MACHINE COMBINATION ANALYSIS PROCEDURE

FOR SELECTING OPTIMAL FACTORY

CELL COMPOSITION

DISSERTATION

Presented to the Graduate Council of the

University of North Texas in Partial

Fulfillment of the Requirements

For the Degree of

DOCTOR OF PHILOSOPHY

By

J. Robert McQuaid, Jr., B.S.M.E., M.B.A.

Denton, Texas

May, 1998

MU AO.

McQuaid, J. Robert, Jr., Machine Combination Analysis Procedure for Selecting

Optimal Factory Cell Composition. Doctor of Philosophy (Management Science), May,

1998, 162 pp., 27 tables, 13 figures, references, 87 titles.

Cellular Manufacturing is a manufacturing strategy that capitalizes on part

processing similarities to improve the performance of the factory. It has extensive

applications in the metalworking and machining industries and is a viable alternative to

traditional functional shop layouts. Research in this area focuses on cell formation,

factory comparisons, scheduling strategies, and planning and control issues.

This research examined the relationship between manufacturing input parameters

and factory performance in a cellular manufacturing environment. The independent

factors investigated include the process structure and product structure represented by

operation capability and work content, respectively. Dependent variables explored

include factory throughput and flow time. C-language programs created raw

manufacturing data used in the manufacturing simulation program.

The study revealed that a relationship exists between the input parameters of the

part/operation matrix and the factory performance. Evidence suggested that operation

capability, represented by the number of parts each operation processed, had a significant

effect on factory performance. In addition, the process structure and product structure

significantly affected the throughput performance of the factories. Under the conditions

assumed in the study, cellular manufacturing performed competitively with a traditional

manufacturing strategy.

The study proposed a cell formation methodology designed to exploit

relationships reported in the operations management literature. The proposed

methodology identifies optimal manufacturing strategies using certain selection criteria.

Traditional methodologies typically do not compare performance variables that are

widely used by operations managers for selecting manufacturing strategies against that of

optimal strategies. The proposed method selects a strategy based solely on its ability to

optimally satisfy criteria desired by the operations managers.

The results of this research revealed potential for future research using the

simulation methodology from this study to gain a more in-depth analysis of the

relationship between cellular manufacturing and traditional strategies. Further

comparative studies using the proposed cell formation method incorporating additional

factory performance criteria into existing methodology warrant attention.

MACHINE COMBINATION ANALYSIS PROCEDURE

FOR SELECTING OPTIMAL FACTORY

CELL COMPOSITION

DISSERTATION

Presented to the Graduate Council of the

University of North Texas in Partial

Fulfillment of the Requirements

For the Degree of

DOCTOR OF PHILOSOPHY

By

J. Robert McQuaid, Jr., B.S.M.E., M.B.A.

Denton, Texas

May, 1998

MU AO.

ACKNOWLEDGEMENTS

I thank my committee chair, Dr. Robert Pavur, for his academic guidance,

extensive support, and friendship prior to and during this effort. Additionally, I

appreciate the tremendous effort and constructive comments of my committee, Drs.

Richard White, Maliyakal Jayakumar, and Alan Kvanli.

Thanks to Drs. Victor Prybutok and Roger Pfaffenberger for their support,

encouragement, friendship, and advice throughout my education. And, to my family and

friends who understood the time and energy required for this effort.

I acknowledge the University of North Texas for the environment and resources

that made this work possible.

Special thanks to my wife, Christine, whose support and encouragement kept me

returning to work.

Finally, thank God for giving me the health, opportunity, and willpower to see

this through to completion.

Ill

TABLE OF CONTENTS

Page

LIST OF TABLES vii

LIST OF FIGURES ix

Chapter

1. INTRODUCTION 1

Problem Definition 2

Example of Cell Formation 5 Purpose of the Research 8 Significance of the Study 9 Framework of the Study 10

2. LITERATURE REVIEW 11

Cellular Manufacturing 11 Benefits of Cellular Manufacturing 13 Early Research in Cellular Manufacturing 16 Cell Formation Techniques 17

Classification and Coding Techniques 17 Production Analysis Flow Techniques 20

Matrix Formulation: Array-Based 21 Matrix Formulation: Similarity Coefficient 25 Graph Theory 26 Mathematical Formulation 27 Other Structures: Systems Simulation 33

Theoretical Development 38 Technology and Structure 38 Focused F actory 41 Process-Product Matrix 42

Proposed Theoretical Model 45 Research Model 48

Product Structure 50 Process Structure 50

Cell Formation 51 Factory Performance 52 Density 53 Product and Process Structure 55

Research Objectives 58 Research Question #1 58 Research Question #2 59 Research Question #3 59 Research Question #4 60 Research Question #5 61

Summary 61

3. RESEARCH METHODOLOGY 62

Proposed Technique 62 Example of Machine Combination Analysis 63 Research Design 66 Simulation Design 67

Programming Language Selection 67 Model Building 68 Computer Programs 69

Program #1: Input Data Generation 69 Program #2: Cell/operation Matrix and Cell/part Matrix Generation 70 Program #3: Combine Cells to Generate Feasible Factories 73 Program #4: Assign Parts to Cells and Establish Number of Machines in Cells 73 Program #5: Manufacturing Simulation 73

Transient Period 76 Model Verification and Validation 77

Verification 77 Validation 78 Test for Poisson Arrivals 80

Data and Analysis 81

4. DATA COLLECTION AND ANALYSIS 82

Input Data 82 Input Data Generation Program Output 83

Cell/Operation Matrix and Cell/Part Matrix Generation Program Output 87 Combine Cells to Generate Feasible Factories Program Output 90 Assign Parts to Cells and Establish Number of Machines in Cells Program Output 92

Analysis of Input Data 93 Manufacturing Simulation Data Analysis 96 Analysis of Samples using Flow Time and Throughput 97 Poisson Analysis Results 105 Summary 106

5. DISCUSSION OF RESULTS 107

Conclusions 108 Research Question #1 109 Research Question #2 109 Research Question #3 110 Research Question #4 I l l Research Question #5 113 Factor Interactions 113 Other Conclusions 114

Limitations 116 Future Research 117

APPENDIX A STATISTICAL TABLES 119

APPENDIX B RESEARCH PRESENTATION TO FOCUS GROUPS 142

APPENDIX C ACRONYMS 153

REFERENCES 156

VI

LIST OF TABLES

Page

Table 1. Typical part/operation matrix 6

Table 2. Cellular part/operation matrix 8

Table 3. Summary of benefits associated with cellular manufacturing 15

Table 4. Common performance parameters used in simulation studies 37

Table 5. Research model operational definitions 53

Table 6. Cell sizes found in the literature 54

Table 7. Example part/operation matrix 64

Table 8. Cell/operation and cell/part matrices 64

Table 9. Feasible factories 65

Table 10. Experimental factors 66

Table 11. Binary equivalent values of M 72

Table 12. Assumptions for manufacturing simulation 75

Table 13. Part/operation matrix (0.4, uniform, uniform) 83

Table 14. Part/operation matrix (0.4, uniform, skew) 84

Table 15. Processing time matrix 85

Table 16. Setup times 86

Table 17. Cell/operation matrix for part/operation matrix in table 13 88

Table 18. Cell/part matrix for part/operation matrix in table 13 89

VII

Table 19. Feasible factories 91

Table 20. Final population of factories in experiment 92

Table 21. Best factory performance at each factor level based on throughput and flow time 98

Table 22. Analysis of variance for the systematic sample sorted on flow time 99

Table 23. Analysis of variance for the systematic sample sorted on throughput 100

Table 24. Analysis of variance for the systematic sample (actual cellularization) 103

Table 25. Analysis of variance for the systematic sample (planned cellularization) 104

Table 26. Nominal significance levels for runs test on Poisson process 106

Table 27. Summary of significant findings for throughput and flow time 108 ratios

VIll

LIST OF FIGURES

Page

Figure 1. Product-process focus continuum 1

Figure 2. Taxonomic review framework for group technology 4

Figure 3. Transformation process model 38

Figure 4. Product-process matrix 43

Figure 5. Cellular manufaturing concept superimposed on product-process

matrix 45

Figure 6. Proposed theoretical model 47

Figure 7. Research model 48

Figure 8. Operational relationships 49

Figure 9. Manufacturing model 69

Figure 10. Manufacturing simulation flowchart 74

Figure 11. Range of feasible cells created in 1000 replications of Programs

#1 and # 2 9 4

Figure 12. Part capability of feasible cells 95

Figure 13 Operation capability of feasible cells 96

IX

CHAPTER 1

INTRODUCTION

Cellular Manufacturing (CM) is a strategy that moves a functional factory which

is process focused toward product focused (see figure 1). A functional or process

focused factory routes parts through several large groups of machines with similar

Process Focus Product Focus

Functional Disconnected Connected Continuous Layout Line Layout Line Layout Layout (Job) (Batch) (Assembly) (Flow)

Cellular Manufacturing

Figure 1. Product-process focus continuum

operations. Typically, in a functional factory, when a part enters an operation, any

machine within that operation can process that part. However, cellular manufacturing

involves methodically clustering dissimilar operations into distinct groups, called cells,

and assigns parts to cells so each produces efficiently. Performance improvement results

from reducing the variation of operation and part types within a cell. Many existing

studies compare functional factories to cellular factories (Suresh 1979; Hyer and

Wemmerlov 1982; Flynn and Jacobs 1987; Wemmerlov and Hyer 1987; Durmusoglu

1993), and the findings are often contradictory. A summary of the findings suggests

further research is needed to investigate the conditions in which cellular layouts

outperform functional layouts.

This study proposes a new method of cell formation in cellular manufacturing. It

uses the proposed method to investigate the relationship between cellular configuration

and factory performance under various conditions. The application of the proposed

method in this manner demonstrates its potential. This chapter contains the problem

definition, an example of cell formation, the purpose of this research, the significance of

this study, and a framework for the remaining chapters.

Problem Definition

Group technology (GT), one of the tenets of the Japanese approach to

management (Schonberger 1982), is a manufacturing principle aimed at improving

economies of production by taking advantage of similarities in parts or processes. There

are considerable advantages of an effective cellular factory over a functional factory

(Greene and Sadowski 1984). These factories typically result in reduced material

handling, tooling, setup time, expediting, floor space, in-process inventory, part

makespan, improved scheduling routines, human relations and operator expertise

(Burbidge 1971; King 1980; Flynn and Jacobs 1987; Guerrero 1987). Suggested

drawbacks generally include increased capital investment and lower machine utilization.

Some studies (Flynn and Jacobs 1987; Shafer, Kern, and Wei 1992) report that the

expected improvements when implementing CM depend on initial conditions or process

control practices, for instance. A study of manufacturing technology in 1,042 US

factories, published by the National Association of Manufacturers in December 1994,

found that 56% of them are experimenting with cellular manufacturing (The celling out

of America 1994). Even though the evidence is inconsistent, industry and academics

remain attracted to the cellular manufacturing strategy. Cellular manufacturing is a

viable alternative to a functional factory.

The application of GT to cell formation has influenced the development of most

of the cell formation techniques. Based on an earlier study (Flynn and Jacobs 1987),

Offodile, Mehrez, and Grznar (1997) identified three GT categories for identifying

machine-part families (see figure 2). Kao and Moon (1995) identify two methods: (1)

Production Flow Analysis (PFA) and (2) Coding and Classification. PFA, originally

introduced by Burbidge (1963), identifies and groups parts that share common operations

and Coding and Classification combines the visual methods and parts coding analysis

categories of Offodile, et al. (1997). Singh (1993) proposes seven categories with similar

features including:

1. coding and classifications for part families 2. machine-component group analysis 3. similarity coefficient based clustering methods 4. mathematical and heuristic methods 5. knowledge-based and pattern recognition methods 6. fuzzy clustering approaches

7. neural network based approaches.

While the terminology varies, the nature of the categories correspond. This study uses

the Kao and Moon (1995) categories overall, but expands PF1A using several sub-

categories identified as Production Flow Analysis in figure 2 (Offodile, et al. 1997).

Dynamic Programming

Visual Methods

Group Technology

Monocode (Hierarchical)

Production Flow

Analysis

Polycode (Chain-type)

Parts Coding Analysis

Linear Programming

Graph Theory

Other Structures

Integer Programming

Mathematical Formulation

Array-Based Method

Fuzzy Set Theory

Matrix Formulation

Neural Networks

Figure 2. Taxonomic review framework for group technology (Offodile, Mehrez, and Grznar 1997)

Visual methods subjectively form part families based on observed part geometry.

While relatively inexpensive, this method relies heavily on the expertise of the analyst

and is rarely used in practice (Offodile, et al. 1997). Parts coding analysis assigns

numerical weights to part characteristics and identifies part families using a classification

scheme. One survey (Hyer and Wemmerlov 1989) reports 62% of surveyed companies

use this method, yet others (Kusiak 1987; Kaparthi and Suresh 1991) suggest this method

is not extensively studied in the research literature. Both visual methods and parts coding

analysis require extensive databases containing detailed part information and neither

consider manufacturing capability. PFA does not require part characteristic information

and it uses manufacturing information to identify the optimal factory.

This study proposes a technique that compares the performance of all factories

given various initial conditions and identifies the optimal cell configuration or functional

factory. The technique does not ignore the effect of the initial conditions on final factory

performance by not presuming the cellular strategy is optimal,. The remainder of this

chapter includes an example of cell formation and the purpose of this research.

Example of Cell Formation

This section illustrates the concept of part family identification and cell formation.

The typical PFA technique manipulates part routings in an effort to segregate the

functional factory into smaller, focused cells. The varying nature of each technique leads

to the subdivisions of PFA shown in figure 2. A relatively constant aspect of the typical

PFA technique is the use of the part/operation matrix as the starting point.

The part/operation matrix is a 0-1 matrix that identifies which parts require which

operations (see table 1). A part requiring a specific operation has a "1" at the intersection

of the row and column for that particular part and operation, respectively. If a part does

not require an operation, then a "0" is placed in that position. These matrices are

described by their cell density such that:

( i . i ) cell density = (number of operationsXnumber of parts)'

where ay = 0 or 1 depending on operation requirements for parts.

A higher cell density indicates more parts require more operations or more "Is" in the

matrix. Density represents the complexity of the part/operation matrix in terms of

control, operational requirements, and management. The density of the matrix in table 1

is 13/35 = 0.371.

Table 1. Typical part/operation matrix

Parts Operations

Parts A B C D E 1 1 1 1 2 1 1 3 1 1 4 1 1 5 1 6 1 1 7 1

Three parameters define the part/operation matrix: work content, operation

capability, and density. The work content for each part is represented by the number of

" 1 s" in each row of the part/operation matrix. A large number of " 1 s" indicates a part

that requires a large number of operations. Depending on how many parts require a large

number of operations relative to others in the factory, the final cellular configuration may

differ or not be cellular at all. The operation capability is defined by the number of "Is"

in each column of the part/operation matrix. A large number of "Is" indicates an

operation that must process a large number of parts in that factory. Depending on the

mix of operations in high demand and those in lower demand, the final cellular

configuration may differ or not be cellular at all. Finally, as the density of the

part/operation matrix increases, the number of off-diagonal "Is" increases. The following

example describes the use of the part/operation matrix for identifying part families and

cells simultaneously.

Cell formation techniques rearrange the rows and columns of the original matrix

to form a block diagonal matrix used to identify part families and cells of dissimilar

operations. A possible solution to the original matrix (see table 1) appears in table 2 after

manipulating rows and columns. The solution identifies operations in cell 1 = {C, B, E}

and cell 2 = {A, D}. Parts 1, 3, and 7 are assigned to cell 1 and parts 2, 4, 5, and 6 are

assigned to cell 2. The density of cell 1 is 0.67 and cell 2 is 0.875.

Not all part/operation matrix solutions are as straightforward as this example. For

instance, in a matrix with a higher original density, the number of off diagonal "Is" may

be high. These "Is" represent parts that can not be processed completely within one cell.

In the above example, if part 5 required operation A and E, both cells 1 and 2 would

require operation E to completely process part 5. There are several solutions to this

problem. One is to purchase additional equipment to complete the processing needs of

every part assigned to each cell. Another solution is to allow intercell flow, increasing

material handling cost and complicating scheduling as parts transfer cells for one or two

operations and return to their assigned cell. A third solution may be to place the

Table 2. Cellular part/operation matrix Operations

Cell 1 Cell 2 Parts C B E A D

1 1 1 1 3 1 1 7 1 2 1 1 4 1 1 6 1 1 5 1

operations shared by several cells in a cell of their own, called a remainder cell. While

this remains a material-handling problem, it allows better scheduling management of the

shared cell.

This example demonstrates the typical PFA technique to form cells based on

similar part processing requirements. The techniques shown in figure 2 illustrate different

methods to achieve the same objective. The existing techniques identify one solution for

each initial part/operation matrix. The proposed technique achieves the objective in

unique fashion recognizing that there may be several cellular matrices associated with

any initial part/operation matrix.

Purpose of the Research

This study has two purposes: (1) to propose a new cell formation methodology

and (2) to investigate the relationship between the initial part/operation matrix and the

ultimate cellularization of the factory. Machine Combination Analysis (MCA) is a

proposed cell formation methodology that stems from the production flow analysis class

of techniques. MCA's objective is to derive the most efficient factory possible for a

given part/operation matrix. It accomplishes this by focusing on the performance of the

overall factory. This focus differs from other techniques that use some interim

performance criteria, such as a clustering measure which is mathematical in nature

(Kaparthi and Suresh 1995). While the factory resulting from MCA may be either

functional or cellular, it may also be a hybrid of these two extremes. The value of MCA

is that it investigates all possible combinations of operations, the subsequent feasible cell

combinations, and finally, the most efficient factory given the initial part/machine matrix.

In addition to investigating various cellular configurations, MCA inherently considers the

functional layout in the analysis.

The second purpose of the research is to investigate the conditions in which

cellular manufacturing performs better than functional factories (Hyer and Wemmerlov

1985; Flynn and Jacobs 1987; Shafer, et. al. 1992). The proposed MCA technique serves

as the platform to investigate the research questions of this study. The study

demonstrates the effectiveness of the MCA technique by investigating the influence of

the part/operations matrix characteristics on the factory process decision

Significance of the Study

Techniques developed for PFA typically do not possess the capability to

investigate a multitude of possible solutions to a given part/operations matrix without

extensive application. By identifying and investigating each possible solution to the

matrix, MCA includes the functional factory as a possible solution in addition to all

10

possible cellular configurations. It reduces the assumptions required by the other

techniques by investigating all efficient factory configurations. The technique is easy to

apply and mathematically uncomplicated making it attractive for practical use. The

ability of the user to understand the methodology limits the use of many existing

techniques. Finally, MCA permits the investigation of the association between the

part/operation matrix and factory performance. By investigating this relationship, it is

possible to identify the conditions under which a cellular configuration is desirable.

Framework of the Study

The literature review in chapter 2 serves as the basis for the theoretical

development. The proposed research model provides the framework for investigating the

affect of the part/operation matrix characteristics on factory performance. The MCA

technique is proposed, demonstrated, and applied to the research model in chapter 3.

Chapter 4 includes an analysis of the data and chapter 5 describes conclusions drawn

from the experiment. The appendices include the complete statistical tables generated

during data analysis, the presentation made to industry focus groups, and a list of

acronyms used throughout this study.

CHAPTER 2

LITERATURE REVIEW

This chapter examines the relevant literature in the area of cellular manufacturing.

The objective is to establish the current state of research in cellular formation techniques

and provide a theoretical foundation to support this study. The chapter gives a brief

historical perspective of cellular manufacturing, discusses pertinent classification and

coding techniques (visual methods and parts coding analysis in figure 2), and

concentrates on an extensive review of the Production Flow Analysis techniques. The

intensive examination of the latter reflects the strong association between the proposed

MCA technique and this category of research. The theoretical model is presented along

with the research model in which all constructs and variables are operationalized and

research questions presented.

Cellular Manufacturing

Cellular Manufacturing involves processing a collection of part families made up

of similar parts on dedicated clusters of dissimilar operations or manufacturing processes

(Wemmerlov and Hyer 1987). A part family is defined as a group of parts requiring

similar operations, processing steps, and/or jigs and fixtures (Greene and Sadowski

1984). The dedicated clusters of dissimilar operations or processes are called cells and

the physical layout of a set of manufacturing cells is known as a cellular layout. By

12

processing part families only within their assigned cells, the efficiencies associated with

continuous flow layouts are approached. Cellular manufacturing research includes cell

formation techniques, cell or factory performance under various conditions and controls,

comparisons of different layouts, and surveys of industry. Due to a lack of industry data

to thoroughly investigate these areas, researchers rely heavily on computer simulation

and proving face validity.

Chase and Aquilano (1992) present the process layout transition toward CM as a

three-phase process. The first phase is to develop a classification and coding scheme for

the parts. Part characteristics such as shape, size, material, manufacturing operations, or

process time determine the classification and coding scheme. The growth of information

management systems has aided the first phase over the past decade. The second phase is

to group parts into families to form cells using a cell formation technique. The level of

difficulty associated with the second phase range from simple rules-of-thumb to complex

mathematical algorithms and programming. The technique developed in this dissertation

addresses this area of application. The final phase is to physically position the cells

relative to each other and is defined by three positions along a continuum: (1) informal

part families - functional layout, (2) formal part families - functional layout, and (3)

formal part families - group layout (Hyer and Wemmerlov 1982). Position 1 requires no

physical re-layout, but scheduling is performed according to tool set-up similarities.

Position 3 is a complete physical cellular re-layout using part family scheduling. Position

2 may adopt any one of an infinite number of configurations between the two bounds.

13

Benefits of Cellular Manufacturing

Extensive research has investigated performance of CM layouts. Reportedly,

improved performance results from the factory's ability to more efficiently process

homogeneous families of parts in cells designed to process the specific families.

Expected performance improvements include reductions in material handling, tooling,

expediting, in-process inventory, flow time, setup time, and others depending on the

purpose of the study (Wemmerlov and Hyer 1986; Flynn and Jacobs 1987; Morris and

Tersine 1990; Jensen, Malhotra, and Philipoom 1996). In addition, CM results in

improved human relations and operator expertise (Greene and Sadowski 1984; Shafer

and Rogers 1991; Hyer and Wemmerlov 1989). Some disadvantages include increased

capital investment, tooling expenses, direct labor costs, floor space, and a reduction in

machine utilization. (Greene and Sadowski 1984; Hyer and Wemmerlov 1989).

The advantages and disadvantages identified from CM are not consistent across

all studies. For example, Shafer and Rogers (1991) list minimized capital investment as

an advantage of CM, but Greene and Sadowski (1984) find an increase in capital

investment as a disadvantage of CM. A few studies indicate the performance of cellular

manufacturing may actually be inferior to functional layouts within certain parameter

ranges (Flynn and Jacobs 1986, 1987; Leonard and Rathmill 1977; Morris and Tersine

1990). Flow time and work-in-process inventory in CM may be higher than efficiently

operated functional factories (Morris and Tersine 1990).

The benefits achieved by CM over a functional factory typically include reduced

setup time, flow time, inventory, market response time, and machine utilization (Flynn

14

and Jacobs 1987; Hyer and Wemmerlov 1989). Setup times reduce through use of part

family tooling and sequencing (Abou-Zeid 1975). As a result of reduced setup times,

flow times improve due to smaller transfer batches, wait time for moves, and move time

within cells. A lower average setup time results in smaller economic batch sizes and

reduced machine utilization for the same throughput equating to an effective increase in

capacity (Knox 1980). The net outcome is the capability to process more product in a

fixed amount of time (Opitz and Wiendahl 1971).

The level of cellularization, defined as the proportion of manufacturing hours

assigned to cells, has its disadvantages. Generally, increased cellularization of a factory

reduces flexibility, which must be measured against gains in other performance variables.

Two other issues associated with a cellular layout may negatively affect flexibility. First,

a cellular layout may include an additional manufacturing area, called a remainder cell,

that is not determined by a part family. This remainder cell is designed to accommodate

those parts and operations that cannot logically or efficiently be placed in a

manufacturing cell. Second, some operations require special placement in a facility due

to a dominant criterion such as toxicity, utility requirements, or physical size regardless

of CM requirements. Consequently, development of a CM layout may result in a hybrid

of cellular and functional factories. Management of this hybrid system is critical,

because it can become as inefficient as the traditional factory from which the hybrid

system originated.

Many of the studies comparing functional and CM layouts are simulation based

(Durmusoglu 1993; Flynn 1987; Flynn and Jacobs 1987; Morris and Tersine 1990). A

15

shortfall of comparison studies is the selection of the scheduling rule used in the

simulation. Complex rules may be difficult to use in a simulation model if the focus of

the investigation is not scheduling rules. Few studies use complex, efficient scheduling

rules such as Shortest Processing Time with Truncation (SPT/T) for the functional

factory (Ramasesh 1990). Simpler rules like FCFS, RANDOM, or DUE DATE, may

compare two, possibly sub-optimal, systems.

A summary of advantages and disadvantages associated with cellular

manufacturing layouts appears in table 3. The disadvantages are cost variables and the

advantages are related to productivity. The trade-off between cost and productivity is the

basic decision criterion for any manufacturing strategy. The objective is to minimize

investment while maximizing productivity. An excellent CM application often results in

no additional capital investment in equipment, but simply rearranges existing operations

to take advantage of similar processing requirements.

Table 3. Summary of benefits associated Advantages

with cellular manufacturing Disadvantages

Reduced material handling Reduced tooling available for each

operation within a cell Reduced work-in-process inventory Reduced flow time for parts Reduced setup changeovers Improved human relations Improved operator expertise Improved market response time Tooling specific to part family Efficient part family sequencing Reduced move wait time within cells Reduced move time within cells Reduced batch sizes

Increased tooling expense Increased capital investment Increased direct labor costs Increased floor space Reduced machine utilization Reduced flexibility

16

Early Research in Cellular Manufacturing

Cellular manufacturing is a subset of Group Technology (GT) which is defined as

bringing together and organizing common concepts, principles, problems, and tasks to

improve productivity (Greene and Sadowski 1984). GT began in the 1940's in the

U.S.S.R. as a manufacturing philosophy intended to capitalize on similar, recurrent

activities (Wemmerlov and Hyer 1987). The early development in U.S.S.R. focused on

the process requirement and routing design subset. In the 1940's, Mitrofanov,

Sokolovskii, and other Russian engineers made inroads into job simplification and setup

time reduction (Greene and Sadowski 1984). Mitrofanov suggested the use of a

composite component approach (Mitrofanov 1966). German and British researchers

further advanced the concepts of GT in the late 1960's and early 1970's (Opitz and

Wiendhal 1971; Greene and Sadowski 1984). In the United States, research began to

appear in the 1960's and 1970's. One of the first methods developed by Burbidge (1963,

1971) was Production Flow Analysis (PFA). PFA was a unique approach in that it did

not use part coding and classification as input data, but relied on the part/operation matrix

and route cards for input. Most of the early PFA research centered on part family

formation techniques and group technology methods (Burbidge 1963, 1971, 1975; Carrie

1973; McAuley 1972; McCormick, Schweitzer, and White 1972). PFA, in many

different configurations (see figure 2), remains today as a standard methodology for cell

formation. As the field progressed, comparisons of formation techniques and integration

of applications from other fields proliferated.

17

Cell Formation Techniques

This section addresses the literature as introduced in figure 2. Since the main

interest of this study is production flow analysis techniques, a brief review of

classification and coding techniques is given followed by an extensive discussion of the

PFA techniques.

Classification and Coding Techniques

The emergence of new technologies including computerized systems, information

based technologies, automated manufacturing equipment, and robotics allows more

efficient application classification and coding techniques. Greene and Sadowski (1984)

identify three subsets of GT as piecepart coding, process requirement and routing design,

and cellular manufacturing. Piecepart coding is accomplished with modern, on-line

information systems and the coding and classification of parts is simplified as well.

Many of the techniques for forming part families include large matrix calculations that

can be handled efficiently with today's computing power.

The mechanism just discussed typically involves categorizing parts into families

based on a part or process characteristic and grouping equipment or processes to

manufacture a given family. Many studies compare the performance of systems based

which methodology was used to develop the part families. There is a fundamental flaw

in this evaluation since none of the methodologies use performance measures as a

developmental criterion. Process time, for instance, is not a performance measure, but a

characteristic of a specific part. Performance measures of interest may be minimizing

on

18

total throughput time or maximizing machine utilization in a cell. There are practical

limitations to the evaluations as some of the algorithms or mathematical programs do

become extremely complex by adding performance criteria to the cell formation method.

Cell formation techniques are used mainly to form families of parts that have

similar design attributes, manufacturing attributes or both (Singh 1993). Part codes

indicating similar characteristics obtainable through MRP systems or design databases

can be used to form part families. After part families are formed, machine groupings and

requirements are identified to complete the cell formation. Classification and coding

techniques require two steps to form cells, use part codes to form part families and then

assign machines to cells. The production flow analysis techniques discussed later often

solve both the part family and machine assignment problem concurrently.

Coding systems categorize parts into major families, then use common traits to

identify base families. A coding scheme proposed by Chen (1989) contains general part

information and has six positions:

1. material type 2. tolerance 3. overall length 4. maximum diameter 5. minimum diameter 6. total number of external primitive form features on the part

Chen s scheme cannot handle internal and facial form features on a rotational part which

limits is use in practice (Chen 1989).

To facilitate parts coding analysis, there are commercially available coding

systems such as BRISCH BIRN, CODE, MICLASS/MULTICLASS, and OPITZ (Hyer

and Wemmerlov 1985). These coding systems are usually add-in software to existing

19

MRP systems to aid in the coding of parts. There are three codes: (1) Monocodes are

hierarchical interpreting each succeeding symbol in the code dependent on the preceding

one, (2) Polycodes are based upon a chain structure and not dependent on the hierarchy of

digits found in monocodes, and (3) Hybrid codes combine the best of poly- and mono-

codes (Guerrero 1987).

Another coding system uses object-oriented modeling principles such as: (1)

generalization with disjoint subclasses, (2) generalization with overlapping subclasses,

(3) classification, (4) generalization with restriction, and (5) aggregation enhance

classification and coding applications. These principles are a derivative of object-

oriented programming code that is prevalent in modern computer languages. Five types

of decision trees (E-trees, N-trees, X-trees, D-trees, and C-trees, respectively) are shown

to be in exact correspondence with these principles (Billo and Bidanda 1995).

While usually considered a production flow analysis category, neural networks

also classifies and codes part families. Several studies successfully developed part

families using back propagation learning rules and binary adaptive resonance theory

(ART1) (Kao and Moon 1995; Chakraborty and Roy 1993; Liao and Lee 1994). The

ART1 neural model takes binary vectors as inputs and forms part families according to

the similarities of parts m terms of machining features. Each part and part family are

then assigned GT codes according to a customized scheme.

Like neural networks, fuzzy set theory has been applied to classification and

coding. Xu and Wang (1989) demonstrate the use of fuzzy subsets and fuzzy clustering

algorithms. Fuzzy logic is valuable as most classification systems can be improved by

20

quantifying subjective descriptors. The objective is to increase the sensitivity of the

classification system to a wide variety of part geometries.

In summary, the classification and coding techniques require extensive databases

of accurate part information and, until recently, significant expertise on the part of the

designer. Recent developments using neural networks and fuzzy logic may eventually

reduce the expertise required, but will still require data. These techniques are designed to

form part families requiring additional procedures for cell formation. The PFA

techniques in the next section are designed to accommodate both concurrently.

Production Flow Analysis Techniques

This section concentrates on production flow analysis techniques. One of the first

problems in the design of cellular manufacturing is the identification of part families and

machine groups and the simultaneous or subsequent evaluation of the related cell

properties (Wemmerlov and Hyer 1986). This identification and evaluation has received

extensive coverage in the literature, especially in the past decade, as computing power

has become increasingly less expensive. The categories of production flow analysis (see

figure 2) identified by Offodile, et al. (1997), serve as structure for this discussion. Since

research m some of the categories is limited and not applicable to this study, only specific

categories of research are discussed. The specific categories of interest include

mathematical programming, systems simulation, and two matrix formulation techniques,

array-based methods and similarity coefficients.

21

Matrix Formulation: Array-Based

Matrix formulation techniques use the initial part/operation matrix to derive part

families and cells. Array based methods manipulate the rows and columns of the original

part/operation matrix. Similarity coefficient methods convert the part/operation matrix to

a table of similarity coefficients and groups of parts or machines are determined based on

a cluster-analytic algorithm. Many models adopt Jaccard's similarity measure (Sokal and

Sneath 1968) for the table of similarity coefficients. The conceptual equation is:

(2.1)

Similarity Coefficient =

number of parts processed on both machines

number of parts processed on both machines + number of parts processed by machine + number of parts processed by machine 2.

This equation results in a value between 0 and 1. As the number of unique parts to either

machine 1 or machine 2 increases, the similarity coefficient approaches 0.

Burbidge (1971) refers to array based methods as Machine Component Group

Analysis (MCGA) and includes techniques based on his Production Flow Analysis

technique (Burbidge 1963, 1971, 1977). PFA involves three steps: (1) factory flow

analysis, (2) group analysis, and (3) line analysis. Factory flow analysis manipulates the

part/operation matrix to define large families. Group analysis further divides the large

families into final production groups for operation scheduling. Line analysis is the

intracell layout process. Both the first and last step focus on minimizing material

handling and maximizing machine utilization (Burbidge 1971). PFA, while effective

22

requires considerable experience in the second and third stage, as poor judgment will

negatively affect ultimate performance (Greene and Sadowski 1984). The following

matrix formulation techniques are considered seminal work in this area:

1. Component Flow Analysis (CFA) (El-Essaway and Torrance 1972) 2. Bond Energy Algorithm (BEA) (McCormick, Schweitzer, and White 1972) 3. Rank Order Clustering (ROC) (King 1980) 4. Rank Order Clustering II (ROC2) (King and Nakornchai 1982) 5. Direct Clustering Algorithm (DCA) (Chan and Milner 1982)

Several other matrix formulation techniques discussed in this section are chiefly

modifications of the originals noted.

Component Flow Analysis (CFA) incorporates material flow simplification in a

three-stage procedure (El-Essaway and Torrance 1972). CFA determines the degree of

complexity and similarity between the operations. CFA then establishes rough groups of

operations and parts based on constraints such as desired cell size, operation or part

characteristics, or other factors. The last step involves a feedback mechanism analyzing

the expected work load of each cell. CFA has similar drawbacks to PFA in that it is

manually intensive and requires tremendous understanding to apply the constraints of a

typical manufacturing system.

Bond Energy Algorithm (BEA) attempts to maximize the total bond strength,

defined as the product of their element values (either 0 or 1), for the part/operation matrix

in two passes (McCormick, Schweitzer, and White 1972). The first pass begins with

either rows or columns and the second pass uses the row or column not used in the first

pass. Two advantages are the final groups are independent of the initial ordering of the

matrix and no number of groups" specification is required as in some of the other

23

techniques. A disadvantage is that the initial matrix density unusually influences the total

bond strength.

Rank Order Clustering (ROC) reads each row and column as a binary word

transforming them into their decimal counterpart (King 1980). The algorithm

successively rearranges rows and columns in descending order until the matrix is

unchanged. All rows that have positive entries in the right-most column move to the top

of the matrix maintaining their relative order. This procedure is repeated for each column

from right, to left. Columns with positive entries move to the far left maintaining their

relative order. The same procedure is used on all columns searching for positive entries

in each row from bottom to top. This method is influenced by the initial order of the

columns and rows. If the same parts or operations were shuffled, a different answer may

result.

A revised procedure of ROC, ROC2 or MODROC, compares adjacent binary

words directly with no decimal transformation (King and Nakornchai 1982) and a

relaxation procedure for bottleneck machines. The authors review and categorize

literature m a variety of approaches including similarity coefficient, set theoretic,

evaluative, and other analytical methods. The ROC2 algorithm in this paper is presented

as an extension to the ROC algorithm which had several limitations when first

introduced. ROC2 is more computationally straightforward and does not necessitate

setting arbitrary limiting values like similarity coefficient methods. It does not include

detailed evaluation of the group formation.

24

The Direct Clustering Algorithm (DCA) proposed by Chan and Milner (1982)

manipulates the part/operation matrix by shifting parts with high numbers of operation

visits to the top of the matrix and operations with high numbers of part capability to the

left in the matrix iteratively. DC A was the most advanced computerized methodology for

initial part grouping in the early 1980's. Designed as a replacement for Burbidge's group

analysis step, DCA has a weakness as it redirects the diagonal in the matrix at each pass,

essentially forcing unacceptable solutions. However, a suggested modification

minimizes the effect of that flaw (Wemmerlov 1984). However, it may still result in

unacceptable solutions if some parts require a large number of operations while others

require very few.

One study proposes a heuristic approach to the economic determination of

machine groups and their corresponding component families in GT (Askin and

Subramanian 1987). Costs considered include WIP and cycle inventory, intra-group

material handling, set-up, variable processing and fixed machine costs. The procedure

consists of three stages: reorder part types based on routings, combine adjacent part

types to reduce machine requirements, and combine groups when economic benefits of

utilization offset those of set-up, WIP, and material handling. This is essentially a

clustering method including economic impact. It first develops a large number of

machine groups and then combines them based on a cost function. Cost based heuristics

suffer from an assumption that presumes constant costs exist over a wide range of

possible variations. This assumption is eliminated by limiting the studies to a narrow

range of possibilities which limits the applicability of these methods.

25

In summary, the enhancement of array based methods corresponds to the

improvement in computing capability. These methods focus on the structure of the cells

and part families. Each method may form different cells from the same initial

part/operation matrix depending on the measure used to stop the method,. The

techniques' objectives include ease of application, computing efficiency, and adequate

cells formed. This study proposes an array based method. It's objective is to form cells

based on the performance of the entire factory.

Matrix Formulation: Similarity Coefficient

The first of these approaches, suggested by McAuley (1972), was drawn from the

field of numerical taxonomy. This procedure uses route information to determine the

degree to which pairs of operations produce the same set of parts. McAuley's approach

employs Single Linkage Cluster Analysis. Items attach to a cluster if their similarity

coefficient exceeds a predetermined threshold level. Sequentially lowering the threshold

provides alternate solutions. McAuley's similarity coefficient is defined as sy = ny / my

where ny is the number of parts processed on both operations i and j, and my is the

number of parts processed on either operation i or j. After computing this coefficient for

each pair of operations, the pair of operations with the highest coefficient groups into a

cell. A new set of similarity coefficients calculates between this cell and all the

computations of the other operations. This process repeats grouping the pair of

operations, operation and cell, or two cells with the highest similarity coefficient together

each time and repeating the coefficient calculation. The weakness of this method derives

26

from its inability to correctly discriminate between clusters when all the coefficients are

small or relatively close in value.

Carrie (1973) employs a similarity coefficient resembling McAuley's, however it

uses the similarity between parts instead of operations. The similarity coefficient is the

proportion of operations required by both parts to the number of operations required by

either part. A single linkage clustering algorithm groups parts into families followed by

the assignment of required machines. These two algorithmic procedures are

uncomplicated to program and apply, however both suffer from the lack of discrimination

when similarity coefficients are small or relatively close in value.

In an extension of earlier work, de Witte (1980) developed three similarity

coefficients that identify related operations (de Beer, van Gerwen, and de Witte 1976).

The operations labeled as one-of-a-kind may occur in more than one cell or appear in

potentially every cell. Visual inspection then determines cell membership. This method

works well for smaller data sets, but requires substantial judgement to apply.

The similarity coefficient methods are popular due to their ease of application, the

extensive clustering techniques available, and their intuitive appeal. Like the array based

methods, these methods focus on the structure of the cells and part families. Factory

performance of the resulting cell formation is not part of the methodology.

Graph Theory

Rajagopalan and Batra (1975) use Jaccard's similarity coefficients discussed

above and graph theory to form machine groups. The vertices of the graphs are shared

27

operations and the arcs are weighted as similarity coefficients. The goal is to achieve

uniformly high machine utilization. The method was tested using hypothetical situations

and there have been no practical applications (Greene and Sadowski 1984).

Chakravarty and Shtub (1984) present a procedure to generate an efficient layout

of machine groups with production lot sizes that match the layout. The first procedure

considers the production planning and lot sizing problems for the case of mutually

independent machine-component groups using clustering techniques. The second

procedure simultaneously integrates the lot sizing cost with the layout cost in parametric

fashion. It does not require independent machine component groups. The proposed

design procedures provide a method of combining layout decisions with production

scheduling decisions, thus integrating the design of batch oriented systems into a single

phase.

Graph Theory research does not appear extensive in the literature. The

methodology is complex and difficult to apply requiring extensive understanding of the

technique. Since there are a number of less complex techniques, the use is very limited.

Mathematical Formulation

Gupta and Dudek (1971) describe the pure flowshop scheduling problem

consisting of scheduling n jobs on M machines. The work is unidirectional and flows in

numerical order from 1 to M. The cost components considered include operation, job

waiting, machine idle, and penalty for late jobs. The development of the four costs and

the calculation of the opportunity cost is often described in detail. Since this study does

28

not include cost variables, more coverage is disregarded. The optimization criteria is

derived from the total opportunity cost equation and sensitivity analysis is performed.

Finally, Monte-Carlo simulation is used to draw conclusions on the optimization

criterion.. The total opportunity cost should be the criteria of choice.

Ballakur and Steudel (1987) define the part family and cell formation problem as

identifying and grouping part families and cells, then assigning families to cells based on

routing sheet information satisfying at least one of several objectives. They present a

heuristic which considers several practical criteria such as within-cell machine utilization,

work load fractions, maximum number of machines that are assigned to a cell, and the

percentage of operations of parts completed within a single cell. Results based on several

examples from the literature show this heuristic performs well with respect to more than

one criterion. They also apply the heuristic to a large sample of industrial data involving

45 work centers composed of 64 machines and 305 parts showing the usefulness of the

heuristic for trading-off several objectives. The heuristic forms part families and

machine cells simultaneously. It indirectly attempts to minimize the total number of

inter-cell moves of parts given machine work load and cell size restrictions.

Choobineh's (1988) paper proposes a systematic two-stage procedure for the

design of cellular manufacturing systems. The author defines group technology as a

philosophy that exploits the proximity among attributes of given objects or situations for

the purpose of performing a known task. Stage one of the procedure is part family

formation. Choobineh states that manufacturing operations and their sequence are the

most relevant attributes in the design phase of GT and should be used to establish a

29

relative measure of sameness among the parts. He modifies the commonly known

Jaccard Similarity Coefficient which uses only manufacturing operations with one that

considers sequences. This proposed special proximity measure is used in a clustering

algorithm to uncover the natural part families. Stage two is the cell formation which is a

integer linear program used to minimize production costs and the cost of acquiring and

maintaining the machine tools. Choobineh recommends against combining the two

stages as it introduces several shortcomings into the final solution. Disadvantages of the

proposed method include it is difficult to use for a large number of parts, does not use

operation sequences, and the economics of the production system are ignored.

The primary objective of Shafer and Rogers' (1991) study is to develop a cell

formation procedure that accurately and realistically addresses more facets of the cell

formation problem beyond the development of formation techniques. Three goal

programming models are presented and an approach for solving the goal programs is

discussed. The researchers discuss four objectives of CM: reduce setup time, produce

within a single cell, minimize investment in new equipment, and maintain acceptable

utilization levels. Setup time reduction is approached as reducing total setup time in a

cell, not the setup time on a specific part. The researchers present a new goal

programming formulation for several reasons. First, before procedures can be developed

to solve cell formulation problems, the problems must be clearly defined (objectives,

constraints, and situation). Second, to directly address as many design objectives and

realistically capture the constraints as much as possible. The proposed model combines

the p-median formulation with the traveling salesman (or shortest route) problem (TSP).

30

The three models are analytically complex and require a heuristic solution procedure by

applying p-median and TSP successively.

The next paper (Ahmadi and Matsuo 1991) addresses a line segmentation

problem (LSP) in a multistage, multimachine production system. LSP determines an

allocation of machines at each stage to families to minimize the completion time of all

jobs. The resulting segmentation of a line constitutes minilines within a line where only

items in a family are produced. LSP is related to three well studied problems including

the constrained resource scheduling problem, the cutting stock problem, and the

concurrent resource scheduling problem. The authors prove the LSP in this application is

NP-hard and develop three lower bounds to begin development of heuristics and provide

benchmarks for performance evaluation. They propose four heuristics to efficiently solve

the problem with LaGrangian Relaxation giving the best results.

The objective of a study by Rajamani, Singh, and Aneja (1992) explicitly

considers the trade-off between the discounted investment in machines and setup costs

which are sequence dependent for cell formation in a manufacturing environment. For

this purpose, the authors developed a mixed integer programming model. It describes the

optimal number of cells to form and the optimal sequence in which to produce the parts

in each cell. If the manufacturing environment is not suited for forming cells, then the

model results in a job shop or flow line. The trade-off that exists between saving on

sequence dependent setup costs and additional investment in new machines was

identified and explicitly modeled. The ideal application of this model is in a repetitive

31

manufacturing environment where a limited number of parts are run in a fixed sequence

and repeated from cycle to cycle.

The main contribution of Adil, Rajamani, and Strong's (1993) work is provide a

mathematical framework which simultaneously considers the trade-off between

investment and operational costs to address cell design in manufacturing. The majority

of cell formation models consider grouping parts and machines based on clustering

techniques exclusive of costs. Cellular systems designed without considering the

operational variables can lead to poor performance. A mixed integer program

considering investment in cell and machines and operational variables was developed.

The model determines the economic number of cells, capacities of processing stages in

each cell formed, part allocation, sequencing and scheduling in these cells. Trade-off

between various costs are illustrated using six examples: low cell investment cost, high

cell investment cost, intermediate cell investment cost, work-in-process, and machine idle

time interactions, and due date interaction. These different situations at the design stage

led to different groupings of parts and machines. They conclude part and machine

grouping should simultaneously consider interactions with costs.

Kusiak, Boe, and Cheng (1993) present an efficient heuristic branch-and-bound

algorithm for solving the identification of machine cells and formation of part families.

In addition, the A* algorithm is developed to obtain optimal machine cells. Whereas the

branch and bound algorithm groups machines and parts simultaneously, the A* algorithm

solves for machine grouping only. The study includes a comparison of the proposed

algorithm with several existing heuristics. The authors state GT can be applied to

32

manufacturing systems in two ways: logical or physical. In the logical layout, machines

are dedicated to part families but their positions in a factory are not altered. In the

physical machine layout, dedicated cells containing different machines are created for

part families to exploit flow shop efficiency.

Clustering is a more practical and easier approach to implement than

classification and coding schemes. The clustering problem can be formulated either

through matrix formulation or integer programming formulation. The clustering

algorithm transforms the initial incidence matrix into a structured form. The integer

programming model is used to determine the type and number of machines in each cell in

the second stage after parts are grouped in the first stage. The overall objective is to

minimize the machine cost and the variable production cost. The cluster algorithm

presented solves only a special case of the GT problem where there are no bottleneck

(shared) parts or machines. The branching scheme removes bottleneck machines and

bottleneck parts from an incidence matrix which prevent the matrix from decomposition.

The comparison of these two proposed approaches to existing published models suggests

they are reliable and require relatively little computational effort.

The mathematical programming techniques have received substantial coverage in

the literature. Strengths of the technique include the capability to consider multiple

objectives and constraints, costs are easily introduced into the decision, and packaged

mathematical programming computer programs are available. Their application is

straightforward and results in definitive solutions to the cell formation problem.

33

However, the techniques require substantial understanding of their theory, technical

programming expertise, and many simplifying assumptions to build the model.

Other Structures: Systems Simulation

The use of simulation enables the researcher to examine many variables in a

controlled environment. Lack of available industry data has constrained researchers to

use simulation and attempt to generalize to real world applications. Many of the

simulation experiments in cellular manufacturing investigate scheduling of parts within

cells and through the factory. Cells are formed using a cell formation technique and

various scheduling rules are applied to these cells to investigate the effect of the rule on

factory or cell performance. Pertinent research reviewed in this area provides evidence to

support the relationships in examined in this study. Specific studies discussed use similar

factors as the experiment discussed in chapter 3.

Recent studies support the post-design focus on scheduling (Jensen, Malhotra and

Philipoom 1996; Mahmoodi, Dooley, and Starr 1990; Wemmerlov and Vakharia 1991).

One study investigated the tradeoff in shop performance between the routing flexibility in

a functional job-shop of non-dedicated operations and the setup efficiency of dedicated

operations in shops that have cell layouts (Jensen, Malhotra, and Philipoom 1996). The

authors investigated traditional and GT-based scheduling procedures to determine the

conditions when GT philosophy should be employed in layout and scheduling decisions.

This study varied the shop layout in three levels from pure cell to pure functional and

applied four scheduling rules (FCFS, APT, EDD, EDD-U) geared toward testing the

34

effect of setup limiting strategies. Two additional factors in this experiment included

machine customization and demand variability. The performance measures evaluated

include flowtime, mean tardiness, and percent tardiness. The authors conclude that all

four factors (shop layout, scheduling rule, customization, and demand) significantly

effect the performance measures; in addition, most of the two-way interaction effects

were significant. They summarize that all four scheduling rules perform similarly for

mean flowtime except one, APT. With limited setup strategy, APT is dominated by the

other scheduling rules. However, EDD with unlimited setup duplication capability is the

best for mean tardiness and percent tardiness performance. Essentially, the authors

conclude that when machine customization is low or when demand variability is high, the

gap between functional and cellularization increases from a customer service perspective.

However, there is a trade-off between flowtime and customer service that must be

considered in the final decision. The findings of the study suggest further evaluation of

the effect of layout on these two scheduling strategies.

Mahmoodi, Dooley, and Starr (1990) compared three order release and two due

date assignment heuristics in combination with six scheduling heuristics showing

controlled release results in deteriorating flow time, lateness, and tardiness performance

and is inferior to both immediate and interval release. The conclusion contradicts the

results of a later study by Mahmoodi, Tierney, and Mosier (1992); in the later study, the

performance of traditional single-stage heuristics was compared to that of the two-stage

group scheduling heuristics. The findings suggest that the interarrival time does have a

major impact on the performance of scheduling heuristics. The findings of the later study

35

were supported by Wirth, Mahmoodi, and Mosier (1993), when they added that cell

performance was also affected by cell loading. The evidence suggests that some form of

controlled release improves the performance both from the perspective of controlled

arrivals and allowable cell load.

In a 1991 study, Wemmerlov and Vakharia compared four job-scheduling

procedures that are oblivious to part families and four part family scheduling procedures

that select subsequent jobs to avoid new setups. The cell formation method integrates the

issues of cell formation and within-cell material flow. A proposed part similarity

coefficient based on operation sequences is used to form part families and cells. Within-

cell operation sequences and machine loads are considered by the method. The study

concludes the part family scheduling procedures generate marked improvements in mean

flow time and lateness measures.

Garza and Smunt (1991) investigated the effect of five factors on mean flow time

and average work in process. The factors investigated include level of intercell flow,

setup time, run time variability, batch size, and setup ratio. The last factor was the ratio

of minor setup to major setup time. They concluded that the performance of the cellular

shop is more sensitive to runtime variability than the job shop, the cellular shop can better

produce smaller batch sizes, and that a sizable reduction in setup times must occur before

considering conversion to cellular manufacturing.

Flynn (1987) modeled a job shop, cellular shop, and hybrid using three scheduling

procedures (FCFS, repetitive lots (RL), and truncated repetitive lots (TRL)). She

examined a number of performance parameters including setup time, utilization, lot size,

36

queue length, work-in-process, waiting time, longest queue, longest wait, and flow time.

The shop layout and scheduling procedure factors were both statistically significant on

the main effects for all the performance parameters measured. However, the interaction

between the two factors was also significant except on machine utilization. Since the

interactions were significant, it was difficult to analyze the true influence of the main

effects. The repetitive lots (RL) scheduling procedure led to lower average setup time,

average machine utilization, and shorter average queue length. The lot size associated

with RL was larger. For the shop type factor, the GT shops had shorter setup times,

lower machine utilization and larger batch sizes. However, the GT shops had longer

queues and higher work-in-process inventory.

One study of selection rules measured job lateness and tardiness, setup time, idle

time, flow time, and proportion of jobs failing to make due date (Mosier, Elvers, and

Kelly 1984). The selection rules involved selection from which queue and then jobs

within that queue. Shop utilization and setup ratio were fixed factors in this study. The

selection rule that performed best under most factor combinations was the total work

content rule. It placed second in the percentage late category behind an economic

selection rule designed to minimize the cost of changing queues.

A brief summary of the representative performance parameters used in several

simulation studies is presented (see table 4). Most studies analyze several parameters as

there is significant trade-off in various systems. The four most common parameters

include flow time, throughput, tardiness, and jobs late. The latter two are strongly

correlated with scheduling rules used in the factory, therefore, this study uses flow time

37

and throughput as primary performance parameters. Other parameters are collected to

investigate the affect of the trade-off just mentioned. The use of parameters typically

used in industry enhances the generalization of the results. Simulation studies are

valuable in that they allow comparisons of multiple alternatives and sensitivity analysis

of the decision criteria.

Table 4. Common performance parameters used in simulation studies Mosier, et al. Flynn (1987) Mahmoodi, Garza and Jensen, et al.

(1984) et al. (1990) Smunt (1991) (1996) tardiness X X X setup time X X

idle time X

flow time X X X X X jobs late X X X proportion utilization X

lot size X

queue length X

WIP X X wait time X

long queue X

long wait X

throughput X X X

In summary, cell formation techniques currently in use include coding and

classification techniques which focus specifically on the part and PFA techniques that

focus on the part and operation requirements. The coding and classification techniques

require substantial part information and expertise to apply. The existing PFA techniques

use the part/operation matrix, but may not identify the optimal factory given that matrix.

The method proposed in this study is a PFA array based method that achieves the optimal

factory given the part/operation matrix.

38

Theoretical Development

The theoretical development for this study begins with the production function

(see figure 3). This model serves as a basis for much of the theoretical development in

many areas encompassing the management of the transformation process. Concepts

developed by Thompson (1967), Skinner (1974), and Hayes and Wheelwright (1979a,

Transformation Process

Figure 3. Transformation process model

1979b) are used to provide a foundation for this research and link the transformation

process model with organization strategy and goals.

Technology and Structure

Pertaining to technology and structure, Thompson (1967) suggests there are both

instrumental and economic reasons to have structure. According to Thompson, a

temporary organization which emerges to resolve some large-scale natural disasters

(synthetic organization) is usually instrumentally rational, in that it gets the job done;

however, the synthetic organization lacks efficiency. As information increases, priorities

39

change; meanwhile resources are juggled to support the changing requirements. The

efficiency of this synthetic organization would improve if the extent of the problem or the

resources required were known in advance.

Organizations pursuing bounded rationality must also facilitate the coordinated

action of the interdependent elements that make up the structure. To assume that an

organization is composed of interdependent parts does not necessarily mean that these

parts rely directly on each other. However, the total organization is jeopardized by the

failure of any of these parts. The situation in which each part renders a discrete

contribution to the whole is called pooled interdependence. Two higher forms of

interdependence include sequential and reciprocal. Sequential interdependence occurs

when output from one part serves as input for another part. The functional factory is an

example of sequential interdependence. In reciprocal interdependence, the flow of output

and input is bidirectional between two parts. All organizations have pooled

interdependence, some may also include sequential, and the most complex include all

three. In order from pooled, to sequential, to reciprocal, the three types of

interdependence become increasingly more difficult to coordinate.

Coordination may be achieved through standardization, p lanning or mutual

adjustment. Pooled interdependence uses coordination by standardization. One

assumption associated with this type of coordination involves the environment. It must

be relatively stable and repetitive to permit matching of situations with appropriate rules.

In addition to coordination, Thompson (1967) notes that components of

organizations could be grouped based on a common purpose or common processes.

40

Thompson posits that under norms of rationality, organizations group positions to

minimize coordination costs. Thompson further points out that in the absence of

reciprocal and sequential interdependence, organizations subject to norms of rationality

seek to group positions homogeneously to facilitate coordination by standardization. To

the extent that the technological core can be buffered from an unstable environment, the

grouping of positions performing similar processes permits coordination to be handled in

the least costly manner. The technological core is the manufacturing operations. It

receives input in the form of raw material, labor, equipment, and management and

produces output in the form of finished product. By standardizing both the parts and the

operations within a cell, cellular manufacturing buffers the technological core from the

effects of environmental influence in the most appropriate manner.

By dividing a functional factory into smaller, more homogeneous elements,

organizations seek to improve standardization within each cell. Increased standardization

then leads to efficient operations based on Thompson's propositions. In addition, by

minimizing inter-cell flow of parts, organizations seek to drive down the complexity

across cells of their structure to that consisting of pooled interdependence. This pooled

interdependence enhances their ability to coordinate operations across the cells consistent

with pooled interdependence. Pooled interdependence of cells combined with sequential

interdependence within cells provides for much higher levels of efficiency

41

Focused Factory

Wickham Skinner (1974) proposed that the conventional factory was attempting

too many conflicting production tasks within an inconsistent set of manufacturing

policies. This had led the United States to not be competitive on an international scale.

Skinner suggested that focusing the entire manufacturing system on a limited task would

provide a more competitive system. The focus would produce synergistic effects

consistent with the company's competitive strategy and capability. The main goal of this

philosophy is greater simplicity and a support organization that are able to focus on the

needs of the manufacturing system.

As part of the focused factory, Skinner proposes developing focus by establishing

a plant within a plant (PWP). One plant would concentrate on standardized products and

customized products in the other. The latter would have modest excess capacity and a

product oriented layout. Work force management would entail creating fewer jobs

requiring a wider breadth of skills and ability to perform a variety of jobs. Skinner

recognizes that there may be more than two PWP's and suggests dividing the facility both

organizationally and physically. Each PWP would concentrate on those limited essential

objectives constituting the PWP's manufacturing task. A focused cell demonstrates

Skinner's focused factory concept. Several cells within a plant is indicative of the PWP

description.

Skinner's focus factory concept provides support for cellular manufacturing. The

focus factory concept, much like CM, offers the opportunity to eliminate compromises

42

associated with general-purpose, do-all plants, thus providing a mechanism to establish

clear goals and sense of direction.

Process-Product Matrix

The product-process matrix is a two-dimensional matrix that suggests a way in

which the product life cycle and the process life cycle can be correlated (Hayes and

Wheelwright 1979a). The four stages of the product lifecycle: introduction, growth,

maturity, and decline, are similar to the four columns of the matrix that range from low

volume, low standardization to high-volume, high standardization (see figure 4).

The four rows of the matrix represents the process life-cycle beginning with a

highly flexible, but inefficient process-focused layout progressing into a very efficient,

capital intensive, and inflexible product-focused layout. The top row of figure 4 is the

job shop process structure. This is an appropriate process strategy for products with low

standardization, high variety, low volume, and flexibility is important. The second row is

a batch operation process structure appropriate for products with similar standard

characteristics grouped to improve the efficiency of the process. The third row is an

assembly line process requiring more part standardization where the discrete parts move

along a fixed line improving the efficiency even more. Finally, the bottom row is a

continuous flow process for highly standardized, high volume commodity products. An

interpretation of the product-process matrix is that selection of a product-process

combination that is off the diagonal shown is not competitive. For instance, attempting to

produce a high volume, highly standardized product in a job shop is unrealistic. Based

43

Product Structure

Low volume - low

standardization,

one o f a kind

Multiple products

low volume Few major products

higher volume High volume - high

standardization,

commodity products

Process Structure

Process life cyc le stage

Jumbled f l ow

(job shop) Commercial

printers J^one

Disconnected line

f b w (batch) Heavy

equipment

Connected line

f low(assembly line) Automobile

assembly

None Con tin uo us f l ow

Sugar

refinery

Figure 4. Product-process matrix (Hayes and Wheelwright 1979b)

on an organization's choice of product and production process, the organization occupies

a particular region in the matrix."

The concept of organizing different operating units so the organization can

specialize on focused portions of the total manufacturing task while maintaining overall

coordination is pertinent to this study. The example presented by Hayes and

Wheelwright (1979a) involves the production of spare parts in support of the primary

products. While increasing volume of primary products may cause the company to move

44

down the diagonal toward a product-focused factory, the ensuing demand for spare parts

may require a combination of product and process structures more toward the upper left

hand corner of the matrix. A company could develop separate factories or simply

separate their production facilities within the same factory to support the product and

process characteristics. The authors' suggest that leaving such production

undifferentiated is probably the least appropriate approach. The application of the

process-product matrix in this scenario supports Skinner's (1974) plant within a plant or

the cellular philosophy.

Hayes and Wheelwright (1979a) suggest that operating units with narrowly

defined, specific locations on the matrix often encounter coordination problems with the

whole system. They proposed individual units manage themselves relatively

autonomously. The researchers suggest that it is desirable to minimize inter-cell flow in

order to maximize the ability of each cell to manage its work load.

In a continuing article Hayes and Wheelwright (1979b) discuss how companies

select strategies for both product and process developments. While an industry usually

progresses down the diagonal of the matrix, it is a less likely pattern for an individual

company to follow. Individual companies tend to make discrete changes in either the

product or process design resulting in a stair-step movement down the diagonal. One

such discrete change may be a decision to divide the plant into more specialized, but less

flexible, PWPs. At the upper left end of the diagonal is the functional factory, while at

the lower right end, is the focused factory for each product produced by the organization.

This concept is explored in detail in the next section.

45

Proposed Theoretical Model

Hayes and Wheelwright's (1979a) model discussed earlier serves as the basis for

the proposed model. Superimposing the cellular manufacturing concept on the product-

process matrix introduces the concept discussed in this section (see figure 5). The

Process Structure

Product Structure

Increasing Number of Part Families

Increasing Number o f Divisible

Operations

Flow shop Flexible

Cellular

Functional (Job shop)

Assembly

Figure 5. Cellular manufacturing concept superimposed on product-process matrix

product structure is represented by the number of part families, and the process structure

by the number of divisible operations. A low number of part families in a shop with only

a few operations should implement a continuous flow strategy (flow shop). A low

46

number of part families in a shop with a large number of operations should implement an

assembly strategy (assembly). A shop producing a high number of part families with

only a few operations should establish a flexible facility (flexible). The cellular

manufacturing concept falls in the area between the functional Gob shop) and the flow

shop. As the number of part families increase, the opportunity for cellularization

increases dependent upon the divisibility of the operations required. There are two "off-

diagonal", non-cellular strategies on this matrix, assembly and flexible. For a high

number of identifiable part families with few operations that are not divisible, the

manufacturing strategy may focus on flexible operations. Thus, the company can

minimize capital investment while maintaining the company's ability to manufacture all

its products competitively. For a low number of identifiable part families with highly-

divisible operations, parallel assembly lines may be the reasonable strategy.

As stated in the prior section, individual companies attempt to move down the

diagonal of the product-process matrix (see figure 4) to gain production efficiency.

Similarly, as the opportunity for cellularization increases and the number of divisible

operations decreases, companies will attempt to move up the diagonal (see figure 5).

The proposed theoretical model is based on the relationship of cellular

manufacturing and the product-process matrix. The theoretical model views a functional

factory as a one-cell factory. As the number of identifiable, discrete part families and the

number of distinct operations increase, the opportunity for increased cellularization is

improved. At the extreme that each part family consists of few part families and there are

47

few divisible operations, the pure flow shop results and contains as many "cells" as there

are part families. This is consistent with others' conclusions (Flynn and Jacobs 1986).

The proposed theoretical model uses process structure as the number of divisible

operations and product structure as the number of parts to produce (see figure 6). The

literature provides support for the notion that cell performance is influenced by the initial

product and process structures mediated by cell formation. Using the concept (see figure

5) discussed previously, the Process and Product Structure determine the extent to which

cellularization is possible. In some cases, these two factors, due to special requirements

of either, can prescribe specific cells that must be included in the factory, factory. The

ultimate factory performance is a consequence of the individual cell performances within

the factory as well as the successful coordination of the parts of the factories. This is a

very important application of Thompson's (1967) pooled

Factory Control Systems

Product Structure

Factory Performance

Cell Formation

Process Structure

Cell Performance

Figure 6. Proposed theoretical model

48

interdependence. Factory coordination must use standardization as discussed previously

to best manage the cellular factories.

Research Model

This section presents the research model used to examine the relationships proposed in

the theoretical model (see figure 7). The experiment investigates the effect of product

and process structure on factory performance as mediated by the cell formation. These

relationships represent the initial conditions which factories encounter and the final goals

toward which factories strive.

Product Structure

Cell Formation

Factory Performance

Process Structure

Figure 7. Research model

Figure 8 exhibits the variables and operational relationships for the research

model. The factory performance parameters, throughput and flow time, were identified

in the literature review and the product and process structure parameters are discussed ii

49

the following sections. Work content required by each part represents product structure

depicted by the operations per part distribution in the part/operation matrix. Process

structure is represented by the operation capability depicted by the parts per operation

distribution of the part/operation matrix. Product and process structures were influenced

by the density of the part/operations matrix, which is included as the third factor in the

experiment. Once cells have been formed, the assignment of parts to each cell effects

factory performance. That is, the cellularization of the factory effects how the factory

Procfoct Structure

Cell Formation

Factory Performance

Process Structure

Parts per operation

Celiulariztion

Operations per part

Methodology Part Assignment

Throughput

Density

Flow time

Figure 8. Operational relationships

performs. The performance in this study is measured by throughput and flowtime.

The research model focuses on the three factors: process structure, product

structure, and density and their effect on factory performance. The factory performance

measures in figure 8 are consistent with those in other studies (see table 4). This research

focuses on the effect of these factors on cell formation. Research of this nature may not

compare the best cellular factory to the best functional factory. Often, comparisons focus

on a functional layout versus the unique cellular layout resulting from the cell formation

50

technique under examination. This study makes that comparison and uses factors

commonly found in the literature. The subsequent discussion concentrates on the

variables specific to this study (see figure 8).

Product Structure

Product structure is a function of the density of the part/operation matrix and the

work content required by each part. The work content of each part is the number of "Is"

in each row of the part/operation matrix and is described by the operations per part

distribution. The density of the matrix is the percentage of "Is" in the part/operation

matrix and is indicative of the complexity of the part processing plan. As the density

increases, the average number of "Is" per row increases and each part requires more

operations. A complex product structure can effect the achievable level of cellularization

and performance of the factory.

Process Structure

Process structure is defined as the variety of operations required to process parts

and is represented by the parts per operation distribution. This is a measure of

operational capability. Operational capability increases as the number of parts an

operation can process increases. The capability of each operation is the number of "Is"

in each column of the part/operation matrix and is described by the parts per operation

distribution. As the density increases, the average number of "I s" per column increases

and each operation is more capable. Complex process structures include a high

51

proportion of operations capable of producing large numbers of parts each. This is not a

question of capacity, just capability.

Cell Formation

Cell formation is the division of a functional factory into smaller, independent

groups of operations. It is affected by the formation methodology, the cellularization,

and the part assignment. Each of these variables are established by management prior to

and during cell formation. The cellularization and part assignment variables are

functions of the desired operating environment.

The methodology used influences the final cells identified. For instance, given

the same part/operation matrix, single linkage clustering techniques (McAuley 1972)

result in different cells than a technique using average linkage clustering (Seifoddini and

Wolfe 1986). The decision of which methodology to use is influenced by the skill of the

user, the type of input information available, and the investment (time) available. These

factors influence whether a visual method, parts coding analysis, or production flow

analysis technique is most appropriate for a specific situation.

The level of cellularization and part assignment variables are related.

Cellularization is the percentage of manufacturing hours produced in cells relative to the

entire factory. A functional cell, one that contains at least one of each operation, is not

included in the calculation of manufacturing hours produced in cells. Therefore, the

assignment of parts to the cells influences the cellularization of a factory. Part

assignment may differ for the same cellular configuration depending on the priority

52

assignment rule used. For instance, if maximum assignment to cells is desirable, leaving

the functional cell available for the purpose of flexibility, then the cellularization of that

factory would be high. If part assignment, was made to balance the workload between all

cells including the functional cell, then the level of cellularization reduces.

Factory Performance

Factory performance is the ability of the manufacturing operation to accomplish

the desired goals. The performance variables selected for this study are consistent with

other studies of this nature (Flynn 1987; Jensen, et al. 1996). The two variables of

specific interest to this study include throughput and flow time. Throughput is the

number of parts completed in a given time period. Flow time is the average time spent in

the system by each part. The experiment described in chapter 3 uses these variables to

analyze the affect of product and process structure on factory performance.

Table 5 summarizes the operational definitions for product structure, process

structure, cell formation and density. The definitions of the measurable variables used in

this study are also defined in the table. The definitions are consistent with those used in

other studies (Flynn 1987).

The following three sections address the experimental levels of the factors used in

the experimental design: density, product structure, and process structure. The

discussion concentrates on how the factor levels were chosen for this study.

53

Table 5. Research model operational definitions Construct Definition Measurable variable Definition Product Variety of parts required Structure to be processed

Density

Operations per part (work content)

Percentage of 1 's in the part/operations matrix Variation in number of operations required by each part represented by the row sums in the part/operation matrix

Process Variety of operations Structure required to process parts

Parts per operation (operation capability)

Variation in number of parts processed on each operation represented by the column sums of the part/operation matrix

C e l l Division of a functional Formation factory into smaller,

independent groups of operations

Methodology

Cellularization

Part assignment

Technique used to develop part families and operation groups

Percentage of manufacturing hours completed in cells, not including the functional cell Designation of parts to cells for processing

Factory Performance

Ability of the manufacturing operation to accomplish the desired goals

Throughput

Flow time

Number of parts completed in given time period

Time spent in system by parts

Density

The density of a matrix is a numerical value representing the complexity of the

part/operations matrix (see equation 1.1). In order to generalize the results of this

investigation, problems from the literature were selected and evaluated to determine the

appropriate levels of density to investigate. The problems selected (see table 6) are the

54

Table 6. Problem sizes found in the literature

Burbidge (1975) 28~ Morris and Tersine (1990) 30 Carrie (1973) 20 Burbidge (1975) 16

King andNakornchai (1982) ig Shafer and Charnes (1993) 15 Shafer and Charnes (1993) 15 Shafer and Charnes (1993) \ 5 Chandrasekharan and Rajagopalan (1986) 8 Chandrasekharan and Rajagopalan (1986) 8 Chan and Milner (1982) 10 Seifoddini and Wolfe (1986) 8 Gupta and Tompkins (1982) 12 Ham, Hitomi, and Yoshida (1985) 10 Shafer and Rogers (1991) 6

Note: the Shafer and Charnes (1993) and Chandrasekharan and three and two problems defined in the same article, respectively

Number Number of of

Operations Parts Size Density (X) (Y) (X*Y)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

50 40 35 43 43 30 30 30 20 20 15 12 8 8 12

1400 1200 700 688 688 450 450 450 160 160 150 96 96 80 72

0.18 0.12 0.19 0.18 0.18

0.196 0.26

0.583 0.38 0.57 0.31 0.36 0.32 0.32 0.49

Rajagopalan (1986) had

same as those selected by previous researchers for comparison (Kusiak, Boe, and Cheng

1993; Vakharia and Kaku 1993). The relationship between size of the overall matrix and

density is documented to establish an acceptable size and density for this study.

The studies in table 6 are sorted according to cell size. The average problem size

is 456. Using the Shafer and Charnes (1993) study as the minimum cutoff for a large

problem, densities for large problems vary from 0.12 to 0.26. The cell density of 0.583

for the third Shafer and Charnes (1993) model is extremely high compared with others in

the large problem category (1 through 8). They specifically investigated this unusually

high density level to create a high level of required intercell flow in their experiment. The

small problems (9 through 15) range in density from 0.31 to 0.57 (see table 6). Using cell

55

size as a weight factor, weighted-average density for small problems is 0.40. The

weighted-average density of the large problems is 0.21. To maintain an integer problem

formulation, this study rounded the low level setting to 0.20 and assigned a high level

setting of 0.40 to the density factor.

The methods studied in problems 9 through 15 are mathematical formulations

(see figure 2) and are a compatible methodology with the array based technique proposed

m chapter 3. The proposed technique investigates a cell size of 100 which is consistent

with the sizes of the smaller problems in table 6.

Product and Process Structure

Variability in product and process structure is the change in relative proportion of

jobs that belong to each part family. This variation may affect cellular manufacturing

cell balance. The extent of its impact on factory performance has not been thoroughly

investigated.

In a study by Jensen, et al. (1996), product structure was investigated at two

levels. The first called for equal probability for part demand from all ten part families.

The second used a weighting factor to increase the probability of arrival of two randomly

selected families to 13%, two others to 7%, and the other six remained at 10%. The

researchers investigated the shop layout, scheduling procedure, possibility of machine

customization, and demand variation for a given factory. While the result indicated

significant impact on performance for that factory, it did not indicate the effect of mix if

the number of cells were reduced, thus increasing the overall flexibility within each cell.

56

Another recent study by Vakharia and Kaku (1993) varied process and product

structure in a mure complex manner. A selected percentage (10, 20, 30, or 40%) of the

existing parts were eliminated and replaced by new parts with completely new routings,

processing times, and demand level. Their technique investigates the ability of a given

cell system to adapt to new products in the mix while deleting old products. The

researchers allowed intercell flow and examined the need for cell redesign in an

environment of long term demand change.

A load imbalance caused by a fluctuation in demand volume for given parts may

make a cell inefficient or obsolete (Wemmerlov and Hyer 1989). Volume variability can

lead to early obsolescence of a specific cell, but, one may be able to avoid this by

decreasing the manufacturing hours assigned to cells. Process variability is the variation

in aggregate demand levels across all families of parts (Jensen, Malhotra, and Philipoom

1996). Jensen, et al. (1996), varied the volume over two levels. The low level had a

constant interarrival rate of one job every ten-time units. The high level randomly

generated part arrivals every day from a Poisson distribution with an average often time

units.

Vakharia and Kaku (1993) modeled volume changes by increasing demand for

10, 20, 30, and 40 % of the total parts by an amount selected from a given discrete

uniform distribution. This experiment controlled for the number of parts for which

volume was allowed to fluctuate, whereas Jensen, et al. (1996), could have all the parts

increased or all the parts decreased.

57

Flynn and Jacobs (1986, 1987) used actual factory data for one demand

distribution of six products and three theoretical distributions. The three theoretical

distributions include: (1) equal demand for all six products, (2) higher demand for parts

requiring more operations, and (3) higher demand for parts requiring fewer operations.

Product structure was tested by allowing parts requiring more operations than others in

the factory. Product structure is represented by the row totals in the part/operation

matrix. The low level for this factor was a uniform distribution of operations per part

where each part required the same number of operations. The high level skewed the

operations per part distribution such that approximately one-third of the parts required

more operations and one-third required fewer operations than at the low level. Process

structure was tested by allowing higher demand for some operations on the floor.

Demand was defined as the total parts processed by each operation represented by the

column totals of the part/operation matrix. The low level of this factor was a uniform

distribution for operation demand where all operations processed the same number of

parts. The high level of this factor skewed the distribution such that approximately one-

third of the operations processed a higher proportion of parts and approximately one-third

of the operations processed a lower proportion of part than at the low level of this factor.

These levels of process and product structure are consistent with the demand variability

introduced in the Jensen, et al. (1996) study, but has been modified slightly to fit this

research design.

58

Research Obi ectives

This study involves the investigation of the affect of the product structure and

process structure with factory performance. Previous research in this area has thoroughly

defined the relationship between product and process structure and the ability to form

cells. However, research is lacking on the effect of factory performance of these factors

The simplest characteristic of the matrix is its density. The initial matrix density

has a major impact on the ability of any of the existing cell formation techniques to

identify independent cells. The density of any matrix is related to the number of

operations required by each part. As the number of operations increases, so does the

density of the matrix. That is, the higher the initial density, the higher the probability of

off-diagonal 1 's in the final matrix. This influence is addressed in the first research

question.

Research Question #1: Is there a significant relationship between the density of

the part/operation matrix and factory performance as determined by throughput

and flow time?

While the density is the most obvious place to begin describing the part/operation

matrix, the demand for parts can affect how the final layout is achieved, A part with low

work content in terms of number of operations required, but containing a high proportion

of the total manufacturing hours, may still require a unique cell. A part requiring many

59

operations that are in high demand by other parts may eliminate the advantages of a cell

layout philosophy. This possibility is addressed in the second research question.

Research Question #2: Is there a significant relationship between the product

structure represented by the operations/part distribution and factory performance

as determined by throughput and flow time?

The next research question addresses the impact of process structure on the

performance of cellular manufacturing. In many manufacturing settings, there are some

operations capable of producing a high number of parts and there are others with limited

capability. From a capacity perspective, this imbalance leads to more complex material

handling, scheduling, and management. As the imbalance becomes more distinguishable

in the distribution of the process structure, factory performance may be affected. This

leads to research question #3.

Research Question #3: Is there a significant relationship between the process

structure represented by the parts/operation distribution and factory performance

as determined by throughput and flow time?

The previous three research questions focus on the average effect the factors have

on average factory performance. This is the optimal manner to examine the relationships

defined in the research model. A representative sample was collected by using the

60

systematic sampling plan described in chapter 3. However, an area of interest is how

different factor combinations influence the performance of the best factories. A primary

advantage of the proposed method is its ability to identify multiple factories which may

demonstrate different performance characteristics. By examining the top performers on

given measures, throughput and flow time, it was possible to examine the variation in

other criteria of interest to the operations managers. The fourth research question

addresses the best performing factories.

Research Question #4: Do the variables investigated significantly contribute to

explaining the variation in factory performance for the best performing factories

based on throughput and flow time?

The proposed method excels in its applicability to practical situations. The

algorithm to identify all the feasible factories is not limited by assumptions, however, the

simulation model to analyze the factories requires assumptions. A major assumptions

used in experimentation that is often violated in practice is to assume an arrival process is

described by a Poisson distribution. The assumption may be violated by batching jobs,

time dependent demand, or other such violations. A modified runs test was presented

(McQuaid and Pavur 1997) to identify the existence of a Poisson process. Like the MCA

algorithm, this test excels in its ease of application to practical situations. The final

research question addresses the use of this test.

61

Research Question #5: Is the proposed test procedure for identifying the

assumptions of a Poisson process for arrival times statistically valid?

The remainder of this study addresses these five research questions. The

investigation of these relationships is supported by the theoretical relationships defined in

this chapter. These research questions are important since factory performance is a

function of the strategy selected.

Summary

This chapter provided a comprehensive review of cellular manufacturing

literature and presented the research model for this dissertation. The early literature

focused on cell formation techniques, progressed through comparisons with traditional

factories using a functional layout, and is now beginning to survey users of the

philosophy. With the development of more powerful computing capability, some of this

path is being revisited using neural networks, fuzzy logic, and other less structured

techniques.

The main goal is to improve productivity by improving output without changing

input. This study focuses on the goal by addressing the product and process structure as

characterized by the Hayes and Wheelwright (1979) matrix. By examining the

relationship this structure has on factory performance, it provides new insight on the state

of nature in which the factory operates.

CHAPTER 3

RESEARCH METHODOLOGY

The purpose of this research was to examine the relationship of factory

performance with the initial part/operation matrix. This study required the development

of a large number of factories that evolved from different possible initial matrices. The

concept of Machine Combination Analysis (MCA) emanated from the need to develop all

possible factories. The MCA technique is a reasonable extension of existing methods

that focused on some specific, and possibly unimportant design criteria. This chapter

presents the MCA technique and describes the experiment to investigate the influence of

the part/operations matrix on factory performance.

Proposed Technique

The creation of independent cells is a common goal for most cellular design

techniques (Burbidge 1975, Wemmerlov and Hyer 1987). MCA results in no planned

intercell flow. MCA is a two-stage procedure. The first stage employs the part/operation

matrix as input and results in a list of possible cell groupings, or factories, capable of

producing all parts in the matrix. The factories range in size from one-cell

(representative of a functional factory) to a maximum equal to the number of parts in the

original part/operation matrix. The collection of feasible factories is reduced in this

stage. Cells that process no parts in their entirety, cells requiring more operations than

63

others to process the same parts, and factories that require more machines of a given

operation than available are removed. The second stage is a simulation of all feasible

factories to determine which cell combination best satisfies the requirements of the

designer such as minimizing flow time or maximizing throughput of the system.

There are advantages of MCA over typical cell design techniques. Other

techniques focus on part characteristics or process similarities in forming cells without

focusing on the system performance. Due to this lack of consideration of overall system

performance during cell design, these techniques may generate a sub-optimal solution.

Since MCA selects from all feasible combinations, the result is optimal for the system

under consideration. Another advantage of MCA is the ability to modify the

manufacturing simulation stage to apply different performance criteria. MCA inherently

compares the operation of an efficient functional factory to all feasible cell combinations.

Other techniques do not use the functional factory as a possible solution to the problem.

By investigating all feasible cell combinations, the MCA considers hybrid factories.

Example of Machine Combination Analysis

An example beginning with a 6 x 4 part/operation matrix is used to demonstrate

the technique (see table 7). The first step of MCA manipulates the part/operation matrix

and identifies eight cells (numbers 0, 1, 2, 3, 4, 6, 8, and 10) capable of producing

complete parts with no intercell flow (see table 8). The other seven (5, 7, 9, 11 12 13

14) are eliminated from consideration. Table 8 contains two matrices. The cell/operation

matrix is a 0-1 matrix that identifies which operations are in each cell. Cell #0 is referred

64

to as the functional cell since it contains all the operations and can produce all parts. The

cell/part matrix is a 0-1 matrix that identifies which parts each cell can process (see table

8).

Table 7. Example part/operation matrix Operation

Part 1 2 3 4 1 1 l I 2 1 1 l 3 1 l l 4 l l 5 1 l 6 1

_ j . .. .J l

Note: a "1" denotes a part requires that operation

Table 8. Cell/operation and cell/part matrices Cell Operations Part

Number l 2 3 4 1 2 3 4 5 6 0 l l l l 1 1 1 1 1 1 l l l l 1 1 2 l l l 1 3 l l l 1 1 1 4 l l l 1 1 1 5 l l 6 l l 1 7 l l 8 l l 1 1 9 l l 10 l l 1 l l l 12 l 13 l 14

\ t . A _ . _ a 1 l

process that part. For instance, cell 10 contains operation 3 and 4 and process part 4 in its entirety.

65

The next step involves forming all possible combinations of cells from table 8

including one cell, two cell, up to six cell factories. The upper limit of six cells results

because if each cell processes at least, and at most, one part, there are six possible cells.

Assuming two machines of each operation exist, table 9 shows the feasible factories

constrained by the number of available machines. The twenty factories listed in table 9

are the only combinations that will satisfactorily manufacture all parts using the available

machines. These factories become the input to the manufacturing simulation stage of

MCA.

Table 9. Feasible factories Factory Number of Cells Number Cells Used

0 1 0 1 2 0,1 2 2 0,2 3 2 0,3 4 2 0,4 5 2 0,6 6 2 0,8 7 2 0, 10 8 3 0,1,2 9 3 0,1,4 10 3 0, 1,10 11 3 0, 2,3 12 3 0 ,2 ,6 13 3 0, 2, 10 14 3 0, 4,6 15 3 0, 6, 10 16 3 0, 8, 10 17 3 1,3,4 18 4 0, 1,2, 10 19 4 1,2,3,4

66

Research Design

The experimental design chosen for this study is a 23 full factorial design. The

experiment examined the three factors at the levels shown in table 10. The purpose was

to investigate how the initial part/operation matrix influenced the performance of the final

factory. As discussed in chapter 2, initial conditions include the density of the

part/operation matrix, the operations per part distribution, and the parts per operation

distribution. A manufacturing simulation discussed in the next section, written in

Microsoft C program language, was used to simulate the factories generated at each

factor level.

A power analysis to determine required sample size was conducted. Using

statistical tables from Cohen (1988), a total sample of 240 was collected to perform the

analysis of variance test. This was based on a = 0.05 and p = 0.20 with a medium effect

size.

Table 10. Experimental factors Factor Level Description

Density Low 0.2 High 0.4

Parts per operation distribution Low Uniform High Skewed

Operations per part distribution Low Uniform High Skewed

67

Simulation Design

Programming Language Selection

Several simulation languages appear in the literature. Early research on

mainframe systems required knowledge of UNIX or FORTRAN. Since the mid-1980's,

several simulation languages evolved that focus on manufacturing systems (SLAM,

WITNESS). FORTRAN and other programming languages are often used in

combination with a simulation package.

Morris and Tersine (1990) compared cell layouts with functional layouts. The

facility planning software MICROCRAFT generated the layouts. A manufacturing

simulation coded in SIMAN evaluated each layout. Other popular packages include

GPSS and GASP IV (Sassani, 1990). A current popular package is SLAM. SLAM used

in much of the recent research, appears accepted as a valid software package (Askin and

Iyer 1993; Flynn and Jacobs 1987; Jensen, et al. 1996; Russell and Taylor 1985).

This simulation coded in Microsoft C increased the flexibility of necessary

calculations, as well as, eased the input and output of the data created by the MCA

technique. At the time of this study, SLAM and GPSS did not have the grouping

flexibility required by this technique to build all the feasible factories. Since a large

amount of program code for subroutines was required, the determination was to write the

entire technique and simulation in Microsoft C.

68

Model Building

This study required a complex manufacturing model able to model any number of

cells, operations, and machines available. The level of detail required for this simulation

was not presented in any published research found. The model requires a flexible

manufacturing simulation able to represent multiple cell factories with varying quantities

of operations within a cell and machines within an operation. Although other complex

models have been presented, none capture the complexity required by the cellular system

for this study (Banks and Carson 1984; Law and Kelton 1991; Shannon 1975).

The manufacturing model used for this simulation is introduced in figure 9. It

possesses the necessary attributes to successfully model complex, flexible factories. The

model contains three cells. Cell 1 has two machines of operations 1, 2, and 3 and one

machine of operation 4. There is a queue before each operation in each cell. When a part

exits a queue, it is processed by one machine in that operation and moves to the next

required operation. Cell 1 is a smaller version of the functional factory. Cell 2 has taken

four machines from cell 1 and cell 3 has taken five machines from cell 1. If a part

required operations 1,2, and 3, the part requires cell 1. However, a part requiring

operations 1 and 3 could be done in either cell 1 or 3. This model is expandable to any

number of cells containing different numbers of machines in each operation. For this

study, an arriving part routes first to an assigned cell. If that cell exceeds an upper limit

in any of its queues, the functional cell is checked for available capacity, and the part

either routes to that cell or exits the factory without processing. Intercell transfers and

rejections are tracked as part of the manufacturing simulation.

69

Cell 1

Cell 2

Cell 3

Operation 1 Operation 2 Operation 3 , Operation 4

= queue

<'" "JS' > = machine

Figure 9. Manufacturing model

Computer Programs

The experiment used five separate programs to generate the part/operation matrix,

form feasible cells and factories, develop reasonable part assignments, and simulate the

factory. The following sections describe the general logic of each program and the

assumptions required to facilitate their execution.

Program #1: Input Data Generation

The purpose of program #1 was to generate the part/operation matrices for each

combination of factor levels (see table 10). Other data created by this program include

70

the processing times for each part on each operation and the setup times required when

preparing a machine for the next part. The program requires input of the information

shown in table 10 regarding the density, part/operations distribution, and operations/part

distribution for each combination of factors.

The part/operation matrix used the density and the matrix size to calculate the

number of "Is" that appeared in the matrix. The part/operation matrix then assigned the

Is in a random manner that satisfied the marginal totals established by the desired

distribution forms input to the program.

Processing times of parts in each operation were deterministic and selected to be

comparable with other simulation studies. The assignment of processing times used a

truncated exponential distribution averaging 120 minutes with a minimum of 30 minutes

and a maximum of 240 minutes. Setup times assigned using a similar distribution

averaged 20 minutes with a minimum of 10 minutes and a maximum of 40 minutes. In

both cases, if the random number generator calculated a time outside the range, then the

program repeated until it determined a satisfactory time. Selection of these times

followed input from operations managers during the model verification and validation

discussed later.

Program #2: Cell/operation Matrix and Cell/part Matrix Generation

This program developed the cell/parts and cell/operations matrix (see table 8)

based on the part/operations matrix for each combination of factor levels. Input required

was the part/operations matrix similar to table 7, but revised using different factor

71

combinations. The output from this program included the operations assigned to each

cell (cell/operations matrix) and the parts each cell produces (cell/part matrix).

Program logic compared each row (part) of the part/operations matrix to the all

rows of the cell/part matrix to see which cells could produce which parts entirely. The

cell/operation matrix (see table 8) includes all possible combinations of operations from

single operations, to pairs, to threesomes, up to the number of operations available.

There is a different cell/operation matrix and cell/part matrix for each part/operation

matrix. The program calculated the maximum number of possible cells (M) using:

(3.1) M = 2k-l

where k = number of operations.

The above formula was used to calculate the number of combinations from one-way,

two-way, through k-way combinations given k items. To investigate all possible

combinations of machines creating the cell/operations matrix, the program iterated M

times. The binary equivalent was calculated for each value as M decremented from M to

0 and assigned machines to a cell based on the "Is" in that binary number (see table 11).

The binary equivalent of the value 11 is 1011. For each binary digit equal to "1", the

value in the bottom row of table 11 is summed. Therefore, 1011 = 8+0+2+1 = 11.

The cell/part matrix was then created by comparing each cell to all rows of the

part/operation matrix. If the cell contained all operations necessary to process any of the

parts completely a "1" was placed in that part's column (see table 11). An example using

the part/operation matrix in table 7 illustrates this process.

72

There are four operations for a value of M = 24-l = 15 possible cells. Table 11

exhibits the binary equivalent and the relationship to operations for these cells containing

a "1". A "1" in a column indicates an operation included in that row's cell. From table 7,

part #5 requires operations 2 and 4, so any cell must contain at least these two operations

to process that part. According to the data in table 11, cells 0,2, 4, and 8 can process this

part. The result of comparing each row of table 11 with each row of the part/operations

matrix is the creation of a cell/parts matrix. The cell/operations matrix is a list of cells

and the operations included in each cell. The cell/parts matrix is the same list of cells and

the parts each can produce (see table 11).

Table 11. Binary equivalent values of M Cell Cell/operation matrix Cell/part matrix

Number M 1 2 3 4 1 2. 3 4 5 6 0 15 1 1 1 1 1 1 1 1 1 1 1 14 1 1 1 0 1 1 2 13 1 1 0 1 1 7 12 1 1 0 0 3 11 1 0 1 1 1 1 1 6 10 1 0 1 0 1 5 9 1 0 0 1 14 8 1 0 0 0 4 7 0 1 1 1 1 1 1 9 6 0 1 1 0 8 5 0 1 0 1 1 13 4 0 1 0 0 10 3 0 0 1 1 1 12 2 0 0 1 0 11 1 0 0 0 1

8 4 2 1 Binary value of M

Note: cell numbers correspond to those listed in table 8.

73

Program #3: Combine Cells to Generate Feasible Factories

Using the cell/operations and cell/parts matrices as input, program #3 combined

the cells into one-cell, two-cell, up to p cell factories, where p is the number of parts. The

program identifies feasible factories defined as those cell combinations capable of

producing all the parts. For example, the two-cell factory made up of cell 1 and cell 2 is

unable to produce parts 1,3, and 4. Therefore, it is not a feasible factory. Any cell

combination that includes cell 0, the functional cell, can produce all the parts. The output

for program #3 is a list of the feasible factories (see table 9), the number of cells in each,

and the cells in the factory referenced by the cell numbers shown in table 8.

Program #4: Assign Parts to Cells and Establish Number of Machines in Cells

The objective of this program was to assign parts to cells in a reasonable manner

and to identify suitable factories considered usable in practice. The primary criterion was

to balance the production hours assigned to each cell. The program accomplished this by

minimizing the standard deviation of the proportion of production hours assigned to each

cell. Program logic identified all possible assignments that used all cells in the factory

and selected the assignment that balanced total process time across cells in each factory.

Program #5: Manufacturing Simulation

The manufacturing simulation followed the model in figure 9. The flowchart

exhibited in figure 10 describes the logic of the program. The program is a discrete event

simulation, incrementing time when a part arrives at the factory or when a part anywhere

74

Part arrives at factory

Identify to which cell part

is assigned

Identify to which cell part

is assigned

Increment time

Identify next operation for

part

Enter queue for that operation

Begin setup and process hg

Is machine available?

Increment time

Part completes processing

similar part in queue?

Any part m queue?

Has part finished all operations?

Figure 10. Manufacturing simulation flowchart

in the factory completes service. Statistics representing throughput, flow time, and

several others were collected during the simulation of each factory. Ten replications of

one year's simulated time were run and the average recorded in output. As shown in

figure 9, the general factory operation required all parts waiting for an available machine

are in a common queue for that cell and operation. Thus, the cell is layout resembles an

efficient functional factory.

75

Several assumptions were required to develop the simulation. Table 12 lists these

assumptions. The operations managers reviewed these assumptions during the

presentation of the verification and validation of the model. Several assumptions were

modified based on the operations managers' feedback. The operations managers

supported the assumptions listed in table 12.

Table 12. Assumptions for manufacturing simulation ~ 1 All operations required to complete a part are available in the cell to which the

part is assigned.

2 Each cell is laid out and functions as a modified flow shop.

3 No specialized machinery is required in more than one cell.

4 Once a part begins production in a cell, it completes production in that cell.

5 Total number of machines available in each operation established based on one set of parts arriving each hour.

6 Feasible factories are constrained based on the option to add up to two machines of each operation to account for imbalance when dividing parts among cells.

7 Arrival rate of parts is based on the maximum arrival rate allowed by any of the functional factories without rejecting parts.

8 Priority for parts in queues is given to a similar part as just processed and, if none are available, use FIFO.

9 Processing times and setup times are deterministic and do not vary throughout simulation.

76

Transient period

Since factories do not generally start with empty queues each day, it was

necessary to run the simulation for a start-up period to bring the factory from an empty

and idle state to a steady state at the beginning of each replication. All performance

variables were set to zero while the system remained in its current state of activity. A

series of pilot runs using the functional factories established a start-up period of six

months. This time period was consistent, if not slightly longer, with other studies. One

study to determine the best scheduling heuristic in a one-cell, five-workcenter system

used a 2,000 hour warm-up period followed by an 8,000 hour simulation run (Mahmoodi

and Dooley 1991 j. Testing each scheduling heuristic used fifty replicates. Flynn and

Jacobs (1987) used a seven-year start-up period followed by twenty years of simulation

gathering data in alternate years for ten independent observations. Other studies included

a 200-hour startup with 2,500 hours of simulation and a 50-job startup with a 500 job

simulation run (Askin and Iyer, 1993; Russell and Taylor, 1985). Based on the studies, it

appeared a startup period of 10% to 33% of the length of the actual simulation run was

adequate.

The transient period for this study was established by collecting statistics using

the functional factory for 2000 hours while varying the transient period time from 200 to

1000 hours. Steady-state appeared to occur with a transient period approximately 650

hours long.

77

Model Verification and Validation

Verification

Verification of the computer programs involved confirming that the programs

processed data correctly. This task was accomplished through several stages. First, by

dividing the programs into five smaller programs, control was improved. This allowed

debugging to be applied in much smaller increments of program code.

Each program was run to verify input files were being read and output files were

written correctly. This was accomplished using a series of print statements. Realtime

output was monitored on queue lengths, machine usage and availability, random part

sequences through the system, and time dependent statistics collection. This step

required writing interim values to a file and manually reviewing the variables for

inconsistencies.

Finally, sensitivity analysis was performed on the program by changing three

system parameters and observing the effect. The first system parameter was the arrival

rate. As it increased beyond the service capability of the system, the programs stopped

abruptly as expected. As arrival rate decreased, the system utilization and throughput

declined as well as other queue and work-in-process statistics. Second, certain operations

were given zero available machines. Queues increased to the maximum limit indicating

parts could not proceed through the factory. Third, the simulation time was varied to

observe the effect on time persistent statistics. These statistics decreased as expected for

the shorter time periods.

78

Validation

The validation effort consisted of establishing face validity and substantiating the

model assumptions. Since CM is not in wide spread use, actual data from manufacturers

are scarce. Scarce data make model validation a speculative task since the model can not

be proven via real life. In an effort to validate this model, presentations were made to

fifteen manufacturing, inventory and planning managers and supervisors at Fortune 100

companies. The managers and supervisors served as focus groups to provide feedback to

revise the original model.

The presentation to the operations personnel is included in appendix B. The

primary feedback was on the setup-time portion of the presentation. The initial

assumptions of the model included that setup time was a percentage of processing time,

10% if a minor setup and 40% if a major setup (Wemmerlov and Vakharia 1991). The

operations managers' input was that setup time was not related to processing time in

general, but was a function of the operation. In fact, some operations took longer to setup

than to actually process the part. As a result of this input, setup time was determined

similar to the processing time. With their agreement, setup time was calculated by a

truncated exponential distribution with a mean of 20 minutes and a range of 10 to 40

minutes per part.

Another initial assumption was that parts could be processed only in the cells to

which they were originally assigned. The operations managers thought that this was an

unrealistic assumption because good managers adjust their system if queues forming in

one area could be completed in another underutilized area. The model was revised to

79

allow parts assigned to overloaded cells to process through the functional cell if it were

available. Otherwise, the part is rejected from the factory.

The final adjustment to the model for this study involved the mean and variation

in process times. The operations managers thought that the mean of 60 minutes with a

range of 15 to 120 minutes was too low. The model was modified to a mean of 120

minutes with a range of 30 to 240 minutes per part.

Some input received from the focus groups was not instituted in this study

because it did not aid the investigation of the theoretical model. A performance measure

the managers thought important was percent tardy by on-time starts. This measurement

indicates when a shop is unable to meet schedule based on starting jobs on-time. In

addition, the operations managers thought that finishing too many jobs early indicated an

over-capacitated shop and was also an undesirable statistic. Another question the

managers raised was what is the effect of changing order quantities in the functional

factory versus a cellular factory? This question involved much more extensive

investigation than the designed purpose of this study; therefore, was not addressed in this

study. Finally, the operations managers were interested in the application of other

secondary part selection decision rules other than the ones used in the model. While the

FIFO rule performs adequately, the operations managers often use work content

remaining as a secondary rule. Again, because of the extensive work required was not

addressed.

Other than the changes discussed, the operations managers thought that the model

and research plan were satisfactory. One of the companies had implemented a cellular

80

process at a division in the northeastern United States. An individual involved in that

implementation process commented that this model would have been valuable prior to

making many of the layout decisions.

The focus groups aided in establishing the validity of this research. They also

substantiated the important assumptions of the model. Those assumptions that were not

verified were modified based on feedback received from the operations managers.

Test for Poisson Arrivals

In addition to model validation, a procedure to test for Poisson arrivals is

explained and used (McQuaid and Pavur 1997). The strength of this test is its ease of use

and power associated with relatively large sample sizes. One violation of the assumptions

of the Poisson process occurs when arrivals are reordered. In most queuing situations,

this violation occurs, yet few researchers test for this assumption. Since this experiment

generates arrivals with exponentially distributed interarrival times, the test is not

absolutely necessary for this study. It is presented as an important prerequisite to

practioner application of MCA.

The proposed test procedure is:

1. Sample the times of the occurrences of a renewal process. 2. Generate a Poisson process with a mean approximately equal to the mean

interarrival times for the same length of time the renewal process ran. 3. Combine the two processes. 4. Perform a runs test on the sequences to determine if the sequence is

nonrandom.

The proposed test procedure uses a generated Poisson process as a comparison

case. The rate for the generated process may be substantially different from the actual

81

process and still provide good conclusions. Finally, the generated data set is observed for

the same length of time as the actual process. The advantage to this test is that violation

of the stationary assumption may affect the number runs even if the assumption of

exponentially distributed interarrival times holds.

Data and Analysis

The data generated by each program were written to several files. Except for the

part/operations matrix and setup and process time information, each file listed the first

column as either a cell number or a factory number. The cell number was used to

identify which cells were in each factory and the factory number was used to identify

which factory to apply each record of data. The data were compiled such that a 2 full

factorial ANOVA test could be performed. A regression analysis on top performing

factories was run. The goal for this analysis was to analyze the relationship between the

top factories performance and the variables and factors. This information may be

valuable to making cellular configuration decisions in different environments. Finally, a

Monte Carlo simulation run demonstrates the robustness and power of the proposed

Poisson process runs test.

CHAPTER4

DATA COLLECTION AND ANALYSIS

This chapter presents the data collected through the simulation experiment and the

feedback received from focus groups of operations managemers in the manufacturing

field. In addition, this chapter discusses how the data analyzed supports the research

questions and hypotheses. Several computer programs discussed in the previous chapter

written in C-code were used to generate data. A Pentium 200 MHz PC was used to

process all the computer programs. This chapter provides examples of output files.

However, the volume of data generated prohibits presenting this information entirely.

The following sections detail the input data development, analysis of input data,

manufacturing simulation data, and analysis of the simulation data.

Input Data

There were four separate programs used to generate input data for the final

manufacturing simulation program. The methodology chapter discusses the design of

each program. This section presents the output from each program. Required input data

includes the part/operation matrix, cell/operation matrix, cell/part matrix, processing time

matrix, setup time matrix, and the number of available machines for each operation.

Each of these data were generated using the first four computer programs.

83

Input Data Generation Program Output

This program generated the initial part/operation matrix, the part processing

times, and the part to part changeover times for each level of the 23 Factorial design. The

input required by the program was the desired density (0.2, 0.4), operations per part

distribution (uniform, skewed), and parts per operation distribution (uniform, skewed)

for each factor level. Table 13 exhibits an example of the output from this program.

Table 13. Part/operation matrix (0.4, uniform,uniform)

Operation Parts

0

1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9 Ops/part

0 0 1 1 0 0 0 0 1 1

1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 1 0

4 4 4 4 4 4 4 4 4

Parts/operation 4 4 4 4 4 4 4 4 4 4 40 Note: For this example, density = 0.4, operations per part distribution and parts per operation were skewed. Shaded area was actual output, other information provided for clarity.

The operations and parts in table 13 are numbered from 0 through 9 because the C

programming language assigns "0" to the initial value in a subscripted variable. This

factor level in the experiment design had four "ones" in each column and each row

because the density was 0.4 and both distributions were uniform. Therefore, each part

84

required four operations and each machine processed four parts. Changing the density to

0.2 would result in each part requiring two operations and each machine processing two

parts.

Table 14 exhibits another matrix with the parts per operation distribution skewed.

This table shows changing the parts per operation distribution to skewed resulted in a

change in the loading on several operations. In this example, operations 0-2 are required

by six parts, operations 3-6 are required by four parts, and operations 7-9 are required by

only two parts. However, all parts still require four operations each. Other part/operation

matrices provided similar output as the initial information for remaining programs.

Table 14. Part/operation matrix (0.4, uniform, skew)

Operation Parts 0 1 2 3 4 5 6 7 8 9 Ops/part

0 1 0 1 0 1 0 1 0 0 0 iisaliii®: 1 0 1 1 1 1 0 0 0 0 0 •llllliii 2 0 1 0 1 1 1 0 0 0 0 4 3 0 1 0 1 0 0 0 0 1 1 4 4 1 1 0 0 0 0 1 0 1 0 4 5 1 0 1 0 0 1 0 0 0 1 4 6 1 0 1 0 0 1 0 1 0 0 4 7 1 0 1 0 1 1 0 0 0 0 4 8 1 1 0 0 0 0 1 1 0 0 4 9 0 1 1 1 0 0 1 0 0 0 4

Parts/operation 40 Note: For this example, density = 0.4, operations per part distribution was uniform and parts per operation was skewed. Shaded area was actual output, other information provided for clarity.

85

The part/operation matrix is related to the processing time matrix in that each

location in the prior matrix containing a "1" will have a positive processing time in the

latter matrix. Table 15 presents an example of the processing times calculated by this

program associated with the part/operation matrix of table 14.

Table 15. Processing time matrix

Part

Operation (time in minutes)

Total part process

time Part 0 1 2 3 4 5 6 7 8 9

Total part process

time

0 25 0 51 0 107 0 130 0 0 0 l l i i l l l l l l

1 0 133 164 22 39 0 0 0 0 0 358

2 0 126 0 237 95 89 0 0 0 0 547

3 0 70 0 24 0 0 0 0 47 192 • l l l l l l 4 50 228 0 0 0 0 86 0 63 0 427

5 218 0 76 0 0 37 0 0 0 114 445

6 160 0 18 0 0 27 0 62 0 0 267

7 180 0 38 0 120 197 0 0 0 0 535

8 55 "191 0 0 0 0 49 216 0 0 511

9 0 73 32 82 0 0 53 0 0 • i l l 240

Total machine 688 821 379 365 361 3501 318 278 110 306 3976 required time

Number machines required

15 18 8 8 8 8 7 6 3 7

Note: Shaded area was actual output, other information provided for clarity

The processing times in table 15 used in the manufacturing simulation as

deterministic processing times were estimated as discussed in the previous chapter. The

number of machines required (bottom row, table 15) were used as input to a later

program (program #4). This is the number of machines available for assignment to cells

based on an efficient functional layout with 80% utilization. To offset the impact of an

86

imbalance in processing times when distributing parts to more than one cell, the later

program allowed the addition of two machines in each operation. For example, operation

2 has eight machines available. When two cells are formed and the work content is

divided, an imbalance may result where one cell requiring 3.7 machines gets four and the

Table 16. Setup times

operation to part 0 0 1 l l i l l 3 4 ' 5 6 7 8 9

0 40 0 0 0 52 59 92 74 74 0

1 0 0 0 0 0 0 0 0 0 0

2 0 0 0 0 0 0 0 0 0 0

3 0 0 0 0 0 0 0 0 0 0 a. 4 33 0 0 0 14 49 51 58 87 0 S 5 35 0 0 0 88 17 46 39 85 0 ,s 6 66 0 0 0 78 107 30 36 31 0

7 30 0 0 0 109 38 58 21 88 0 8 57 0 0 0 80 116 44 36 11 0 9 0 0 0 0 0 0 0 0 0 0

operation to part 1 0 i l l ! 12 l l l i 4 i 5 • i l l 7 • H I 9

i i i i i i i i 0 0 0 0 0 0 0 0 0 0 i 0 34 61 108 36 0 0 0 41 58 2 0 83 23 94 90 0 0 0 59 94 3 0 102 31 36 78 0 0 0 103 32.

cd OH 4 0 44 34 38 10 0 0 0 61 104 6 <*•*) 5 0 0 0 0 0 0 0 0 0 0 w

q-H 6 0 0 0 0 0 0, 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 8 0 35 92 72 95 0 0 0 32 107 9 0 75 64 59 93 0 0 0 83 10

operation to part 2 0 (1111 2 3 | . 4 1 5 llill na i l l l i l l 9 0 16 • H i ! 0 0 0 31 81 43 0 32 1 87 : io 0 0 0 43 33 33 0 30 2 ... ... Hill i i i i i i Hill! ... | IIIIIS ... 11111 ...

Note: Shaded area was actual output, other information provided for clarity.

87

other cell requiring 4.3 machines gets five for a total of nine machines required. This

would be accommodated for up to two additional machines of each operation, if

necessary.

The last set of data created by matrix.c is the part to part changeover times. Table

16 exhibits an example for the first two machines (0 and 1) related to the part/operation

matrix in table 14. There are eight other matrices (machines 2 through 9) in this data set.

These setup times are used in the simulation to represent the amount of time taken to

change the setup from the last part processed on a given machine to the current part. A

minor setup occurs when the changeover is from and to the same part. In table 16, setting

up part #1 on an operation #1 machine when the last part was a part #1 takes 34 minutes.

A major setup occurs when the changeover is to a different part. In table 16, setting up

part #1 on an operation #1 machine when the last part was a part #2 takes 83 minutes.

The previous chapter discusses the estimation of setup times. This data set has ten

matrices of setup times; one matrix for each machine showing the setup time to change

from and to all parts on that machine.

Cell/Operation Matrix andCell/Part Matrix Generation Program Output

This program uses the part/operation matrices for each combination of factors

from program #1 as input. Its purpose is to generate all feasible combinations (cells) of

machines that are capable of producing at least one part in its entirety. Each factor

combination results in different feasible cells. Output at each factor level is in two

separate data sets; the combination of machines in each feasible cell and the combination

88

of parts in each feasible cell. The part/operation matrix combines these cells into multiple

cell factories capable of producing all possible parts. Output for these two data sets is

shown in tables 17 and 18.

Table 17. Cell/operation matrix for part/operation matrix in table 13

Cell Operation Total Operations Number 0 1 2 3 4 5 6 7 8 9

Total Operations

0 1 1 1 1 1 1 1 1 1 1 10

1 1 1 1 1 1 1 1 1 1 0 i l w I I B l

2 1 1 1 1 1 1 1 1 0 1 • M i l l 3 1 1 1 1 1 1 1 1 0 0 H H f i H M I 4 1 1 1 1 1 1 1 0 1 1 5 1 1 1 1 1 1 1 0 1 0 WBKSSBM 6 1 1 1 1 1 1 1 0 0 1 7 1 O i l 1 1 1 0 0 0 • • l l i l i s 8 1 1 1 1 1 1 0 1 1 1 9 1 1 1 0 1 1 0 1 1 0 7

i l l i l ! 1 1 0 1 1 1 0 1 0 1 7

l i 1 1 0 0 0 1 0 1 0 0 4

12 1 0 1 1 1 0 0 0 1 1 6 13 1 0 1 0 1 0 0 0 1 0 4 14 1 0 1 1 1 0 1 1 0 1 7 15 1 0 1 0 1 0 1 0 0 0 4 16 0 0 0 1 1 0 0 1 0 1 4 17 1 1 1 1 0 1 1 0 1 1 8 18 1 1 1 1 0 1 1 0 1 0 7 19 1 1 0 1 0 1 1 0 0 1 6 20 1 0 0 1 0 1 1 0 0 0 4 21 0 0 1 1 0 0 0 0 1 1 4 22 0 1 1 0 0 0 1 0 1 0 4 23 0 1 0 0 0 1 1 0 0 1 4 24 0 1 0 0 1 0 0 1 1 0 4 25 0 0 0 1 0 1 0 1 0 1 4

Note: For this example, density = 0.4, operations per part distribution and parts per operation were uniform. Shaded area was actual output, other information provided for clarity.

89

Cell Part Total Parts Number 0 1 2 3 4 5 6 7 8 9

Total Parts

0 1 1 1 1 1 1 1 1 1 1 10

1 0 1 1 1 0 1 0 1 0 1 6

2 0 1 1 0 1 1 1 0 1 0 6

3 0 1 1 0 0 1 0 0 0 0 i l l l l l l l l l

4 1 0 1 1 1 1 0 0 0 1 H M B & H :5'' 0 0 1 1 0 1 0 0 0 1 • • • • S i

6 0 0 1 0 1 1 0 0 0 0 I l i l l B l l l !

7 0 0 1 0 0 1 0 0 0 0 K l H t M l

8 1 1 0 0 0 0 1 1 1 1 WKBSSM 9 0 1 0 0 0 0 0 1 0 1 WBttBBM

ilia 1Q .0 1 0 0 0 0 1 0 1 0 • -3

11 0 1 0 0 0 0 0 0 0 0 1

12 1 0 0 0 0 0 0 0 0 1 2

13 0 0 0 0 0 0 0 0 0 1 1

14 0 0 1 0 0 0 1 0 0 0 2

15 0 0 1 0 0 0 0 0 0 0 1

16 0 0 0 0 0 0 1 0 0 0 1

17 1: 0 0 1 1 1 0 o o o 4 18 0 0 0 1 0 1 0 0 0 0 2

19 0 0 0 0 1 1 0 0 0 0 • . 2

20 0 0 0 0 0 1 0 0 0 0 1

21 1 0 0 0 0 0 0 0 0 0 1

22 0 0 0 1 0 0 0 0 0 0 1 23 0 0 0 0 1 0 0 0 0 0 1 24 0 0 0 0 0 0 0 1 0 0 1

i n ' - 0 0 0 0 0 0 0 0 1 0 1

distribution and parts per operation were uniform. Shaded area was actual output, other information provided for clarity.

For the combination of factors in tables 17 and 18, cell #16 has operation numbers

3, 4, 7, and 9 (see table 17), and can produce part #6 (see table 18). When this cell is in a

factory, it requires other cells in the factory capable of producing the other nine parts or

that factory is not feasible.

90

Combine Cells to Generate Feasible Factories Program Output

Program #3 uses the cell/operation and cell/part matrices as input to identify all

feasible factories made of combinations of cells from one-cell through ten-cell factories.

The only restriction at this point is that a feasible factory must be capable of producing all

the parts in the part/operation matrix. The number of feasible factories at each factor

level given no restriction on the number of available machines is extremely large, literally

millions. The next program (program #4) imposes an additional restriction limiting the

number of additional machines available per operation and, thus, limits the feasible

factories. Table 19 shows a partial output for the factories capable of producing all parts,

with no machine restrictions, for the information provided in tables 17 and 18. All

factories shown except #26 contain the functional cell (cell 0). The factories that contain

cell 0 have more flexibility in the part assignment strategy. If a part arrives at its

assigned cell and that cell is at full capacity, the factories containing cell 0 have the

option of reassigning that part.

The cell numbers in table 19 correspond with the cell numbers shown in tables 17

and 18. For example, factory 26 contains cells 4 and 8 (see table 19). Cell 4 contains all

operations except 6 and cell 8 contains all operations except 6 (see table 17). These two

cells combined can produce all the parts in the factory (see table 18). Parts 2, 3,4, and 5

must be assigned to cell 8 and parts 1, 6, 7, and 8 must be assigned to cell 4. Either cell

could process part 9. Therefore, there are only two feasible part assignments for this

combination of cells.

91

Table 19. Feasible factories Cell numbers included in factory (reference table 17 and 18)

Factory Number Cell Cell Cell of cells #1 #2 #3

0 ••••111 0 • • i l l M H I 0 B M B

mtm illlllili 0 •••••• lillllll ; 2 . 1 0 IllllHl • l l l i l l iiiiiiiin 0 • • • • • 1 1 1 s a s i i i i ••••111 0 n i M

6 • i r t i i i i 0 IBIlllll !•••!• ' 2 ;• • 0 ••i l i i i

8 • 2 0 8 M i i — l i M i 0 • • i l l

10 H M k n i • • I I I 10 n wmm ••111 M N H 12 wmm • i l i i i 12 13 •llllSlIi 0 13 14 — l i M • I r a 14 15 H r i h r n 0 15 16 •IliMllS! 0 16 17 illlSfcSISI 0 17 18 2 0 18 19 2 0 19 20 • • • • i l l 0 20 21 '2- 0 21 22 m n s M H E 0 22 23 0 23 24 liiifciii! 0 24 25 • • • i l l 0 25 26 2 4 8 27 3 0 l i l l l l l l 2 28 3 0 iiiiiiii 3 29 3 0 l l l l l B l 4 30 •illilll! 0 • l l l i l l 5 31 •iiiiiiii 0 llllllllil! 6 32 3 . 0 l l l i i l l l l l 7

Note: Shaded area was actual output, other information provided for clarity. These data continue until factories with ten cells have all been identified

92

Assign Parts to Cells and Establish Number of Machines in Cells Program Output

This program inputs the feasible factories, part/operation matrices, cell/operation

matrices, cell/part matrices, and processing times to accomplish several final steps prior

to the manufacturing simulation. The main purpose of the program is to make part

assignments to each cell of a feasible factory while accounting for limited available

machines. Each cell must produce at least one part, and the assigned processing times to

each cell in a given factory must be as balanced as possible. Results indicate these

limitations substantially reduce the number of feasible factories to a reasonable number

of factories to simulate. Table 20 shows the final number of factories simulated for

experimental purposes.

Table 20. Final population of factories in experiment Density 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4 Parts/op U U S S U U S S Ops/part U S U S U S U S # cells in factory

1 1 1 1 1 1 1 1 1 2 125 127 537 609 26 26 66 53 3 3367 4508 49946 50796 354 360 2083 1294 4 0 0 0 0 10 122 0 11 5 0 0 0 0 0 0 0 0

Total 3493 4636 50484 51406 391 509 2150 1359 Note: U=uniform distribution, S=skewed distribution

The total number of feasible factories is restricted by the lack of available

machines. The number of cells included in any factory has been reduced from ten to four

because there are not enough machines available to distribute to more cells. This is a

93

substantial reduction because there are millions of possible factories containing five or

more cells.

Analysis of Input Data

Program #1 produces a large number of part/operation matrices depending on the

random number seed used. Each matrix generates a different number of feasible cells.

The inherent danger is that within a combination of factor levels, the quantity of possible

cells formed has a wide range. Programs #1 and #2 ran for 1000 replicates at each of

eight factor level combinations. The purpose of this analysis was to establish a

representative number of feasible cells as shown in tables 17 and 18. Figure 11 displays

the results of this experiment.

The information in figure 11 is critical in the decision of random number seeds to

generate the part/operation matrix. The random number seed could result in a feasible

number of cells for factor level #2 (FL2) of 37 when the maximum possible is 170 while

comparing this to factor level #5 (FL5) at its maximum of 41 cells. This may lead to

spurious results with respect to the available factories at these factor levels. Prior to

establishing the desired number of feasible cells from which to form factories, some

general comments about figure 11 follow.

At the higher factor level for density, 0.4, the distribution of feasible cells perform

in a predictable manner. All four combinations are normally distributed or skewed

slightly at this factor level. At the lower level of density, 0.2, there is a wide range of

feasible cells possible, depending on the initial part/operation matrix. The

94

Frequency

Factor levels Number of feasible

cells created

Factor level FL1 FL2 FL3 FL4 FL5 FL6 FL7 FL8

Density 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4

Parts/op U U S S U U S S Ops/part U S U s u S U S Maximum 132 170 205 209 41 54 70 67

3rd Quardle 100 112 144 139 29 30 48 43

median 82 89 127 121 26 26 43 38

1st Quartile 67 67 105 100 24 22 39 33

Minimum 37 37 57 51 19 14 23 20

Average 83.4 92.0 124.8 121.4 26.2 26.3 43.6 38.4 Std Deviation 9.5 10.1 11.9 11.7 5.2 5.2 6.7 6.3

Figure 11. Range of feasible cells created in 1000 replications of programs #1 and #2

distributions are extremely irregular. However, the median and mean of feasible cells

possible for all eight-factor combinations are very close indicating at most a central

tendency. With this indication, the random number seed for program #1 to create the

part/operation matrix for each factor level combination was selected to produce the

median number of cells indicated in figure 11.

Two other interesting results were obtained while investigating the range of

feasible cells possible. The average number of parts produced by feasible cells and the

95

average number of operations required by feasible cells were remarkably consistent

across the eight factor level combinations.

The average number of parts produced by feasible cells was between 3.2 and 4.6

for all eight combinations (see figure 12). Few cells can produce a high number of parts

and only one cell can produce all ten parts. The factor combinations with uniform parts

per machine appear more jagged and unpredictable.

20 Cell is

Frequency io

Factor level

Figure 12. Part capability of feasible cells

7 Number of parts a cell is capable

of producing

The average number of operations available in the feasible cells varies between

6.7 and 7.7. The distribution of operations in feasible cells follows approximately the

same distribution across all factor combinations (see figure 13). The range of operations

per cell for the higher density level is essentially between 6 and 9 operations per cell,

while the lower level is between 5 and 9 operations per cell.

96

Frequency is-

Factor level

Figure 13. Operation capability of feasible cells

Number of

operations

a cell contains

Manufacturing Simulation Data Analysis

In appendix A, table A1 exhibits an example of the simulation output.

Performance measures throughput and flow time were the main statistics analyzed. A

large amount of other data was collected to aid in the analysis of factory performance.

Table A1 lists this data.

A correlation matrix was calculated for each combination of factor levels (FL1

through FL8) on statistics collected for all factories simulated (see appendix A, tables A2

through A9). The correlation values revealed several interesting observations. The

number of machines in each factory was not significantly correlated with either flow time

or throughput for any of the factor combinations. Flow time and throughput were not

significantly correlated to the number of transfers allowed during the operation. The only

two variables not significantly correlated with any of the other performance measures

within each factor level were the number of transfers and the number of machines

97

available. The correlation between actual cellularization and throughput increased in

magnitude from an average of -0.24 at a 0.2 density level to -0.46 at the 0.4 density level.

While a similar difference existed in the correlation between actual cellularization and

flow time, it was not substantial. A general examination of these eight correlation

matrices reveals correlation values that would be expected given the nature of the

measures other than those just discussed.

Table 21 presents information related to the best performing factories in each

factor level based on flow time and throughput. The performance of the functional (one

cell) factory is listed for reference. It is interesting to note that the functional factory was

the top performer in throughput for only one factor level (density 0.2, skewed

operations/part distribution, uniform parts/operation distribution).

Analysis of Samples using Flow Time and Throughput

The research questions deal with the relationship of the part/operations matrix as

defined by density, parts/operation distribution, and operations/part distribution and the

resulting factory performance. In order to make valid comparisons across factor levels,

pure flow time and throughput were not compared. The ratio of each measure relative to

the actual factory performance in the associated factor level was used as the dependent

variable. Two different levels of analysis were performed on each parameter. First, based

on the parameter of interest, the observations within each combination of factor levels

were sorted. A systematic sample of these sorted factories was taken on one level of

analysis. The best factory was included in the sample and every k-th factory after

98

<D a o

SH

T?

0

is4

DO S3

I CS O

X3 CO cd

JD T3 > jy

4 o 4-* cS M-H cl cS <U td <L> o C3 cS <2 S3 OH

b o +-> o ,cs +-» c/j <D CQ

<N <D I f—1

Actual Cellularization

oo co O o> Ti-ro o

O o o d O V) ©

o © ©

m o o

(Nl m o

00 SO o o o os m d

OO m Tf d o OO •rt d

Tf SO d

so rN oo d CN SO SO d

oo ro d <N in d

Utilization r-00 Tj-©

Os 00 Tt © o oo sD o

00 Tf © Tf <N r~ © <N r-o

00 m o ON m SO o

m m d r-SO d

rN d

m TJ-d ON m m d

"<fr in d co so m d

ON oo in d Percentage of minor setups

ro (N 00 o 00 ro 00 o

Os SO O OO 00 SO O

o co so o r-SO o

Tf 00 SO o

r-NO o 00 o oo d

s 00 d m so OO d

ON d

rN rf so d ON SO r-d

«n SO d ON SO SO d

Rejects (parts) o o o o <N o o o o o o o o o o o

Transfers (parts) so

Os o ro

Tf 00 o rf

o ON sO rN t Tf ON rj-«n in oo so

m m SO o o o o o o o o

Setup Time

(minutes) CO o rN

(N O (N <N O SO fN so

(N SO SO <N

p Tf <N Os SO (N

p s 00 oo p <N rN d rN "<r d cn

oo in (N CO OO <N CO

ON rN Maximum

work in process (parts)

in NO

co <N 00 SO

r-s

fN rf in r» <N m r-SO m rs

in SO ro SO m oo m

<N m TJ-tn Os ON CO Os SO Os o o

Work in Process (parts)

a ro o 00 co ro <N r-

ro oo in m 00 m 00 r- s CN

o m <N Os rs ON

(N cn so

ON in CO SO rN SO

Maximum Wait

(minutes) 00 £ ON

m <N VO <N CO Tf IT) Os

m in ro O vo o rf oo un

oo m R E m

m Tt <N

C*~i m i> T)-m

Os 00 OS 00 m

< N Os r-V O R A

VO in SO CO rN SO O N OO S O

T F m r-T F " 3 -00

TT in Tf

Maximum Queue (parts)

© m (N O m ON

3 oo o m r-

S O in © o S O S O

<N r-<N o o •*f

zz ZZ! CO in m oo

Queue Length (parts)

m ro rt

3> Tf ro

o co m © OO o ro (N

o m in m

m Os •n m

oo Tf in rf so

o o m sd m

ON os Os OO m rn TT oo o d

(N o d

cn Os d

so r-d

o ON d

ro rf ro d Time in Queue

(minutes) co © o 5 so

o so r-so 00 ••st

r-SO "t VO o s r-

SO as (N m <N SO

r~-rn m

m oo so <N rn 00 ro c-

00 oo r-o co

Throughput ratio to functional "St <N O O

o o p so co p

rr m m Tf (N in p r-

Tf p

o o p o p SO Os OO d o p o o o p o p

<N O O

Throughput (parts) Tf o ro

r-o Tf

l*-» in Tf

o CO ro

m (N SO Tt

00 in Tf

m (N m m NO m rN m

Tf r -Os m

Tf OO oo m ON 00 so <N

Os oo SO rN o ON SO <N

oo oo so <N

oo oo so rN ON CO SO rN

Flow time ratio to functional TT "st r-in

r-ro O ro o o p Tf fN ro

rn (N O

Os 00 m <N so in o o <N

r-r-

Os r-Os d o <N as d

SO 00 d ON oo d

s Os d o oo d

CN rN ON d Os OO so d

Flow time (minutes)

O O in ON

oo sO Os m <N <N co

Os co so Tf

O in oo o <N r-oo r-~

O as Os <N m so

sO SO

oo o oo r-r-<N

•n r-~ rN Tf ON m

f-«n m r ON m

OO OO m

Number of machines

O "sD in NO

oo SO SO o\ r-00 m O m oo cs m

m SO in so SO (N O o rN o

OO 00 Number of cells co co - ro <N <N rn (N fN m CI ro CO co ro

Factory Identification

Number o co rf

oo as so o -5-

r- SO oo oo m OO ro »n m m o «N

<N r-rr» m Ol

S O r-CO

r-o rf CO ON r-

Tf OO r-

Factor Level J

UH

rN J UH

co J UH

J UH

m J U~

S O J UH

r-UH

oo J fcu J UH

(N J U-—1 -J U*

m J fcu so J l-u

r-J U-OO hJ u-

Sorted by throughput Sorted by flow time

99

was selected where k-(total factories in sample)/30. The purpose in this sampling plan

was to insure selection of an equivalent cross section of factories across factor levels.

An Analysis of Variance was performed on the combined total sample of 240 factories

all eight-factor levels. The second level of analysis selected the top 30 factories based

flow time and throughput (separate samples) and regressed the other variables on flow

time and throughput. All conclusions were drawn using a = 0.05.

Table 22 presents the ANOVA table with the flow time ratio as the dependent

variable. The parts/operation distribution and the interaction between density and

parts/operation distribution are significant. No other effects are significant. Since

interaction effects are significant, interpretation of the main effects is limited.

Table 22. Analysis of variance for the systematic sample sorted on flow time S o u r c e SS Df MS p SiT~

Density 26.864 l 26.864 0306 0.580

Parts/op 3528.322 1 3528.322 40.241 0.000

Ops/part 11.129 1 1 U 2 9 0.127 0.722 Density* 24,6.275 , 2 4 1 6 . 2 7 5 2 7 . 5 5 g

0 ' 5 7 ' 0 1 5 7 0 0 0 2

4581 ' 4581 0052

SS 117569 ' ,17-569 '•*' Parts/op

in

on

Error 20341.483 232 Total 55396.709 240

87.679

100

Table 23 presents the ANOVA table with the throughput ratio as the dependent

variable. All three factors and the interaction between density and operations/part are

significant relative to the throughput ratio. Since interaction effects are significant,

analysis of the main effects is limited.

Table 23 Analysis of variance for the systematic sample sorted on throughput Df MS" F Sig_

ouuitc Density 0.414 1 0.414 26.759 0.000

Parts/op 0.0869 1 0.0869 5.608 0.019

Ops/part 0.0644 1 0.0644 4.155 0.043

Density x parts/op

0.0276 1 0.0276 1.783 0.183

Density x Ops/part

0.117 1 0.117 7.527 0.007

Ops/part x Parts/op

0.0036 1 0.0036 0.023 0.879

Density x Ops/part x Parts/op

0.0002 1 0.0002 0.01 0.919

Error Total

3.593 183.985

232 240

0.0155

The set of samples using the top thirty factories were then analyzed using a

stepwise regression procedure regressing variables which had been collected during the

simulation runs on flow time and throughput, independently. A correlation analysis

between the top factories sorted by flow time indicated a high correlation with the

number of entities arriving, throughput, maximum work-in-process, maximum queue,

101

average queue length, average time in queue, and work-in-process. The correlation of

these variables to flow time is expected and serves as some validation of the model. The

flow time ratio was regressed on these seven variables using a stepwise procedure with

entering probability < 0.05 and removal probability >0.10. The resulting regression

equation was:

(4-1) y = _25.891 + 0.0414*,-0.00272x2 +0.00452*3 +0.00210X4

where y = flow time ratio xi = average queue length (parts) X2 = average time in queue (minutes) X3 = maximum work-in-process (parts)

and X4 = throughput (parts).

For this regression, the R2 = 76.6%. Since the dependent variable is a proportion with

values close to 1.0, the coefficients tend to be extremely small in magnitude. This is

acceptable since the objective is to predict the effect of the independent variables on a

cellular factory relative to a functional factory.

The following result is obtained when the three factors are included in addition to

the original variables in the previous regression on flow time ratio.

(4.2) y = i .011 - O.lOlx, - 0.0696X2 - 0.076x3

where y = flow time ratio xi = density X2 = parts/operation

and X3 = operations/part.

For this regression, the R2 = 78.4% and none of the performance measures previously in

the equation were included by the stepwise procedure. Equation 4.2 shows the that as

any of the three factors increase to a high level, the flow time ratio declines.

102

A simil&i analysis using the throughput ratio uses the number of entities arriving

at the system, the maximum queue, the number of intercell transfers, the average queue

time, and the flow time in the initial stepwise analysis. The regression equation is:

( 4- 3 ) y = 0.603 + 0.00003133x

where y = throughput ratio

x = number of arriving parts.

The R2 = 0.189 shows this model is not strong in the assessment of throughput

performance. However, it is interesting to note that none of the other variables entered the

model.

The addition of the factor levels as variables to this regression substantially

changes the regression equation.

(4.4) y - 0.313+ 0.349x, + 0.00004459x2 +0.01846x3

+ 0.000005891x4 - 0.000034x5

where y = throughput ratio xi = density X2 = number of arriving entities X3 = operations/part X4 = number of intercell transfers

and X5 =maximum queue.

This model has an R2 = 67.7% which is a significant improvement from the previous

model. The stepwise procedure included two factor level variables in the model, X| and

x3. Therefore, based on equation 4.2 and 4.4, it appears the factor levels are important in

predicting the performance of the best factories.

The relationship between cellularization and utilization was investigated with the

three factor levels to complete the data analysis associated with the research questions.

Using the systematic samples, analysis of variance was used to examine three different

103

relationships. The factor effect on cellularization was divided into two types of

cellularization, actual and planned. These differ in that planned cellularization is based

on assigned production hours prior to the simulation and actual cellularization is a result

of the production hours in cells since the simulation allows intercell flow if required. The

effect of the factors on utilization was also examined.

Table 24 presents the analysis of variance table for actual cellularization for both

flow time and throughput samples. While the density is the only significant effect on

actual cellularization for throughput, the three-way interaction is also significant for flow

time. The other factor levels have no effect on the actual cellularization.

Source s s df MS F Sig

1.9020 1 1.902 64.760 0.000 0.01072 1 0.01072 0.365 0.546 0.000003 1 0.000003 1.248 0.992 0.0075 1 0.0075 0.256 0.613 0.0367 1 0.0367 1.248 0.265 0.0988 1 0.0988 3.364 0.068 0.140 1 0.140 4.755 0.03 6.815 232 0.0294 66.560 240

<L> S £ _o E

Density Parts/op Ops/part Density x parts/op Density x Ops/part Ops/part x Parts/op Density x Ops/part x Parts/op Error Total

3 & bO 3 O J3 H

Source SS df MS F Sig

Density 1.433 1 1.433 41.455 0.000

Parts/op 0.0124 1 0.0124 0.358 0.550 Ops/part 0.00358 1 0.00358 0.104 0.748 Density x parts/op 0.00257 1 0.00257 0.074 0.785 Density x Ops/part 0.0302 1 0.0302 0.874 0.351 Ops/part x Parts/op 0.0115 1 0.0115 0.333 0.564 Density x Ops/part x Parts/op 0.123 1 0.123 3.558 0.061 Error 8.02 232 0.0346 Total 67.230 240

104

A similar analysis was performed for the factor effects on planned cellularization.

The results are notably different from those for actual cellularization. While density

remains significant on both flow time and throughput samples, the throughput sample

includes the parts/operation distribution and the interaction between density and

parts/operation distribution (see table 25). The flow time sample includes density,

parts/operation distribution, the interaction between parts/operation and operations/part,

as well as the three-way interaction term.

Source s s df MS F Sig

4.568 1 4.568 81.271 0.000

0.425 1 0.425 7.569 0.006

0.00260 1 0.00260 0.046 0.830

0.0218 1 0.0218 0.388 0.534 0.041 1 0.041 0.730 0.394 0.426 1 0.426 7.577 0.006 0.270 1 0.270 4.811 0.029 13.041 232 0.05621 174.142 240

<D .§

£ E

Density Parts/op Ops/part Density x parts/op Density x Ops/part Ops/part x Parts/op Density x Ops/part x Parts/op Error Total

Source SS df MS F Sig

Density 5.229 1 5.229 87.036 0.000

Parts/op 0.417 1 0.417 6.946 0.009

Ops/part 0.0162 1 0.0162 0.269 0.605

Density x parts/op 0.249 1 0.249 4.150 0.043

Density x Ops/part 0.00762 1 0.00762 0.127 0.722

Ops/part x Parts/op 0.0722 1 0.0722 1.203 0.274

Density x Ops/part x Parts/op 0.130 1 0.130 2.168 0.142

Error 13.939 232 0.06008 Total 164.084 240

3 £ OA 3 o

H

105

A correlation on the systematic sample was the final step in the analysis of the

data provided by the manufacturing simulation. The purpose of the examination was to

identify the relationship between the performance measures and the factor levels (see

appendix A, tables A10 and A11). For the factories that performed well on throughput,

there was a high correlation between throughput and the number of entities arriving and

the number of parts rejected. However, there was no significant correlation with the

number of machines available. For these same factories, flow time was highly correlated

with the work-in-process and queue statistics. For the top flow time factories, the same

relationships hold. The factor levels have a very low correlation with the throughput or

flow time samples.

Poisson Analysis Results

The Monte Carlo simulation was run at three time lengths equal to 50,100, and

400. The nominal alpha levels were established as 10, 5, and 1%. Nine different

distributions were examined. The first three consisted of exponentially distributed

interarrival times with varying means. The remaining six were not exponentially

distributed. The results are shown in table 26. The first three distributions should have

values close to the nominal alpha value in the first column. For the remainder of the

distributions, the value represents the power of the test to identify non-Poisson

distribution. The nominal alpha is close to the empirical values, especially for higher

sample sizes and the power of the test is adequate for many of the distributions.

106

Table 26. Nominal significance levels for runs test on Poisson process

r/} C/3 ^ l i e

•I T n - | ^ | 1 § ^ g "3 "3 3 * w c?< o cq n§/T .H ts *+3 ^ ^ - s ^ g _ w <u i M Ch fi ?? "O S S £ C S fi r j u

oJ u u y 22 u c 1-1 ° o 2 o S c ^ ~ 6 ^ ^ S? *1 .2 "I .2 | -c

03 Cl, o O O <U (N <+H

100 400

100 400

100 400

inen

tial =

0.2

5 IT) ©

1! 13 es <D a

m

3 15 <L> £ O

Ord

ered

exp

onen

tial

= 0

.25

V O. X PJ

o £ w

o* X W

Ord

ered

exp

onen

tial

= 0

.25

10.7 8.9 10.7 56.1 8.3 10.3 9.7 63.6 10.6 9.8 11.4 33.3 5.0 4.7 7.0 50.8 4.7 4.7 4.7 59.2 4.8 4.4 5.6 26.8 0.8 0.8 3.1 41.3 0.7 0.9 1.6 50.5 0.7 1.0 1.4 16.8

£ a cx a g< *g o *3 'S ^ o *o *S h2 w g $ £j w W O II ^ P S Z O . ^ O h Z >

10% 50 10.7 8.9 10.7 56.1 26.6 100.0 19.8 61.2 26.3 41.8 100.0 56.7 61.2 63.6 90.1 100.0 100.0 75.2 90.9

5% 50 5 0 4 7 7.0 50.8 15.0 100.0 11.7 50.8 17.2 28.6 100.0 45.3 50.0 59.2 83.7 100.0 99.9 66.2 82.9

1% 50" 0 8 0.8 3.1 41.3 4.6 100.0 4.0 31.0 4.3 10.7 100.0 25.0 32.0 50.5 61.5 100.0 99.9 '50.1 65.4

Summary

This chapter reviewed the data analysis pertinent to analyzing the research

questions. Simulated factory performance measures, flow time and throughput, were

analyzed using a three-way factorial experiment. The performance measures of the top

thirty factories for each performance measure were analyzed using multiple regression

analysis. A Monte Carlo simulation study was conducted to validate the effectiveness of

the proposed test procedure to assess the appropriateness of the assumption of Poisson

arrivals. Statistical tables generated using SPSS are available in the appendix for more

detailed analysis.

CHAPTER 5

DISCUSSION OF RESULTS

This dissertation conducted an intensive simulation experiment to investigate the

relationship between product and process structure and factory performance. It

introduced a new cell formation method using the product and process structure as input

to determine the optimal cellular factory based on substantive performance criteria. In

some cases, the new method may demonstrate that a cellular factory is inferior to a

functional layout given the same initial conditions. A distinguishing attribute of the

proposed method over the traditional cell formation methodologies is its ability to

identify when a functional layout is superior to a cellular configuration.

In addition to introducing the MCA methodology, a 23 full factorial experiment

was conducted to examine the relationship between the initial conditions used by the

majority of cell formation techniques and factory performance. The experiment resulted

in several significant findings relevant to manufacturing strategy selection that have gone

uninvestigated.

There are two principal contributions of this work. First, previous research

typically has not associated factory performance criteria used in manufacturing strategy

selection to the technique used to layout the factory. The connection is often lost in

layers of strategies and budget constraints. The proposed method effectively

accomplishes this connection. Second, the outcome of the experiment supported the

108

relationships discussed in the theoretical model. Since these relationships were identified

through an extensive literature review, the conclusions serve to bolster the existing

research in the area.

The rest of this chapter presents conclusions of the research questions, the

limitations of the study, and the intended extensions of this stream of research.

Conclusions

The Analysis of Variance tables (see tables 22 and 23) are summarized with

reference to throughput ratio and flow time ratio (see table 27). The ratios were

calculated relative to the functional factory performance for both throughput and flow

time to allow fair comparisons across factor combinations. Significance was concluded

for a = 5%. This information is used to draw conclusions for research questions #1

through #3.

Table 21. Summary of significant findings for throughput and flow time ratios ~ Throughput ratio ~ Flow time ratio

Density x

Process Structure x x

Product Structure x

Density x Process Structure x

Density x Product Structure x Process Structure x

Product Structure Density x Process Structure

x Product Structure

109

Research Question #1

Is there a significant relationship between the density of the part/operation matrix and factory performance as determined by throughput and flow time?

The density of the part/operation matrix is an indication of the inherent

complexity in the product structure for a manufacturing firm. Higher densities imply

more operations required by parts. As the number of required operations increase

throughout the factory, the potential for negative interaction within the factory increases.

Parts cross paths more often interfering with each part's progress and inefficiencies in the

system flourish.

The findings of this study suggest that the effect of density on factory

performance is dependent on the performance measure used. Density had an affect on

throughput of a factory, but was not a factor when considering flow time. As density

increases, throughput decreases due to increased processing complexity and associated

increase in interaction. Flow time is not associated with density because the operational

capacity established before a physical layout includes a capacity cushion. This capacity

cushion eases the impact of part interaction in the factory for higher density levels.

Research Question #2

Is there a significant relationship between the product structure represented by the operations/part distribution and factory performance as determined by throughput and flow time?

110

The product structure is a function of the process flow characteristics in the

factory. This study examined a balanced system in which all parts had approximately the

same requirements and an imbalanced system in which some parts required more

operations and others less. The latter system represents a factory where parts requiring

fewer operations could get through the factory faster if not for the higher work content

parts. Product structure did not significantly affect flow time. An explanation for this

may involve the ability of cells to ease the congestion in complex factories by assigning

the low work content (low operations per part) parts to independent cells. Possibly, the

one-cell functional factory was affected by this factor, but this experiment did not single

out the functional factory for this analysis.

The product structure did have an affect on throughput. This is consistent with

expectations in that the more balanced the operations required, the better the factory is

able to balance the work content across all cells. By balancing the work content,

operations are better utilized and able to recover from minor fluctuations that may occur.

Research Question #3

Is there a significant relationship between the process structure represented by the parts/operation distribution and factory performance as determined by throughput and flow time?

Process structure significantly affected both flow time and throughput. This is

consistent with the theoretical model. Process structure is an indication of operation

capability. As operations are able to process a variety of parts, routing complexity

through the factory increases. In addition, the operations actually become less divisible if

I l l

there are some operations that can only process a few parts; this has a negative affect on

both flow time and throughput. In essence, the less capable machines cannot be

separated from the more capable machines in cells. This limitation restricts the ability of

a factory to take advantage of cellularization.

Research Question #4

Is the proposed test procedure for identifying the assumptions of a Poisson process for arrival times statistically valid?

The regression analysis indicates that the factor combinations do have a

significant effect on the performance of the best factories based on throughput and flow

time. The regression for flow time explained 78.4% of its variation with density, product

structure, and process structure in the model. Even when other variables were included in

the stepwise regression, the other variables did not enter the model. Therefore, the

factors have a significant effect on the flow time performance of cellular factories. Also,

all the coefficients in the equation are negative. So, as the factors increase to the high

level (density = 0.4, skewed operations/part distribution, skewed parts/operation

distribution), which implies a more complex processing requirement, the flow time ratio

decreases. When the factors were not included in the stepwise regression, but other

performance variables were regressed, the resulting regression also had a high explained

variation (76.6%). The variables included in this model were average queue length,

average time in queue, maximum work-in-process, and throughput. The association

between the queue statistics and the maximum work in process is expected. As work in

112

process increases, given a constant number of available machines, the amount of work in

queues also increases. Given the other variables in the model, as the average time m

queue increases, the flow time ratio decreases. The explanation for this is that the flow

time ratio is relative to the functional factory which is influenced less by work m process

than cells that divide the work and specify which operation can do which. There may be

parts in queue in the cellular system that could be processed if an available machine in

another cell was used. In a functional factory, this problem would not arise.

The stepwise regression of throughput ratio on all the variables except the three

factors resulted in a very week model. When the three factors were included in the

stepwise analysis, this condition changed. Two factors, density and product structure,

entered the model along with the number of arriving entities, intercell transfers, and

maximum queue. The number of arriving entities are of little interest since factories

generally do not have control over this variable. The intercell tranfers coefficient is

positive indicating throughput increases as intercell transfers increase, given the other

variables in the model.

Analyzing the top factories at each combination of factors (see table 21)

introduces some other characteristics of the best performing factories. Characteristics of

top factories based on flow time included a higher number of cells, lower throughput,

minimal queue time and length, very low work in process, and no cell transfers compared

to those factories based on throughput. In addition, the actual cellularization of flow time

factories was much higher than throughput factories. Only one of the throughput top

performing factories and none of the flow time top performing factories rejected any

113

parts. Therefore, factories that have a higher number of specialized cells are more

efficient at producing efficiently, but do not produce as high a quantity m the same period

of time. Throughput benefits from transferring parts between cells when necessary.

Research Question #5

Does the modified runs test effectively identify the existence of a Poisson distribution of arrival times?

The modified runs test successfully identified all the Poisson distributions for the

medium and large process time lengths. For the small1 process time length, it was not

effective at when the mean of the Poisson distribution differed from the mean of the

comparison'distribution at the 1% nominal significance level. This indicates that as the

length of time sampled decreases, it is important to estimate the mean of the actual

process as closely as possible.

The power of the test for identifying non-Poisson distributions is very good for

long process time lengths. As the time length decreases, the power of the test to identify

non-Poisson distributions decreases. Even at small time length samples, the test is able to

distinguish between some distributions extremely well, but overall it weakens

substantially. This is consistent with many statistical tests given small sample sizes.

Factor Interactions

Flow time was not significantly affected by density, however, the interaction of

density and process structure was significant on flow time. The reason for this relates to

114

the discussion for research questions #1 and #3. The density issue is resolved in the

initial capacity analysis before physical layout. However, when combined with the

process structure, the interaction of a large number of parts requiring operations that are

imbalanced between high and low capability operations becomes significant. The

operations become inseparable and are required by a higher number of parts in the

system, which affects flow time. No other interaction terms were significant for flow

time.

Density and product structure significantly affected throughput ratio, however, the

interaction between density and product structure was significant also. As parts requiring

more operations and the number of operations required generally increases, throughput

declines. More conflicts arrive especially when the operations become linked by parts

requiring several in one cell. The parts that do not require many operations have

difficulty flowing through the system as it is processing higher work content parts.

Other Conclusions

Higher density levels decrease the number of cells that can produce at least one

part, but increase the range of feasible cells substantially. Process structure has a similar

affect, whereas product structure has minimal affect. This indicates that as density

increases, there are fewer factories to investigate depending on other imposed limitations.

The number of parts a cell can process and the number of operations in a cell both

averaged between six and nine across all factor combinations. This is an interesting

conclusion since there were some parts in the skewed product structure that required only

115

one operation and the maximum number of operations a part may require was six. This

indicates that cells with a variety of operations tended to result no matter what the factor

levels were.

Density and process structure had a tangible influence on the number of feasible

factories formed in this experiment. The high-density level and uniform process structure

reduced the overall number of feasible factories that could be developed. Density

decreases the number of feasible factories because as the number of operations increases,

it is either forcing more operations per part or parts per operation. Either situation will

make the operations less separable and results in fewer cells from which to derive

feasible factories. As the process structure skewed, some of the parts only require a few

operations, increasing the number of cells that can process at least one part. Hence, there

are more cells available to form factories.

A stepwise regression was run to determine the important relationships for the

higher performing factories. Of particular interest is that density was the first variable

that entered the equation when trying to predict flow time (see equation 4.2). This factor

was insignificant when examined in the factorial experiment. An explanation is that this

factor affects higher performing factories. Process structure was also a significant factor

on throughput in the factorial experiment, but did not enter the regression equation at all

when predicting throughput. This may indicate the high performing factories are not as

affected by the process structure as the average factory.

116

Limitations

The simulation experiment was conducted to maintain a high level of validity for

the study. A power of 80% was used in the factorial experiment to establish the

minimum required sample size. Since, the simulation study controlled the reliability of

treatments and measures, no environmental influences were in the study. The simulation

study was conducted so the assumptions of the models were valid. The use of common

random number streams in the experiment controlled for bias in the data.

Internal validity of the experiment was also controlled for. The computer

simulation was verified through a series of stages to insure the gneration of reasonable

data. Several secondary variables were monitored during the simulation runs to protect

against unknown relationships from affecting the factors of interest.

A limited number of parameter values were selected for this study.

Generalizability of the experimental results may depend upon other constructs not

included in this study. The focus of the simulation study was to gain insight into the

relationships that existed between variables and factors of interest. The validation step

during model building process controlled for inconsistent behavior of the data. Since

only one form of measurement was used to examine the relationships proposed in the

theoretical model, there is a possibility that either inadequate construct definitions or

confounding of constructs may affect the generalizability of the study.

Finally, the issue of external validity is always a major consideration associated

with simulation. However, two elements work in favor of this study. An experienced

manufacturing person with some background in its use wrote the simulation. Also, the

117

model was presented to manufacturing managers and revised based on feedback from

these meetings. The proposed method was designed to be used by practitioners for

developing cellular layouts using real data. In spite of the lack of real data during the

experiment, the fundamental relationships remain the same.

Future Research

Perhaps the best outcome of this dissertation is the opportunity to expand it and

use it as the basis for other research. The manufacturing simulation itself is a powerful

tool able to be modified and tailored to many manufacturing research projects. While the

primary focus was on a new method for cell formation, other research will proliferate

from this program.

Of main interest is to find some real applications to apply the new method. By

introducing real world data into the model, the new method can be validated and applied

simultaneously. In addition, with the existing program, there is a possibility of a

longitudinal study taking a functional factory and developing a cellular factory over time

to test the theoretical relationships.

A mathematical representation of cellular manufacturing could be investigated.

This would support further theoretical development and definition of the theoretical

relationships examined in this dissertation.

A study of particular academic interest is to program several existing techniques

to determine if they identify the best factory given the part/operations matrix as input.

118

The program from this dissertation can be used to identify where the traditional technique

scores on several factory performance measures.

Finally, a survey of manufacturing managers to determine performance measures

of specific interest to them combined with the current study could be used to develop an

objective function with multiple performance measures. This would aid in determining

the best factories on more than one dimension at a time as done in this study.

APPENDIX A

STATISTICAL TABLES

120

*0 <D t S tr> o q\ O ^

Cd f-H CD s

V->

£ o

53

0> 0

1 §

> tw O V3

*00

"c3 C <

< J& " • §

H

^ — o

4-» 1)

8 I 1 § ° b Z £

<D O C3 ce o s "S #W) GO

§ 1 <L> 3 S cr ^ 00

xt

H ^ X K o g o> C £d a S 3 >> 5 CT< H 0 0 c/3

o o o

m 00 o

o o o

m VO O

Os OS OS

O i/~) o

VO <-< uo -H O <N d d

VO vo r -00 o CN r-H m (N r—* d d o d m m

oo <N CN i—i O UO "3-in o o CO

d d 1—1 <N

o o © d

o o o

o 00 ir>

O O o d

(N <N r -

o o o

vo VO ON d

oo d

oo ^r <N

VO vo T-« 00 o "3-*-"I CO <N d d d CO CO

r -<N 00 CN (N r-H »n o «r> r f

»ri o O co i> o o CN

oo CN co d vo ON OO <N

"3* VO CO VO <N

<N <N co oo CN m co

Os CN

in r -<N VO t-H Tf (N

in

d

—< OS oo vo tn »n

OS r -vq i> oo

CN co (N

O "3-<N

Os co CM

00 Tf (N Os t - Os CO Os T—1 CN VO <N <N r - ID 00 VO oo O 00 CO 00 CO '—* (N uo !> CO d vo oo VO d l> I VO VO

CN (N F-H r—< f»4 •"Sf OS Os *r> Tf C-4 CO CO oo CO <N o in vo CM (N <r> CN

Q-<D O

H 55 §

a

CU o 55 H C* < Oh

H <

a, oo PH O

cu O 5) H Dd < Cu X

H E73 £ w Q

H 0^ < a, 5) Ou O x > H oo 2 w Q

tS

55 a, O x 0h o 55 H P < ou

H P< < Ph 5) a. O x Ph O tn H od < a< x >< H So

w Q

§ w o H

o H T3 0) o Q> fc o O

00 O

un <N ^ © O „

5 &

« ts bJO 3 d

3 < h3 ^ £ m 3 CN 6 O S ii O CN

U Pi

ca

121

z £

O ON O ON O ON

O

m 0 0 m o m (N s o o o s o i n <N t >

d d d d

m *-* m i n o o d d

s o m m

d o SO

ON 0 0 i n i n o m r - ; SO »—;

s o i n r f <N

m r -o o f N l > i n

m o <N «—• o p d d

u *

cd •+-»

c u

OX) 3 o £ <2.

<D o

. 1

c3 >

<4H O

CO

1 3 c

<

fN <

a>

H

EU <+h o = ° 2 <u c cd a £ 3

r5 cr H 0 0 <Z3

o o o

o o o

ON

o d

c n Tf o

r n r » ON ON o o o r - r-H

o 0 0 ON d d d d

SO i n m d o s o

ON OO i n c n c n o i n O m o o (N <N r-H

r - SO •—i i n O o SO i n r—J r > d d (N

r-H r-H Tf o 0 0 »—H

SO d ON r »

d

r - SO (N i > o o m SO t—H SO r - T-H o o s o <N S o o O

d d d

s o o s o m o o o

d

i n ON * n 1—< O O o

ON

IT) ©

d

(N O c n ^ f N <N

ON c n (N

O

d

^ t-~ s o (N r -o o *—< o o c n s o <— s o r t s o r > *—

£ d © 8 S o

s o o SO c n o o o

in m in rf ON ON oo o in in ON rn o o

rn rn 00

n-

o d

Qh <l> o

H So £ w Q

p -

O

5 5 H Pc* <

Ou

H c * <

OH 0 0 PH O

a. O

5 o H P^ <

a . X

>*

5 ? £ w Q

c2 g CO PH O X

H

c75 £ w Q

f2

o o a , O x

PH O

c/5

S *

H P£i

< PH

0 0 OH o

X

OH o

I O H

< PH X

> H

CO

Z L-H o

w fc: o Q w H

- 3 o

H

"O CD 4-» o <u fc o

U

O

IT) r-H

® o

2 &

S - 8 « t o 0 0 3

. s ^

3 ^ w v o

3 J~l . 0,0

S II O <N

O Pi

O T 3

122

j

3

C/3

£

< 8 x

J <4-1

s

J D C+H

I d

£ CS o

• p«4

" 5 f H o>

fcj o o

J H 3 0 3

• rH

J s c ^ o

c5

^3

w O

D oo

D C/3 C

C O

c

J h ? -

r«J 03

H O ,

0 )

O h ' o w

t ;

g

—I

© NO © m © co

" - 1 ©

© ON ON © r - <N © © <—<

© ©

co co NO <N © ©

rf NO © © ©

o

—I ©

o NO m O ON » O 00 O —I © ©

<n ON © r-co <n —< -h o m ©

in O © ©

O ON O Tt- On <N ON o ON © m fS — ' -r O OO O <—; O «n ©

~ o — ' o o o ©

<N On o

© r - On Tf —< r - (N © 00 OO 00 in <rm+ Tf* © OO ON 00 © <—1 in

—i © © © © © ©

o O oi o r -

©

*=t <n

© <N NO © r-~ OO <N © ID Tf r - r- NO © m m in IT) <N

© © © © © ©

—h so co CO rf 00 oo co —«

© © ©

l> r -o

© Tf rs ON Tt r- © m © m OO m ON m OO <N © © © m »—I fN •—1 rf »—t

© © © © © © © CD

o o o

r» NO © ON r-~ © r - <N iri m IT) OO CM OO © OO ^O rf Os MD OO VO oo m © rf

© © © © © © © © © ©

© © ON OO r - m TJ- NO NO ON »RI © © <N r - rr VN ON ITJ m Ti- ON © MD 1—4 (N V~i »r» VL in *S~> •—11 ro co

© © © © © © © © © © ©

00 <N NO 8 . O NO in

— " o o

« m oo m

,-h rO m

«n on (N -H ON CO m <— O

ON O »—H rf rf O

o o o o

© OO ON 00 <N 1-H NO CO ON © Tf © r - 0 0 © rf CO m © in VO On © Tt On NO o

—J © © © © © © © © 3

©

m <N co r- co o o © ©

NO r -tn no Tf —H

© o

© *-* © co CO VO co ON NO m <N fN CO © (N NO © ON 00 NO rf NO fN in m m Tf (N NO NO © NO in Tt- NO © OO t— NO so ^o NO co © Tf •—<

© © © © © © © © © © © © © © ©

© r- —< © © Tf © rf On

^ O O

m —H Tt ©

r - CO r - 00 m rsi m NO © CO r- co © •n © m in «n so CO

ON o —i 00 m NO »n NO <N © CO r-4

© © © © © © © © © © © ©

© —I ©

.£• D

- £ * 2

3 X .5

£ - £ £

rf vo -h r~. r- On © ©

P ^ CO ^

r- ON © 1-H © r~ © T-* © co NO NO co ON <N r- 00 00

NO NO m NO CO in r - o\ 00 ON

© © © © © © © © © ©

© VO ©

©

1—1 rf r» ON NO 00 NO m —< OO co OO On fN NO CO Tf Tf © © © CO On © rf ON r- OO r- 00 CO © in —4

© © © © © © © © © © © ©

or ^

X X

£ £

£ =

.5" sS * J

5* tJU Bi

o o o

1 2 3

S3

a.

£

E

CT

ctf

a cs

.2 Js 13 fc o o

JD

3

.s

"S c

> • £ 03

D JZ5 "ST £

D

Q .

X

o o o

o o o — o

<N

O On ^ ©

o o o

o © o

On <N m 00 00 00 r»- so r»

-« o o o ©

o o o

rfr m NO ©

o o o

<i

3

<u Oh '

czj ts

cj cd E-"1 Qh

o o o

o o o m o — —I ©

£ <g x .5 £ £

—1 © o

o o p s

m r-M

ON ON

© o O

o o p

m m NO

Tf r-<N

m

m

o Tf NO

© © O o

o o p

NO ON in

r— CN TT

ON r-

<N oo t;

ON O IT)

© © © o O

m "=t M

NO o NO

< N M ON

CTi NO

fN r-<N O^

© © © © o o

O OS Tf

NO On ro

m O NO

& O

o m oo

oo On NO

© © © o O O

NO m

< N < N m

ON F N OO

in Tf

oo M M r-

© © © o O o

m 00 NO

< N oo in

NO Ti-

M o rr NO

< N 00 «n

© © cs © o o i

r-O M

r-oo NO

»n oo ON

try NO o

NO M

oo *n ON

On <N O r-~ -h r- —<

m ?N to <N © © © ©

\0 <N 00

— ON oo © NO NO

00 © — r- oo oo no m no © © ©

s <N ©

f--*3-

in © NO NO o ©

no m (N m Tf (N

m m m NO ON © 00 ON

o ©

o o o o

© © © oo m

—' ©

© © © m ON

m in ©

—1 © ©

o © ©

<N (N ©

OO *3-in

ON NO m

© © ©

ON oo ©

m m ©

ro m Tf

m ©

o © • © ©

m

o

NO ©

NO m rf

NO <N

© © © © i

ON © Tf in ©

in rn •*t

OO <N ©

© © • © ©

r-(N ©

- »n en

(N 3]

© © • © © i

NO (N

CO 00 © Tt

<N © fNI

© © © ©

m

<N 9

m in

rr © ©

© © © ©

CN m

m <N ©

© <N ©

oo © NO

© © © ©

© <N ©

©

OO oo rn

m

<N © © © ©

S ©

© (N m

m ©

o © © o

r-m

•n ©

NO m m

(N rr ©

© © © ©

NO (N <N

ON fN ©

m '=5-<r\

00 in fN

© © © ©

(N NO m

m © in

oo ON

© © © ©

D ^ 00 "e? £ £ 5

cr £ X X £ E

o —< © o

no cn NO <N oo o o © © ©

(N On fN

OO <N

en 00 c*~> <N O OO O Tf *-<

© o

Tfr o

c/> E M - .§ *W I

£ i s I ! f | 3 1 xc/d 3 cr cr ? C (8 +:

o o o

124

C3

*-i

a

.2

13 fc o o

D. £

cr x £

D CO

O

D t/3

D 00

•§ « *-H

Js o

o5 • 3»h

cl>

< J i ^

•2 ^ o3 Oh

o o o

8 P O Tt

^ o

o o o

so ••n O o —< <N

o o

on o *st

00 oo 00 00 (N r -

O S a vo Tf o oo v> —4 m ~ d d © © ©

3

ro oo m ro i n oo <—< o fN m r - © as oo h O n - O; T i ^

o © o © o o o

o o p

ON r-» »r>

sO <N ITi

CO n-V~>

OS •sD

m so 00

r -

t -r f r -

00

sq so SO VO

—1 o d © © o o o d d ©

o o o

m <N oo

oo

o C-4 m

o "3" m

Tf-(N 1 -

oo oo

m ^r <N

r^ SO sO

oo sO rn

m Tf rt-

s rn

_* O o o o O o o o o o ©

O rn

— o

m m ^ m o o r ^ - — —> — ^ r r f N O O ^ j D r N T t

o o o o o o

as © O - . o as —1 ©

o as ©

*T) <J\ O

o o p o

o o o

(N */"> ro

ro m oo SO Tf" V> vo r - so d © d

o so on m

fN oo oo to oo Tf

o

£ C0

X

B

D

C/D

£ £

—V TO

CO ^ +2 x x 2 E S

o o p

r -•Ct rs

d

O O p

fN SO O

TJ-o

o d

o o p

o <N O

r -rsi

Tf ir>

'— o o d

so SO p

m m o

oo oo m

00 m p

© o d • d

Ti-es p

oo T|-o

ON m

oo <N

© o o d

oo so o

rh

o

o ON m

r -ro O

© o d i

d

rs o

i n (N O

r -as m

© O o d i

Tl"

<N 3 <N

SO ON <r> §

O O d d

ON SO

OO rs

o ON m

(N

S

O O d d

SO (N rf

CN g l/~i

o

r -

r -

© O d d

CN ON

o r -o

SO SO m

oo Os

O o d d

Tf

o

so o

r -

m

o as o

o o d d

r -o

Tf oo o

o

m

Os g

o o d d

o o C4

ON m

Os SO <N

ir> ir> <N

o o d d

OS Os r i

Os so O

<N r -Tt

S <N

p o d d

o r -

P

ON o <N

m *r> O

fN ON

o O d d

<r) (N O

(N IT) O

r -ON CO

ITJ

O O d d

o Os

r -r -o

<N ON ro

o r -

o o o o

5 5 S . H d cr cr > 53

125

O oo © oo O —I ©

B 1

T3 CD

£ <L>

(Z)

C/5 Cr o

' 3 u< <D Dh O

" d <u £ <D

t/3

<N O

w a <u

T3

'I (Z> <1>

O r 0 3 <H-H

3 *5? cd

.<D <4-H

1 3 J-*

a a

.2 j 2 1 3 ts o o <U

| . 2 13

* J-M V© <D < &

J i ^ x> t : rcS c3 H Oh

a. "5

cr x B

ZD W o

GO c

a, "5 x B

© o —. o

CN sO £ S o

o

v£> On ro

o I s O fS oo OO --O On O m Tl- fNt p oo O <—< O rn p ^ © o © d

o o o

o r~ ~ o

8 O

*-< —i r-

<N O OO 00 O C O

© © O " -

ON S O S O 0 0 rf r-~ rt- r-m m m rs

—< (N oo m Tf o

o o o

o O p p p p o o o

o o p

(N m o

ON TI-

o-oo m ON O

m oo NO ON o

sO rs m

o in p m *n o

in

o CS o O o o p p d p

o o o sO

On On fO

r-<N ON

m rf sO

r-(N OO

o Tf SO oo rN oo

rn Tf <N

OO m o

sO o m

<N O <N

— p O p O o o o d p d d

o o p m r -

Os <N

r-m

r-oo r-

so <NI r-SO r-sO

<N r-rr r -SO

Tf Tf r--<N O

oo C4

o <N O

- * © © p p o O o o d d p p

o o p

oo r-00

rr IT)

Tf r-o Tf

rf rs so rr r -

o NO

rn oo ON IT) SO SO NO r-i p

r -rs co

r-> m p

© o © O O o o o o d d d d

o o o

m nO TT oo r-NO

oo ON OO

"if Tf rN

"ft OO oo oo

rr l/~L

»r, r-sO

oo m ITi

SO r-so

m m <N

o o

<N (N

so <N

— © d d O o o p o O O p d d p

o o o SO <n <r,

r-iri

rn W,

rr m sO

oo 0 o rs V", oo

On rs R -

r-~ r~-vO NO' ON NO

M NO NO m rr

ON <N CN{

R S

M

O R S

— © O p d o o o p p O p o d d d

o o o o oo rn oo

r-CN

SO NO •"St

m NO sO

o m rs ON m rn

o oo TJ-(N

rf r-ro

o rf (N

r -r-m

m (N O

oo m

oo so o

NO m CA

— © o © p © © o O p O O o d d i d d

o o p

CN r- (N SO

00 r-xf

SO r-

8! NO

r-in ( N OS ro SO tn

On <N r~~

NO 00 ON

ON OO

00 00 On

NO m 00

( N < N

m o

00 r-ro

re

- • d © 1 © o © © O o i p O o O o d d d d i

•rf on SO On <N SO

oo so SO

oo oo-oo so

OO r-r-

r-} oo ON o m

rf rt

ON */-> ON

<N <n r~-

rf r--00 o V) r--

r-oo < N

(N Tf O m m

r-r--

p © o o d p © o o o o p p d p d d d

mx

wip

min

SU

maj

SU

totS

U

mxq

mxw

ait

"E? xfe

rs

Sut

im

3 qle

ng

qtim

wip

flw

tim

actc

ell

totm

ac

mns

dv

pinc

ell

126

8 jC Cl

O O O

O o r -o

O rr O fN — o o — — l o o

N OO OO

4—t JD 3 "00

csS

£ cc

C u -

*5

£ X S

cr X B

O fN ~ O

8 o — o

o o

VO <— " Tf

o

00 rf On O vO Th o o

VO o _ . . O" 0 0 0 ~ o

On fN m ~ fN

- . s o VO Tj-O O - O

c3 j~h

£ £ .2 J 5 1 5 fc o o

JD

• i—H Ir? ^ « o

K> od

_ • Vh c^- <u C Ph ^ o J 2 ^ - o tS r<tf c3 H PL)

O © O O O ON —; ©

0 o o

ON V> On O tT r-O ©

rj- 00 r~~ —< 00 l> _« — VO

in rf o r~» vo <N O O

o o O '

m cn -—>• fN VO OO Tf — VO

D *2 o

D C/3

- 0 0 0 0 0 0 0 0 0

O O p fN VO s

0 0 ON vO

rf in

VO VO *n

0 m

fN r-0

00 r*~i

vO in O

O 0 O O O O 0 0" O O

0 0 0

ON m 0

r -Tf

m m oc

m tN v-j 00 VO

00 <N

ON r~ VO

00 TI" Tf

m On O

O 00 Tf

O «n

* - 0 0 0 O O O O O O © O

0 0 0

iT) On m

(N O vO in O IT)

r -00 (N rs r - vO

rn On VO

rs VO

m O O

O Tf m

O ON m

m m (N

— 0 O O 1 0 0 O O O O 0 0 O

0 0 0

m Tf r-

00 m

C> m O t> <n r4

Tt"

00 r-r-

r~-vO

ON r-r-

(N in vO s fN

vo 0

ON 3

m

0 O O O O 0 O 0 O O O 0 1 O

0 0 0

m tn 0 00 r-

m in O

ON rr 00

vO vO ro

r-~ 00 m vo ro

O OO m vO fN fN m

0 m TJ-—; O 0 O 0 O 0 O O 0 O O O 0 O

0 0 0

m ON m

(N m ON vO (N

<N f -

(N 8

n-vO t> C4 00 00

VO On 1r>

m m r-<N m VO

00 r-4 r -

fN VO VO O r-0

0 m r-

NO l> vO

O O O i O O 0 0 O 0 O 0 O 0 0 O

0 0 0 CN

O VO VO

O »T) m

<Ti Tf* m

OO 00 <N

ON m *n

r— ON VJD

00 0 (N

00 0^

0 <N

<N 00 r«-j

On m fN

NO 00 O

fN in fN

(N ON fN

m 00 O

—; O O 0 0 O O O 1

0 0 O O O O 0 O O

0 0 0

ON 0 Tf

O VO VO

r- 0 0 00 00 00 vO

fN O »n rr Tj-VO

Tf rj-r -

(N ir» *r>

0 r-Ov

VO ON

O ON ON rf ON

>n ON

Tf ON 0

fN O r- S

O 0 0 0 O O O 0 O O 0 O O O 0 0 O

0 </•)

m fN

rn Tf 00

"t m 00 r-ro 00

(N 0 m On

On O O r-

<N VO On OO in in

00 m 0

in O vo

«n r-

fN xr m •n VO O

VO r-»n 00 rr m

O O 0 O 0 O O O 0 O O 0 0 0 0 O O O

mx

wip

min

SU

maj

SU

totS

U

mxq

mxw

ait

"J? xfer

s

Sut

im

util

qlen

g

qtim

wip

flw

tim

actc

ell

totm

ac

mn

sdv

pinc

ell

j C ~ci

127

o o o

O OS 3 ; O m o o o o

c n

<D

Vh O +-»

J < - w

3 • i o n c d

t H

< 2

c

.2

" 5 fcj o o

3 .2

c 3 >

o o <

J £

"§

H

+2 §

D t /5 ' a ? £

D

<N (N e n

a

.2 0 3 f-H CD C U ' o

E a,

o m O Os O <N v_J v »

o © o

s o m s o m Tf o s <n ©

o o o \£)

©

<N Os OS

- - b b o i

o o

o o p

SO m OS

8 p

o Os

O

r -f N m

m

m

b b b b b

o o p

r-4 0 0 o o

r f

Os 0 0 o o

r -Os p

CO m (N

SO r~~ TJ-

•rr ( N (N

b b b b b b b

o o p

m

ir>

o o »Ti

o

sO

m V ) r - -

<N r n v q

i n m m

o SO

3 » n

O b b b b b b b

o o o

m « n

cn r -Wi

o

v o

r ~ m VD

0 0 o SO

* n o

CM r n o

SO

3

<N

* n

© O b b b b i

b b b

o o p

0 0

«N

m SO O

t n o sO

r -r -m

sO

I D

(N 0 0 m

r n o

m o (N

Tf m

o SO

b © o b b b b b b b

o o o

Os m o

r -

m

SO Tf 0 0

m m m

sO m r -

v o r -ir>

KTi s o r f T t

Os

o

Os TJ-"st-

m r n TT

b © b o b b b b b b b

o o o

i n ©

" t

o r -IT)

(N eN r n

m r s

o o s q

Os

• n

o o <N SO » n

o o o

r n O m

r -

m

» n

© © b p o b b b b b b b

O O O

r -m r -

« n m m

o o t n

r -o m

r -o

m

r -OO ir>

o r - -

o o i n

ON Tf (N

m o o o

m m i n

s o r -m

b b © o b o b b b b b b b

o o © Os

0 0 m

Os s o OO

o » n (N

Os o o o o

Os r s j

Os i n v >

fNt o •^t

i n «n i n

s o m m

sO m f N

SO

Tf

o

b b b O O o p b b b b b b b

m » n m

rM o i n

o s o <N

(N o v q

OO

o

o SO 0 0

SO m o o

SO Tf ITi

m Os SO

sO m SO

o Os SO

i n <N r -

» n f N <N

m sO r^-

o o s O

© b O b b © O o b b b b b b b

r i -Os i n

OS sO (N

i n OS O

Os Os m

o o

i n O s sO

VO 0 0

m Os

o s m o

o o r f o

>n OS O

r— o

o

<N 3

b © b o © O o o b b b b b b b

0 0 V ) m

>n O r—

m

SI0

(N CM * n

OS

m

r n « n sO

Os

SO

SO *fr Os

SO o OS

o o 0 0 OS

* n O Os

"3-m CN

o m O

OS m m

<N O m

b b © © b b O i

b b b b b b b b

o o o Os

o s O m r*~i

<N m Os ©

OS Os m

Os m Os

OS *n

o o o o o

r -r -SO

s o o

o

i n i n

m r -

O © O © b b o b b b b b b b b

3: ^

3 £ .s fi- £ £

+2 p a - £ x x £ £

£

a *

E =5 |

£ p £ i s c

2 £

o o o

o so o o © ©

128

T3 <d £ CD

M w

i

C o ii u* <D Pm O

«s • f-H a 3

d II >> 4-* *5o C3 <D T2 JC

£ C/3 <D

O fcd <4-i J52 3 *00 cd t£> <+H

£ 'I

S CT

cd O <4H G O •jH J3 13 £ o Q -SJ 3 S c3 c o > *4-* cd cK cK <D < Pu O <D en 3 t; cd cd H a

o o o

o »-O <N o on —J ©

o o —I ©

o on o r-o o ©

so fN Os

O ©

so rri o Tf o o o fN O <N SO O © O O O

vO Tf O - Tf t O «r> —<

CN Tt OO —* fN o ~ © o o o o OO (N VO - o ©

o v> © —< 0\ rn rf »n m r- —< © s

rf O ro r*i — tn m «jri m — o o o o

o — — o

o p r-r- r-rf o Tf r-in rr ir« d d d d d

o o p sO m fN 00 m ro

oo ON m 'Cf Tf

so Tf o rr m» oo

© d d d d d

o o p fN OO *n m ON m o so TJ-fN oo r~- fN o

o Ch r-r-r-00

— d O d d d d d

o o © sO fN rf m o-

>n oo oo fN o r-sO in O m Tf o sO

oo o rn d d d o d d d d

o o p m fN m sO SO oo oo O o 00

SO ON SO m Tf «n in in r-

oo r-in — d d d d d d d d d in r--m rn oo m

o ro OO rn oo oo SO CO •n

so so in oo r-ON

0 ro ON in •r o oo ON

o r-o

SO m O

sO r~~ m m oo *n fN oj m fN V) *n fN m ©

s so r-so

On fN On ON O (N

SO oo ON

3 00 c

o o o

D ~ I s ? e 2 a •I" *

£ c;

o fN Tf

© © o o O ON t— ON O m fN -"3-—« —< o —• © o o ©

Q\ ON ON «n fN <N in — o d

On so SO

s -a

JE a.

1 2 9

T 3 <D £

<D

in

Is

on C

. 2

cd J-H <D a , o ~ a

<L>

£

00

O

00 S3 <U

£ £ 00 <D

O tcd <4H

CD

V 1 1 (

£

cd <4H l-H

J-t

<2 a

.2 J 5 1 3 fcJ

o o

I

c3 >

0 < <u

1

H

£ o

o V> -J ©

e

.2 13 ?-t <D Oh ' . O oo

S Oh

00 o

ZD 00

o o> CN ° 3 ^ o o vo —: o o

fN r-so

«-H O SO

o o o o o —1 o

SO VO (N

o o o

o o

<r> <N so Os Os

O oo Os —; © o o o

g £ 2 o O in

o d

—> r-co ~ n-

o o o

o — o o o —

O

O o p

0^ »r> rs

Tf sO v>

d p

O O p

o SO co

r--"Sf in

— O d d

O O p

Tf CO <N

0^ »r> O

r-co 0^

Tf <N Tf

O o d d

O O p

fN OO 00 CO

« o fN -r

oo

SO

—4 d d d d d

O O O

g r-

CO O

O oo CO

SO r^ co

00 Os fN r~-

d d d d d d

O O p o

CO

so rr CO

uo Os

r^ oo CO

CO fN Os oo

CN OO <N

d © d d d d O

o o p

SO fN SO <r>

IT) r-CO

tr» r-i r-

O O o

CO so

CM V~i oo

O sO

—' d o d d d d d O

r-OO O

CO oo

O <N O

MO r-

oo Os sO

»r> Os "D;

(N CO sO

fN co un

OO SO O

d d d d d d d d d

r- *r> SO

rt-co

O CN Os

vo <N

r-00 rf 00

Os rf I— ir> oo «—« iri co o d d

oo m «r> Tt vO — sO — — en Os — o p d d d d

co m co

00 CN o — o —«

d

fN OS co

OS CO 00 T}- CN O CM m <r~>

o © o

o ^ VO Tfr (N © O fs| Tf o d d

ti-d

SO CO <N Os SO O d d

O) OO CO so to O O rf- O o d d

ro t-- co co Os SO SO (N CO oo

co oo Os oo co r~--r- <N sO —- rO OS m

SO d

co v> IT) OS d d

•co r~- p-— o

00 Os d d

fN oo fN so r- <n © so —< (N o o d d d d

(N VI r~- r - r<i O os SO r- TI-so co sO Os oo Os i—< <r> fN SO

«r~j SO r- OS Tf Os <—t •—<1 Os •r> r-d d d d d d d d d d d d

.9r O - £ <g 3 X .5 s- e e

E w •J5 — c 3 ^ 4>

>r> — O

i o % ~

OO so os rt o r**-o m o

o o o

S I 2 E

130

Table Al l . totceils

Correlation of systematic sample sorted by throughput dens pts/op ops/pt entity tput mxwip minSU majSU totSU mxq mxwait

totceils 1.000

dens 0.137 1.000

pts/op -0.062 0.000 1.000

ops/pt 0.137 0.000 0.000 1.000

entity -0.185 0.053 -0.231 0.075 1.000

tput -0.213 0.073 -0.213 0.038 0.975 1.000

mxwip 0.108 0.090 -0.016 0.026 -0.429 -0.538 1.000

minSU 0.151 0.801 -0.057 0.111 0.342 0.311 0.226 1.000

majSU -0.195 0.791 -0.075 -0.074 0.360 0.424 -0.284 0.537 1.000

totSU 0.000 0.906 -0.074 0.035 0.398 0.410 0.004 0.908 0.841 1.000

mxq 0.080 0.032 -0.120 0.043 -0.356 -0.398 0.742 0.130 -0.235 -0,033 1.000

mxwait -0.179 -0.031 -0.115 0.009 -0.430 -0.462 0.661 0.001 -0.199 -0.098 0.763 1.000

rej 0.073 -0.266 -0.004 -0.078 -0.921 -0.913 0.457 -0.462 -0.507 -0.548 0.394 0.505

xfers -0.129 0.363 -0.054 0.001 0.159 0.172 0.465 0.535 0.314 0.499 0.422 0.404

Sutim -0.136 0.645 0.039 -0.066 0.222 0.306 -0.462 0.233 0.872 0.582 -0.355 -0.306

util -0.264 0.679 -0.129 0.026 0.696 0.731 -0.323 0.688 0.863 0.870 -0.262 -0.288

qleng -0.059 0.017 0.001 0.004 -0.465 -0.554 0.961 0.131 -0.288 -0.059 0.721 0.703

qtim 0.138 0.051 0.082 -0.005 -0.673 -0.734 0.898 0.074 -0.355 -0.128 0.635 0.608

wip 0.106 0.064 0.006 0.016 -0.492 -0.589 0.984 0.171 -0.303 -0.040 0.724 0.668

flwtim 0.144 0.083 0.084 -0.007 -0.669 -0.728 0.898 0.100 -0.328 -0.098 0.633 0.604

actcell 0.358 -0.386 0.036 0.019 -0.420 -0.454 0.092 -0.373 -0.639 -0.556 0.151 0.081

totmac 0.229 0.963 -0.006 -0.101 0.048 0.070 0.054 0.731 0.768 0.850 0.012 -0.087

mnsdv -0.090 0.344 -0.141 0.016 0.424 0.475 -0.496 0.179 0.642 0.433 -0.435 -0.408

plncell 0.198 -0.511 0.144 -0.028 -0.360 -0.373 0.061 -0.452 -0.674 -0.625 0.167 0.131

rej xfers Sutim util qleng qtim wip flwtim actcell totmac mnsdv plncell

rej i .000

xfers -0.200 1.000

Sutim -0.407 0.047 1.000

util -0.766 0.372 0.682 1.000

qleng 0.516 0.468 -0.457 -0.346 1.000

qtim 0.676 0.303 -0.463 -0.482 0.903 1.000

wip 0.518 0.440 -0.464 -0.374 0.978 0.933 1.000

flwtim 0.662 0.318 -0.439 -0.458 0.900 0.999 0.932 1.000

actcell 0.464 -0.504 -0.472 -0.649 0.066 0.018 0.111 0.162 1.000

totmac -0.277 0.317 0.651 0.621 -0.033 0.013 0.030 0.046 -0.345 1.000

mnsdv -0.467 -0.070 0.611 0.566 -0.515 -0.510 -0.516 -0.497 -0.629 0.355 1.000

plncell 0.432 -0.433 -0.493 -0.642 0.072 0.155 0.086 0.136 0.763 -0.471 -0.627 1.000

131

Table A12. Correlation of systematic sample sorted by flow time totcells deiis pts/op ops/pt entity tput mxwip minSU majSU totSU mxq mxwait

totcells 1.000

dens 0.069 1.000

pts/op 0.069 0.000 1.000

ops/pt 0.173 0.000 0.000 1.000

entity -0.215 -0.002 -0.293 0.072 1.000

tput -0.226 0.038 -0.272 0.035 0.975 1.000

mxwip -0.017 0.017 -0.073 0.048 -0.368 -0.502 1.000

minSU 0.050 0.798 -0.162 0.105 0.346 0.340 0.153 1.000

majSU -0.187 0.839 -0.047 -0.049 0.308 0.373 -0.245 0.646 1.000

totSU -0.067 0.900 -0.119 0.036 0.361 0.392 -0.037 0.919 0.895 1.000

mxq -0.075 -0.003 -0.080 0.025 -0.339 -0.417 0.756 0.057 -0.184 -0.062 1.000

mxwait -0.330 -0.019 -0.121 -0.030 -0.392 -0.444 0.656 -0.040 -0.119 -0.084 0.797 1.000

rej 0.095 -0.213 0.050 -0.086 -0.917 -0.916 0.446 -0.469 -0,467 -0.515 0.405 -0.488

xfers -0.204 0.364 -0.081 0.034 0.223 0.209 0.428 0.559 0.382 0.524 0.398 0.408

Sutim -0.092 0.740 0.128 -0.058 0.124 0.203 -0.403 0.353 0.866 0.654 -0.269 -0.210

util -0.253 0.702 -0.176 0.035 0.656 0.699 -0.302 0.753 0.881 0.895 -0.256 -0.246

qleng -0.121 -0.006 -0.067 0.014 -0.399 -0.513 0.976 0.117 -0.244 -0.057 0.758 0.700

qtim 0.037 0.020 0.006 -0.002 -0.623 -0.702 0.901 0.042 -0.306 -0.133 0.658 0.598

wip -0.007 0.024 -0.053 0.035 -0.432 -0.549 0.986 0.138 -0.248 -0.047 0.760 0.673

flwtim 0.037 0.055 0.009 -0.003 -0.618 -0.695 0.900 0.072 -0.275 -0.100 0.658 0.597

actcell 0.318 -0.459 0.034 0.001 -0.385 -0.408 -0.002 -0.481 -0.664 -0.625 0.015 -0.074

totmac 0.139 0.962 0.008 -0.110 -0.022 0.026 -0.029 0.727 0.807 0.843 -0.028 -0.057

mnsdv -0.187 0.430 -0.064 -0.048 0.381 0.444 -0.410 0.302 0.686 0.531 -0.351 -0.275

plncell 0.194 -0.493 0.150 -0.012 -0.377 -0.376 -0.048 -0.545 -0.634 -0.646 -0.025 -0.065

rej xfers Sutim util qleng qtim wip flwtim actcell totmac mnsdv plncell

rej 1.000

xfers -0.274 1.000

Sutim -0.340 0.121 1.000

util -0.742 0.424 0.683 1.000

qleng 0.484 0.456 -0.397 -0.310 1.000

qtim 0.674 0.267 -0.396 -0.446 0.911 1.000

wip 0.498 0.430 -0.395 -0.331 0.988 0.929 1.000

flwtim 0.660 0.285 -0.368 -0.418 0.910 0.999 0.929 1.000

actcell 0.454 -0.590 -0.490 -0.660 -0.025 0.122 0.006 0.099 1.000

totmac -0.206 0.319 0.736 0.642 -0.057 -0.014 -0.017 0.021 -0.427 1.000

mnsdv -0.441 0.099 0.626 0.638 -0.413 -0.421 -0.418 -0.404 -0.671 0.412 1.000

plncell 0.442 -0.536 -0.418 -0.630 -0.048 0.070 -0.031 0.049 0.764 -0.466 -0.648 1.000

132

Table A13. Correlation of best factories sorted by throughput — — — • — : T : : — • O T T M N ; C I I

totcells dens pts/op ops/pt entity tput mxwip minSU majSU totSU mxq mxwait

totcells 1.000

dens -0.199 1.000

pts/op 0.112 0.000 1.000

ops/pt -0.026 0.000 0.000 1.000

entity -0.256 -0.183 -0.836 -0.007 1.000

tput -0.307 -0.200 -0.786 -0.093 0.957 1.000

mxwip 0.236 0.122 0.451 -0.173 -0.483 -0.383 1.000

minSU -0.084 0.882 -0.054 0.031 -0.096 -0.114 0.221 1.000

majSU -0.423 0.918 -0.103 -0.008 -0.013 0.003 -0.029 0.684 1.000

totSU -0.269 0.980 -0.084 0.013 -0.061 -0.063 0.110 0.924 0.911 1.000

mxq 0.337 0.047 0.581 -0.118 -0.597 -0.520 0.837 0.152 -0.120 0.023 1.000

mxwait -0.467 0.281 0.218 -0.063 -0.148 -0.049 0.345 0.166 0.410 0.309 0.255 1.000

rej 0.053 0.096 0.083 -0.096 -0.086 -0.087 0.149 0.193 -0.012 0.103 0.146 0.022

xfers 0.070 0,092 0.619 0.062 -0.652 -0.524 0.801 0.110 0.009 0.067 0.747 0.458

Sutim -0.448 0.675 0.024 -0.058 -0.112 -0.093 -0.112 0.282 0.855 0.607 -0.179 0.397

util -0.643 0.834 -0.228 0.012 0.196 0.211 -0.115 0.701 0.921 0.879 -0.233 0.412

qleng -0.066 0.139 0.368 -0.071 -0.345 -0.264 0.912 0.240 0.046 0.160 0.710 0.430

qtim 0.226 0.135 0.467 -0.110 -0.511 -0.441 0.925 0.264 -0.059 0.119 0.725 0.260

wip 0.235 0.138 0.400 -0.129 -0.415 -0.341 0.971 0.254 -0.017 0.135 0.773 0.345

flwtim 0.212 0.186 0.454 -0.121 -0.507 -0.440 0.922 0.309 -0.010 0.170 0.714 0.270

actcell 0.478 -0.368 -0.292 0.003 0.231 0.123 -0.316 -0.209 -0.504 -0.382 -0.245 -0.730

totmac 0.053 0.935 0.015 -0.127 -0.235 -0.246 0.225 0.810 0.820 0.888 0.158 0.209

mnsdv -0.099 0.288 -0.396 -0.064 0.403 0.383 -0.462 0.133 0.437 0.304 -0.427 0.115

plncell 0.433 -0.459 -0.076 0.019 0.058 -0.004 -0.079 -0.272 -0.586 -0.460 0.041 -0.578

rej xfers Sutim util qleng qtim wip flwtim actcell totmac mnsdv plncell

rej 1.000

xfers 0.063 1.000

Sutim -0.104 0.018 1.000

util 0.012 -0.091 0.726 1.000

qleng 0.129 0.786 -0.042 0.050 1.000

qtim 0.180 0.773 -0.155 -0.123 0.881 1.000

wip 0.167 0.776 -0.126 -0.089 0.931 0.937 1.000

flwtim 0.187 0.759 -0.119 -0.077 0.882 0.998 0.937 1.000

actcell -0.034 -0.508 -0.540 -0.462 -0.422 -0.254 -0.324 -0.266 1.000

totmac 0.138 0.122 0.598 0.655 0.148 0.204 0.234 0.254 -0.290 1.000

mnsdv 0.000 -0.531 0.417 0.367 -0.493 -0.489 -0.424 -0.465 -0.261 0.307 1.000

plnceil -0.019 -0.153 -0.594 -0.538 -0.149 -0.074 -0.102 -0.097 0.808 -0.390 -0.530 1.000

n :

Table A14. Stepwise regression output for best throughput factories not using factor levels as variables -

Model Summary Standard Error of

Adjusted the

Model R R2 R2 estimate

1 0.435* 0.189 0.186 0.0476

a. Predictors: (constant), ENTITY

ANOVAD

Model SS df MS F Sig.

1 Regression 0.126 1 0.126 55.586 0.000a

Residual 0.539 238 0.02266

Total 0.665 239

a. b. Dependent variable: throughput ratio

Coefficients® Unstandardized Standardized

Coefficients Coefficients

Model B Std. Err Beta t Sig

1 (constant) 0.603 0.056 10.770 0.000

ENTITY 0.00003133 0.000 0.435 7.456 0.000

a. Dependent variable: throughput ratio

Excluded Variables

Model Beta In t Sig. Partial

Correlation

Collinearity Statistics

Tolerance

1 MAXQ -0.114a -1.574 0.117 -0.102 0.643 XFERS 0.123a 1.598 0.111 0.103 0.575 QTIME 0.028" 0.417 0.677 0.027 0.739 FLOWTIME 0.065" 0.958 0.339 0.062 0.743

a. b. Dependent variable: throughput ratio

134

Table A15. Stepwise regression output for best throughput factories using factor levels as

variables —

Model Summary

Model R R2 Adjusted

R2

Standard Error of

the estimate

1 0.5633 0.317 0.314 0.0437

2 0.785b 0.617 0.614 0.0328

3 0.812° 0.659 0.655 0.0310

4 0.818d 0.669 0.664 0.0306

5 0.823e 0.677 0.670 0.0303

a. b. c. d. e.

Predictors: (constant), DENSITY, ENTITY Predictors: (constant), DENSITY, ENTITY, PARTSKEW Predictors: (constant), DENSITY, ENTITY, PARTSKEW, XFERS Predictors: (constant), DENSITY, ENTITY, PARTSKEW, XFERS, MAXQ

ANOVA

Model SS df MS F Sig.

1 Regression 0.211 1 0.211 110.551 0.000'

Residual 0.454 238 0.001909 Total 0.665 239

2 Regression 0.411 2 0.205 190.857 0.000s

Residual 0.255 237 0.001075 Total 0.665 239

3 Regression 0.439 3 0.146 152.118 O.OOO1'

Residual 0.227 236 0.0009611 Total 0.665 239

4 Regression 0.445 4 0.111 118.977 0.000'

Residual 0.220 235 0.000936 Total 0.665 239

5 Regression 0.451 5 0.09013 98.223 O.OOO1

Residual 0.215 234 0.0009176 Total 0.665 239

to* h.

J-k.

Predictors: (constant), DENSITY Predictors: (constant), DENSITY, ENTITY Predictors: (constant), DENSITY, ENTITY, Predictors: (constant), DENSITY, ENTITY, Predictors: (constant), DENSITY, ENTITY, Dependent variable: throughput ratio

PARTSKEW PARTSKEW, XFERS PARTSKEW, XFERS, MAXQ

135

Table A15 - Continued

Model

Coefficients"

1 (constant) DENSITY

Unstandardized Coefficients B Std. Err

0.931 0.297

0.009 0.028

Standardized Coefficients

Beta

0.563

t 104.414 10.514 9.322

Sig 0.000 0.000 0.000 (constant)

DENSITY ENTITY

0.381 0.350

0.00004010

0.041 0.000 0.557 13.619 0.000

(constant) DENSITY ENTITY PARTSKEW

0.369 0.350

0.0000402 0.02163

0.039 0.020 0.000 0.004

0.665 0.558 0.205

(constant) DENSITY ENTITY PARTSKEW XFERS

0.274 0.352

0.00004655 0.02082

0.00000353

0.052 0.020 0.000 0.004 0.000

0.669 0.647 0.198 0.134

9.527 17.213 14.444 5.404 5.278 17.529 12.886 5.257 2.706

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.007

(constant) DENSITY ENTITY PARTSKEW XFERS MAXQ

0.313 0.349

0.00004459 0.01846

0.00000589 -0.000034

0.054 0.020 0.000 0.004 0.000 0.000

0.663 0.619 0.175 0.224 -0.141

a. Dependent variable: throughput ratio

5.803 17.480 12.152 4.563 3.621 -2.387

0.000 0.000 0.000 0.000 0.000 0.018

136

Table A15 - Continued

Excluded Variables'1

Collinearity Partial Statistics

Model Beta In t Sig. Correlation Tolerance

1 ENTITY 0.557' 13.619 0.000 0.663 0.966

MAXQ -0.3611 -7.457 0.000 -0.436 0.998

XFERS -0.268' -5.242 0.000 -0.322 0.991

QT1ME -0.2821 -5.541 0.000 -0.339 0.982

FLOWT1ME -0.2871 -5.593 0.000 -0.341 0.965

MACHSKEW -0.4361 -9.550 0.000 -0.527 1.000

PARTSKEW 0.202' 3.872 0.000 -0.244 1.000

2 MAXQ -0.050"1 -0.996 0.320 -0.065 0.639

XFERS 0.154m 2.949 0.004 0.189 0.574

QTIME -0.009"1 -0.191 0.849 -0.012 0.737

FLOWTIME -0.019m -0.409 0.683 -0.027 0.734

MACHSKEW 0.109m 1.429 0.154 0.093 0.276

PARTSKEW 0.205m 5.404 0.000 0.332 1.000

3 MAXQ -0.011" -0.227 0.821 -0.015 0.624

XFERS 0.134" 2.706 0.007 0.174 0.571

QTIME 0.023" 0.514 0.608 0.034 0.725

FLOWTIME 0.016" 0.355 0.723 0.023 0.719

MACHSKEW 0.113" 1.574 0.117 0.102 0.276

4 MAXQ -0.141° -2.387 0.018 -0.154 0.393

QTIME -0.116° -1.905 0.058 -0.124 0.374

FLOWTIME -0.124° -2.058 0.041 -0.133 0.383

MACHSKEW 0.082° 1.135 0.257 0.074 0.268

5 QTIME -0.077p -1.204 0.230 -0.079 0.334

FLOWTIME -0.087p -1.376 0.170 -0.090 0.343

MACHSKEW -0.097" 1.346 0.179 0.088 0.266

Predictors: (constant), DENSITY m. Predictors: (constant), DENSITY, ENTITY n. Predictors: (constant), DENSITY, ENTITY, o. Predictors: (constant), DENSITY, ENTITY, p. Predictors: (constant), DENSITY, ENTITY, q. Dependent variable: throughput ratio

PARTSKEW PARTSKEW, XFERS PARTSKEW, XFERS, MAXQ

137

Table A16. Correlation of best factories sorted by flow time totcells dens pts/op ops/pt entity tput mxwip minSU majSU totSU mxq mxwait

totcells 1.000

dens 0.361 1.000

pts/op 0.271 0.000 1.000

ops/pt 0.338 0.000 0.000 1.000

entity -0.595 -0.577 -0.578 0.003 1.000

tput -0.626 -0.578 -0.578 -0.022 0.999 1.000

mxwip -0.420 -0.432 -0.614 0.121 0.963 0.951 1.000

minSU 0.319 0.851 -0.076 0.153 -0.343 -0.344 -0.208 1.000

majSU 0.172 0.956 -0.093 -0.029 -0.450 -0.447 -0.320 0.734 1.000

totSU 0.240 0.981 -0.093 0.039 -0.440 -0.438 -0.299 0.886 0.965 1.000

mxq -0.434 -0.547 -0.567 0.118 0.976 0.965 0.991 -0.317 -0.438 -0.421 1.000

mxwait -0.929 -0.406 -0.409 -0.284 0.731 0.760 0.570 -0.245 -0.248 -0.264 0.581 1.000

rej

xfers

Sutim 0.182 0.946 -0.075 -0.310 -0.491 -0.486 -0.372 0.690 0.983 0.936 -0.485 -0.270

util -0.246 0.777 -0.288 -0.103 -0.048 -0.033 0.021 0.747 0.852 0.869 0.009 0.228

qleng -0.681 -0.555 -0.576 -0.052 0.991 0.996 0.929 -0.319 -0.417 -0.407 0.940 0.810

qtim -0.565 -0.540 -0.584 0.044 0.997 0.994 0.977 -0.298 -0.416 -0.398 0.984 0.706

wip -0.496 -0.413 -0.633 0.062 0.975 0.968 0.994 -0.189 -0.290 -0.271 0.982 0.642

flwtim -0.529 -0.356 -0.653 0.032 0.967 0.962 0.983 -0.135 -0.227 -0.207 0.962 0.674

actcell 0.180 -0.333 0.318 0.042 -0.112 -0.111 -0.183 -0.065 -0.517 -0.377 -0.120 -0.128

totmac 0.537 0.952 0.012 -0.057 -0.618 -0.627 -0.446 0.744 0.883 0.889 -0.551 -0.575

mnsdv -0.081 0.370 -0.301 -0.025 0.043 0.039 0.132 0.102 0.531 0.401 0.069 0.040

plncell 0.001 -0.408 0.373 0.015 0.129 0.125 0.080 -0.165 -0.508 -0.409 0.135 0.030

rej xfers Sutim util qleng qtim wip flwtim actcell totmac mnsdv plncell

rej 1.000

xfers 1.000

Sutim 1.000

util 0.815 1.000

qleng -0.457 0.020 1.000

qtim -0.462 -0.018 0.985 1.000

wip -0.341 0.083 0.955 0.986 1.000

flwtim -0.278 0.162 0.955 0.978 0.996 1.000

actcell -0.504 -0.473 -0.122 -0.129 -0.201 -0.232 1.000

totmac 0.892 0.602 -0.625 -0.584 -0.447 -0.406 -0.303 1.000

mnsdv 0.529 0.445 0.043 0.063 0.141 0.168 -0.895 0.353 1.000

plncell -0.527 -0.393 0.112 0.122 0.062 0.030 0.695 -0.398 -0.678 1.000

Note: shaded region has no correlation because there were no transfers or rejects for the top 30 factories based on flow time.

138

Table A17. Stepwise regression output for best flow time factories not using factor levels as variables

Model Summary Standard Error of

Adjusted the

Model R R2 R2 estimate

1 0.429a 0.184 0.181 0.0713

2 0.479° 0.229 0.223 0.0695

3 0.66 l c 0.437 0.43 0.0595

4 0.875d 0.766 0.762 0.0385

a. Predictors: (constant), yLfcNU i h b. Predictors: (constant), QLENGTH, QTIME c. Predictors: (constant), QLENGTH, QTIME, MAXWIP d. Predictors: (constant), QLENGTH, QTIME, MAXWIP, TPUT

ANOVA1

Model SS df MS F Sig.

1 Regression 0.273 1 0.273 53.722 0.000e

Residual 1.212 238 0.005091 Total 0.1485 239

2 Regression 0.341 2 0.17 35.289 0.000'

Residual 1.144 237 0.004828 Total 1.485 239

3 Regression 0.649 3 0.216 61.094 0.000g

Residual 0.836 236 0.003542 Total 1.485 239

4 Regression Residual Total

1.137 0.348 1.485

4 235 239

0.284 0.001841

191.888 0.000"

e. Predictors: (constant), QLENGTH f. Predictors: (constant), QLENGTH, QTIME g. Predictors: (constant), QLENGTH, QTIME, MAXWIP h. Predictors: (constant), QLENGTH, QTIME, MAXWIP, TPUT L Dependent variable: Flowtime ratio

139

Table A17 - Continued

Coefficients'1

Unstandardized Standardized Coefficients Coefficients

Model B Std. Err Beta t Sig

1 0.88100 0.005 161.453 0.000

0.00968 0.001 0.429 7.330 0.000

2 0.88800 0.006 157.330 0.000

0.03685 0.007 1.633 4.987 0.000

-0.00014 0.000 -0.122 -3.733 0.000

3 0.71500 0.019 37.284 0.000 0.15400 0.014 6.810 10.954 0.000

-0.00129 0.000 -10.968 -10.142 0.000

0.00283 0.000 4.757 9.331 0.000

4 -25.89100 1.466 -17.658 0.000 0.04140 0.011 1.835 3.771 0.000

-0.00272 0.000 -23.089 -23.875 0.000

(constant) 0.00452 0.000 7.595 20.814 0.000

ENTITY 0.00210 0.000 14.329 18.147 0.000

a. Dependent variable: Flow time ratio

Excluded Variables" Collinearity

Partial Statistics Model Beta In t Sig. Correlation Tolerance 1J ENTITY -0.626 -1.435 0.153 -0.093 0.01790

TPUT -0.260 -0.392 0.695 -0.025 0.00783 MAXWIP -0.237 -1.496 0.136 -0.097 0.13600 MAXQ -0.458 -2.701 0.007 -0.173 0.11600 QTIME -0.122 -3.733 0.000 -0.236 0.03032 WIP -0.053 -0.269 0.788 -0.017 0.08807

2k ENTITY 6.128 5.700 0.000 0.348 0.00248 TPUT 7.285 6.069 0.000 0.367 0.00196 MAXWIP 4.757 9.331 0.000 0.519 0.00918 MAXQ 5.023 5.640 0.000 0.345 0.00363 WIP 2.735 7.253 0.000 0.427 0.01877

31 ENTITY 12.416 17.036 0.000 0.743 0.00202 TPUT 14.329 18.147 0.000 0.764 0.00160 MAXQ 9.274 14.526 0.000 0.688 0.00310 WIP -18.324 -10.779 0.000 -0.575 0.00056

4111 ENTITY -23.250 -3.650 0.000 -0.232 0.00002 MAXQ -2.592 -1.649 0.100 -0.107 0.00040 WIP -1.684 -0.871 0.384 -0.057 0.00027

j. Predictors: (constant), QLENGTH k. Predictors: (constant), QLENGTH, QTIME 1. Predictors: (constant), QLENGTH, QTIME, m. Predictors: (constant), QLENGTH, QTIME, n. Dependent variable: Flowtime ratio

MAXWIP MAXWIP, TPUT

140

Table A18. Stepwise regression output for best flow time factories using factor levels as variables

Model Summary

Model R R2 Adjusted

R2

Standard Error of

the estimate

1 0.6403 0.410 0.408 0.0607

2 0.778b 0.606 0.602 0.0497 3 0.784c 0.615 0.610 0.0492 a. b. c.

Predictors: (constant), MACHSKEW, PARTSKEW Predictors: (constant), MACHSKEW, PARTSKEW, DENSITY

ANOVAg

Model SS df MS F Sig. 1 Regression 0.609 1 0.609 165.548 0.000"

Residual 0.876 238 0.004 Total 1.485 239

2 Regression 0.900 2 0.450 182.102 0.000e

Residual 0.585 237 0.002 Total 1.485 239

3 Regression 0.913 3 0.304 125.730 0.000s

Residual 0.572 236 0.002 Total 1.485 239

d. Predictors: (constant), MACHSKEW e. Predictors: (constant), MACHSKEW, PARTSKEW f. Predictors: (constant), MACHSKEW, PARTSKEW, DENSITY g. Dependent variable: Flow time ratio

Coefficients1

Un standardized Coefficients

Standardized Coefficients

Model B Std. Err Beta t Sig (constant) MACHSKEW

0.953 -0.101

0.006 0.008

172.121 -0.640

0.000 -12,867 0.000

(constant) MACHSKEW PARTSKEW

0.988 -0.101 -0.070

0.006 0.006 0.006

177.795 -0.640 -0.442

0.000 -15.705 -10.843

0.000 0.000

(constant) MACHSKEW PARTSKEW * DENSITY

1.011 -0.101 -0.070 -0.076

0.011 0.006 0.006 0.032

91.851 -0.640 -0.442 -0.097

0.000 -15.860 -10.951 -2.393

h. Dependent variable: throughput ratio

0.000 0.000 0.018

141

Table A18 -- Continued

Excluded Variables

Model Beta In t Sig. Partial

Correlation

Collinearity Statistics

Tolerance

I1 ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY PARTSKEW

0.066 1.087 0.278 0.070 0.666 I1 ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY PARTSKEW

0.083 1.366 0.173 0.088 0.666 I1 ENTITY

TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY PARTSKEW

-0.043 -0.687 0.493 -0.045 0.623

I1 ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY PARTSKEW

-0.019 -0.319 0.750 -0.021 0.678

I1 ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY PARTSKEW

0.090 1.484 0.139 0.096 0.668

I1 ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY PARTSKEW

0.017 0.282 0.778 0.018 0.659

I1 ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY PARTSKEW

0.000 -0.007 0.994 0.000 0.599

I1 ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY PARTSKEW

-0.097 -1.953 0.052 -0.126 1.000

I1 ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY PARTSKEW -0.442 -10.843 0.000 -0.576 1.000

2J ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY

0.068 1.367 0.173 0.089 0.666 2J ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY

0.069 1.381 0.169 0.090 0.666 2J ENTITY

TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY

0.043 0.826 0.410 0.054 0.608

2J ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY

0.059 1.174 0.242 0.076 0.664

2J ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY

0.056 1.121 0.264 0.073 0.666

2J ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY

0.047 0.929 0.354 0.060 0.657

2J ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY

0.045 0.858 0.392 0.056 0.596

2J ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP DENSITY -0.097 -2.393 0.018 -0.154 1.000

3" ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP

-0.031 -0.444 0.657 -0.029 0.333 3" ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP

-0.030 -0.427 0.670 -0.028 0.332 3" ENTITY

TPUT MAXWIP MAXQ QLENGTH QTIME WIP

-0.037 -0.590 0.556 -0.038 0.421

3" ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP

-0.038 -0.567 0.571 -0.037 0.365

3" ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP

-0.046 -0.675 0.500 -0.044 0.358

3" ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP

-0.059 -0.881 0.379 -0.057 0.365

3" ENTITY TPUT MAXWIP MAXQ QLENGTH QTIME WIP -0.030 -0.488 0.626 -0.032 0.425

i. Predictors: (constant), MACHSKEW j. Predictors: (constant), MACHSKEW, PARTSKEW k. Predictors: (constant), MACHSKEW, PARTSKEW, DENSITY 1. Dependent variable: Flow time ratio

APPENDIX B

RESEARCH PRESENTATION TO FOCUS GROUPS

143

Machine Combination Analysis Procedure for Selecting Optimal

Factory Cell Composition

Research Presentation

J. Robert McQuaid, Jr.

August 29, 1997

Purpose of Today's Presentation

Main purpose is to validate the assumptions and operational factors in the simulation model

To present the Machine Combination Analysis technique of cell formation

To receive input from industry on variables of interest

144

Introduction

* What is Cellular Manufacturing? • Methodology

- Example of Cell formation - Research Design

• Purpose of Research • Experimental Factors

• Proposed Technique • Performance Measures

- Example of MCA - Expected Results

• Research Questions • Future research

What is Cellular Manufacturing?

Partitions a traditional (functional layout) into ceils

- A cell is a combination of dissimilar machines or operations capable of producing a subset of all the parts in a factory

Purpose to improve productivity

- greater degree of similarity among parts processed within cells

- flow of parts within cells tends to be more product focused

Advantages

- reduce total setup time

- improve flow time

- reduce inventory

Disadvantages

- increased capital investment

- decreased machine utilization

145

Functional and Cellular Layouts

A B

A C

D E F

FUNCTIONAL FACTORY

A B D E A

r>

A C B

JD

C

D

D F C F

E F C D E

CELLULAR FACTORY

Example of Cell Identification

Machines Machines 1 2 3 4 5 3 2 5 1 4

- i • i 1 1 1 1 1 2 1 1 3 1 1 3 1 1 7 1 1

Parts 4 1 1 Parts 2 " 1 j j 5 1 4 1 1 6 1 1 6 1 1 7 1 1 5 j 1

Original Part/Machine Matrix Solved Part/Machine Matrix

146

Purpose of Research

Introduce Machine Combination Analysis

Investigate the effect of various initial conditions on the optimal degree of cellularization

Investigate the effect of various initial conditions on several system performance variables

Establish a model from which to investigate both existing and future studies in terms of applicability of cellular manufacturing

Proposed Technique

Two stage procedure

- identify all feasible cellular factories

- identify the optimal factory under various conditions

Constraints reducing investigation requirements:

- eliminate cells with no part processing capability

- eliminate cells that process the same parts than other cells with fewer machines

- eliminate factories that require more machines of a given type than are available for the functional factory

147

Machine Combination Analysis Example Original Part/Machine Matrix

Parts

. ....

2 3 4 5 6 7

Machines 2 3

T l

l l

Machine Combination Analysis Example Possible Combinations and Capability

Cell • Number

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15

Machine Combinations

Part 3 4 5 T~™T * l

l 1 1

148

Machine Combination Analysis Example Feasible Factories

Factory Number of Cells Factory Number of Cells

Number Cells Used Number Cells Used

_ _ j 1 12 3 1,2,11

2 2 1,2 13 3 1,3,4

3 2 1,3 14 3 1,3,7

4 2 1,4 15 3 1,3,11

5 2 1,5 16 3 1,4,9

6 2 1,7 17 3 1,5,7

7 2 1,9 18 3 1,7,9

8 2 1,11 19 3 1,7,11

9 3 1,2,3 20 3 1,9,11

10 3 1,2,5 21 4 1,2,3,11

11 3 1,2,9 22 4 2,3,4,5

Basic Assumptions for this Research

All operations required to complete a part are available in the cell to

which that part is assigned

Each cell is laid out as a modified flow shop

No specialized machinery (one of a kind) is required in more than one

cell

While multiple cells may be capable of producing a given part, it is always routed to the cell originally assigned

149

Specific Model Operational Assumptions

Initial part processing times are distributed exponentially with a mean of 60 minutes per operation, a minimum of 15 minutes per operation (25% of mean), and a maximum of 120 minutes per operation 200% of mean)

Upon selection from queues, part processing times may vary +/- 10% of the mean for each operation performed.

Number of machines required calculation based on a theoretical arrival rate of one entire set of parts per hour (if 20 part types under consideration, then arrival rate set at 20/hour). To allow for imbalance created by assigning parts to cells, one machine of each type added to available resources

Feasible factories are constrained by the number of machine types available from previous calculations

Specific Model Operational Assumptions

Simulated arrival rate varied using theoretical number of machines

required in a functional factory until factory utilization of 75%

achieved. Resulting arrival rate will be used throughout simulation

Part assignment to queues based on balancing cell utilization at one

level of analysis and maximizing cell utilization at the other

Queue priority given to selection of same part type as just processed.

If no similar part type available, FIFO used.

If similar part type selected from queue, setup time = 10% of process time. If dissimilar part type selected from queue, setup time = 40% of process time.

150

Research Questions

What impact does the density of the original part/machine matrix have on the optimal degree of cellularization of the factory? What effect does the original density have on the optimal factory given the remaining factors in the experiment?

Does part assignment to cells have an impact on degree of cellularization of the factory? What effect does the part assignment have on the optimal factory given the other factors in the experiment?

Does variation in product mix have an impact on degree of cellularization of the factory? What effect does this variation have on the performance of the optimal factory given the other factors in the experiment?

Research Questions (Continued)

What is the relationship between the distribution of machine capability and the degree of cellularization of the factory? What effect does the machine capability have on the optimal factory given the other factors in the experiment?

What effect does the performance measure used to select the optimal factory have on the selection? What effect does the performance measure have on the degree of cellularization of the optimal factory?

151

Methodology

• 24 Full Factorial Design

• Experimental Factors

- Density 0.2

0.4

- Machine Capability Uniform

Skewed

- Part assignment goal Balance all workcells

Maximize cellularization

- Product Mix Variability Constant each period

Varying each period

• Fixed factors levels established comparable to other published research

• Simulate each feasible factory using C program

Performance Measures

Performance measures selected are representative of those used throughout published research in the area, although not ail articles use all measures and some hybrid measures are used.

- Average setup time

- Average number of parts completed

- Average machine utilization

- Average queue length

- Average waiting time

- Average work-in-process

- Average flow time

- Productivity (relative to available machine hours)

152

Expected Results

Important conclusions pertaining to partial cellularization of a factory

Define relationships between the optimal degree of cellularization and

the experimental factors investigated

Define relationships between performance measures and the degree of

cellularization

Develop a platform from which to compare current research capacity to distinguish optimal from satisficing solutions

Future Research

Application of proposed MCA using goal programming

Application of proposed MCA using neural networks

Comparison of existing cell formation techniques

Attempt to develop mathematical programming model which defines feasible space to replace individual identification of each feasible factory

Procure real factory data to apply to proposed MCA and prove its capability in real application

APPENDIX C

ACRONYMS

154

ANOVA

ART1

BEA

BRISCH BIRN

CFA

CM

CODE

DCA

DUE DATE

EDD

FCFS

FIFO

FORTRAN

GASP IV

GPSS

GT

LSP

MCA

MICLASS/MULTICLASS

MICROCRAFT

MODROC

MRP

Analysis of Variance

Adaptive Resonance Theory

Bond Energy Algorithm

Commercial parts coding software

Component Flow Analysis

Cellular Manufacturing

Commercial parts coding software

Direct Clustering Algorithm

Part selection from queue based on due date

Earliest Due Date

First Come, First Serve

First In, First Out

Programming Language

Manufacturing simulation programming language

Manufacturing simulation programming language

Group Technology

Line Segmentation Problem

Machine Combination Analysis

Commercial parts coding software

Facility planning software

Rank Order Clustering II

Material Requirements Planning

155

OPITZ Commercial parts coding software

PFA Production Flow Analysis

PWP Plant Within a Plant

RANDOM Part selection from queue random

RL Repetitive Lots

ROC Rank Order Clustering

ROC2 Rank Order Clustering II

SIMAN Manufacturing simulation programming language

SLAM Manufacturing simulation programming language

SPT/T Shortest Processing Time with Truncation

TRL Truncated Repetitive Lots

UNIX Mainframe programming language

WIP Work In Process

WITNESS Manufacturing simulation programming language

REFERENCES

Abou-Zeid, M. 1975. Group technology. Industrial Engineering 7: 32.

Adil, G., D. Rajamani, and D. Strong. 1993.A mathematical model for cell formation considering investment and operational costs. European Journal of Operational Research 69: 330-341.

Ahmadi, R. and H. Matsuo. 1991. The line segmentation problem. Operations Research 39: 42-55.

Askin, R. and S. Subramanian. 1987. A cost-based heuristic for group technology configuration. International Journal of Production Research 25: 101-113.

Ballakur, A. and H. Steudel. 1987. A within-cell utilization based heuristic for designing cellular manufacturing systems. International Journal of Production Research 25: 639-665.

Banks, J. and J. Carson. 1984. Discrete-event system simulation. New Jersey: Prentice Hall.

Billo, R. and B. Bidanda. 1995. Representing group technology classification and coding techniques with object oriented modeling principles. HE Transactions 27: 542-554.

Burbidge, J. 1963. Production flow analysis. The Production Engineer 42: 742.

. 1971. Production flow analysis. The Production Engineer 50: 139-152.

. 1975. The Introduction of Group Technology. London: Heinemann.

. 1977. A manual method for production flow analysis. The Production Engineer 56: 34-38.

Carrie, A. 1973. Numerical taxonomy applied to group technology and plant layout. International Journal of Production Research 11: 399-416.

Chakraborty, K. and U. Roy. 1993. Connectionist models for part-family classifications. Computers & Industrial Engineering 24, no. 2: 189-198.

157

Chakravarty, A. and A. Shtub. 1984. An integrated layout for group technology with in-process inventory costs. International Journal of Production Research 22. 431-442.

Chan, H. and D. Milner. 1982. Direct clustering algorithm for group formation in cellular manufacturing. Journal of Manufacturing Systems 1: 64-76.

Chandrasekaran, M. and R. Rajagopalan. 1986. MODROC: An extension of rank order clustering for group technology. International Journal of Production Research 24: 1221-1233.

Chase, R. and N. Aquilano. 1992. Production and Operations Management. Boston: Irwin.

Chen, C. 1989. A form feature oriented coding scheme. Computers & Industrial Engineering 17, no. 1-4: 227-233.

Choobineh, F. 1988. A framework for the design of cellular manufacturing systems. International Journal of Production Research 26: 1161-1172.

Cohen, J. 1988. Statistical power analysis for the behavioral sciences. New Jersey: Lawrence Erlbaum Associates.

de Beer, C., R. van Gerwen and J. de Witte. 1976. Analysis of engineering production systems as a base for product-oriented reconstruction. CIRP Annalen 25: 439-441.

de Witte, J. 1980. The use of similarity coefficients in production flow analysis. International Journal of Production Research 18: 503-514.

Durmusoglu, M. 1993. Analysis of the conversion from a job shop system to cellular manufacturing system. International Journal of Production Economics 30: 427-436.

El-Essawy, I. and J. Torrance. 1972. Component flow analysis. The Production Engineer 51: 165-170.

Flynn, B. 1987. Repetitive lots: the use of a sequence dependent setup time scheduling procedure in group technology and traditional shops. Journal of Operations Management 7. no. 1: 203-216.

Flynn, B. and F. Jacobs. 1986. A simulation comparison of group technology with traditional job shop manufacturing. International Journal of Production Research 24: 1171-1192.

158

Flynn, B. and F. Jacobs. 1987. An experimental comparison of cellular (group technology) layout with process layout. Decision Sciences 18, no. 4: 562-581.

Garza, O. and T. Smunt. 1991. Countering the negative impact of intercell flow in cellular manufacturing. Journal of Operations Management 10, no. 1: 92-118.

Gongaware, T. and I. Ham. 1981. Cluster analysis applications for GT manufacturing systems. Proceedings: IX North America Manufacturing Research Conference. SME: 503-508.

Greene, T. and R. Sadowski. 1984. A review of cellular manufacturing assumptions, advantages, and design techniques. Journal of Operations Management 4, no. 2: 85-97.

Guerrero, H. 1987. Group Technology: I. The essential concepts. Production & Inventory Management Journal 28, no. 1: 62-70.

Gupta, R. and R. Dudek. 1971. Optimality criteria for flowshop schedules. AIIE Transactions 3: 199-205.

Hayes, R. and S. Wheelwright. 1979a. Link manufacturing process and product life cycles. Harvard Business Review 57. no. 1: 133-140.

.1979b. The dynamics of process-product life cycles. Harvard Business Review 57, no. 2: 127-136.

Hyer, N. and U. Wemmerlov. 1982. MRP/GT: a framework for production planning and control of cellular manufacturing. Decision Sciences 13: 681-701.

. 1985. Group Technology oriented coding systems: Structures, applications, and implementation. Production & Inventory Management Journal 26, no. 2: 55-78.

. 1989. Group technology in US manufacturing industry: a survey of current practices. International Journal of Production Research 27: 1287-1304.

Jacobs, F. and D. Bragg. 1988. Repetitive Lots: Job Flow Considerations in Production Sequencing and Batch Sizing. Decision Sciences 19: 281-294.

Jensen, J., M. Malhotra, and P. Philipoom. 1996. Machine dedication and process flexibility in a group technology environment. Journal of Operations Management 14, no. 1: 19-39.

159

Jordan, P. and G. Frazier. 1993. Is the full potential of cellular manufacturing being achieved? Production & Inventory Management Journal 34, no. 1: 70-72.

Kao, Y. and Y. Moon. 1995. Feature-based memory association for group technology. Computers & Industrial Engineering 29, no. 1-4: 171-175.

Kaparthi, S. and Suresh, N. 1991. A neural network system for shape-based classification and coding of rotational parts. International Journal of Production Research 29: 1771-1784.

. 1995. Performance of selected part-machine grouping techniques for data sets of wide ranging sizes and imperfection. Decision Sciences 25: 515-539.

King, J. 1980. Machine-component grouping in production flow analysis: An approach using rank order clustering algorithm. International Journal of Production Research 18: 213-232.

King, J. and V. Nakornchai. 1982. Machine-component group formation in group technology: Review and extension. International Journal of Production Research 20: 117-133.

Knox, C. 1980. CAD/CAM and group technology: the answer to systems integration. Industrial Engineering 12: 66.

Kusiak, A. 1985. Part families selection model for flexible manufacturing systems. Proceedings of the 1983 Annual Industrial Engineering Conference: 575-580.

. 1987. The generalized group technology concept. International Journal of Production Research 25: 561-569.

Kusiak, A., W. Boe, and C. Cheng. 1993. Designing cellular manufacturing systems: branch-and-bound and A* approaches. IIE Transactions 25: 46-56.

Law, A. and W. Kelton. 1991. Simulation modeling and analysis. New York: McGraw-Hill.

Leonard, R. and K. Rathmill. 1977. The group technology myths. Management Today: 66-69.

Liao, T. and K. L ee. 1994. Integration of a feature-based CAD system and an ART1 neural model for GT coding and part family forming. Computers & Industrial Engineering 26, no. 1: 93-104.

160

Mahmoodi, F. and K. Dooley. 1991. A comparison of exhaustive and non-exhaustive group scheduling heuristics in a manufacturing cell. International Journal of Production Research 29: 1923-1939.

Mahmoodi, F., K. Dooley, and P. Starr. 1990. An Evaluation of Order Releasing and Due Date Assignment Heuristics in a Cellular Manufacturing System. Journal of Operations Management 9, no. 4: 548-573.

Mahmoodi, F., E. Tierney, and C. Mosier. 1992. Dynamic group scheduling heuristics in a flow-through cell environment. Decision Sciences 23: 61-85.

McAuley, J. 1972. Machine grouping for efficient production. The Production Engineer 51: 53-57.

McCormick, W., R. Schweitzer and T. White. 1972. Problem decomposition and data reorganization by clustering techniques. Operations Research 20: 993-1009.

McQuaid, J. and R. Pavur. 1997. Evaluation of a proposed goodness-of-fit test for a Poisson process. Proceedings of the 1997 Decision Sciences Institute 2: 1023-1025.

Mitrofanov, S. 1966. Scientific principles of group technology. Boston Spa: National Lending Library.

Morris, J. and R. Tersine. 1990. A simulation analysis of factors influencing the attractiveness of group technology cellular layouts. Management Science 36, no. 12: 1567-1578.

Mosier, C., D. Elvers, and D. Kelly. 1984. Analysis of group technology scheduling heuristics. International Journal of Production Research 22: 857-875.

Offodile, O., A. Mehrez, and J. Grznar. 1997. Cellular manufacturing: a taxonomic review framework. Journal of Manufacturing Systems 13: 196-220.

Opitz, H. and H.Wiendhal. 1971. Group technology and manufacturing systems in small and medium quantity production. International Journal of Production Research 9: 181-203.

Rajagopalan, R. and J. Batra. 1975. Design of cellular production systems: A graph-theoretic approach. International Journal of Production Research 13: 567-579.

161

Rajamani, D., N. Singh, and Y. Aneja. 1992. A model for cell formation in manufacturing systems with sequence dependence. International Journal o Production Research 30: 1227-1235.

Ramasesh, R. 1990. Dynamic job shop scheduling: a survey of simulation research. Omega 18, no. 1: 43-57.

Rana, S. and Singh, N. 1994. Group scheduling jobs on a single machine: A multi-objective approach with preemptive priority structure. European Journal of Operational Research 79: 38-50.

Sassani, F. 1990. A simulation study on performance improvement of group technology cells. International Journal of Production Research 28: 293-300.

Schonberger, R. 1982. Japanese manufacturing techniques: Nine hidden lessons in simplicity. New York: The Free Press.

Seifoddini, H. 1989. Duplication process in machine cells formation in group technology. HE Transactions 21: 382-388.

Shafer, S., G. Kern, and J. Wei. 1992. A mathematical programming approach for dealing with exceptional elements in cellular manufacturing. International Journal of Production Research 30: 1029-1036.

Shafer, S. and D. Rogers. 1991. A goal programming approach to the cell formation problem. Journal of Operations Management 10, no. 1: 28-43.

Shannon, R. Systems simulation - the art and science. New Jersey: Prentice-Hall.

Singh, N. 1993. Design of cellular manufacturing systems: An invited review. European Journal of Operational Research 69: 284-291.

Skinner, W. 1974. The focused factory. Harvard Business Review 52. no. 3: 113-121.

Sokal, R. and P. Sneath. 1968. Principles of Numerical Taxonomy. San Francisco: W.H. Freeman and Co.

Suresh, N. 1979. Optimizing intermittent production systems through group technology and an MRP system. Production and Inventory Management 20: 76.

The celling out of America 1994. Economist 333(7894): 63-64.

Thompson, J. 1967. Organizations in Action. New York: McGraw-Hill Book Company.

162

Vakharia, A. 1986. Methods of cell formation in group technology: A framework for evaluation. Journal of Operations Management 6. no. 3: 257-271.

Vakharia, A. and B. Kaku. 1993. Redesigning a cellular manufacturing system to handle long-term demand changes: a methodology and investigation. Decision Sciences 24: 909-929.

Waghodekar P. and S. Sahu. 1984. Machine-component cell formation in group technology: MACE. International Journal of Production Research 22: 937-948.

Wemmerlov, U. 1984. Comments on the Direct Clustering Algorithm for group formation in cellular manufacture. Journal of Manufacturing Systems 3: vii-ix.

Wemmerlov, U. and N. Hyer. 1986. Procedures for the part family / machine group identification problem in cellular manufacturing. Journal of Operations Management 6. no. 2: 125-147.

.1987. Research issues in cellular manufacturing. International Journal of Production Research 25: 413-431.

Wemmerlov, U. and A. Vakharia. 1991. Job and family scheduling of a flow-line manufacturing cell: A simulation study. HE Transactions 23: 383-393.

Wirth, G., F. Mahmoodi, and C. Mosier. 1993. An investigation of scheduling policies in a dual-constrained manufacturing cell. Decision Sciences 24: 761-788.

Xu, H. and H. Wang. 1989. Part family formation for GT applications based on fuzzy mathematics. International Journal of Production Research 27: 1637-1651.