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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
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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
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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
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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
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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
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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
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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
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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
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