 1-2-2 2-1-2 2-2-1 2-2-2

Card Allocation

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1

2

3

1, 2

1, 3

2, 3

47


2.000

2.500

3.000

3.500

4.000

4.500

5.000

5.500

6.000

6.500

1 2 3 1, 2 1, 3 2, 3

Bottleneck Location

Ob

serv

ed W

IP (

Bat

ches

)1-1-1

1-1-2

1-2-1

2-1-1

1-2-2

2-1-2

2-2-1

2-2-2

Figure 3.10: WIP Analysis of 3 Machine Kanban Lines– Card Allocation Constant

Figure 3.10 provides the observed WIP for feeder lines managed under a kanban

system with constant card allocations. The following experimental results were obtained


• The WIP variances of single bottleneck kanban systems decrease or remain

constant as the bottleneck is moved upstream.

• In 21 out of 24 statistical comparisons, the WIP variances of dual bottleneck

kanban systems decrease or remain unchanged, as the bottlenecks are both

located further upstream.

• The WIP means of kanban systems increase or remain unchanged as the

bottleneck is moved further upstream, given the same card allocation.

48


2.000

2.500

3.000

3.500

4.000

4.500

5.000

5.500

6.000

6.500

1-1-1 1-1-2 1-2-1 2-1-1 1-2-2 2-1-2 2-2-1 2-2-2

Card Allocation

Ob

serv

ed W

IP (

Bat

ches

)

1

2

3

1, 2

1, 3

2, 3

Figure 3.11: WIP Analysis of 3 Machine Kanban Lines– Bottleneck Position Constant


system with constant bottleneck locations. The following experimental result was

obtained using an α level of 0.05. In 112 out of 114 statistical comparisons, increasing the

number of cards in the systems increase WIP means, given identical bottleneck locations.

49


600

800

1000

1200

1400

1600

1800

2000

1 2 3 1, 2 1, 3 2, 3Bottleneck Location

Cyc

le T

ime

(S

eco

nd

s /

Ba

tch

)1-1-1

1-1-2

1-2-1

1-2-2

2-1-1

2-1-2

2-2-1

2-2-2

Figure 3.12: Cycle Time Analysis of 3 Machine Kanban Lines– Card Allocation Constant

Figure 3.12 provides the observed cycle time for feeder lines managed under a

kanban system with constant card allocations. The following experimental results were


• The cycle time means of the system increase as the bottleneck stations move

further downstream, given identical card allocation.

• The cycle time means of single bottleneck kanban systems with the bottleneck

on the final workstation, is less than the cycle time of dual bottleneck kanban

systems with the initial bottleneck on the first workstation.

50


600

800

1000

1200

1400

1600

1800

2000

1-1-1 1-1-2 1-2-1 2-1-1 1-2-2 2-1-2 2-2-1 2-2-2Card Allocation

Cyc

le T

ime

(S

eco

nd

s /

Bat

ch)

1

2

3

1, 2

1, 3

2, 3

Figure 3.13: Cycle Time Analysis of 3 Machine Kanban Lines– Bottleneck PositionConstant


system with constant bottleneck positions. The following experimental result was

obtained using an α level of 0.05. In 125 out of 132 statistical comparisons, increasing the

number of cards in the systems increase the cycle time means, given identical bottleneck

location.

3.3 CONWIP Feeder Line

The CONWIP feeder lines contain three variables that effect the performance

indicators: the number and position of the bottlenecks, and the number of cards allocated.

Unlike the other systems analyzed, the WIP is held constant as defined by the number of

cards allocated. To identify effects of the bottleneck and the number of cards allocated,

51

two separate analyses were carried out for each parameter. In the first section the number

of cards allocated is held constant while the bottleneck locations are varied, and in the

second section the bottleneck location is held constant while the number of cards allocated

is varied.

Figure 3.14: Throughput Analysis of 3 Machine CONWIP Lines– Cards AllocatedConstant


CONWIP system with a constant number of cards allocated. The following experimental

results were obtained using an α level of 0.05.

• The throughput variances of CONWIP systems are equal regardless of

bottleneck location or amount, given the number of cards allocated to the

system are less than six. When the number of cards allocated to the systems

equals six, the throughput variances of these CONWIP systems are equal


0.000

0.050

0.100

0.150

0.200

0.250

1 2 3 1, 2 1, 3 2, 3

Bottleneck Location

Ob

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1

2

3

4

5

6

52

regardless of bottleneck location, provided the systems have same number of

bottlenecks.

• The throughput means of CONWIP systems increase as the number of cards

allocated to the system increases.

• The throughput means of single bottleneck CONWIP systems having five cards

allocated are equal to the throughput means of single bottleneck CONWIP

systems with six cards, given identical number of cards allocated.

• The throughput means of CONWIP systems are equal, given identical number

of bottlenecks and cards allocated.

• The throughput means of CONWIP systems decrease as the number of

bottlenecks increase, given identical number of cards allocated.

Figure 3.15: Throughput Analysis of 3 Machine CONWIP Lines– Bottleneck PositionConstant


0.050

0.070

0.090

0.110

0.130

0.150

0.170

0.190

0.210

1 2 3 4 5 6Number of Cards Allocated

Ob

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(Bat

ches

/Min

ute

) 1

2

3

1, 2

1, 3

2, 3

53


CONWIP system with constant bottleneck location. The following experimental results

were obtained using an α level of 0.05.

• As the number of cards allocated to CONWIP systems increase, the

throughput variances of the CONWIP systems increase, given identical

bottleneck positions.

• The throughput variances of single bottleneck CONWIP systems at five cards

are equal to the throughput variances of single bottleneck CONWIP systems at

six cards, given the bottleneck positions are identical.

• The throughput variances of dual bottleneck CONWIP systems at four, five,

and six cards are identical, given identical bottleneck positions.

• The throughput means of CONWIP systems increase as the number of cards

increase regardless of the number of bottlenecks, given identical bottleneck

positions.

54


600

800

1000

1200

1400

1600

1800

2000

1 2 3 1, 2 1, 3 2, 3

Bottleneck Location

Cyc

le T

ime

(S

eco

nd

s /

Ba

tch

)1

2

3

4

5

6

Figure 3.16: Cycle Time Analysis of 3 Machine CONWIP Lines– Cards AllocatedConstant


CONWIP system with constant number of cards allocated. The following experimental

results were obtained using an α level of 0.05.

• The cycle time variances of CONWIP systems are equal regardless of the

number of and location of the bottlenecks, given idential number of cards

allocated.

• In 30 out of 36 statistical comparisons, the mean cycle time of CONWIP

systems with equal numbers of bottlenecks are equal, given identical number of

cards allocated.

• Increasing the number of bottlenecks in the CONWIP system increases the

mean cycle time, given idential number of cards allocated.

55


600

800

1000

1200

1400

1600

1800

2000

1 2 3 4 5 6

Number of Cards Allocated

Cyc

le T

ime

(Seco

nds /

Bat

ch)

1

2

3

1, 2

1, 3

2, 3

Figure 3.17: Cycle Time Analysis of 3 Machine CONWIP Lines– Bottleneck PositionConstant


CONWIP system with constant bottleneck locations. The following experimental results

were obtained using an α level of 0.05.

• Increasing the amount of cards allocated increases the cycle time variances,

given identical bottleneck positions.

• As the number of cards increase, the cycle time means also increase regardless

of the bottleneck postions.

3.4 Feeder Line Production Control Systems Summary and Conclusions of Findings

The basic findings of the feeder line analysis is that under any pure production

control system increasing the number of bottlenecks generally increases WIP, and cycle

time, and decreases throughput. This is an expected finding since the addition of the

56

bottleneck to the system automatically increases cycle time. Utilizing Little’s law given

constant WIP and increased cycle time results in deceased throughput, and given constant

throughput and increased cycle time results in increased WIP.

In push and pull systems starving the bottleneck station results in the system’s

throughput being reduced. In push systems bottleneck starvation can occur when raw

material is not delivered to the feeder lines fast enough. Therefore, as the interarrival

times are increased the throughput of the system decreases. In pull systems bottleneck

starvation can occur if the kanban cards are not allocated optimally. Therefore, as

additional cards are added to the system throughput increases. In a pull system, when the

bottleneck is starved the addition of cards will generally increase cycle time, WIP, and

throughput. An additional card decreases the amount of time the bottleneck is starved

thus results in an increase in throughput. The additional card also increases the maximum

number of batches in the system, and since more batches are in the system to be

processed, the cycle time increases.

The feeder analysis also indicates a reduction in system variance as the bottleneck

is moved downstream. Since the simulation uses an exponential distribution as a unit

mean process time distribution, moving the bottleneck station downstream would have the

same effect of moving a higher variable workstation downstream, and thus moving a

bottleneck station downstream can reduce system variation.

The analyses of the three production methodologies revealed characteristics of the

MRP and CONWIP systems that made them ideal for the analyses of assembly systems.

The MRP feeder lines’ throughput and WIP have equal mean and variance

regardless of bottleneck location, given identical number of bottlenecks and interarrival

57

times of 300 to 305. Additionally the MRP feeder lines show no discernable statistical

pattern that indicates that the position of the bottleneck influences the cycle time. Since

the interarrival time of raw material, not the location of the bottleneck, affects the

throughput and WIP, any alteration of the assembly system’s throughput and WIP using a

constant interarrival time is the result of the assembly station or the bottleneck’s position

relative to the assembly station.

The CONWIP system feeder lines’ throughput and cycle time are equal in mean

and variance regardless of the bottleneck postion given identical number of cards. In the

kanban system the allocation of the cards in relationship to the bottleneck influences

throughput. Since it is desireable in this paper to observe the effects of the bottleneck in

relation to the assembly station and not the effects of the bottleneck in relation to the

allocation of cards, the CONWIP production system will be used in constructing the pull

portion of the assembly systems.

58

CHAPTER 4

ASSEMBLY SYSTEM ANALYSIS

There are four full assembly systems under analysis: a pure push assembly system

with a batch synchronization procedure, a pure push assembly system without a batch

synchronization procedure, a pull-push system, and a hybrid pull/push-push system. Each

assembly system will be fully described prior to its respective analysis.

The feeder lines used in the construction of the assembly system had to have at

least an average throughput of 0.197 batches per minute. The throughput rate chosen is

the maximum throughput attainable from the MRP feeder line systems without

experiencing exploding inventories. The maximum throughput rate occurred at the

interarrival times of 300 and 301. The interarrival time of 301 was chosen to reduce WIP.

Since the assembly system study includes two bottlenecks, different card allocations must

be assigned to the CONWIP feeder lines with different amounts of bottlenecks. To

achieve at least 0.197 for the CONWIP feeder lines four cards were allocated when there

was no bottlenecks, six cards were allocated when there was one bottleneck, and thirteen

cards were allocated when there were two bottlenecks.

The assembly system is broken into three distinct segments: the assembly line, the

bottleneck feeder lines and the nonbottleneck feeder lines. The assembly line follows the

production control rules of a push system. The bottleneck feeder lines follow either the

MRP production rules with an interarrival time of 301, or the CONWIP production rules

with card settings of six, or thirteen depending on the number of bottleneck stations in the

feeder line. The nonbottleneck feeder lines follow either the MRP production rules with

59

an interarrival time specified in the assembly system, or the CONWIP production rules

with four cards allocated. In the assembly system, the assembly station acts as the

customer and removes finished products from the each feeder lines, but only if there is at

least one finished product in each of the feeder lines’ out-queues.

To aid review of the assembly system statistical analysis, table 4.1 provides

identification of systems with both bottlenecks in a single feeder line, with one bottleneck

in a feeder line and the second bottleneck in the assembly line, and with two bottleneck

feeder lines.

Table 4.1: Assembly System Types

System description Bottleneck locations

Systems with both bottlenecks are located

in a single feeder line.

(1 ,2), (1, 3), and (2, 3)

Systems with one bottleneck located in a

feeder line and the second bottleneck

located in the assembly line.

(1, 10), (1, 11), (1, 12), (2, 10), (2, 11),

(2, 12), (3, 10), (3, 11), and (3, 12)

Systems with two bottleneck feeder lines. (1, 4), (1, 5), (1, 6), (2, 5), (2, 6), and (3, 6)

60

4.1 Pure Push Assembly Systems Using a Synchronization Process

This pure push production will serve as the base push assembly system. In this

system the interarrival times for the delivery raw material is set uniformly in all feeder lines

to 301. The batches entering the system in synchronization will combine at the assembly

station.

Throughput Analysis

0.1972

0.1974

0.1976

0.1978

0.198

0.1982

0.1984

0.1986

1,2

1,3

1,10

1,11

1,12 2,

3

2,10

2,11

2,12

3,10

3,11

3,12 1,

4

1,5

1,6

2,5

2,6

3,6

Bottleneck Location

Ob

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(Bat

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/ M

inu

te)

Figure 4.1: Throughput Analysis of Base Push Assembly System

Figure 4.1 provides the observed throughput for the push assembly system with

the batch synchronization process. The following experimental results were obtained


61

• In 61 out of 66 statistical comparisons, the throughput variances of systems

with a single bottleneck feeder line are identical.

• The throughput variances of systems with two bottleneck feeder lines are

identical.

• The throughput means of systems with both bottlenecks in a single feeder line

are identical.

• The throughput means of systems with one bottleneck feeder line and the first

bottleneck in the first workstation are identical.

• The throughput means of systems with two bottleneck feeder lines are

identical.

Figure 4.2: WIP Analysis of Base Push Assembly System

WIP Analysis

15

20

25

30

35

40

45

1,2

1,3

1,10

1,11

1,12 2,3

2,10

2,11

2,12

3,10

3,11

3,12 1,4

1,5

1,6

2,5

2,6

3,6

Bottleneck Location

Ob

serv

ed W

IP (

Bat

ches

)

62

Figure 4.2 provides the observed WIP for the push assembly system with the batch

synchronization process. The following experimental results were obtained using an α

level of 0.05.

• The WIP variances of systems with bottlenecks located in two separate feeder

lines are identical.

• The WIP means of systems with both bottlenecks located in a single feeder line

are identical.

• The WIP means of systems with two bottleneck feeder lines are identical.

• If one bottleneck is located in a feeder line and the other one is in the assembly

line, then the WIP of these systems are identical.

• The WIP means of systems where one bottleneck is located in a feeder line and

the second bottleneck is located in the assembly line, are identical to the WIP

means of systems with both bottlenecks located in separate feeder lines.

63

Figure 4.3: Cycle Time Analysis of Base Push Assembly System

Figure 4.3 provides the observed cycle time for the push assembly system with the

batch synchronization process. No statistically discernable patterns were evident in cycle

time mean or variance at an α level of 0.05.

4.2 Pure Push Assembly Systems with No Synchronization Process

In the base push system synchronizing the sub-components for the assembly station

actually occurred when raw material was dispatched to the feeder lines. A consequence of

this action is the accumulation of batches in the nonbottleneck feeder lines’ out-queues.

This increase of system WIP ties in additional capital that could be used elsewhere.

In the DBR control system, the bottleneck is scheduled to ensure its complete

utilization. Thus the highest throughput is achieved while the WIP and cycle time of the

system is reduced. In the assembly system the assembly station does not necessarily need

Cycle Time Analysis

0

2000

4000

6000

8000

10000

12000

1,2 1,3 1,10 1,11 1,12 2,3 2,10 2,11 2,12 3,10 3,11 3,12 1,4 1,5 1,6 2,5 2,6 3,6

Bottleneck Location

Cyc

le T

ime

(Sec

on

ds

/ Bat

ch)

64

to be completely utilized, but the nonbottleneck feeder lines’ products should always be

available when the bottleneck feeder lines’ product becomes available. Using the DBR

methodology, this analysis attempted to balance the bottleneck and the nonbottleneck

feeder lines’ throughput in order to achieve decreased system WIP, without sacrificing

throughput. This was accomplished by gradually increasing the interarrival times of raw

material to the nonbottleneck feeder lines, while maintaining an interarrival time of 301 to

the bottleneck feeder lines.

The results indicate an interesting phenomenon at the assembly station that we

term as a pure-birth process. If the bottleneck feeder lines’ throughput differed from the

nonbottleneck feeder lines’ throughput, the difference would be the pure-birth process rate

of unmatched batches. To compute the total number of unmatched batches the “Final

Inventory Status” equation was used for each of the feeder lines.

To demonstrate how the pure-birth process can be hidden figures 4.4, 4.5, and 4.6

will be presented for assembly systems with one bottleneck feeder line and figures 4.7, 4.8,

and 4.9 will be presented for assembly systems with two bottleneck feeder lines. Figures

4.4 and 4.7 are the summed total of final inventories for the bottleneck feeder lines’

products. Figures 4.5 and 4.8 are the summed total of final inventories for the

nonbottleneck feeder lines’ products. The total final inventories of all the feeder lines’

products are in figures 4.6 and 4.9.

65

Figure 4.4: Unmatched Inventory after 4000 Batches - Bottleneck Feeder Line

Figure 4.5: Unmatched Inventory after 4000 Batches - Dual Nonbottleneck Feeder Lines

Last Status of Available Unjoined Inventory at Assembly Station from Bottleneck Feeder Lines

0

10

20

30

40

50

60

70

80

90

301 302 303 304 305 306 307

Interarrival Time

WIP

(B

atch

es)

1, 2

1, 3

1, 10

1, 11

1, 12

2, 3

2, 10

2, 11

2, 12

3, 10

3, 11

3, 12

Last Status of Available Unjoined Inventory at Assembly Station from Nonbottleneck Feeder Lines

0

10

20

30

40

50

60

70

80

301 302 303 304 305 306 307Interarrival Time

WIP

(B

atch

es)

1, 2

1, 3

1, 10

1, 11

1, 12

2, 3

2, 10

2, 11

2, 12

3, 10

3, 11

3, 12

66

Figure 4.6: Unmatched Inventory after 4000 Batches - Assembly Systems with OneBottleneck Feeder Line

Figure 4.7: Unmatched Inventory after 4000 Batches - Dual Bottleneck Feeder Lines

Last Status of Available Unmatched Inventory at Matching Station from All Feeder Lines

0

10

20

30

40

50

60

70

80

90


WIP

(B

atch

es)

1, 2

1, 3

1, 10

1, 11

1, 12

2, 3

2, 10

2, 11

2, 12

3, 10

3, 11

Last Status of Available Unjoined Inventory at Assembly Station from Bottleneck Feeder Lines

0

20

40

60

80

100

120

140

160

180

301 302 303 304 305 306 307

Interarrival Time

WIP

(B

atch

es)

1, 4

1, 5

1, 6

2, 5

2, 6

3, 6

67

Figure 4.8: Unmatched Inventory after 4000 Batches - Nonbottleneck Feeder Line

Figure 4.9: Unmatched Inventory after 4000 Batches - Assembly Systems with TwoBottleneck Feeder Lines

Last Status of Available Unjoined Inventory at Assembly Station from Nonbottleneck Feeder Lines

0

2

4

6

8

10

12

14

16

301 302 303 304 305 306 307

Interarrival Time

WIP

(B

atch

es)

1, 4

1, 5

1, 6

2, 5

2, 6

3, 6

Last Status of Available Unmatched Inventory at Matching Station from All Feeder Lines

0

20

40

60

80

100

120

140

160

180


WIP

(B

atch

es)

1, 4

1, 5

1, 6

2, 5

2, 6

3, 6

68

The pure-birth process is insidious in two manners. First, as illustrated in figures

4.4 and 4.7 this process can remain hidden. Second, as illustrated in figures 4.4, 4.5, 4.7,

and 4.8 the buildup of unmatched inventory appears to occur either in the bottleneck

feeder lines or the nonbottleneck feeder lines. In this analysis there does not appear to be

an interarrival time that the nonbottleneck feeder line can use, that will not generate

unmatched products. Because of the unchecked buildup of unmatched products at the

assembly station, unsynchronized assembly systems do not achieve steady state and thus

statistical analysis cannot be provided.

4.2.1 Process Analysis of Unmatched Feeder Line Inventory

TOC provides one major simplification for the proceeding analysis - subordinating

all processes to the bottleneck. The bottleneck feeder lines have the lowest throughput of

all the feeder lines. The assembly station requires the same amount of raw material from

each of the feeder lines; it cannot begin processing until this matched set is collected.

Since the joining process requires zero time, the arrival rate to the assembly station is

defined by the arrival rate (throughput) of products from the bottleneck feeder lines.

It is known that if the service rate of a process is less than the arrival rate, the

process’ queue will increase to infinity. If this occurs, the process is unstable and it can be

described as a birth process. Since the bottleneck feeder line’s throughput rate equals the

arrival rate of batches to the assembly station, the nonbottleneck feeder lines experience a

birth process.

69

4.2.2 Verification of Analysis

Arrival Rate to Assembly Station (λA)= min(Throughput of feeder lines)

Arrival Rate of Line i (λi)= Throughput of Line i

Birth Rate of Line i’s Product (λ’ i)= λA – λi

Expected Inventory of Line i's Product at time t = λ’ i * t

Figure 4.10: Assembly Station Raw Material Combination

Table 4.2 was generated from the simulation series with the bottleneck on the 1st

and 4th workstations. The table demonstrates the validity of this process analysis. If the

simulation were allowed to run for an infinite period of time the build up of unmatched

feeder line products would become infinite in number. To avoid this, rescheduling of the

production process must occur.

λ1

λ2

λ3

λA

Line 1

Line 2

Line 3

Matching Assembly Station

70

Table 4.2: Series Comparison of Actual Feeder Line Inventory to the Predicted Value

Feeder Line Throughputs Feeder Line Birth RatesInterarrival Time 1 2 3 1 2 3

301 0.1991 0.1985 0.1993 0.0006 0.0000 0.0007302 0.1986 0.1985 0.1986 0.0001 0.0000 0.0000303 0.1992 0.1990 0.1979 0.0013 0.0011 0.0000304 0.1992 0.1990 0.1972 0.0020 0.0018 0.0000305 0.1991 0.1992 0.1966 0.0025 0.0026 0.0000306 0.1991 0.1990 0.1960 0.0031 0.0030 0.0000307 0.1980 0.1987 0.1954 0.0026 0.0033 0.0000

Time ofSimulation Run

Observed Final Inventory Expected Final Inventory

Seconds 1 2 3 1 2 31209874 11 0 15 11.3 0.0 15.01210431 1 0 0 2.1 0.0 0.91213771 26 23 0 25.3 22.7 0.01217855 41 36 0 41.1 35.9 0.01222144 50 53 0 50.0 52.6 0.01225511 64 62 0 64.3 62.3 0.01229527 54 69 0 53.2 68.6 0.0

The “Expected Final Inventory” was determined from the “Expected Inventory of

Line i” equation derived in section 4.2.and used the “Simulation Run Time” and the

“Feeder Line Birth Rates” as inputs.

4.3 Pull-Push Assembly Systems

Desiring to reduce the assembly system’s WIP and maintain throughput, the

CONWIP system is used to manage all feeder lines. When the synchronization of one

product from each of the feeder lines can occur, these items are joined together in a single

ten item batch and transported to the assembly station. Following the matching the cards

71

associated with the feeder lines’ products are released back to the initial workstations of

each respective feeder line.

The cards associated with each feeder line are dependent on the number of

bottlenecks resident therein. If no bottlenecks exist four cards are assigned to the feeder

line, if one bottleneck exists six cards are assigned to the feeder line, and if two

bottlenecks exist thirteen cards are assigned to the feeder line.

Figure 4.11: Throughput Analysis of Pull-Push Assembly System

Figure 4.11 provides the observed throughput for the pull-push assembly systems.

The following experimental results were obtained using an α level of 0.05.

• In 60 out of 66 statistical comparisons, the throughput variances of assembly

systems are equal.

• The throughput means of systems with both bottlenecks located in the same

feeder line are equal.

• The throughput means of systems with one bottleneck in the feeder lines are

equal.

Throughput Analysis

0.194

0.195

0.196

0.197

0.198

0.199

0.2

1,2

1,3

1,10

1,11

1,12 2,3

2,10

2,11

2,12

3,10

3,11

3,12 1,4

1,5

1,6

2,5

2,6

3,6

Bottleneck Location

Ob

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72

• The throughput means of assembly systems with both bottlenecks in one feeder

line are equal to or less than assembly systems with one bottleneck in the

feeder lines.

• The throughput means of systems with both bottlenecks in separate feeder lines

are equal.

• The throughput means of systems with both bottlenecks located in separate

feeder lines are less than the throughput means of systems with one bottleneck

feeder line.

Figure 4.12: WIP Analysis of Pull-Push Assembly System

Figure 4.12 provides the observed WIP for the pull-push assembly systems. The

following experimental results were obtained using an α level of 0.05.

• The WIP variances of systems with both bottlenecks in the same or different

feeder lines are equal.

• In 34 out of 45 statistical comparisons, the WIP variances of systems with one

bottleneck in the feeder lines are equal time.

WIP Analysis

05

10152025303540

1,2

1,3

1,10

1,11

1,12 2,3

2,10

2,11

2,12

3,10

3,11

3,12 1,4

1,5

1,6

2,5

2,6

3,6

Bottleneck Location

Ob

serv

ed W

IP (

Bat

ches

)

73

• The WIP variances of systems with one bottleneck in the feeder lines are

greater than systems with both bottlenecks located in one feeder line.

• In 39 out of 45 statistical comparisons, the WIP means of systems with one

bottleneck in the feeder lines are equal.

• The WIP means of systems with both bottlenecks in a single feeder line are less

than or equal to systems with only one bottleneck in the feeder lines.

• The WIP means of systems with both bottlenecks in separate feeder lines are

less than systems with the bottlenecks located elsewhere.

Cycle Time Analysis

0

2000

4000

6000

8000

10000

12000

1,2

1,3

1,10

1,11

1,12 2,3

2,10

2,11

2,12

3,10

3,11

3,12 1,4

1,5

1,6

2,5

2,6

3,6

Bottleneck Location

Cyc

le T

ime

(Sec

on

ds

/ Bat

ch)

Figure 4.13: Cycle Time Analysis of Pull-Push Assembly System

Figure 4.13 provides the observed cycle time for the pull-push assembly systems.

The following experimental results were obtained using an α level of 0.05.

• The cycle time variances of systems with both bottlenecks in one feeder line

are identical.

• The cycle time variances of systems with both bottlenecks in separate feeder

lines are identical.

74

• The cycle time variances of systems with both bottlenecks is separate feeder

lines are less than systems with the bottlenecks located elsewhere.

• The cycle times of systems with both bottlenecks in separate feeder lines are

less than in systems with the bottlenecks located elsewhere.

4.4 Hybrid Pull/Push-Push Assembly Systems

Desiring to further reduce the assembly system’s WIP and maintain throughput,

the DBR approach used in section 4.3 is re-evaluated. In that section scheduling the

arrival of nonbottleneck feeder lines’ product led to uncontrolled buildup of unmatched

product. To avoid this instabili ty the CONWIP system is used to manage the

nonbottleneck feeder lines. Spearman et al. [14] developed a similar method of using the

CONWIP and MRP production system rules to simulate a DBR system. The difference is

that Spearman used the system to manage a bottleneck station, and here the system

manages an assembly station.

As in section 4.3, when the synchronization of one product from each of the feeder

lines occurs, these batches are joined together in a single ten-item batch and transported to

the assembly station. Following the synchronization process the cards associated with the

nonbottleneck feeder lines’ products are released back to the initial workstations of the

nonbottleneck feeder lines. Four cards are allocated to the nonbottleneck feeder lines to

ensure the availabili ty of product at the assembly station.

Little’s Law is applicable in many situations, but because of how the cycle time is

defined for the assembly systems it seems to fail for the hybrid pull/push-push system. In

this system the cycle time is defined along the bottleneck feeder lines and the assembly

75

line. Changes to the nonbottleneck feeder lines’ WIP does not necessarily affect the

systems’ throughput or cycle time means, but will affect the systems’ WIP. If the cycle

time of the assembly systems were defined using the average of the feeder lines’ cycle

times, Little’s Law would apply.

Throughput Analysis

0.1978

0.1979

0.198

0.1981

0.1982

0.1983

0.1984

1,2

1,3

1,10

1,11

1,12 2,3

2,10

2,11

2,12

3,10

3,11

3,12 1,4

1,5

1,6

2,5

2,6

3,6

Bottleneck Location

Ob

serv

ed T

hro

ug

hp

ut

(Bat

ches

/ M

inu

te)

Figure 4.14: Throughput Analysis of Hybrid Pull/Push-Push System

Figure 4.14 provides the observed throughput for the hybrid pull/push-push

assembly systems. The following experimental results were obtained using an α level of

0.05.

• The throughput variances of systems with both bottlenecks in a single feeder

line are identical.

• The throughput variances of systems with two bottleneck feeder lines are

identical.

76

• In 152 out of 153 statistical comparisons, the throughput variances of systems

regardless of bottleneck location are identical.

• The throughput means of systems with one bottleneck on the first workstation

of a feeder line and second bottleneck in the assembly line are identical.

• The throughput means of systems with one bottleneck on the second

workstation of a feeder line and second bottleneck in the assembly line are

identical.

• The throughput means of systems with one bottleneck on the third workstation

of a feeder line and second bottleneck in the assembly line are identical.

• In 64 out of 66 statistical comparisons, the throughput means of systems with

one bottleneck feeder line are identical.

• The throughput means of systems with both bottlenecks located in separate

feeder lines are identical.

• The throughput means of systems with one bottleneck feeder line are less than

or equal to the throughput means of systems with two bottleneck feeder lines.

77

WIP Analysis

24

25

26

27

28

29

30

31

32

33

34

1,2

1,3

1,10

1,11

1,12 2,

3

2,10

2,11

2,12

3,10

3,11

3,12 1,

4

1,5

1,6

2,5

2,6

3,6

Bottleneck Location

Ob

serv

ed W

IP (

Bat

ches

)

Figure 4.15: WIP Analysis of Hybrid Pull/Push-Push System

Figure 4.15 provides the observed WIP for the hybrid pull/push-push assembly

systems. The following experimental results were obtained using an α level of 0.05.

• The WIP variances of systems with one bottleneck feeder line are identical.

• The WIP variances of systems with two bottleneck feeder lines are identical.

• In 147 out of 153 statistical comparisons, the WIP variances of systems with

two bottlenecks are identical.

• The WIP means of systems with two bottlenecks are equal regardless of the

number of feeder lines.

78

Cycle Time Analysis

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

1,2 1,3 1,10 1,11 1,12 2,3 2,10 2,11 2,12 3,10 3,11 3,12 1,4 1,5 1,6 2,5 2,6 3,6

Bottleneck Location

Cyc

le T

ime

(Sec

on

ds

/ Bat

ch)

Figure 4.16: Cycle Time Analysis of Hybrid Pull/Push-Push System

Figure 4.16 provides the observed cycle time for the hybrid pull/push-push

assembly systems. The following experimental results were obtained using an α level of

0.05.

• The cycle time variances of systems with one bottleneck on the first

workstation of a feeder line and the second bottleneck located in the assembly

line are identical.

• In 20 out of 21 statistical comparisons, the cycle time variances of systems

with one bottleneck on the second workstation of a feeder line and the second

bottleneck located in the assembly line are identical.

• If the first bottleneck is on the first workstation of the system, the cycle time

means increase as the second bottleneck moves further downstream.

79

4.5 Assembly System Summary and Conclusions of Findings

Much of the feeder line analysis can be used to predict the assembly systems’

responses to bottlenecks. In the feeder line analysis, increasing the number of bottlenecks

decreases throughput. In the assembly system analysis, increasing the number of

bottlenecks in the same feeder line decreases throughput. In the feeder line analysis, WIP

variance is zero in CONWIP systems while it is present in push systems. In the assembly

system analysis, systems using CONWIP techniques experience less WIP variability than

systems reliant purely on push systems.

Sometimes the feeder line analysis cannot be used to infer the results of assembly

systems’ responses to bottlenecks. If both bottlenecks are located in separate feeder lines,

the pull-push assembly systems experience a decrease in throughput. From the feeder line

analysis, it is known that both bottleneck feeder lines have identical throughputs. The loss

of throughput results from the probability of both bottleneck feeder lines finishing a

product at the same time being equal to zero. Even though all two bottleneck feeder line

assembly systems experience this batch matching delay only systems that manage the

bottleneck feeder lines with a pull system experience a significant reduction in throughput.

The pure push assembly systems provide impressive results in regards to

throughput and WIP. Statistically, the throughput means of these systems are not

necessarily identical but the difference between the maximum throughput and the

minimum throughput is 0.0007. The WIP means of the push systems are also consistent

with a difference only becoming evident when both bottlenecks are located in the same

feeder line. The pure push assembly system does have its shortcomings. It has the

80

potential to be unstable. To avoid this instability, the pure-birth process, this type of

assembly system requires the use of a batch synchronization procedure.

The pull-push assembly systems provide impressive results in regard to system

variability. In these assembly systems the throughput, WIP, and cycle time variances are

consistent regardless of the bottleneck locations. The throughput and WIP means are

effected by the positions of the bottleneck stations in relation to the assembly station. If

one bottleneck is in the assembly line the pull-push systems experience its greatest average

throughput and WIP; if both bottlenecks are in a single feeder line the throughput and

WIP are reduced; and if two bottleneck feeder lines exist the throughput and WIP are

significantly reduced.

The pull-push assembly system is significantly affected by the batch matching

delay. The additional wait time increases the bottleneck feeder lines’ cycle time and the

probability for the bottlenecks to starve. The combination of bottleneck starvation,

constant feeder line WIP, and increased bottleneck feeder line cycle time results in a

significant reduction in the assembly system’s throughput, WIP, and cycle time. Little’s

Law still applies. The law must be applied to the feeder and assembly lines separately.

The bottleneck feeder lines experience increased cycle time, while maintaining a constant

WIP. Using Little’s Law this combination results in lower feeder line throughput. The

assembly line now has an increased interarrival time between batches. The increased

interarrival time reduces the assembly lines’ WIP and cycle time. Apparently the reduction

in the assembly lines’ WIP and cycle time is greater than the increased WIP and cycle time

associated with a two bottleneck feeder line assembly system and batch matching delay

compared to systems with one bottleneck feeder line and no batch matching delay.

81

The hybrid pull/push-push systems provide superior results in regard to throughput

and WIP. Statistically, the throughput means of these systems are not necessarily identical

but the difference between the maximum throughput and the minimum throughput is

0.0006. Additionally the throughput variances and the WIP means and variances of these

systems are consistent. Since this system uses a push technique to manage the bottleneck

feeder lines, the batch matching delay does not have a noticeable effect. In fact, it is

shown that systems with two bottleneck feeder lines achieve greater throughput rates than

the hybrid systems with a single bottleneck feeder line. Thus, the delay experienced for

batch matching is less than the delay experienced at the second bottleneck located

downstream from the first bottleneck. The hybrid assembly system does have its

shortcomings. If the nonbottleneck feeder lines are not managed properly this system

could also experience a pure-birth process.

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CHAPTER 5

ASSEMBLY SYSTEM COMPARISON ANALYSIS

Of the assembly systems originally analyzed, only the three systems that achieved

equilibrium are compared. The parameter settings of these systems were derived from the

feeder line analysis in chapter three. In chapter four it was determined that bottleneck

position does effects the performance indicators of assembly systems using a pull system

to manage the bottleneck feeder lines. Given the information in chapter three, it is known

that the pure push and hybrid assembly systems are achieving their optimal throughput

values. Given the information from chapter four, it is known that the pull-push systems

analyzed in this chapter are not at their optimal settings.

The following results are broken into three sections where comparisons between

the performance indicators are carried out. After the results this chapter is summarized.

Figures 5.1, 5.2, and 5.3 provide observed throughput, WIP, and cycle time means for the

assembly systems.

83

System Throughput Analysis

0.1960

0.1965

0.1970

0.1975

0.1980

0.1985

0.1990

0.1995

1,2

1,3

1,10

1,11

1,12 2,3

2,10

2,11

2,12

3,10

3,11

3,12 1,4

1,5

1,6

2,5

2,6

3,6

Bottlneck Location

Th

rou

gh

pu

t (B

atch

es/ M

inu

te)

Pull-Push SystemAverageThroughput

MRP SystemAverageThroughput

Hybrid SystemAverageThroughput

Figure 5.1: Throughput Comparison Analysis of Assembly Systems

System Inventory Analysis

15

20

25

30

35

40

45

50

55

60

1,2

1,3

1,10

1,11

1,12 2,

3

2,10

2,11

2,12

3,10

3,11

3,12 1,

4

1,5

1,6

2,5

2,6

3,6

Bottlneck Location

WIP

(B

atch

es)

Pull-PushSystemAverage WIP

MRP SystemAverage WIP

HybridSystemAverage WIP

Figure 5.2: WIP Comparison Analysis of Assembly Systems

System Cycle Time Analysis

15

2015

4015

6015

8015

10015

12015

1,2

1,3

1,10

1,11

1,12 2,3

2,10

2,11

2,12

3,10

3,11

3,12 1,4

1,5

1,6

2,5

2,6

3,6

Bottlneck Location

Cyc

le T

ime

(S

eco

nd

s/B

atch

)

Pull-PushSystemAverageCycle Time

MRP SystemAverageCycle Time

HybridSystemAverageCycle Time

Figure 5.3: Cycle Time Comparison Analysis of Assembly Systems

84

5.1 Push and Pull-Push Assembly Systems

The push and the pull-push assembly systems differ in that the push assembly

systems manage all the feeder lines with synchronized dispatches of raw material and the

pull-push assembly systems manage all the feeder lines with a CONWIP system. The

following experimental results were obtained using an α level of 0.05.

• The WIP means and variances of pull-push systems are less than the equivalent

push systems.

• The throughput means of pull-push assembly systems with one bottleneck

located in the assembly line are greater than or equal to the equivalent push

systems.

• The throughput means of pull-push assembly systems with both bottlenecks in

a single bottleneck feeder line are less than or equal to the equivalent push

assembly systems.

• The throughput means of pull-push assembly systems with two bottleneck

feeder lines are less than or equal to the equivalent push assembly systems.

• The cycle time variances of pull-push assembly systems with both bottlenecks

in a single bottleneck feeder line are less than the equivalent push assembly

systems.

• The cycle time means of pull-push assembly systems with two bottleneck

feeder lines are less than or equal to the equivalent push assembly systems.

85

5.2 Push and Hybrid Pull/Push-Push Assembly Systems

The push and the hybrid assembly systems differ in the following manner. Push

assembly systems manage the bottleneck and nonbottleneck feeder lines with synchronized

dispatches of raw material. Hybrid assembly systems manage the bottleneck feeder lines

with synchronized dispatches of raw material and the nonbottleneck feeder lines with

CONWIP systems. The following experimental results were obtained using an α level of

0.05.

• In 16 out of 18 statistical comparisons, the push and hybrid assembly systems

have equal throughput means and variances, given identical bottleneck

positions.

• The WIP means and variances of push assembly systems with both bottlenecks

in the same feeder line are greater than the equivalent hybrid systems.

• The cycle time variances of push and pull-push assembly systems with both

bottlenecks in a single feeder line are identical, given identical bottleneck

positions.

5.3 Hybrid and Pull-Push Assembly Systems

The pull-push and the hybrid assembly systems differ in the following manner.

Pull-push assembly systems manage the bottleneck and nonbottleneck feeder lines with

CONWIP systems. Hybrid assembly systems manage the bottleneck feeder lines with

synchronized dispatches of raw material and the nonbottleneck feeder lines with CONWIP

systems. The following experimental results were obtained using an α level of 0.05.

86

• The WIP means and variances of hybrid assembly systems are greater than the

equivalent pull-push assembly systems.

• The throughput means of hybrid assembly systems with one bottleneck in the

assembly line are less than or equal to the equivalent pull-push assembly

systems.

• The throughput means of hybrid assembly systems with two bottleneck feeder

lines are greater than the equivalent pull-push assembly systems.

• The cycle time variances of hybrid assembly systems with both bottlenecks in

one feeder line are identical to the equivalent pull-push assembly systems.

• The cycle time means of hybrid assembly systems with two bottleneck feeder

lines are greater than the equivalent pull-push assembly systems.

5.4 Assembly System Comparison Summary of Findings

The pull-push assembly system has demonstrated that it is capable of high levels of

throughput at reduced WIP. This assembly system has also demonstrated some of its

fallacies. If the number of cards allocated to the CONWIP system is insufficient to

properly ensure the bottleneck is always working, the systems experiences a loss in

throughput. Additionally the use of this assembly system’s management technique

requires additional cards assigned to the bottleneck feeder lines when there are two or

more bottleneck feeder lines feeding an assembly station.

The push and the hybrid assembly systems demonstrate equivalent throughputs.

But the hybrid assembly system is able to achieve those throughputs at lower levels of

87

WIP and variability than the push system. The similarity and dissimilarity of these systems

can be tied to how the hybrid system is constructed. The bottleneck feeder lines control

the throughput of the system. In both the push and hybrid systems these lines are

managed identically with a push systems. The nonbottleneck feeder lines in both of these

systems are managed to ensure that its product is always ready for the assembly station

when the bottleneck feeder lines’ product becomes available. In the push system this

management resulted in higher WIP and variability than when it is managed by the

CONWIP system.

88

CHAPTER 6

CONCLUSIONS

The factors that determine how well an assembly system performs are: types of

control systems are used; the amount and location of bottlenecks; and if a synchronization

process is implemented.

If the entire assembly system is managed via a push system, a synchronization

process must be implemented. If this does not occur the assembly system will become

unstable. In Agnetis’ [2] paper this instabili ty resulted in tardy jobs, in this paper the

instabili ty is the result of a pure-birth process occurring at the assembly station. The pure-

birth process was shown to exist in all unsynchronized push assembly systems studied. In

the unsynchronized push assembly system, WIP becomes unmanageable unless production

rescheduling is continually provided.

Managing the nonbottleneck feeder lines with a pull system can eliminate the need

for the synchronization process. In order to eliminate the need, the nonbottleneck feeder

lines are managed in such a way that if left unhindered will achieve a greater throughput

than the bottleneck feeder lines. Since the bottleneck feeder lines determine when the

nonbottleneck feeder lines release a card, the throughput and the WIP of the

nonbottleneck feeder lines remain in check. An additional advantage of managing the

nonbottleneck feeder lines with a pull system is reduced system WIP. Even with these

advantages, the hybrid pull/push-push control system does have its shortcomings. If the

89

nonbottleneck feeder lines are not managed properly, a pure-birth process will result.

Also, given that the nonbottleneck feeder lines are managed properly, the maximum

throughput attainable in the hybrid systems is identical to the equivalent assembly systems

managed by a synchronized push system.

Given that the flow lines are properly managed, to eliminate the possibility of a

pure-birth process, and to possibly achieve greater system throughput the bottleneck

feeder lines must also be managed by a pull system. In this analysis the pull-push assembly

system did not always achieve the highest throughput of the assembly systems, but its card

settings are not optimally set. The lost throughput can be overcome with additional cards

allocated.

The use of pull systems to manage the assembly station is derived from the TOC

philosophy. In this situation the assembly station is not necessarily the bottleneck, it is a

process that can potentially lead to infinite-sized buffers. This technique was derived after

observing the instability of unsynchronized push assembly systems.

Through the analysis performed in this paper, the following three statements have

been shown to be true for assembly systems. Given that the flow lines are in equilibrium,

by managing the assembly system with a push system, batch synchronization must occur to

prevent a pure-birth process from developing. Given that the flow lines are in equilibrium,

by managing the nonbottleneck feeder lines with a pull system, the WIP of the system can

be reduced. Given that the flow lines are in equilibrium, by managing all feeder lines with

a pull system, the WIP of the system can be reduced, a pure-birth process cannot occur,

and increased throughput may by achieved.

90

System robustness, the ability for the system to achieve equivalent production rates

(throughput) if the bottleneck station shifts location, is a critical factor in managing an

assembly system. If the bottleneck shifts within its feeder or assembly lines no significant

change in throughput is expected in any of the assembly systems examined. If the

bottleneck station shifts to a different flow line this results in a misidentification of the

bottleneck feeder line and can result in changes in the assembly systems’ throughput and

equilibrium status.

Misidentification of the bottleneck feeder line and thus the mismanagement of this

line can result in a birth process and / or lost system throughput. In the pure push

assembly system with batch synchronization (MRP system) shifting of the bottleneck

station to different flow lines will not significantly effect the systems’ throughput or

equilibrium. In the pull-push assembly system shifting of the bottleneck station to different

flow lines, without reallocation of system cards, can result in decreased system throughput

but equilibrium will be maintained. In the hybrid assembly system shifting of the

bottleneck station to different flow lines, without altering how the assembly system is

managed, can result in a combined decrease in system throughput and a pure-birth

process. Thus in regards to robustness, the pure push assembly system with batch

synchronization is the most stable, and the hybrid system is the least stable.

The findings indicate that prior to the implementation of production management

techniques to assembly systems. The system should be studied to determine the location

and any shifting properties of the bottleneck station or stations. If the bottleneck stations

regularly shift in regards to different flow lines a MRP management system may be the

most appropriate. If consistent nonbottleneck feeder lines exist, management of these

91

flow lines with CONWIP systems will reduce the system’s WIP and not effect the

system’s throughput. If the bottleneck station does not shift between flow lines,

management of all feeder lines with CONWIP systems can result in higher system

throughput and reduced system WIP.

92

GLOSSARY OF TERMS

This thesis uses a variety of terms that the reader may not be aware of or that

differ from literature source to literature source. These terms are defined when first used,

but are supplied here to aid the reader.

Term DefinitionAssembly Line A serial line of production stations with one or more

assembly stationsAssembly Station The station which two or more workstations feed with

different products. The products of the workstationsare then combined into a unique product.

Assembly System Production system containing one or more assemblystations.

Batch One or more units to be processed on a station that aregrouped together.

Bottleneck A machine whose throughput directly effects thethroughput of the system.

Bottleneck Feeder Line Feeder line containing a bottleneck station.Bottleneck Line Serial line of workstations with one or more

bottlenecks.Cycle Time The average time it takes for a batch to be processed on

the production system.Downstream A station or stations that proceeds the current station.Feeder Line Serial line whose end product is used at the assembly

stationSynchronization Process A synchronization process occurs when each

component used in the assembly station’s product wasintroduced to the manufacturing system to specificallycombine with one another.

Nonbottleneck Feeder Line Feeder line not containing a bottleneck station.Nonbottleneck Line Sequential production line without a bottleneck.Process Time The time it takes to product one unit of product.Production system The set of manufacturing processes that are required to

transform raw material into a end product.Raw Material The input to a production system.Throughput The number of units produced per unit of time. This

93

unit of measurement can be observed at the workstationor system level. The final workstation’s throughput isthe production systems throughput.

Upstream A station or stations that precede the current station.Work in Process Inventory at a workstation’s in-queue, out-queue, and

being processed.Workstation A production station with one input and one output per

product type.

94

LIST OF REFERENCES

[1] Altug, M. S. “Design and Performance Evaluation of Mixed MRP, Kanban, andCONWIP Production Systems Using Emulated Flexible ManufacturingLaboratory.” M.S. Thesis, University of Florida, Gainesville, 1997

[2] Agnetis, A., Pacifici, A., Rossi, F., Lucertini, M., Nicoletti, S., Nicolo, F., Oriolo, G.,Pacciarelli, D., & Pesaro, E. “Scheduling of flexible flow lines in an automobileassembly plant.” European Journal of Operations Research, Vol. 97, 348-362,1997

[3] Bonvik, A. M., Couch, C. E., & Gershwin, S. B. “A comparison of production-linecontrol mechanism” International Journal of Production Research, Vol. 35, No. 3,789-804, 1997

[4] Cook, D. P. “A simulation comparison of traditional, JIT, and TOC manufacturingsystems in a flow shop with bottlenecks.” Production and Inventory Management,Vol. 35, 73-78, 1994

[5] Dallery, Y., Liu, Z. & Towsley, D. “Properties of fork/join queuing networks withblocking under various operating mechanisms.” IEEE Transactions on Roboticsand Automation, Vol. 13, No. 4, 503-518, August 1997

[6] Gstettner, S. and Kuhn, K. “Analysis of production systems kanban and CONWIP.”International Journal of Production Research, Vol. 34, No. 11, 3253-3272, 1996

[7] Goldratt, E. The Goal: A Process of Ongoing Improvement, Great Barrington, MA:North River Press Inc 1984.

[8] Guide, V. D. R. “Scheduling using drum-buffer-rope in a remanufacturingenvironment” International Journal of Production Research, Vol. 34, No. 4, 1081-1091, 1996

[9] Huang, M. Wang, D. & Ip, W. H. “Simulation Study of CONWIP for a cold rollingplant.” International Journal of Production Economics, Vol. 54, 257-266, 1998

[10] Kleinrock L., Queuing Systems Volume I: Theory, New York: Wiley, 1976

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[11] Krejewski, L.J., King, B.E. Ritzman, L. P., and Wong, D. S., “Kanban, MRP, andshaping the Manufacturing Environment.” Management Sciences, Vol. 33, 39-57,1987

[12] Luppen, R. T. Just-in-time Manufacturing New York: McGraw-Hill BookCompany, 1998

[13] Rao, S. S., Gunasekaran, A., Goyal, S. K., & Martinkainen, T. “Waiting line modelapplications in manufacturing.” International Journal of Production Economics,Vol. 54, 1-28, 1998

[14] Spearman, M. L. Woodruff, D., & Hopp, W. J. “CONWIP:a pull alternative tokanban.” International Journal of Production Research, Vol. 5, 879-894, 1990

[15] Spencer, M. S., & Cox III, J. F. “Master production scheduling development intheory of constraints environment.” Production and Inventory ManagementJournal, First Quarter, 8-13, 1995

96

BIOGRAPHICAL SKETCH

Tim Elftman was born in Cleveland, Ohio on January 24, 1973. Prior to finishing

high school, he attended Driffield School as an exchange student in England, from 1989 to

1990. In 1991, he graduated from Midview High School in Grafton, Ohio. In 1994, he

attained an Associate of Arts Degree in Engineering from Central Florida Community

College in Ocala, Florida. From 1995 to 1997, he attended the University of Florida and

specialized in industrial and systems engineering. After obtaining a Bachelor of Science

degree, he continued at the University of Florida further specializing in operations research

at the Department of Industrial and Systems Engineering. He will receive a Master of

Science degree from this department in May of 1999.

examination of the effects of bottlenecks and …

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