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2, LIBRARY
2002 Michigan State
University

This is to certify that the
dissertation entitled

Pnooucr COMPLEXITY: THEORETICAL Raunousmps TO Dunno AND
Sumv CHAIN Cons

presented by

Mark A. Jacobs

has been accepted towards fulfillment
of the requirements for the

Ph. D. degree in Operations and Sourcing
Management

 

 

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W or Professor’s Signature
22 July 2008

 

Date

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5/08 K:lProleoc&Pres1CIRC/DateDue.indd

PRODUCT COMPLEXITY: THEORETICAL RELATIONSHIPS T0 DEMAND AND SUPPLY
CHAIN COSTS

BY

MARK A. JACOBS

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Department of Operations and Sourcing Management

2008

ABSTRACT

PRODUCT COMPLEXITY: THEORETICAL RELATIONSHIPS TO DEMAND AND SUPPLY
CHAIN COSTS

By

Mark A. Jacobs

Researchers have suggested that product portfolio complexity effects firm performance
but that the effects are not well understood. This study enhances the understanding by
clearly defining the construct, developing a typology, applying the theoretical framework
of Theory of Performance Frontiers, developing measures or complexity factors
descriptive of the construct, and testing several hypotheses informed by the definition and

theoretical perspective.

From a thorough grounding in the literature, product portfolio complexity is defined to be
the state of possessing a multiplicity of, and relatedness among, products within the
portfolio. Complexity is found to possess two dimensions: multiplicity and relatedness.
Relatedness contains three subdimensions: similarity, interconnectedness, and

complementarity.

Several measures of multiplicity and similarity are created and are informed by the
definition and theoretical perspective. Hypotheses which relate these measures to various

costs and sales volume are tested using panel data regression by analyzing longitudinal

product portfolio and cost data provided by a designer and manufacturer of data

processing equipment.

The results reveal that measures of multiplicity are more effective at predicting cost than
measures of similarity. Additionally, models measuring changes in cost or volume rather
than absolute levels are superior. On average, complexity variables used to measure

changes in cost or volume explain 10% of variance and the full models explain over 50%.

Thus this research fills a portion of the gap in understanding that exists about the
relationship between product portfolio complexity and firm performance by providing a
theoretically grounded understanding of complexity’s relationship to cost and sales
volume. Further, a typology of complexity is developed, two of its dimensions
operationalized, and the Theory of Performance Frontiers extended to intangible assets.
Beyond the academic contribution of the research is the benefit offered to the business
community. Specifically, this research provides an approach to quantifying the most
profitable configuration of a portfolio. Thus the research both advances theory and offers

benefit to the practitioner community.

Copyright by
MARK ALLEN JACOBS
2008

DEDICATION & ACKNOWLEDGMENTS

THERE ARE FEW THINGS THAT STAND IN ISOLATION. MOST ARE RELATED TO SOMETHING ELSE AT LEAST AT SOME
POINT. IN THE CASE OF THIS UNDERTAKING, THERE ARE MANY CONNECTIONS OF DIFFERING KINDS; THUS IT
MANIFEST S THE VERY CONSTRUCT IT SEEKS TO EXPLICATE. HERB SIMON INFORMED US IN 1961 THAT NEARLY
EVERY SYSTEM 15 DECOMPOSABLE TO INTEGRATED PARTS. IN THE CASE OF THIS RESEARCH, SOME OF THOSE
PARTS ARE APPARENT AND SOME NOT. THE APPARENT PARTS ARE CALLED ATTENTION TO IN THE BIBLIOGRAPHY;
THE FOUNDATION OF KNOWLEDGE PROVIDED BY PRIOR SCHOLARS. THE PARTS THAT ARE NOT APPARENT ARE

MANY AND A FEW OF THE MOST SIGNIFICANT ARE HIGHLIGHTED BELOW.

THE SEED WAS PLANTED FOR THE PURSUTT OF DOCT ORAL STUDIES WHEN AS A YOUNG CHILD I WATCHED MY
FATHER EARN HIS DOCTORATE. I LEARNED OF THE DOCTORAL STATUS OF MY UNCLES AND FINALLY OF THE
DOCT ORAL STUDIES OF MY MOTHER. I WAS INCULCATED IN THE VALUE OF EDUCATION THROUGH LIVING IN
GRADUATE STUDENT HOUSING WHILE MY FATHER EARNED HIS DOCTORATE, BEING RAISED IN A NEIGHBORHOOD
POPULATED BY PHYSICIANS AFTER HE COMPLETED THE DEGREE, AND BY THE CONSTANT REMINDING BY MY
PARENTS OF THE IMPORTANCE OF EDUCATION. THIS INITIAL PUSH AND THE EXPECTATION OF ATTAINING MY

PERSONAL BEST HAS ENABLED ME TO BE IN A POSITION TO UNDERTAKE THIS DISSERTATION.

LATER IN LIFE I WAS EXPOSED TO THREE ACADEMICS WHO CAST A VISION OF A CAREER IN ACADEMIA. THE FIRST
WAS RALPH MORGAN, FOR WHOM I WORKED ON A RESEARCH PROJECT WHILE AT CAL POLY. HE ENCOURAGED ME
TO PURSUE GRADUATE STUDIES, BUT I FANCIED MYSELF FOLLOWING A PATH MORE SIMILAR TO HIS OWN; SEVERAL
YEARS RUNNING A BUSINESS AND THEN LATER EARNING A DOCTORATE AND ENTERING ACADEMIA. THE SECOND
AND THIRD WERE FRED BEIER FOR WHOM I ALSO WORKED ON A RESEARCH PROJECT WHILE AT THE UNIVERSITY
OF MINNESOTA AND MY UNCLE, CARL ADAMS. FRED AND CARL WERE GENEROUS WITH THEIR TIME AND
INSTRUMENTAL IN HELPING ME WORK THROUGH THE DECISIONS OF WHETHER AND WHERE TO PURSUE A
DOCTORATE AND IF A LIFE IN ACADEMIA WAS RIGHT FOR ME. WITHOUT THE ASSISTANCE AND ADVICE OF FRED

V

AND CARL AND THE EXAMPLE OF RALPH MORGAN, IT IS UNLIKELY I WOULD BE WRITING THIS DISSERTATION.

THE FACULTY AT MICHIGAN STATE, IN PARTICULAR MY Two ADVISORs MORGAN SWINK AND SHAWNEE VICKERY,
HAVE PREPARED ME WELL TO EXECUTE THIS DISSERTATION AND PROSECUTE A PRODUCTIVE RESEARCH AGENDA.
WITHOUT THEIR TRAINING AND IN PARTICULAR THE GUIDANCE 0F MORGAN SWINK, MY COMMITTEE CHAIR, THIS
RESEARCH COULD NOT HAVE BEEN UNDERTAKEN. MORGAN HAS BEEN CAPTAIN, COACH, CHEERLEADER,
COUNSELOR, CRITIC, AND COMRADE AT VARIOUS AND APPROPRIATE TIMES. I AM INDEBTED TO HIM FOR THE
INVESTMENTS HE HAS MADE IN MY DEVELOPMENT As A SCHOLAR. I AM ALSO INDEBTED TO MY COMMITTEE,
ROGER CALANTONE, DAVE CLOSE, AND BOB HUBBARD FOR THEIR CONTRIBUTIONS IN FUNDING AND REVIEWING

THIS RESEARCH, ADVISING ME IN ITS EXECUTION, AND ENCOURAGEMENT ALONG THE WAY.

THE MOST IMPORTANT CONNECTION TO THIS RESEARCH IS MY WIFE BARBARA AND DAUGHTERS SARAH AND
LAURA. THEIR WILLINGNESS TO FOREGO THE LUXURIES OF LIFE, MOVE AWAY FROM FAMILY AND FRIENDS, AND
TOLERATE MY STRESS LEVELS AND WORK SCHEDULE THROUGHOUT A SEVEN YEAR TRANSITION PERIOD HAS
ALLOWED THIS DISSERTATION AND ULTIMATELY THE DOCTORATE TO BE REALIZED. BARBARA IN PARTICULAR HAS
MADE SACRIFICES WHICH ARE TOO MANY TO LIST. HER SUPPORT AND BELIEF IN ME, MORE THAN ANY OTHER
REASONS, ARE WHY THIS DISSERTATION HAS BEEN COMPLETED. WITHOUT THEM, NONE OF THE EVENTS ABOVE

WOULD HAVE MATTERED.

vi

1.0

2.0

3.0

4.0

TABLE OF CONTENTS

Overview .............................................
1 . 1 Introduction ....................................
1.2 Objectives
1 .3 Definitions ....................................
1 .4 Motivation ....................................
1.5 Form of research questions ..................
1.6 Overview of the research methodology

1.7 Research contribution ........................
1.8 Plan of Work ....................................
Literature Review ....................................
2. 1 Introduction ....................................
2.2 Typology of product complexity .........
2.3 Portfolio level complexity ..................
2.4 Summary ....................................
Theory Development ....................................
3.1 Two theories ....................................
3.11 Theory of Performance Frontiers .........
3.12 Transaction Cost Economics ..................
3.13 Summary ....................................
3.2 Hypotheses ....................................

3.21 Effects of multiplicity on supply chain costs .
3.22 Effects of similarity on supply chain costs

3.23 Effects of multiplicity on sales volume ......
3.24 Effects of similarity on sales volume ..........
Research Design and Methodology ..................
4.1 Unit of analysis ...........................
4.2 Operationalizations of variables .........
4.21 Independent variables ..................
4.22 Control variables ...........................
4.23 Dependent variables ...........................
4.24 Models ....................................
4.3 Data .............................................
4.4 Analytical Method ...........................
4.41 Overview of panel data regression .........

4.42 Justification of choice of panel data regression
4.43 Analytical protocol ...........................

vii

5.0 Results ............................................. 82

5.1 Hypothesis 1 .................................... 83
5.2 Hypothesis 2 .................................... 94
5.3 Hypothesis 3 .................................... 100
5 .4 Hypothesis 4 .................................... 106
5.5 HypothesisS 118
5.6 Hypothesis 6 .................................... 1 19
5.7 Hypothesis 7 .................................... 126
6.0 Discussion ............................................. 129
6. 1 Introduction .................................... 129
6.2 Interpretations and explanations ......... 130
6.21 High level interpretation .................. 130
6.22 Hypothesis 1 .................................... 133
6.23 Hypothesis 2 .................................... 135
6.24 Hypothesis 3 .................................... 137
6.25 Hypothesis 4 .................................... 140
6.26 Hypothesis 5 .................................... 142
6.27 Hypothesis 6 .................................... 144
6.28 Hypothesis 7 .................................... 146
7.0 Concluding remarks .................................... 149
7.1 , Introduction .................................... 149
7.2 Contributions .................................... 149
7.2 1 Research .................................... 149
7.22 Managerial .................................... 151
7.3 Implications .................................... 151
7.3 1 Theory .................................... 151
7.32 Operationalizations ........................... 152
7.4 Managerial Implications .................. 154
7.5 Limitations .................................... 157
7.6 Future research ........................... 159
7 .61 Address limitations ........................... 159
7.62 Address remaining gaps .................. 159
7.63 Extensions .................................... 161
7.63 Additional research questions emerging
from this study ........................... 161
7.7 Summation of dissertation .................. 162
Appendix ...................................................... 164
Bibliography ...................................................... 167

viii

LIST OF TABLES

Table 1: Complexity Definitions .................. 7
Table 2: Plan of Work .................. 19
Table 3 Summary of Literature .................. 34
Table 4: Variables ........................... 62
Table 5: Models ........................... 70
Table 6: Data categories ........................... 72
Table 7: Correlation Matrixes .................. 80
Table 8: Model 1a — Warranty — no lag ......... 84
Table 9: Model 4a — Delta Warranty — no lag ......... 85
Table 10: Model 4a — Delta Warranty — lag 1 ......... 86
Table 11: Model 5a — Delta Warranty — lag 1 ......... 87
Table 12: Model 5a — Delta Warranty — lag 2 ......... 88
Table 13: Model 4a — Delta Inventory — lag 2 ......... 95
Table 14: Model 5a — Delta Inventory — no lag ......... 96
Table 15: Model 5a — Delta Inventory — lag 2 ......... 97
Table 16: Model 4a — Direct Cost — no lag ......... 101
Table 17: Model 5a — Direct Cost — no lag ......... 102
Table 18: Model 5a — Direct Cost — lag l ......... 103
Table 19: Model 1a — Indirect Cost — prior 1 ......... 107
Table 20: Model 1a — Indirect Cost — no lag ......... 108

ix

Table 21:

Table 22:

Table 23:

Table 24:

Table 25:

Table 26:

Table 27:

Table 28:

Table 29:

Table 30:

Model 4a — Delta Indirect Cost — no lag ......

Model 4a — Delta Indirect Cost — lag 1 .......

Model 5a — Delta Indirect Cost - lag 1 .......

Model 5a — Delta Indirect Cost — lag 2 . ......

Model 1b — Sales Volume — no lag ..........

Model 1b — Sales Volume — lag 1 ..........

Model 4b — Delta Sales Volume — no lag

Model 5b - Delta Sales Volume — lag 1

Model 2b — Sales Volume — no lag .........

Summary of Findings

109

110

111

112

120

121

122

123

127

130

Figure 1:
Figure 2:
Figure 3:
Figure 4:
Figure 5:
Figure 6:
Figure 7:
Figure 8:

Figure 9:

Figure 10:
Figure 11:
Figure 12:
Figure 13:
Figure 14:
Figure 15:

Figure 16:

LIST OF FIGURES

Dimensions of Complexity ..................
Typology ............................... ' .....
Research Focus ...........................
Relationship of Price to Market Share .......
Cumulative Market Share ..................
Hypothesis 1 Model 1a ..................
Hypothesis 1 Model 4a — No Lag .........
Hypothesis 1 Model 4a — Lag 1 .........
Hypothesis 1 Model 5a ..................
Hypothesis 2 Model 5a ..................
Hypothesis 3 Model Sa ..................
Hypothesis 4 Model 1a ..................
Hypothesis 4 Model 4a — No Lag .........
Hypothesis 4 Model 43 — Lag 1 .........
Hypothesis 6 Model 5b ..................

Hypothesis 7 Model 2b ..................

xi

11
22
22
58
59 '
90
92
92
93
99
105
114
116
117
125

128

1.0 Overview of the research

1.1 Introduction

The proposed dissertation draws upon engineering, marketing, and supply chain
literatures to develop theoretical explanations for produCt complexity’s impact on
components of product demand and various supply chain costs. Specifically, this
research focuses on the dimensions of complexity represented in business unit product
portfolios reflecting the design and manufacturing of tangible, discrete, assembled
products. Hypotheses which specifically relate portfolio complexity factors to product
demand and supply chain outcomes are tested using historical product, sales, and cost
data. This is the first research to empirically assess the effects of multiple dimensions of

product complexity on both sales volume and cost in a large scale manner.

This chapter is organized as follows. First, the concept of product complexity is defined.
Then the motivation for performing the research is discussed. The hypotheses are
presented and discussed next followed by a discussion of the methodology. The chapter

concludes by discussing the research contributions.

The subsequent chapters address in greater detail the topics introduced in this chapter.
Chapter Two provides significant detail regarding the current literature. Chapter Three
provides the theoretical underpinning of the research and formally presents the research
hypotheses. Chapter Four describes the research design. Chapter Five reviews the
analysis process and results. Chapter Six offers the conclusions and management

implications.

1.2 Objectives

There are multiple objectives for this research. The first is to develop a robust definition
of the construct ‘complexity’. Second is the development of a typology that
contextualizes current and future research on the topic. Third is the establishment of the
functional forms of various dimensions of complexity in regards to cost and sales

volume.

1.3 Definitions

For science to advance at the maximal rate, there must be consensus (Kuhn, 1963). There
must be commonly used definitions and descriptions of the phenomenon under
consideration (Wacker, 2004). The study of product complexity has been hampered by
the lack of a precise definition. My goal is to establish a basis for consensus beginning
with a formal and robust definition of the construct ‘complexity’. To do so I investigate
several different disciplines to gain a comprehensive understanding of how complexity
has been conceptualized. These findings are discussed below and summarized in Table

1.

Whereas the concept of a product portfolio is well defined and understood to be the
complete set of possible product configurations offered by a business unit at a given point
in time (McGrath, 2001; Meyer & Lehnerd, 1997), consensus regarding a definition of
complexity has yet to emerge, possibly in part because complexity is a multifaceted
concept. To begin the process of developing a formal definition of complexity, one place

to look is in a dictionary. Therein, Webster (1964) defines complexity as “1a: the quality

or state of being composed of two or more separate or analyzable items, parts,
constituents, or symbols 2a: having many varied parts, patterns or elements, and
consequently hard to understand fully 2b: marked by an involvement of many parts,
aspects, details, notions, and necessitating earnest study for examination to understand or
cope with”. Thus the complexity of an item stems from a multiplicity of elements, as
well as from relationships among those elements expressed in “patterns” and
“involvement.” Further, this combination of multiplicative and relational aspects creates
difficulties requiring resources (e.g., mental or otherwise) to be expended in order to
achieve comprehension, or processing, of the item in question. These dimensions,
multiplicity and relatedness, have been addressed in a variety of academic disciplines

including product design, organizational design, chemistry, complex systems, and others.

1.31 Product Design

 

The product design literature consistently associates multiplicity with complexity. For
example, Baldwin and Clark (2000) maintain that the complexity of a system is
proportional to the total number of design decisions required (Baldwin & Clark, 2000).
The association of complexity with multiplicity also relates to the context of product
features (Griffin, 1997b) and components (Gupta & Krishnan, 1999). Kaski and Heikkila
(2002) also focus on multiplicity, in the context of physical modules, but add that the

degree to which they exhibit dependency is also related to product complexity.

1.32 Organizational Design

Organizational design researchers refer to complexity as the number of structural
components that are formally distinguished (Blau & Shoenherr, 1971; Price & Mueller,
1986), the degree to which the structures are differentiated (Price & Mueller, 1986), or
the number of elements which must be addressed simultaneously (Scott, 1992).

Similarly, Dafi (1983) states that the number of activities or subsystems within the
organization influences complexity. He goes on to indicate that these activities or
subsystems could be reflected in the number of levels in the organizational chart,
departments within a division, or geographical diversity; thus touching on the hierarchical

nature of complex systems.

1.33 Complex Systems

 

Both Boulding (1956) and Simon (1962) address the concept of multiple levels of
complex systems. Simon (1962) identifies hierarchy as a means to describe more clearly
the complexity inherent within the system. The complex systems literature also
addresses complexity in terms of differentiation and connectivity (Klir, 1985). This is a
parsing of Simon’s (1962) original notion that a complex system is one comprised of a

large number of parts that interact in a non-simple way.

1.34 Business

 

Hill (1972; 1973) typifies the marketing perspective in suggesting that product
complexity is a result of product diversity, technology, newness, and bundled attributes

such as after sales service. Very similar to the marketing perspective is that of

Management Information Systems which considers the depth and scope of required
technical activities in assessing the degree of complexity (Meyer & Curley, 1991). The
project management literature considers projects that have many varied inter—related parts
as complex (Baccarini, 1996). These are all similar in that they tap the underlying

dimensions of multiplicity and relatedness.

1.35 Hard Sciences

 

The disciplines of Chemistry and Physics pay particular attention to the connections
between entities. Chemists use the term complex when referring to a state in which
certain transition metals share electrons from one of the metal’s outer valences with one
or more anions (Kotz & Treichel, 1996; Whitten & Gailey, 1984). Researchers in both
computational physics and evolutionary biology associate complexity with the degree of
coupling or interactions among the elements within a system (Dooley & Van de Ven,
1999). It is these connections that are implied by Operations Research scholars when
they refer to constraints; the more constraints represented in a problem, the greater the

complexity (Eglese, Mercer, & Sohrabi, 2005).

1.36 Decision Sciences

 

Information processing theory suggests that complexity is a function of the diversity of
information and the rate of information change (Campbell, 1988). Similarly, Wood
(1986) reports that complexity is a function of the number of information cues that must

be processed.

1.37 Operations Management

 

The operations management literature suggests the existence of two dimensions of
complexity; I have characterized them as multiplicity and relatedness. Multiplicity and
relatedness are represented in the characterization of supply chain complexity as a
reflection of the number of parts and the degree of unpredictability (Bozarth, Warsing,
Flynn, & Flynn, 2007); note that unpredictability is a fimction of the interconnections
between the parts because as the number of connections increase the number of potential
outcomes increases. Of the concepts of multiplicity and relatedness, the more developed
of the two dimensions is multiplicity which is conceptualized most frequently in the
literature as the number of components (Gupta & Krishnan, 1999; Ramdas, 2003).
Complexity is considered to increase as the number of components increases. This is
reported to be the case whether it is total part count (Novak & Eppinger, 2001) or number
of unique parts (Collier, 1981; Rutenberg, 1971; Rutenberg & Shafiel, 1971). The same
principle of increased number is manifested at the product level. Griffin (1997a) and Du,
Jiao and Tseng (2001) report that the number of options or features represented within a
product is another dimension of multiplicity. The last manifestation addressed is at the
portfolio level. Ulrich (1995) and Randall and Ulrich (2001) identify the number of
product versions as a dimension of multiplicity. This is articulated by Ramdas (2003) as
product mix. Related to the product mix is the rate at which the products within the
portfolio are replaced; the more frequent, the higher the complexity (Fisher, Ramdas, &
Ulrich, 1999). The other main dimension of complexity is that of relatedness. The

degree to which components, subassemblies, or other architectural representations are

interconnected is a representation of relatedness; thus complexity is proportional to

interconnectedness (Novak & Eppinger, 2001; Tatikonda & Stock, 2003).

Table 1

Complexity Definitions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Discipline Source Definition: Complexity is
Rhetoric Webster (Webster, 1a: the quality or state of being composed of
1964) two or more separate or analyzable items,
parts, constituents, or symbols 2a: having
many varied parts, patterns or elements, and
consequently hard to understand fully 2b:
marked by an involvement of many parts,
aspects, details, notions, and necessitating
earnest study or examination to understand
or cope with.
Baldwin & Clark Proportional to the total number of design
(2000) decisions
Griffin (1997a; The number of functions designed into a
Griffin, 1997b) product
Kaski & Heikkila Represented by the number of physical
Product (2002) modules and also by the degree of
Design dependency '
Gupta & Krishnan The number of components
(1999), Ramdas
(2003)
Tatikonda & Stock Pr0portional to the interdependence of
(2003) technologies
Blau & Schoenherr The number of structural components that
(1971) are formally distinguished
. . Price & Mueller The degree of formal structural
Orgamzatronal . . .
Design (1986) differentration. . .
Dafi (1983) Number of actrvrtres or subsystems across
levels or geographies
Scott (1992) The number of elements that must be
addressed simultaneously
Simon (1962) A system comprised of a large number of
parts that interact in a non-simple way
Complex Flood & Carson Difficult to understand
Systems (1 98 8)
Klir (1985) A system manifesting differentiation and

 

 

connectivity

 

Table 1

Continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Marketing Hill (1972; Hill, The degree of product standardization,
1973) technology complexity, newness of product,
amount of purchase history, newness of
application, installation ease, and amount of
after sales service required
Management Meyer & Curley The depth and scope of technical activities
Information (1991) required
Systems
Project Baccarini (1996) A project comprised of many varied
Management interrelated parts
Chemistry Whitten & Gailey The sharing of valence electrons by certain
(1984), Kotz & transition metals with one or multiple anions
Treichel (1996)
Physics & Dooley & van de Ven The degree of coupling or interactions
Biology (1999) among the elements within the system
Operations Eglese, Mercer, and A synonym for constraint or difficulty; the
Research Sohrabi (2005) more constraints represented in a problem,
the more complex it is
Gailbraith (1977) The difference between information required
Information and present to perform a task
P . Wood (1986) The number of information cues which must
rocessrng
Theory be processed . _ . .
Campbell (1988) A function of the drversrty of Information
and the rate the information changes.
Choi & Kraus (2006) Manifested in varied number of types of
suppliers and their interactions
Bozarth, Warsing, The number of parts and the degree of
Flynn & Flynn (2007) unpredictability.
S . Fisher, Ramdas & Manifested in number of systems and the
upply Charn . . . .
O tions Ulrrch (1999) rate at WhJCh products In the portfolro are
pera
Management replaced
Novak & Eppinger Represented by three facets: number of
(2001) components, extent of interactions, and
degree of product novelty
Rutenberg & Shaftel Represented by the number of modules and
(1971) markets

 

 

 

 

Based upon a review of the literature, there appears to be harmony amongst the uses of
the word complexity in the academic literature. This harmony is evidenced by the
emergence of three themes; multiplicity, relatedness, and difficulty of comprehension.
However, difficulty of comprehension is an outcome of multiplicity and relatedness and
hence, in the interest of creating a criterion free definition, will be omitted from this
research. There also appears to be implicitly represented, consistent with systems theory
(Boulding, 1956) and hierarchically nested systems (Simon, 1962), multiple levels where
these dimensions are manifested; the portfolio, product, and component levels.

Therefore, I propose the following definition of complexity.

Complexity is the state of possessing a multiplicity of elements manifesting

relatedness.

Complexity in a product is manifested by both the multiplicity of, and relatedness among,
elements contained within the product portfolio or the product itself. An element could
be a component, subassembly, feature, design template, etc. Ceteris paribus, one product
is considered more complex than another if it contains a greater number of elements or if
elements are more interconnected than the other. I therefore define product complexity

as follows:

Product complexity is a design state resulting from the multiplicity of and

relatedness among, product architectural elements.

Applying this logic to product portfolios, reveals that the greater the combinatorial
possibilities and degree of interconnection represented between items, the greater the

complexity. As such, complexity in a product portfolio is defined as follows:

Product portfolio complexity is the state of possessing a multiplicity of and

relatedness among, products within the portfolio.

Multiplicity relates to the enumeration of items. However, as can be seen in Figure 1,
relatedness has three dimensions; similarity, interconnectedness, and complementarity.
Similarity includes sharing technological characteristics such as part geometries or
components, offering the same functionality, fulfilling the same strategic role in the
portfolio as a prior product, or any other such indication of a like kind relationship.
Interconnectedness relates to a connection via an interface such as those identified by
Ulrich’s (1995) slot, bus, and sectional typology. The gist is that there is a physical
connection between two elements which may be mechanical or electrical. The
interconnectedness of elements includes not only the physical connections, but also
conceptual relationships. Thus two products in a portfolio may not be physically related,
but rather related in a familial way. For example, a product that supplants another in the
portfolio, the proverbial new and improved product, is connected to the old though the
similarity of position in the portfolio, functionality offered, market segment targeted, or
other logical connection. Complementary relatedness is used in the economic sense. The

demand for one product influences that of another. The stronger this relationship, the

10

more complimentary the products are. For example, computer servers and data storage

devices are compliments as are mp3 players and digital music.

Figure 1
Dimensions of Complexity

 

  

Relatedness

Inter-
Connectedness

     

  
  

   
 

Complementarity

 

 

 

It should be noted that in this study the term complexity is used in lieu of the term
‘commonality’. There are many works which address commonality; however
commonality is merely a descriptive term for one aspect of complexity. Specifically,
commonality is a state of increased relatedness in conjunction with a state of decreased

multiplicity. For example, when resistors of multiple tolerances are replaced with one

11

resistor that has a tolerance consistent with the most stringent application. Because this
resistor is used in more locations than before it replaced the others, it is more inter-
related. There are more connections it has to differing parts of the product. The
multiplicity is decreased because the total number of unique parts in the product has been
reduced. Hence the conceptualization of product complexity presented herein subsumes

commonality.

Within the context of this research, the focus is the portfolio of products. However, this
research may offer insights to other levels e.g. subassemblies, modules, or components

and in other contexts e. g. process steps or social systems.

1.4 Motivation

Prior research has shown that increased product complexity can be beneficial to efforts to
increase sales revenue (Kekre & Srinivasan, 1990; Lancaster, 1979; Quelch & Kenny,
1994). However, the revenue increases at a diminishing rate and the increased costs
associated with added complexity may eventually dominate the revenue gained (Baumol,
Panzar, & Willig, 1982; Kotler, 1986; Lancaster, 1979; Moorthy, 1984; Quelch & Kenny,
1994; Robertson & Ulrich, 1998; Sievanen, Suomala, & Paranko, 2004). Thus the
combination of diminishing sales returns and increasing costs due to complexity imply
there is an optimal level of product portfolio complexity. Hence, finding and maintaining
near optimal complexity levels is an implied, but difficult, management task. The task is

difficult because the drivers of complexity have not been articulated, their impacts

12

quantified, and the models and heuristics presented to date do not sufficiently capture the

scope of the problem.

Researchers have addressed product complexity somewhat myopically, and often with
the perspective that less complexity is always better. For example, some have suggested
the inventory and risk pooling benefits from component commonality (Fisher et al., 1999;
Hillier, 2000). Others have suggested that procurement cost reductions resulting fiom
reducing part count (Meyer and Mugge (2001). Another research stream studies the
influence of the product architecture on the firm's ability to communicate effectively and
coordinate design activities (Galvin & Morkel, 2001; Meyer & Mugge, 2001; Sanchez &
Mahoney, 1996; Ulrich & Tung, 1991). Yet another line of research relates to measures
of research and development (R&D) effectiveness and the degree of modularity within a
production process (Meyer, Tertzakian, & Uttcrback, 1997; Qiang, Mark, Ragu—Nathan,
& Bhanu, 2004). Several studies examine the level of flexibility that various design
architectures facilitate (Baldwin & Clark, 1997; Chang & Ward, 1995; Galvin & Morkel,
2001; Sanchez & Mahoney, 1996; Ulrich & Tung, 1991). Lastly, researchers have
examined the effects of complexity on product development costs (Clark & Fujimoto,
1991). These studies identify design strategies including component standardization and
reuse schemes, modular-based product architectures, and platform-based design
approaches by which the operational costs of supplying a complex product portfolio can
be reduced. These strategies enable inventory reductions, unit price acquisition curbs,
redundancy of suppliers (Langlois & Robertson, 1992; Robertson & Langlois, 1995), and

new schemas for organizing resources within the firm that can decrease cost (Meyer &

13

Mugge, 2001). However, the literature lacks studies that address the management of

product portfolio complexity in a more comprehensive way.

The appropriateness and robustness of these strategies has not been rigorously examined
empirically. Therefore, it is important to study complexity from a broader perspective to
develop principles to apply in conjuction with other strategies. With market demands
constantly driving toward more complexity and resource requirements suggesting less
(Lawton, 2007; Patton, 2007), it is important that managers understand which strategies
are effective for moving a business unit’s product portfolio closer to profitable, if not

optimal, levels of complexity.

The search for the right amount of complexity has spawned research that appears to reach
contradictory conclusions. There is one body of literature which suggests that
complexity reduction is desirable. There is another established body of literature that
posits that firm performance is increased through more product complexity. The
evidence provided by both camps is compelling. Thus there appears to be an unresolved
gap in the literature in relation to complexity. This demonstrates the need to provide,
from a theoretical basis, greater understanding of the advantages and disadvantages of the

differing complexity dimensions.

In part, the lack of clarity is a result of an imprecise definition of complexity. For
example, sometimes it seems that researchers are addressing the multiplicity dimension

of complexity and sometimes the relatedness dimension. However, they speak in generic

14

terms. This is problematic in that the ramifications of the two different types of
complexity may be very different. Therefore an important first step in the

reconceptualization is an improvement on the definition of complexity

This study provides a timely and first step toward improved clarity regarding complexity
in that it investigates the relationship between product portfolio complexity, sales volume
and cost. This is the first research to empirically assess how product complexity
influences both sales volume and cost. It also addresses the gaps identified by Ramdas
(2003), Krishnan and Ulrich (2001), and Yano and Dobson (1998). It does so by
providing a theoretical base to explain the relationship between product complexity and
cost and product complexity and sales volume by extending two well accepted theories;
Performance Frontiers (Schmenner & Swink, 1998) and Transaction Cost Economics

(Coase, 1937; Williamson, 1981, 1991, 1996, 2002).

1.5 Form of research questions
This dissertation develops and tests hypothesized relationships to address the following

objectives:

0 Identify and develop measures of the multiplicity and similarity dimensions of
complexity that are predictive of various costs and volume effects.
0 Test the relationship between the measures of complexity developed and various

costs and sales volume.

15

0 Determine the nature of the relationship between various dimensions of complexity

and various costs and sales volume

To address these objectives, the study integrates the engineering, marketing, and
operations management literatures to develop theoretical explanations for product
complexity’s impacts on the supply chain performance outcomes of cost and sales
volume. The development of specific hypotheses are informed by past conceptual,
analytical, and empirical research and are grounded in two well established theoretical

frameworks. These hypotheses take the following general form:

0 Complexity type X has a non-linear effect on supply chain non-recurring and
recurring costs.

0 The functional form of the relationship between complexity type X and resulting
supply chain non-recurring and recurring costs Y will be nonlinear.

0 Complexity type X has a positive and non-linear effect on sales volume

1.6 Overview of the research methodology

The data provided by a large designer and manufacturer of data processing equipment
computer manufacturing firm includes financial statements, product configuration, and
sales information for four brands. This data reflects quarterly activities for each brand for
the most recent three years. The data set is organized as products nested within models

nested within brands.

16

Fixed effect multiple regression models, time series regression, and panel data regression
are used as appropriate to test the hypothesized relationships between sales or cost data

and complexity factors.

1.7 Research Contribution

Little empirical work has been performed on the subject of product complexity (Bayus &
Putsis, 1999; Lancaster, 1990; Ratchford, 1990) that can guide management practices.
While studies investigating various complexity management strategies can provide some
insight to the larger topic of product complexity e. g. Galvin and Morkel (2001), Meyer
and Mugge (2001), Nobeoka and Cusumano (1997), Robertson and Ulrich (1998), and
Sanchez and Mahoney (1996), they do not directly address or empirically validate
relationships between product complexity and cost or sales volume. Nor do they, in any
rigorous sense, provide explanations or quantifications of the conclusions proposed.
None of these research studies provide theoretical explanations or identify specific

metrics that are predictive of cost or sales volume.

Given the nature and focus of published research to date, there remains a gap. Research
is needed to determine the optimal level of product complexity in the face of conflicting
cost and revenue implications (Fisher, Iain, & MacDuffie, 1995; Fisher & Ittner, 1999).
Fisher and Ittner (1999) go on to say that there is a general lack of understanding about
the specific mechanisms through which complexity affects costs. Ramdas (2003) echoes

this when she calls for research investigating the non-linear impact of complexity on cost.

17

Ishii, J eungel, and Eubanks (1995) also corroborate the call for a need for greater

understanding of how product complexity affects supply chain costs.

In light of these calls for additional insight, this study provides significant contributions
to the research community. It provides a clear definition of complexity so that future
research can more effectively build on the work of others and prior work can be
reconceptualized thereby allowing the findings to be made more specific. This research
establishes a sound theoretical framework by which complexity can be studied. This in
conjunction with a more precise definition of complexity will facilitate an acceleration in
advances on the topic. Additionally, this research will provide a theoretical basis that
explains the functional forms of the relationship between different dimensions of
complexity and various costs and sales volume. Maybe most significantly, this research
will identify the functional relationship between complexity and sales volume and cost.
Knowing the functional relationships of will enable managers to identify the optimal

level of complexity in the portfolio to maximize either sales volume or profit.

1.8 Plan of Work

This research project follows the time table presented in Table 2.

18

Table 2
Plan of Work

 

Activity

Target Completion Date

 

Frame research

January 1, 2007

 

Draft dissertation topic
proposal

September 15, 2007

 

Defend dissertation topic

October 15, 2007

 

Gather data

November 30, 2007

 

Analyze data

February 29, 2008

 

Synthesize findings

June 15, 2008

 

Defend dissertation

July 15, 2008

 

 

Final edits completed

 

July 31, 2008

 

19

 

2.0 Literature review

2.1 Introduction

The literature relating to product complexity is quite broad. It spans four major
disciplines; marketing, engineering, operations, and organizations (Krishnan & Ulrich,
2001) and is informed by the mathematical and hard science literatures. Since the
literature base is so wide, this review will address it relative to several focused areas. The
areas that are pertinent include portions of the marketing, engineering, and operations
management literatures relating to various aspects of product platforms, modularity,

commonality, engineering design, portfolio theory, and product diversification.

The remainder of this chapter is organized as follows. First, a typology of product
complexity is presented and the areas focused upon in this research are highlighted.
Next, the current state of the pertinent literatures relating to product portfolio complexity

is discussed. Last, there is a summation of the chapter.

2.2 Typology of Product Complexity

As defined prior, product complexity represents a multiplicity of related elements. Per
the complex systems literature (Boulding, 1956; Simon, 1962) product portfolio
complexity could be represented on several levels ranging from the portfolio of a firrn’s
offerings down to the individual component level of the products within the portfolio.
Complexity represented at the portfolio level is exemplified by the number of different
models represented in the product portfolio (multiplicity) (Fisher et al., 1999). It is also

represented by the rate of replacement (churn) of the products within the portfolio

20

(Ramdas, Fisher, & Ulrich, 2003). At the individual product level, which is addressed by
Griffin (1997a) and Mac Cormick and Rusnick (2006), it is characterized as the number
of features or functions embodied in a product (multiplicity) and their interconnectedness
(relatedness). Lastly, there is complexity at the component level which has two
dimensions; part count (Gupta & Krishnan, 1999) and interconnectedness (Tatikonda &
Stock, 2003). For example, a product portfolio’s complexity may be increased by
increasing the total number of components it comprises (multiplicity) (Gupta & Krishnan,
1999), by increasing the number of technical fimctions (or “features”) embodied in it
(Griffin, 1997a), or by increasing the degree of interconnectedness among its constituent
components, modules, or products (relatedness) (Tatikonda & Stock, 2003). Thus the
typology contains four categories of complexity at each of three levels as shown in Figure
2. There is multiplicity complexity and three dimensions of relatedness complexity:
similarity, interconnectedness, and complementarity. Each of these appear at each
distinct level of complexity: portfolio, product, and component. This research will focus

on multiplicity and similarity at the portfolio and product levels as depicted in Figure 3.

21

Figure 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Typology
Portfolio
Product
Complimentarity
Component Interconnectedness
Similarity
l 9%
6‘66 @600
(as ea»
Figure 3
Research Focus
Product
Portfolio
Complimentarity
Component Interconnectedness
Similarity

Multiplicity Relatedness

22

2.3 Portfolio Level Complexity

A portfolio of products represents the mix of products offered to the market, their stage of
lifecycle, and competitive position (Day, 1977). It is one of the most strategic elements
of the firm as it reflects resource allocation decisions e. g. decisions about which products
and projects the firm should fund (Cooper, Edgett, & Kleinschmidt, 1997a). Applying
the definition of complexity to the product portfolio yields the following insight. A
portfolio that is complex will have a large number of products and / or the products
within the portfolio will be highly related in some way. Therefore the decisions about
additions, deletions, and the inter-relationships among the products within the portfolio

are of strategic importance.

Decisions about products entering, exiting, and replacing others within the portfolio are
made with two objectives in mind; balancing the funding requirements of the firm and
risk mitigation (Cooper et al., 1997a; Henderson, 1970, 1972a, 1972b). Firms seek a
portfolio that can both generate large amounts of cash currently and offer significant long
term sales growth potential. This has traditionally been accomplished by satisfying as
many customer preferences as possible with the ultimate goal being the creation of the
ideal product for each segment (Dobson & Kalish, 1988). Within this context firms seek
to minimize risk from exposures to threats such as economic events, political or
regulatory vagaries, or supply disruption (Day, 1977). However this leads to a revenue /
sales volume focus and a failure to take into account the requirements of providing the
product to the customer. The result is a one sided analysis with a reduction in profit as a

potential outcome.

23

Portfolio theory (Markowitz, 1959) emerged as a means to model and quantify the risks
within a portfolio of products. As such, it provides a theoretical basis for the forces
driving product portfolio complexity. Portfolio theory Suggests that products can be
treated as investments; each yielding a unique revenue / sales volume stream subject to
volatility. The objective is to minimize the variability of financial returns (risk) or
maximize the return for a given level of risk. The latter forms an efficient frontier of
project investment (Cardozo & Smith, 1983). One means by which risk can be mitigated
is the assembly of a portfolio containing products exposed to different market segments,
geographies, etc. Historically, this has meant providing a product tailored to each of
these niches. However, once the portfolio is large enough there are no longer benefits to
adding more items since the average rate of return will tend to the true mean and adding
one more cash flow stream will not significantly change it. Also, the efficient frontier
hints at the existence of a correct or optimal configuration. Hence, diversification beyond

a certain point may not be advantageous.

The genesis of product complexity resides within the portfolio level. The twin objectives
of funding requirements (generating large amounts of cash currently and long term sales
growth potential) and risk mitigation (Henderson, 1970, 1972a, 1972b) are powerful
forces driving added levels of complexity. Firms are pressured to introduce product
variants into additional markets to offset economic or political risks as well as offer
broader lines in the hope of increasing the chance of a runaway success. There are

further forces such as competitive positioning and responses, reward structures,

24

organizational structure, data management maturity, and governance that work to cause
firms to offer more products (Closs, Jacobs, Swink, & Webb, 2007). These forces
potentially have costly ramifications including increases in the costs of production,
inventory, warranty, shipping, development, administrative support, marketing, and

financing.

Peter Drucker (1963b) observed the difficulty domestic firms were having competing in
global markets and hypothesized that the market performance of the products of U. S.
firms was hindered by portfolios that were too broad. Specifically, he proposed that
focusing on fewer products would enhance competitive strength. Drucker’s work
spawned several approaches to finding the mix of products to hold in the portfolio that
maximized revenue / sales volume and growth opportunities. Several approaches were
proffered e.g. Wright (1978), Allen (1979), Wind (1975), but the one gaining the most
widespread adoption and attention was the cash flow matrix from the Boston Consulting

Group (Henderson, 1970).

The solution presented by Drucker (1963b), when viewed in the context of portfolio
theory, essentially suggests a shifting of the position of the portfolio along the risk /
return fiontier. By reducing the scope of the portfolio, returns can be increased, but at the
expense of added volatility. This led to two questions: is there a way to garner the gains
from reduced portfolio scope yet not relent on the drive to increase revenue / sales

volume, and how can the problem be modeled to gain greater insight. The complexity

25

management strategies of standardization, product platforms, and modularity are the

answers that have been offered so far to the first question.

The first of these three complexity management strategies to be investigated was
standardization; the use of common components (Evans, 1963; Lee & Tang, 1997). The
first significant research into this strategy was the operationalization of the construct
(Collier, 1981). Researchers used this and measures developed in subsequent articles
(Martin & Ishii, 1997; Wacker & Treleven, 1986) to ascertain the benefits of increased
standardization. Unfortunately, the research focused upon inventory costs and
availability almost exclusively, although this aspect of the topic is extensively covered by
many researchers e. g. (Baker, Magazine, & Nuttle, 1986; Collier, 1982; Farrell &
Simpson, 2003; Fisher et al., 1999; Fisher & Ittner, 1999; Hillier, 2002; McClain,
Maxwell, Muckstadt, Thomas, Weiss, & Collier, 1984; Rutenberg, 1971; Swink & Closs,

2006). This leaves open the need to investigate total cost implications.

The revenue impacts of too much customer perceived standardization were researched
empirically by Kim and Chhaj ed (2000) and analytically by Desai, Kekre,
Radhakrishnan, and Srinivasan (2001). They report that high levels of perceived
standardization can influence the price, or the consumer’s perception of value, by putting
downward price pressure on the high price product and upward price pressure on the low
price product. However, remaining to be researched are implications of other types or

measures of portfolio complexity.

26

Product platforms were the next complexity management strategy to be explored. The
product platform is presented as a means to migrate products from one quadrant of the
ECG matrix to another (Meyer & Lehnerd, 1997; Sanderson & Uzumeri, 1995) and thus
improve the quality of the portfolio as related to revenue / sales volume grth and risk
mitigation. In particular, the implied objective is to maximize the number of stars given
the ftmding available from the cash cows. The platform enables the entry into new
markets (the chance to create new stars) while facilitating cash cows through scale
economies (Farrell & Simpson, 2003; Krishnan, Singh, & Tirupati, 1999; Sanderson &

Uzumeri, 1995).

There appear to be limits however to the benefits that can accrue from a complexity
management strategy entailing platforms. Krishnan and Gupta (2001) found limits to the
benefits from platforms that were brought about by increased component costs
attributable to standardization and design costs. They found that increased
standardization was beneficial as long as the unit cost of the component being
standardized was not too high relative to alternative suitable components (multiplicity).
This leads to the conclusion that there is a diminishing benefit to reducing product
complexity. Similar findings are reported in the engineering literature where product
performance is used as the guide to finding the ideal number of platforms to deploy
across a product portfolio (Nelson, Parkinson, & Papalambros, 2001; Seepersad, Mistree,
& Allen, 2002; Simpson, Seepersad, & Mistree, 2001b). Since the consensus is that a
portfolio of higher performing products entails a greater number of components, this is

effectively an investigation into the tradeoffs between the complexity dimensions of

27

similarity and multiplicity. Again, the pattern of diminishing returns to decreasing
complexity is expected. Thus, one interpretation of these findings is that a level of
complexity in the portfolio greater than the theoretical minimum is requisite because it is

not economical to standardize on one platform.

A different group of researchers (Farrell & Simpson, 2003; Krishnan etal., 1999; Meyer
& Lehnerd, 1997; Sanderson & Uzumeri, 1995) contend that platforms can be
advantageous to cost effectively pursuing additional market segments. Thus it would
appear there are increasing returns to decreasing complexity. This finding is not
necessarily paradoxical to that of Krishnan and Gupta (2001). A more likely conclusion

is that the benefit realized from reducing levels of product complexity may be concave.

Modularity is another complexity management strategy that has been explored in the
literature. Modularity emphasizes minimization of strong interdependencies within a
product (Baldwin & Clark, 1997, 1999). Modularity is a systems concept that defines the
degree to which elements can be combined to create a wide variety of end items (Evans,
1963; Lampel & Mintzberg, 1996; Pine, Victor, & Boynton, 1993; Schilling, 2000;
Ulrich, 1995; Walz, 1980). Thus, like product platforms, modularity is proposed to be a
means by which a broad product portfolio can be offered. Also like product platforms,
there is research revealing both beneficial and detrimental outcomes to its use. The
benefits include economies of scale (Pine et al., 1993), inventory reductions (Fisher et al.,
1999; Kim & Chhajed, 2000; Meyer & Mugge, 2001; Mirchandani & Mishra, 2002;

Ramdas & Randall, 2004; Swink & Closs, 2006; Tu, Vonderembse, Ragu-Nathan, &

28

Ragu-Nathan, 2004), engineering efficiencies (Collier, 1981), and improved coordination
(Danese & Romano, 2004; Galvin & Morkel, 2001; Nobeoka & Cusumano, 1997;
Sanchez & Mahoney, 1996; Schilling, 2000). However, the benefits are a function of the
cost of the components being standardized (Fisher & Ittner, 1999; Karmarkar & Kubat,

1987; Ramdas et al., 2003).

Along with efforts to find effective strategies to manage the impacts of complexity is a
stream that uses mathematical modeling to find the ideal portfolio composition. The
modeling approach was initially pursued by researchers who were concerned that the
cash flow techniques offered by consultants suffered from substantial amounts of
subjectivity. This led to the attempt to model the problem analytically e.g. Green and
Krieger (1985), McBride and Zufryden (1988) or Dobson and Kalish (1988) or through
optimization techniques e. g. Archer & Ghasemzadeh (1998; 1999), Baker (1974), Baker
& Pound (1964), Danila (1989), Ghasemzadeh & Archer (2000), and Liberatore (1988).
Unfortunately none of these models were put to the test for feasibility (Cooper et al.,

1997a)

There are limitations to pursuing mathematical models. The analytical models such as
those reported by Green and Krieger (1985), McBride and Zufryden (1988) or Dobson
and Kalish (1988) are limited by several assumptions. The analytical models assume
there is only one product considered with one attribute of interest to the consumer, the
customer always prefers more than less, the segments are ordered the same at every level

of the attribute under consideration, and there is no cost of production (Dobson & Kalish,

29

1988). The extensive assumptions are required due to the extremely high levels of
difficulty in solving problems with unconstrained and unstable boundaries. More recent
literature (Dobson & Kalish, 1993; Nair, Thakur, & Wen, 1995) has focused on
numerical models and heuristics. For example, Rao, SWaminathan and Zhang (2004) use
an optimization approach to study certain aspects of product complexity. In their
research they model and develop heuristics for the effect of demand variance and benefits
of substitution on inventory levels and production set ups. However, these too did not

consider production costs and therefore may lead to untenable solutions.

In conjunction with the portfolio of products represented at the firm or brand level, there
is a related portfolio; the portfolio of projects under development that may enter the
product portfolio. Scholars (Dean & Nishry, 1965; Moore & Baker, 1969; Bonini, 1975;
Utterback & Abernathy, 1975) began to address this level shortly after Drucker’s (1963a)
article appeared. Several researchers have made the attempt to model the problem
analytically or through optimization techniques (Archer & Ghasemzadeh, 1998; Archer
& Ghasemzadeh, 1999; Baker, 1974; Baker & Pound, 1964; Danila, 1989; Ghasemzadeh
& Archer, 2000; Liberatore, 1988). Unfortunately none of these models were put to the
test for feasibility (Cooper et al., 1997a). This could possibly be due to the fact that
interrelationships between new and existing products are very difficult to quantify
(Cooper, Edgett, & Kleinschmidt, 1997b). The lack of practical value to the analytical
and optimization approaches is demonstrated by a lack of both use and interest among the
firms represented in a review of 205 major US. firms (Cooper et al., 1997b; Cooper,

Edgett, & Kleinschmidt, 1999). However, managers of these firms did express interest in

30

decision tools and rules of thumb to guide decisions about which products should enter,

exit, or remain in the portfolio (Cooper, Edgett, & Kleinschmidt, 2001).

Product platforms, modularity, and standardization are all strategies to manage the level
of product and component level complexity (Choi & Krause, 2006). Using the example
of the bicycle industry Galvin and Morkel (2001) present a case for the benefits of
standardization. Since interfaces are standardized in the bicycle industry, a manufacturer
that cannot obtain a supply of sprockets fiom company X can easily secure the product
from company Y. The result is that supply disruptions are minimized and the price of
sprockets is kept low. This illustrates the power of standardized interfaces. Standardized
interfaces enable inventory reduction, unit price acquisition curbs, and redundancy of
suppliers enabling a decrease in supply interruption risks. The result is affordable high
quality products that are widely and readily available (Langlois & Robertson, 1992;
Robertson & Langlois, 1995). Thus there appear to be significant benefits to increasing

the similarity represented within a product or portfolio of products.

The literature also presents examples of benefits resulting from reduced multiplicity.
One is the leveraging of a product platform across the product line (Meyer & Mugge,
2001). The result is new schemas for organizing resources within the firm that can
increase effectiveness and decrease costs. Several other researchers explore the
relationship between multiplicity and inventory (Collier, 1982; Fisher et al., 1999; Fisher
& Ittner, 1999; Ramdas et al., 2003) and find that reduced multiplicity leads to lower

inventory costs and better service levels. Ramdas and Randall (2004) report that reduced

31

multiplicity leads to improved quality. Thus benefits to reducing product multiplicity

appear to be well established.

However, research has shown that product complexity Can increase sales revenue (Kekre
& Srinivasan, 1990; Lancaster, 1979; Quelch & Kenny, 1994; Sanderson & Uzumeri,
1995). Revenue / sales volume will grow incrementally for each variant because each
variant can be targeted at an untapped niche. Thus the marketing literature has
established the benefit to the firm of increased levels of portfolio complexity. While it is
desirable to grow revenue or sales volume, some have postulated that the costs associated
with increased product complexity resulting from additional variants will eventually
overcome the benefit from increased revenue or sales volume (Kotler, 1986; Sievanen et
al., 2004; Suomala, Sievanen, & Paranko, 2004); the result being a concave profit
function (Lancaster, 1990). However, unknown is the precise shape of this curve. One
group of researchers has begun to address this question, but have yet to go beyond
exploratory research hypothesizing that the kurtosis and skewness of the curve will vary
by industry and over time (Closs et al., 2007). Closs et al. (2007) and Lancaster (1990)

imply that product complexity greater than the theoretical minimum may be beneficial.

Yano and Dobson (1998) report that the effect of product complexity on profit has
seldom been considered. Similarly, few industries have developed effective analytical
tools to manage both the revenue or sales volume from variety and the countervailing
costs simultaneously in product portfolio decision making (Otto, Tang, & Seering, 2003).

These analytical tools should account for the scope economies recognized from multiple

32

customer and market segments and the reduction of scale economies in designing and

delivering the product (Yano & Dobson, 1998).

Ramdas (2003) states that the prescriptive models for product variety, presented in the
literature, often have limited use due to a focus on narrow tradeoffs within functional
silos which ignore important interdependencies. She adds that simply adding terms to
existing models will not remedy this problem. Developing practical models will require
understanding (and quantifying) the underlying factors that intertwine different functions,

such as product architecture (Krishnan & Ulrich, 2001).

Since the literature characterizes as beneficial both increases and decreases in
complexity, there is a need to reconceptualize the apparent paradox (Van de Ven, 1989).
This is implicitly supported by Gershenson (2003) who finds a need to illuminate this
topic and hence calls for studies to validate the benefits of complexity management
strategies such as modularity. Qiang, Mark, Ragu-Nathan, and Bhanu (2004) further add
that identifying new theory in this area is growing in importance. An example of this
need is found in the work of Randall and Ulrich (2001) who show that complexity is
related to differing supply chain outcomes. However, they do not offer a means to
quantify the relationship and thus cannot make predictions. This points to the need to
conduct theory building research that can provide a more complete understanding of the

topic.

33

Table 3
Summary of Literature

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Author Journal Year Title Findings
The supply base
and its complexity:
Implications for Platforms, modularity
transaction costs, and standardization are
Journal of risks, all strategies to manage
Operations responsiveness, product / portfolio
Choi & Krause Management 2006 and innovation complexity
Multiple forces such as
Toward a theory of competitive positioning,
competencies for IS maturity, and
Journal of the management of governance combine to
Closs, Jacobs, Operations product complexity: impact the number of
Swink & Webb Management 2007 Six case studies products offered
The Measurement
and Operating
Benefits of Presented a metric to
Component Part quantify the degree of
Collier Decision Sciences 1981 Commonality commonality
Aggregate safety
stock levels and Safety stock diminishes
Management component with an increased level
Collier Science 1982 commonality of commonality index
A product variety A method is presented
ASME Design tradeoff evaluation to evaluate the tradeoff
Engineering method for a family between commonality
Conner, De technical of cordless drill and an individual
Kroon & Mistree Conference 1999 transmissions product's performance
Product
differentiation and
commonality in
Desai, design: Balancing Excessive customer
Radhakrishnan, Management revenue and cost perceived commonality
& Srinivasan Science 2001 drivers influences price
Feature proliferation
Heuristics for arises through drive to
pricing and satisfy as many
Management positioning a customer preferences
Dobson 8. Kalish Science 1993 product-line as possible
Concurrent Architecture of
Engineering: Product Family: Introduce a measure of
Du, Jaio & Research and Fundamentals and variety of choice at the
Tseng Application 2001 Methodology product family level
Product platform Provides a procedural
Journal of design to improve approach to determining
Farrell 8. Intelligent commonality in the optimal number of
Simpsom Manufacturing 2003 custom products platforms

 

 

34

 

Table 3
Continued

 

Platform selection
under performance

A model is presented to
generate the optimal

 

 

Fellini, Journal of bounds in optimal number of products to
Kokkolaras & Mechanical design of product offer the market subject
Papalambros Design 2006 families to performance bounds
Component sharing
in the management Sharing of components
of variety: A study is largely a factor of
Fisher, Ramdas of automotive volume. Lower volumes
& Ulrich MS 1999 breaking systems result in greater sharing.
Product
architecture
assessment: a tool
to link product,
process, and Presented a means to
supply chain design operationalize
Fixson JOM 2005 decisions 'connectedness'

 

On the benefits of
risk pooling and the

Increased demand
variability increases the
risk pooling benefits of

 

 

 

 

 

 

 

variability of commonality in most
Gerchak & He IIE Transactions 2003 demand circumstances
Component Deploying commonality
Gerchak, commonality with is beneficial to
Magazine 8. Management service level maintaining service
Gamble Science 1988 requirements levels
Product variants are
The product introduced to offset
Henderson Perspectives 1970 portfolio economic risks
Component
commonality in Commonizing more
multi-period expensive parts isn't
Naval Research assemble to order always recommended in
Hillier Logistics 1999 systems multi-period cases
Component
commonality in Commonizing more
multi-period expensive parts isn't
assemble to order always recommended in
Hillier llE Transactions 2000 systems multi-period cases
Provides a model based
A methodology of approach to developing
developing product a product family
Journal of family architecture architecture. This PFA
Intelligent for mass can be leveraged for
Jiao & Tseng Manufacturing 1999 customization commonality
Understanding
product family for
mass customization
Journal of by developing
Engineering commonality Proposes a
Jiao & Tseng Design 2000 indices commonality measure

 

 

 

 

 

35

 

Table 3

 

 

 

 

 

 

 

 

 

 

 

 

 

Continued
Measuring product Develops a dependency
International structures to index that can be used
Journal of improve demand- to determine the
Technology supply chain strength of relationships
Kaski & Heikkila Management 2002 efficiency between modules
Commonality in
product design:
European Journal Cost saving, Excessive customer
of Operational valuation change perceived commonality
Kim & Chhajed Research 2000 and cannibalization influences price
A metric for
Kota, Journal of evaluating design Presented a metric to
Sethuraman 8. Mechanical commonality in operationalize
Miller Design 2000 product families commonality
Appropriateness
and impact of There a limits to the
platform-based benefits of platforms
Krishnan & . Management product imposed by the cost of
Gupta Science 2001 development components
International Mass
Journal of Flexible customization: Introduces metrics that
Manufacturing Metrics and quantify the degree of
Kumar Systems 2005 modularity customization
The economics of Increased product
Marketing product variety: A complexity increases
Lancaster Science 1990 survey sales revenue
Feature substitution is
acceptable if costs are
equivilent. Eliminating
Product hardware features for which there
International complexity and its is low demand is
Lin, Breitwieser, Journal of Flexible impact on inventory superior to elimination
Cheng, Eagan, & Manufacturing and customer on of features for which
Ettl Systems 2000 time delivery there is a low usage
Exploring the
Relationship
Between Product
Architecture and
Organizational Presented an approach
MacCormick 81 Form: A Test of to calculate
Rusnak POMS conference 2006 "Conway's Law" 'connectedness'
ASME Design Design for variety:
Engineering Development of Offers a method to
technical complexity indices quantify process
Martin & Iishi Conference 1997 and design charts commonality

 

 

36

 

Table 3
Continued

 

Design for variety:

 

 

 

 

 

 

 

 

 

 

developing
standardized and Presented several
Research in modularized metrics for
Engineering product platform operationalizing
Martin 8. Iishi Design 2002 architectures commonality
This paper introduces a
Capturing the mathematical model,
Degree of termed the
The Journal of Modularity modularization function,
Product Embedded in for analyzing the degree
Innovation Product of modularity in a given
Mikkola Management 2006 Architectures product architecture.
This paper introduces a
Managing mathematical model,
Modularity of termed the
IEEE Product modularization function,
Transactions on Architectures: for analyzing the degree
Mikkola 8. Engineering Toward an of modularity in a given
Gassman Management 2003 Integrated Theory product architecture.
A nonlinear optimization
model is presented to
generate the optimal
Multicriteria number of products to
Nelson & Journal of optimization in offer the market based
Parkinson & Mechanical product platform upon performance
Papalambros Design 2001 design characteristics\
Sourcing by design: Vertical integration of
Product complexity production and
Novak & Management and the supply complexity of design are
Eppinger Science 2001 chain complements
Prescriptive models in
the literature addressing
Managing product portfolio variety focus on
variety: An narrow tradeoffs and
Production and integrative review ignore important
Operations and research interdependencies
Ramdas Management 2003 directions limiting their usefulness
Presents a linear
program formulation to
guide the determination
Managing variety fo of components to
assembled commonize. Reduced
products: Modeling multiplicity leads to less
Ramdas, Fisher component inventory and better
8. Ulrich MSOM 2003 systems sharing service levels

 

 

37

 

Table 3
Continued

 

Product variety,

 

supply chain

structure, and firm Established the

performance: relationship between

Analysis of the US supply chain structure
Randall & Ulrich MSOM 2001 bicycle industry and product complexity

Multproduct

inventory planning
with downward

With nonzero setup
costs, optimal inventory

 

Rao, substitution, levels may increase with

Swaminathan 8. stochastic demand component

Zhang IIE Transactions 2004 and setup costs standardization
Production-

inventory systems
economy using a

Presented several

 

 

 

 

 

 

 

 

 

component metrics for
Midwest DSI standardization operationalizing
Roque conference 1 977 factor commonality
Modularity, product
variety, production Proposes two types of
volume, and modularity -
component combinitorial &
Salvador, Forza Journal of sourcing: theorizing component swapping -
& Operations beyond generic that can reduce impact
Rungtusanatham Management 2002 prescriptions of variety on operations
Platforms can be
Managing Product leveraged into
Families - The additional niches to
Sanderson 8. Case Of The Sony- generate revenue
Uzumeri Research Policy 1995 Walkman growth
A quantitiative Relates the result of
approach for using a goal
ASME Design designing multiple programming technique
Engineering platforms for an to determine the ideal
Seepersad, technical evolving portfolio of number of platforms for
Mistree & Allen Conference 2002 products a family
Costs of adding items to
the portfolio will
Sievenan, Industrial eventually subsume the
Suomala 8 Marketing Product profitability: revenue gains from the
Paranko Management 2004 Causes and effects addition
Assessing variable
levels of platform Suggests the use of
Concurrent commonality within deviation functions to
Engineering: a product family measure the level of
Simpson 8. Research and using multiobjectlve commonality across a
D'Souza Application 2004 genetic algorithm product family

 

 

38

 

Table 3
Continued

 

Balancing
commonality and
performance within

Developed a non-
commonality and
performance deviation

 

 

 

 

 

 

 

 

 

Concurrent the concurrent index to quantify the
Simpson, Engineering: design of multiple tradeoff between
Conner & Research and products in a commonality and
Mistree Application 2001 product family performance
A methodology to
support product Introduces the use of a
family redesign genetic algorithm using
ASME Design using a genetic shape and assembly
Thevenot, Engineering algorithm and factors from the product
Nanda & technical commonality to determine the optimal
Simpson Conference 2005 indices degree of commonality
Develop a linear
Optimal program to determine
Thonemann 8 Operations commonality in the optimal level of
Brandeau Research 2000 component design component commonality
Component part
standardization: an
analysis of Presented several
commonality metrics for
Wacker & sources and operationalizing
Treleven JOM 1986 indices commonality
2.4 Summary

In summary, topics related to product portfolio complexity management have been active

in the literature since the late 1950’s. However, the bulk of the literature pertaining to

product complexity, no matter the level of analysis (portfolio, product, component), is

focused narrowly on inventory effects. Even the research creating measures of

complexity is done so with the intent of using the measures to gain insight to inventory

effects. There has been a small amount of research in the engineering literature

investigating the impact of complexity on product performance and development project

39

 

timing. When viewed retrospectively through the lens of product complexity, each
work addresses only a portion of the topic, e. g. considering revenue in isolation of cost.
My contention is that the underlying dimensions of interest are multiplicity and
relatedness and that, although admirable, prior research'has failed to simultaneously
address these underlying dimensions. This has prevented the development of robust
theory that can guide both research and application. Pervasive in the literature is the tacit
acknowledgement that there is an optimal level of complexity e. g. portfolio breadth,
market diversity, etc., but the research most always approaches the topic from the

perspective that less is better.

There are clear gaps that become apparent from the literature review. First is the need to
improve the definition of complexity since the existing research lacks clarity due to
inconsistent meanings. Second is the need for heuristics addressing production costs
since current ones consider revenue or market share in isolation (Dobson & Kalish, 1993;
Nair et al., 1995). The models published to date are limited by assumptions: one product
considered with one attribute of interest to the consumer; the customer always prefers
more than less; the segments are ordered the same at every level of the attribute under
consideration; and there is no cost of production (Dobson & Kalish, 1988). These
assumptions are due to the extremely high levels of difficulty in solving problems with
unconstrained and unstable boundaries. Empirical research into complexity management
strategies has shown there are relationships between product complexity and the
competitive priorities of cost, quality, flexibility, and delivery (Jacobs, Droge, Vickery, &

Calantone, 2006; Jacobs, Vickery, & Droge, 2007). However, it does not provide insight

4O

into the functional nature of and relationships between the various dimensions of

complexity as they pertain to competitive performance.

41

3.0 Theory Development

There are two theoretical perspectives that provide insights regarding the effect of
product portfolio complexity has on sales volume and cost. Both perspectives offer a
predictive element, in a directional sense, as well as some rationale for the predicted
outcome. These two perspectives are the Theory of Performance Frontiers (Clark, 1996;
Hayes & Pisano, 1996; Schmenner & Swink, 1998; Skinner, 1996) and Transaction Cost

Economics (TCE) (Coase, 1937; Williamson, 1981, 1991, 1996, 2002).

3.1 Two Theories

3.11 Theormf Performance Frontiers

 

The Theory of Performance Frontiers (TPF) is based in the neoclassical school of
economies, which holds that economic growth arises from technological progress and
output can be represented by a production function (Meade, 1962). Several economists
built upon this foundation to establish that there is a diminishing return to investments,
and that substitutions of resources were possible which could positively impact
productivity (Keynes, 1936; Leontif, 1941; Pareto, 1906; von Bohm-Bawerk, 1889).
Thus there is a limit to the performance an organization can achieve given a chosen set of
assets. Schmenner and Swink (1998) refer to this limit as the “asset frontier.” There is a
second performance limit, interior to the asset frontier, determined by the policies and
procedures of the organization, called the “operating frontier” (Schmenner & Swink,
1998). The theory states that an organization may move its operating frontier closer to
the asset frontier by revising the organization’s policies and procedures in ways that more

fully utilize its assets. The resulting increased effectiveness should be reflected in gains

42

in productivity and financial performance (Clark, 1996; Hayes & Pisano, 1996;
Schmenner & Swink, 1998; Skinner, 1996). However, this gain is nonlinear. The gain
increasingly diminishes as the operating frontier approaches the asset frontier. Similarly
the cost to move the operating and asset frontiers closer together grows exponentially as
the gap is narrowed (Schmenner & Swink, 1998). Putting the relationship between the
asset and operating frontiers into the context of product complexity, TPF suggests that
product designs, which are intangible assets of the firm, will be reused as often as is
practical given the assumption that the designer deems the existing design to be
compatible with the objectives of the new development project. Reusing a design is the
equivalent of moving the operating frontier closer to the asset frontier, as it enables a
fuller utilization of the organization’s assets. TPF implies that better financial
performance will result when assets are better utilized; hence better performance from
design reuse. Design reuse is manifested by the reuse of components, assemblies, and
systems. Taken a step further, TPF may predict the use of modular architectures as this
architectural form may offer the greatest opportunity for asset utilization. Modularity
enables increased utilization of the intangible design assets and additional hard and soil
assets in the supply chain that are dependent upon design. For example, product support
personnel can be more productive in the field because problems are easier to diagnose
and resolve (Karmarkar & Kubat, 1987) fewer unique problems are expected and entire
modules can be interchanged rather than repaired at the customer site. Also, equipment
to produce the modules may be more fully utilized due to the ability to build modules to
stock and assemble them in configurations consistent with customer demand (F eitzinger

& Lee, 1997; Pine et al., 1993; Worren, Moore, & Cardona, 2002).

43

Theory of Performance Frontiers and the similarity dimension of complexity are related
in the following way. First, consider the case where the production equipment is the
asset. For example, a lathe is an asset of the firm. It seems evident that a more fully
utilized lathe builds more products and thus scale benefits are recognized. Hence unit
cost can reach its theoretical minimum. There are clearly exceptions to this case, such as
labor that becomes increasingly more expensive the longer the lathe produces products,
thus it should not be construed here as a universal law, but rather as an effect seen

generally.

Further developing the example of the lathe, consider that the lathe supports two products
and that each time production calls for a change in products, a set up is incurred. This set
up consumes some percentage of the total available productive time of the equipment.
The result is that a structural element arises, represented by the gap between the operating
and asset frontiers. Hence the operating frontier can never reach the asset frontier.
Therefore maximum performance can never be attained. This scenario is replicated
throughout production facilities hundreds of times as the numbers of tools and other
productive assets increases, and the number of unique products to be produced upon them
increases. This fact leads to the realization that multiple dissimilar products lead to
multiple unique or uniquely configured production assets whereas multiple products
sharing design characteristics tend to result in increased utilization of fewer unique
assets. Thus moving the operating frontier closer to the asset frontier by designing

additional products with similar geometries leads to improved financial performance and

increasing the number of separate products tends to push the operating frontier away

from the asset frontier with the result being diminished financial performance.

The diminished financial performance is reflected in him ways. First, it may be reflected
in the decrease in the sales volume theoretically possible. The proverbial lathe spends a
certain amount of time inactive, and thus not providing parts for sale. Second, the time
spent setting up must be paid for. An employee is thus earning wages for performing
non-revenue generating work. This cost is then amortized over the products produced
with the effect of increasing the per unit transfonnation cost relative to the fully utilized

scenario.

Granted, there is no consideration of the value of the products produced, and assumptions
include hourly pay not piece work, and the ability to sell everything manufactured. These
assumptions and simplifications are consistent with traditional assrimptions of economics
and they enable the revelation of the primary principle; the similarity dimension of
complexity has significant operational impacts which lead to certain sales volume and

cost implications.

Now consider the case where product designs are assets of the firm. They are included
within the asset class of intangibles and intellectual property and represent the
irreversible work of engineers and other technical professionals. This labor creates the
product design which is represented by an asset frontier; there is only so much benefit

that can be realized from that design and it is constrained by the very nature and quantity

45

of the labor that created it. If a product design is used once and then abandoned, there is
a given amount of benefit the organization will recognize. However, if the design can be
used a second time (i.e. for a second product) then greater benefit is anticipated. Thus the
reuse of the design increases the utilization of the design. Hence the operating fiontier
has moved closer to the asset frontier; the benefit being primarily recognized as
decreased engineering expense and possibly decreased tooling costs and increased scale

economies.

Theory of Performance Frontiers predicts that complexity in the relatedness dimension
will lead to better cost outcomes. This occurs through the enhanced utilization of
existing resources; both tangible and intangible. However, the benefits will increasingly

diminish with ever greater levels of relatedness.

3.12 Transaction Cost Economics

 

Transaction Cost Economics is generally used to explain the governance of firms and
why they choose certain business transactions over others. Williamson (1991) indicates
that TCE is also useful for explaining organizational structures within a firm. If a product
portfolio is taken to posses a given structure, then it is appropriate to apply TCE to
explain the structure of a portfolio of products. The premise of TCE is that organizations
will act to minimize costs. These costs include both out of pocket expenses and costs
associated with risk. The three risks that TCE identifies are asset specificity,

environment, and opportunism.

46

There are a variety of out of pocket costs that will increase with increasing levels of
product portfolio complexity. Examples include marketing and advertising costs. These
will increase with both total number of products and with increased rates of replacement
due to the design and execution of additional marketing campaigns. The additional
campaigns result in increased advertising and accompanying increases in media buys,
promotional materials, and sales training. The extra number of products, both new and
replacement, require a higher level of managerial oversight to coordinate the various
sales and marketing campaigns, delivery channels, and other aspects of the business. The
result is an increase in cost. Beyond the sales and marketing impacts there are cost
ramifications deeper within the organization. These include increases in the areas of

manufacturing operations and product development.

Learning curve theory provides insight to the mechanisms that cause increases in cost
with increased numbers of transactions. For example, within manufacturing operations,
out of pocket costs increase because a larger number of separate items results in less
experience with any given item. Learning curve theory indicates that the number of
defects will be higher and productivity lower because the process is not as far down the
experience curve (Wright, 193 6). These defects will result in the out of pocket costs of

scrap or rework.

Another manner by which increasing the number of transactions increases cost can be
seen in the effects on inventory. Assuming the total demand is constant, increasing the

number of products makes forecasting more difficult due to a relative increase in demand

47

variability across products (Bendoly, Blocher, Bretthauer, & Venkataramanan, 2007;
Caplin, 1985). Inventory theory indicates that to maintain a consistent service level in the
presence of increased variability, the amount of available inventory must increase (Mize,
White, & Brooks, 1971). This impairs short term cash flow and raises financing costs.
Additionally, procurement costs might increase as a greater number of requisitions must

be processed.

Within the product development organization, there are additional non-recurring costs
incurred from the added design, certification, qualification, and related efforts that arise
fiom additional products or those that are more robust. Thus TCE predicts that an

increase in portfolio complexity will negatively impact out of pocket cost.

TCE holds that there are costs associated with certain kinds of risk. The first of these is
asset specificity. If the product design is considered to be the asset then the more finely
focused a niche at which the product is targeted, and the more the product is the only
asset satisfying the demand from that particular niche, the more specific that asset has
become. Thus TCE predicts that increased complexity in the multiplicity dimension will
increase asset specificity and its attendant costs. In contrast, the relatedness dimension of
complexity will work to decrease asset specificity. Products are related when designs are
re-used e. g. shared platforms or modules. Design reuse reduces the number of
engineering hours incurred to design a product (Monteverde and Teece (1982) use
engineering hours as a proxy for asset specificity). Some have argued that engineering

hours is a poor proxy (Ulrich, Sartorius, Pearson, & Jakiela, 1993), but it is clearly an

48

indication of firm resources being dedicated to a specific task. Furthermore, once spent,
these hours cannot be recovered. There is only one means by which the specificity can
be mitigated and that is to reuse the design. The reuse of the design constitutes a
reduction in asset specificity since the underlying asset (engineering hours) is no longer
tied to a single revenue / volume stream (product), but is distributed across two or more.
Thus, the risk (and accompanying costs) of asset specificity is increased with increasing

levels of multiplicity, but decreased with increasing levels of relatedness.

The second risk category addressed by TCE is that of environmental uncertainty.
Environmental uncertainty includes such things as the vagaries of markets, and
competitive responses to a product introduction. It also includes the environment within
the firm thereby capturing such things as quality, equipment performance, and the
capabilities of personnel. Environmental uncertainty will be impacted by complexity
differently depending on the dimension of complexity. For example, an increase in the
number of dissimilar products exposes the firm to higher levels of uncertainty and hence
cost. These costs are manifested in a variety of ways. One such example is poorer
quality attributable to lack of experience with a product. Additionally, equipment may be
stressed by an increase in the variety of parts processed; the increase in variety leading to
additional setups that impair the productivity and ultimately impact the ability to schedule
maintenance. Alternatively, complexity in the relatedness dimension will have a
beneficial impact on uncertainty and the accompanying costs. There are several reasons
for this which can be seen fiom the example of design reuse. Reusing a design reduces

environmental risk because the cost, quality, and demand history are known to a greater

49

degree for the existing design than that of a new design. There are potentially fewer
problems that will arise in the transfer from the design team to the manufacturing group
and the quality level is understood and should continue to improve due to learning curve
effects. This leads to a reduction in the risks of recall Or product failure in the market.
Forecasts can be more accurate, which translates to greater product availability and hence
improved delivery performance. The risk of purchasing equipment that does not perform
at the desired level is avoided since the same manufacturing infrastructure is utilized. To
the extent that the reused design does not fall into the category of ‘over-designed for the
application’, costs can be expected to diminish as discussed above. Thus, environmental
risk is reduced through increased relatedness complexity. It should be noted that this
conclusion is likely to be contingent on a variety of factors including scale economies,
conformance quality levels, the cost of engineering hours, and total variable cost for the
new verses the reused design. Hence TCE offers theoretical explanations for the impact

of complexity on cost.

3.13 Summary

 

There are four principles emerging from TPF and TCE that influence cost / volume
interactions; 1) diminishing returns; 2) utilization; 3) learning / experience; and 4)
uncertainty. Diminishing returns results from the nonlinear relationships between
improvement and cost as the gap between operating and asset frontiers is narrowed by
changes in product complexity. Utilization is improved or diminished as the operating
frontier is moved closer to or farther from the asset frontier. The change in utilization

can be reflected in scope economies whereby a common infrastructure is shared by

50

several products or scale economies whereby one product is produced in larger and larger
quantities. Learning and experience accrue through increased design utilization. TCE
raises the issue of uncertainty by suggesting that a lower level of risk is preferable.

Uncertainty and its associated risks may be reduced through risk pooling.

In conclusion, both Theory of Performance Frontiers and Transaction Cost Economics
suggest that product complexity impacts supply chain performance outcomes. TPF
suggests nonlinear cost curves (diminishing benefits to increasing levels of utilization)
whereas TCE implies linear relationships (incremental increases for additional
transactions). Unresolved is which theory better explains the relationships between
multiplicity and similarity and the supply chain performance outcomes of cost and sales
volume. Identifying the functional form of the relationships between various complexity

factors and cost will reveal which theory better explains the phenomenon.

3.2 Hypotheses

Four areas of supply chain performance outcomes are characterized in the literature
(Hayes & Wheelwright, 1984; Skinner, 1974a): flexibility, delivery, quality, and cost.
This research focuses on the facets of cost that are posited to be most sensitive to aspects
of product complexity, and for which data can be obtained. Additionally, this research
will investigate relationships between dimensions of product complexity and sales

volume.

3.21 Effects of Multipliciy on Supply Chain Costs

51

Conformance quality is the degree to which production outputs conform to product
design specifications (i.e., absence of defects). As multiplicity increases, the effort
dedicated to maintaining consistent quality levels through inspection activities,
certification, and the like must increase. For example,'with increasing numbers of items
to sample, the number of samples must increase if a constant detection rate is to be
maintained (Grant & Leavenworth, 1980; Kapur & Larnberson, 1977). While the effort
dedicated to ensuring conformance quality through inspection increases with increasing
multiplicity, the level of conformance quality actually produced is expected to decrease.
This relationship is an application of the learning curve effect. Production learning
increases with experience (output) at a decreasing rate (Wright, 1936). As multiplicity
increases, fewer numbers are produced of each separate product. Thus, there is less
opportunity for learning and associated quality related process improvements; learning
being one mechanism by which the operating frontier can be pushed toward the asset
frontier. Thus when learning is diminished, the operating frontier recedes from the asset

frontier resulting in a diminished average outgoing quality level.

Failure theory predicts that increasing the number of items contained in a system will
reduce reliability because the probability of a failure within the system is a multiplicative
function of the failure rates for all items in the system (Kapur, 1982). In the case of this
research, the items represent products or product families and the system represents the
portfolio of products. Thus as the number of products within the portfolio increases, the

number of failures will increase at a decreasing rate since all rates are expressed on a zero

52

to one scale. This indicates a non-linear relationship between failure and multiplicity;

failures will increase at a decreasing rate in the presence of increasing multiplicity.

The number of products in the portfolio, or that may enter the portfolio, has an impact on
the engineering resources that can be committed to any single product. Given a fixed
level of available engineering resources, there will be reduced design and testing
resources available for each product when the number of products in the portfolio
increases. Alternatively, more intense design and testing activity is possible if the total
number of products is reduced. The net effect is that any given product is likely to be

less reliable given a larger more divergent portfolio of products.

Therefore the combined effects of increased failure modes and a lower level of reliability
for any given product, brought about from increased multiplicity, will lead to more
product failures in the field, and higher associated warranty costs. This logic leads to

hypothesis one.

H1: As product multiplicity increases, product warranty costs increase at a

decreasing rate.

As additional products are added to a portfolio, inventory is added and safety stock levels
increased. Assuming a uniform service level, inventory on hand increases following a
square root function (Hadley & Whitin, 1963). Given the scenario of a fixed level of

demand being met with a greater number of separate products (increased multiplicity),

53

there is reduced demand per product. As the scenario moves from a lower to a higher
level of multiplicity, additional inventory is requied to support the new products. The
inventory increases as a function of demand and deletions attributable to reduced volume
for existing products. Thus total inventory required to Support a given level of demand
should increase since growth from new products overcomes the reductions from reduced
demand for existing products. This effect arises because of the nonlinear nature of the
inventory requirements curve. New products added to inventory are at the beginning of
the curve, which has a steep slope, whereas reductions in levels required for existing
inventory are based upon a section of the curve which is flatter. The implication of this is
an increase in the holding and financing costs. These cost impacts are consistent with the
predictions of both TCE and TPF; TCE indicating an increase in costs from additional
transactions and TPF a decrease in return on investment. The decreased return on
inventory investment results from the increase in inventory required to maintain the same

sales level. Thus hypothesis two.

H2: As product multiplicity increases, inventory costs increase at an increasing

rate.

Adding new products to the portfolio has several ramifications to manufacturing
operations that can be translated into cost. Learning curve theory indicates that labor
productivity is diminished since there is less experience manufacturing each separate
product (Wright, 1936), hence direct labor increases. There is also an increase in scrap or

rework since the worker is more likely to create defective products. The increased

54

number of products may result in smaller purchase volumes with any given supplier and
consequently may mean that pricing discounts are foregone. Direct manufacturing costs,
e. g. materials required and the labor to transform and assemble, will increase with
increasing levels of multiplicity in a nonlinear manner because of the inability to capture
quantity discounts, increased assembly effort, and the productivity diminishing effects of

the experience curve. Therefore hypothesis three is offered.

H3: As product multiplicity increases, direct manufacturing costs increase at

an increasing rate.

Overhead costs grow nonlinearly with multiplicity, due to scope economies and the
addition of overhead resources in amounts larger than the immediate need. For example,
when storage capacity must be added to accommodate an increase in units, it is added by
bringing on additional storage facilities. Generally these facilities are seemed with the
ability to handle additional growth. Similarly, procurement organizations will add
additional resources when the number of part numbers to manage exceeds its capacity.
These resources generally add capacity beyond the immediate need. For example a buyer
to process requisitions is added before there is a full forty hours of work and e-
procurement systems are introduced that can process more transactions than required at
the time of installation. Then as the workload increases, the utilization of the buyer or e-
procurement system increases. These are concrete examples of changes to the asset base
and the utilization improvements through scale economies. This is representative of the

performance frontier moving toward the asset frontier via improved utilization for a given

55

asset level. Beyond these costs are engineering, development, certification, and
qualification costs which will increase from providing additional products to the market.
Further into the organization, there will be inventory increases, additional production
tooling secured, and a host of other costs such as those’from the increase in requisitions

that must be processed, reconciled, and paid. Therefore hypotheses four is offered.

H4: As product multiplicity increases, indirect costs increase at a decreasing

rate.

3.22 Effects of Similarity on Supply Chain Cost

 

Across the supply chain, costs increase when there is less experience with the items
manufactured. Replacing a product with one that has minor differences partially
mitigates the deleterious impacts of the experience curve since much of the old product is
retained. This allows personnel to apply their knowledge from the old product more fully
to the replacement product; the result being better productivity, quality, and delivery.
Existing manufacturing processes may be kept largely intact, thereby minimizing the
purchase of additional equipment and enabling amortization of capital expenditures over
a larger unit base, when products reuse in substantial form the architectural elements of
the prior product. Since there is already some related experience with the product,
forecasting will be more accurate, although there will remain some demand variability
from the uncertainty of the market’s response to the replacement product. Implications of
improved forecasting include better utilization of productive assets because labor and

equipment are not idle due to stock outs or overcapacity. Within the product

56

development organization, there will be fewer additional costs incurred from the added
design, certification, qualification, and related efforts that arise from additional products.
In essence, the existing infrastructure is better utilized. Thus TPF predicts diminishing
costs down to the point where the operating and asset frontiers meet. This is represented

in hypothesis five.

H5: As product similarity increases, direct manufacturing costs decrease at a

decreasing rate.

3.23 Effects of Multiplicity on Sales Volume

The principles of economics provide insight to the impacts on sales volume by the
addition of products to the portfolio (McConnell, 1981). The first principle is that the
demand curve is not linear. For example, if percentage of market supplied is on the Y-
axis and a measure such as price is on the X-axis, the demand curVe will be concave
beginning at 100% served when the price is zero and decaying to 0% at some price
greater than zero (see Figure 4). A similar relationship will exist with number of
products offered to the market. There is one product which can meet the largest segment
of demand, but not 100%, and other products that continue to vie for an ever smaller
share of the remaining market. This is illustrated in Figure 5. This logic assumes that
firms rationally choose to release products to capture as large a share of the target market
as possible, that there is no cannibalization of the products currently on the market, and
that the market size is fixed. These assumptions are necessary since the relationships

between current products and those entering the market are extremely difficult to describe

57

with certainty (Cooper et al., 1997b) and some simplification is required to illustrate the
point. An alternative to the single product scenario discussed above is that a firm releases
a suite of products into the market in an attempt to gain greater total share. This occurs
when it is strategically infeasible to compete with a single model. In either case, the
result is that additional models result in additional sales (Kekre & Srinivasan, 1990;
Lancaster, 1979; Quelch & Kenny, 1994). This principle is consistent with the utilization
principle revealed by TPF, where the market size is analogous to capacity (asset frontier)
and sales volume generated analogous to machine utilization (operating frontier).

Therefore hypothesis six is offered.

H6: As product multiplicity increases, sales volume increases at a decreasing

 

rate.
Figure 4
Relationship of Price to Market Share

l 1.2
l
l 1
l

0.8
I i o.
‘ (I)

32
0.4
0.2

 

 

 

Price ‘

 

 

58

Figure 5
Cumulative Market Share

..L
N

 

_L

90.0.0

Cumulative market share
0 N its CD on

 

 

 

o 1 2 3 4 5 6 i
Multiplicity i

3.24 Effects of Similarity on Sales Volume

TPF implies better financial performance from improved asset utilization. This is seen in
the example of the lathe presented in chapter 3. If the tool creates saleable parts 100% of
the time, then the sales volume for the firm will be higher under full utilization than if the
lathe is idled for setups required due to differing part geometries, materials, etc.
Similarity acts to reduce the percentage of time that the lathe is idle through the reuse of
product designs. The improved utilization of the manufacturing infrastructure, as
represented by the lathe, is an illustration of the performance frontier moving closer to
the asset frontier. Since similarity works to move the performance frontier toward the
asset frontier, then all else being equal, similarity should have a positive impact on sales
volume. However, other researchers have found that whether a product line replacement
(similarity) will be successfirl depends on a large number of factors (Montoya-Weiss &

59

Calantone, 1994; Reddy, Holak, & Bhat, 1994). For example, some replacement
products which are very similar to the predecessor are wildly successfiIl, like Gillette’s
Mach 3 razor, while others such as ‘new’ Coke are detrimental (Smith, Perrier, & Grimm,
2001). In fact, many product improvements or replacements may be revenue / sales
volume neutral and designed to stave off a decay in sales that is perceived to be imminent
(Mohan & Krishnaswamy, 2006). Since the variance in success is explained by a large
number of known and unknown factors, there may not be enough variance explained by
similarity to reach a level of statistical significance. Therefore hypothesis seven is

presented as follows.

H7: Changes in similarin will not be associated with sales volume.

60

4.0 Research Design and Methodology

4.1 Unit of Analysis

The unit of analysis for this research is the product portfolio. Specifically it is the
portfolio of data processing devices offered to the market by a global designer and
manufacturer of data processing equipment. Thus the conclusions about the impacts of

complexity on supply chain costs and sales volume relate to the product portfolio.

4.2 Operationalizations of Variables

There are three categories of variables that are used in this research: independent
variables (reflective of the two dimensions of complexity), control variables, and
dependent variables. These variables can be found in Table 4 and rationales for their
inclusion follow. Since the data set for this research comprises quarterly observations by

brand, there are values for each of these variables across each brand and time period.

61

 

Table 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variables
VariableNane DeschptI'oT Cduhion Category
#available “’6 launch OfF‘Od‘m “we “the initial+added Miltiplicity/ Static
%add Tlepetoertageoftheportfolroadbdma ll l/irn'tial “1.1.. /12 .
period
%growth Tiednngeinportfbliosize (adtbd-tmrimtims)/initial Mfltiphdty/Wnnic
Paoertage Tlemlafivedegeeofdifieemtnsedm gm / . . .
1 .5 . ageintl‘e “O (2P. VP.) (Inn) Smilmty/Statrc
Tiepemertageoftlep'odntsinthe . . . . .
0
/oupdated Eliotl'atarel . las | Lpthtesm/totalm SIthIy/Statrc
. Tiepaoatageofpodnsbeingackledina . . . . .
0
Aiupdatese'ramg 'Itlntarerpdates rpchtesertenng/totalatemg Srmlmty/Dymmc
'I/unit Totalnatenalsoostfortl‘emtssoldmtle totalrmtaialsoost/ l :1 l
pencdonaperunrttmrs
Manateials/LritlIedarrgemnaterialsoostperuit (II/htaial/urr't),-(lVIaterial/uit),l Calml
volume Nmrberofunitssoldintlepenod' Grvm' Sam“ Ukperrht
DeltaVolurre Tiedmgeinmitssold Volrrra-Volurii-H V 'II/ I
lit ll'etotalarrbrntspertmtlepaiodon 3. E 1 V 'II
warrarty
DeltaWarIarry ”IIed'angeintleuanartyequafiitue W-MJ DeperrhtVarialie
Tierhllararmnofinvertorylrrld 3. .“
3 (imludesKil,WlP,&Raw) I V
Delralrrvertory "liedrangzininvatayinvestrm May-Max, WVariable
I 1' Cost Tietotaloostrrmredmtl‘epa'rodfir 00$ij lSold-E' Cost 13 l V 'II
nrlmectoost
DeltalrrlirectCost Tirednngeinirriireotoost IrrlirrectOost,-Iridiriect('.’ost,_l quarhtVariable
. TIBtotaloostirmredintlepaiodfor . .
DrectCost Mm Given anerrhrVamHe
DeltaDmct' Cost Tiedmgeindimaoost Direct' Cod-Died CostH DeparhtVanable'

 

 

 

 

 

62

g=podnis%ofpatfi)lioage
n=nnrberofpodmsinportfolio

4.21 Independent variables

 

Multiplicity

Measures that address multiplicity quantify the size of the portfolio by considering the
portfolio in total and the additions to the portfolio. Larger values for these measures are
consistent with an increase in portfolio complexity. Three separate measures of
multiplicity are used. ‘Number of products available’ assesses issues pertaining to
workload / resource requirement and scope / scale economies. ‘Percent added’ and
‘percent growth’ tap issues pertaining to learning and impacts that arise from changes to
the portfolio size. ‘Number of products available’ is calculated by adding the number of
products carried over from the prior period and those added to the portfolio during the
period. It is the totality of products available to a customer in the period. ‘Percent
added’ is the number of products entering the portfolio in the period divided by the
number of products in the portfolio at the beginning of the period. ‘Percent growth’ is
determined by subtracting the number of products withdrawn fio‘m the number of
products added and dividing the result by the number of products in the portfolio at the

beginning of the period.

Similarity

The three measures of similarity used in this research are presented in Table 4. They all
measure the utilization of the existing infrastructure, but capture differing aspects. Two
of the measures, ‘percent updated’ and ‘percent updates entering’ capture some variance
pooling benefits. Both of these measures exploit the fact that entrances of products to the

portfolio consist of products that are completely new and those that have little or no

63

changes from a previous product. The study firm characterizes products as either new,
refresh, or speed bump. New products are those that are brand new designs. Refi'eshes
and speed bumps reuse existing design architecture. For example, speed bumps consist
of an increase in the processor’s clock speed; all else 'stays the same. Refreshed products
could include nominal changes such as different warranty terms or the exchange of
components possessing hazardous materials for those that are non-hazardous. This study
aggregates speed bumps and refreshes and refers to them as ‘updated’ products. Thus
greater levels of these ‘updated’ products within the portfolio correspond to greater levels
of portfolio similarity. Thus the proportion of updated products is a measure of the

similarity dimension of complexity.

Where measuring the percentage of updates will reveal more immediate impacts, 3 third
measure of similarity, percentage diversification, captures differences between products
that accumulate over time. The measure takes advantage of the fact that the data used in
this research represent technologically dynamic products. Since the technology is
changing rapidly, products released in year one may bear little resemblance to those
introduced in year three. Later products may reflect advances in processing power, data
storage technologies, communications technologies, or operating system software hard
coded into the electronics. For example, processing technology has recently advanced
from single core to multi-core architectures. Processors of a wholly different architecture
were also introduced as technology from external sources became more advanced and
widely accepted. Data storage has advanced from magnetic, to optical, and within optical

the technology has advanced to allow greater storage density. Communications

technologies have changed from electronic signals sent via copper wire to pulses of laser
light sent across fiber optic cable. These technological differences drive physical and
architectural differences at the product level. Therefore, greater differences in the age of
products represented in the portfolio imply greater degrees of difference between
products. Thus a higher level of age diversification implies a lower level of similarity.
Age diversification is measured with an entropy calculation (2 pi*Ln l/pi) where p,- is the
percentage of the total age represented within the portfolio by product i. This function
has a maximum value of Ln n, n being the number of products summed. This property is
used to make the measure comparable across brands by dividing the value of the entropy
calculation by Ln n to arrive at the percentage of diversification. Thus lower percentages

of age diversification imply greater levels of portfolio similarity.

4.22 Control variables

 

There are four explicit control variables used in this research: material cost per unit, sales
volume, change in unit materials cost, and change in sales volume. Materials cost and
change in materials cost are accounted for since they may influence several dependent
variables of interest. A higher warranty cost could be associated with more expensive
materials through the replacement of components under warranty. Inventory investment
will increase with the cost of materials. Indirect cost may be influenced since the
procurement organization may manage the supply chain more closely when unit cost of
materials increases. Sales volume and the change in sales volume will impact all of the
dependent variables. Volume increases may be associated with warranty cost increases

since the absolute number of failures is likely to rise with volume. Volume increases will

65

lead to increased inventory per the economic order quantity calculation. Direct and.
indirect costs may be impacted by learning curve effects and from an overall increase in

workload.

4.23 Dependent Variables

Warranty

Warranty cost is a supply chain cost that is passed up the supply chain when problems
arise with goods or services downstream. Warranty costs increase because customers
return or request service for products that fail to function as expected. These failures may
be from lack of conformance to manufacturing specification or fi'om faulty materials that
were not detected at the time of receipt. Customers will also initiate action when a
product does not perform as expected. Thus the costs of warranty incorporate many
types of quality issues. Warranty costs may occur from the time a product is delivered
until the end of the warranty period. As such, time lags are incorporated in the analysis
of warranty cost. The time lags are constrained to two periods in length due to the overall
size of the data set. However, since electronic equipment often fails early in its life and
since customers should be able to determine equipment functionality within this time
window, the two period lag duration should be sufficient for detecting impacts of
multiplicity and similarity on warranty cost. Since the cost of warranty relates to a direct
linkage between customer and manufacturer, it is a supply chain cost and hence a

variable of interest.

66

The warranty cost values in the data set used for this research include the total cost of
materials for making repairs, the labor for completing the repair, and any shipping
charges incurred in a given period. Additionally, the category captures any losses
incurred due to customer returns of functional products e. g. the customer finds

performance is too low and exchanges for a more powerful model.

Inventory

Inventory investment changes with changes in the number of unique stock keeping units
required to assemble a product or a portfolio of products. Inventory investment is a
supply chain outcome in that it represents the linkage between supplier and manufacturer.
The investment will be directly related to the costs of inventory: holding, spoilage,
stranding, and shrinkage. Hence insights gained measuring inventory investment will be

directly transferable to inventory costs.

Effectively managing inventory has implications for improved financial performance at
the manufacturer and influences supplier relationships. Inventory changes are likely to
occur prior to products being released to market since raw materials inventory will grow
in anticipation of demand and finished goods may be built ahead to ensure timely product
delivery. Over time the inventory levels may be adjusted to account for better
forecasting, different delivery lead times, or to better match demand. As such this study
incorporates time lags of negative one, one, and two periods for the analysis the impacts

of multiplicity and similarity on inventory.

67

The inventory values in the data set used for this research represent the aggregated dollar
values of raw materials, work in process, and finished goods that are owned by the

manufacturer.

Cost of goods sold

There are two categories of cost of goods sold used in this research; direct and indirect.
Direct costs are those that are directly attributable to the product transformation process,
for example assembling and mounting a power supply. The values for direct cost used in
this data set include the cost of the materials required to build the product and the labor to
assemble and transform them. The impact of multiplicity and similarity on direct cost
should be seen in the initial period due to the immediacy of direct cost. It is incurred
when the product is built. One and two period time lags are also investigated in addition

to the initial period to determine the enduring effects of complexity changes.

Indirect costs are those that accrue from activities not related to the transformation
process on a unit proportional basis, for example the cost of a commodity manager
focusing on the supply of transformers. The values for indirect cost used in this data set
are determined by subtracting the total direct cost from the total cost of goods sold. The
residual, indirect cost, includes categories of costs such as the cost of procurement and
engineering support. Where direct cost is incurred upon the assembly of a product,
indirect cost is not constrained in this way. There could be long term effects found as
employees adjust to different workloads or work that may have been postponed to

accommodate the release of new products is performed in subsequent periods. Hence

68

time lags of negative one, one, and two periods are employed in the analysis of the effects

of multiplicity and similarity on indirect cost.

Sales volume

The number of units sold is an important outcome to measure because it represents the
level of activity in the supply chain. Additionally, it is an indication of market success;
products with higher sales volumes being more successful than those with lower sales
volumes. In the data set used for this research, the sales volume represents the number of
orders shipped. It is the shipping of a unit that invokes booking revenue and all costs
associated with the production of the unit. The sales volume may not immediately
change or respond firlly to changes in the product portfolio. The market may take a while
to embrace or become aware of products. As such, time lags of one and two periods are

employed in the analysis of the effects of multiplicity and similarity on sales volume.

4.24 Models

 

The variables described above were combined to create ‘static’ and ‘dynamic’ models.
The static models explain impacts of multiplicity and similarity on total costs whereas the

dynamic models explain cost changes. These models are shown in Table 5.

69

Table 5

 

 

Models

Static
ID Indepentent Variables ‘ Dependent Variables
Multiplicity

# avail + # availAZ + % divsfid + % updt + Warranty, Inventory, Indirect Cost,
Model la mtls + vol Direct Cost

# avail + # availAZ + % divsfid + % updt +
Model lb mtls Volume
Similarity

Warranty, Inventory, Indirect Cost,

Model 2a % updt + % updt/‘2 + # avail + mtls + vol Direct Cost
Model 2b % updt + % upthZ + # avail + mtls Volume

% divsfid + % divsfid"2 + # avail + mtls +
Model 3a vol Direct Cost
Model 3b % divsfid + % divsfidAZ + # avail + mtls Volume
Dynamic
ID Indepentent Variables Dependent Variables
Multiplicity

% add + % add"2 + % updt ent + dlta mtls Change in: Warranty, Inventory,
Model 4a + delta vol Indirect Cost, Direct Cost
Model 4b % add + % add/‘2 + % updt ent + delta mtls Change in: Volume

% growth + % growth"2 + % updt ent + Change in: Warranty, Inventory,
Model 5a delta mtls + delta vol Indirect Cost, Direct Cost

% growth + % growth"2 + % updt ent +
Model 5b delta mtls Change in: Volume
Similarity

% updt ent + % prod add + delta mtls +
Model 6a delta vol Change in: Direct Cost
Model 6b % updt ent + % prod add + delta mtls Change in: Volume

70

4.3 Data

The data for this study comes from a designer and manufacturer of data processing
equipment. Four product lines, referred to as brands, are represented and together
represent a coherent segment of the business. These four brands represent 12% of the
total revenue for the study company and 51% of revenue derived from manufactured
goods. Each brand is targeted at a different market niche. The brand Brand 1 is targeted
at the consumer market where volumes are high and average price is on the order of
$4,000. These products tend to have shorter lives and as a consequence a greater amount
of churn in the portfolio. Another brand, Brand 2, is focused on the high performance
market and offers a scalable highly robust single package solution. A typical customer is
an IT department and several of these units would be purchased in a single transaction.
The average price for products within Brand 2 is on the order of $60,000. A third brand,
Brand 3, uses proprietary architecture and open source software. The product is a
multiprocessor architecture and offers energy economies over alternatives. The average
price for Brand 3 products is on the order of $30,000. The final brand, referred to as
Brand 4, comprises storage systems that can stand alone or be integrated with the other
three brands. The primary customer is the corporate IT buyer who buys several units at a
time. The average price for a Brand 4 product is $20,000. The four brands comprise the

portfolio of products offered to several niches by a division of a larger organization.

The data come from a variety of sources which include financial statements for each
brand, strategic planning documents, internal analyses of supply chain performance, and

the like. For each brand, data are available for each of the twelve calendar quarters in the

71

years 2004 through 2006. The data set is organized as products within models and
models within brands. There are no missing data points. The data include not only brand
level financial and sales information, but also similar information at the model level. The
raw data collected that is pertinent to this research proj ect includes the items listed in

Table 6.

Table 6
Data Categories

 

Data Categories
Number of products and models
Introduction dates for products and models
Termination dates for products and models
New vs. Replacement designation
Revenue for products and models
Sales volume for products and models
Gross profit by brand and model
Total cost by brand
Direct cost by brand
Indirect cost by brand
Materials cost by brand
Inventory cost by brand
Shipping cost by brand
Warranty cost by brand

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The data were transmitted as several dozen individual files. The files are primarily in
spreadsheet form, but some are PowerPoint files. The PowerPoint files consist of
presentations made to management as part of the company’s regular planning process.

The spreadsheets are those that are used in the process of managing the business and

72

those supporting the PowerPoint presentations. These files are highly confidential as
they provide information about release and withdrawal dates, sales volume, cost, and
revenue data. The data were not disguised in any way by the company prior to its

transmission for use in this research project.

The information within these files was combined, synthesized, and used in the creation of
complexity measures. Since there were multiple data points from several different
sources within the company, cross validation of the data was possible. There were very
few data inconsistency problems. Most of the inconsistencies were related to
misinterpretations and were resolved through discussions with personnel at the company.
Any data that remained seemingly anomalous and unsubstantiated by the representatives
of the company was not used. The result is a comprehensive and coherent data set for

each of the four brands studied in which confidence can be placed relating to accuracy.

Confidence in the accuracy of the data set is possible for several reasons. First and
foremost is the cross validation. Second is the discussion with multiple people from
multiple functions within the company that were in positions to provide informed
answers and opinions. Third is the understanding resulting fi'om my personal experience

working with similar data while employed by the company.

The data set includes quarterly observations of products, models, and brands; replications

of the same units over time. For example direct manufacturing cost and sales volume are

73

recorded at the end of each calendar quarter for each product and model. Therefore panel

data regression is the method that is most appropriate for this research project.

4.4 Analytical Method

4.41 Overview of Panel Data Regression

 

Panel data regression is an econometric technique that offers several advantages over
generic time series or cross sectional techniques. Panel data regression incorporates both
of these techniques (Baltagi, 2001) thus enabling the detection and measurement of
effects that are not discemable with time series or cross sectional analyses in isolation.
Panel data regression also yields improved internal validity relative to the simultaneous
evaluation of cross sections (F inkel, 2000; Keeves, 1988) through the use of effects that
account for latent or omitted variables (Woolridge, 2002, 2003). This is important since
omitted variables can lead to the biasing of parameter estimates. Panel data regression
accounts for the omitted variables by partitioning the error into an unobserved effect plus
idiosyncratic error which results in a more consistent parameter estimate (Woolridge,

2003).

Within panel data regression there are two options; fixed and random effects. An effect
is fixed if it is time invariant and it is not the result of random variation, e. g. a brand
retains its identity across time or seasons. A random effect is the result of random
variation and must be uncorrelated with the regressor variables. The effects may be
correlated across time or across groups. If there are correlations across either time or

groups, then the analysis is considered to be a one way panel regression. If there are

74

correlations with both time and groups, then the analysis is considered to be a two way

panel regression.

4.42 Justification of Choice of Panel Data Regression

Panel data regression with fixed effects is the method employed for the analysis of the
data collected for this study. The data for this study could be analyzed using time series
methods, cross sectional methods, or panel data regression. Panel data regression is the
preferred choice for four reasons (Baltagi, 2001). The first is that it controls for
heterogeneity due to brands. Panel data regression has the ability to account for
differences between these brands. Second, panel data regression is an effective technique
to reveal changes over time attributable to a given driver. Hence it is used in this
research to investigate changes to outcome variables attributable to changes in the level
of product portfolio complexity. The third reason panel data regression is preferred is
that it results in greater efficiency of estimators by accounting for omitted variables
(Hsiao, 1986). Fourth, panel data regression offers the ability to detect and measure
effects that cannot be found using time series or cross sectional techniques in isolation.
An examples of such effects is measuring the effectiveness of fifth grade teachers within
a school district. To do so fully requires the consideration of both time and classroom
effects. Using time alone would not allow for comparisons between teachers, and using
classroom alone would not capture changes in effectiveness (possibly measured by
amount of knowledge mastered by a student) over time. Thus when there are changes
over time and comparisons across groups or dissimilar groups are used, panel data

regression is better suited than other techniques to explicate the relationships.

75

Since panel data regression was chosen as the analytical method, the determination of
whether to use fixed or random effects was required. The choice depends on the
interpretations that the researcher plans to make, the nature of the data collected, and
assumptions made by the researcher about the data. One of the clearest distinctions about
whether to use fixed or random effects entails the inference that will be drawn from the
final results. If the intent is to infer population properties from the analysis of a sample
of that population, then random effects are appropriate. However, if the intent is to make
inference only about the population analyzed, then the use of fixed effects is
recommended (Kennedy, 2003). The use of random effects requires the effects be
attributable solely to random variation and be orthogonal to the independent variables.
However, the fixed effects approach allows for endogeneity of regressors with the effect.
Fixed effects are preferred when the number of time periods is large and the number of
observations small. It is also preferred when the number of tirne periods is small and the
number of observations large, given the condition of nonrandom cross sectional variation.
In the event of uncertainty about the correlation between cross sectional variation and
independent variables, using fixed effects is the more conservative approach since the

estimates will remain unbiased.

There are three relevant assumptions pertinent to the use of fixed effects within panel
data regression. The first is that the effect is not the result of random variation. Second
is that the effect is time invariant. Last, the errors are assumed to be Gaussian and

independently and identically distributed.

76

This study is not designed for the purpose of drawing inference to a larger population.

As such inferences will be constrained to the data set. In the data set, the number of time
periods is large relative to observations. The data manifest time invariant properties
which are not random 6. g. a product retains its identity across time and is rationally
placed into a particular brand rather than whimsically assigned. Therefore, given the data
for this study and the prudence of erring on the side of conservatism, the use of fixed

effects in panel data regression was chosen for this study.

4.43 Analfiical protocol

The data set was checked for outliers per the protocol recommended by Hair, Anderson,
Tatham, and Black (1998). The data were standardized and checked to see if any data
points exceeded 2.5 standard deviations from the mean. There were two periods within
one brand where the number of products introduced exceeded this threshold and one
point that came near it. As a result, related measures such as the percentage of new
products in the portfolio and number of products available were also beyond the 2.5
sigma cutoff. Hair et al. indicate that the data points should be removed only if there is
strong theoretical rationale for doing so. In this case there is justification for the removal
of the data points. A conversation with the person who has tracked this data for the last
six years at the study company revealed that the elevated levels are attributable the E.U.’s
requirement that all products be free of hazardous substances. Additionally, the new
product introductions were significantly elevated due to the introduction of several new

models; each model having multiple products. The company was also slower than

77

normal to remove products from the portfolio due to regional differences in the reduction
of hazardous substances across marketing regions. Collectively these events are
considered within the study company to be anomalous. They have not occurred in such
magnitude prior or since. Thus there is sound reasoning to remove the three records

associated with quarters two through four of 2006.

The data were then mean centered because nonlinear terms were going to be used. Mean
centering is recommended with nonlinear terms because it eliminates extreme
multicollinearity and renders all the regression coefficients meaningful (Cohen, Cohen,

West, & Aiken, 2003).

Data analysis continued with the use of a Chow test (Chow, 1960) to ascertain the
poolability of the data. Next, the appropriateness of a fixed effect for time and brand
was established using an F test. In most cases both brand and time effects were indicated.
The regression was then performed using either one or two way fixed effects as
determined in the prior step. The overall model significance was determined with an F
test and the significance of coefficients with T tests. Additionally, the covariance ratio
was monitored to ensure no that no deleterious impacts to estimation efficiency were

present.

Collinearity was checked by calculating variance inflation factors (VIP) for each model.
The VIF’s for models four through six were between one and two with one exception of a

VIP of 2.3. However, the VIF’s for models one through three, although generally less

78

than 3.0, were slightly elevated but acceptable. Model 1A had two VIP ’3 above 3.0; one
at 3.2 and the other at 3.9. Model 2A also had two VIF’s above 3.0; one at 5.2 and the

other at 4.2. Model 3A had one VIF at 3.6.

Even though individually the VIP scores were acceptable, the impact of collinearity can
be cumulative. To further, and more strenuously, test for collinearity partial and semi
partial correlations were calculated and compared. Large differences between these two
values indicate the presence of collinearity. There is only one instance where this
comparison indicated the presence of collinearity; the prediction of a negative one period
lag for indirect cost by model 1A. For this case, the use of weighted least squares was
employed with direct cost per unit as the weight. This choice of weight was made
because of its negative correlation with indirect cost and all of the independent variables
except materials cost per unit. A reanalysis of the model using weighted least squares
resulted in VIF’s below 2.0 and no significant differences between the partial and semi
partial correlations. Thus all results reported relating to model lA’s prediction of the
negative one period lag of indirect cost are based on the application of weighted least

squares.

79

Table 7
Correlation Matrixes

Static Model Variables

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80

Table 7
Continued

Dynamic Model Variables

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81

5.0 Results

The panel data regression results reported below were created using the Proc Panel
procedure in SAS 9.1. Other regressions and correlations were carried out using SPSS
16.0. The panel data regressions were carried out in a hierarchical manner with control
variables and fixed effects entered first, followed by the linear complexity variable, and
lastly the nonlinear complexity term entered. All of the p-values are based upon two tail

IBSIS.

Post hoc analyses were carried out to confirm that the relationship found when analyzing
the four brands together was consistent with the relationship found within each brand.
This was required since the fixed effects account for only intercept changes and not
changes to the slope. Discrepancies between individual brands and the amalgam of the

brands only appeared in testing hypotheses two and four.

The analyses incorporated significant efforts to detect and ameliorate the effects of
collinearity. Collinearity was a concern since several correlations (see Table 7) were
high. Specifically, within the static models, the correlation between the number of
products available and warranty cost, number of products available and indirect cost,
percentage of updated products and its squared term, sales volume and direct cost, and
indirect cost and warranty cost. The high correlations within the data influenced which
measures of complexity could be used within this research. Several were set aside due to

elevated levels of collinearity.

82

5.1 Hypothesis 1

Hypothesis 1 states that warranty cost will increase at a decreasing rate with increasing
levels of multiplicity. Three Operationalizations of multiplicity were used to create
models describing the impact of multiplicity on warranty cost: 1) the number of products
in the portfolio, 2) the percentage of products added to the portfolio in a given period, and
3) percentage of portfolio growth. Warranty and the change in warranty costs were
regressed on the independent and control variables with and without lagged effects.
Tables 8 — 12 display the hierarchical regression results for the models with significant

coefficients for the multiplicity variables.

83

Table 8

Model 1a - Warranty — no lag

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 1a
DV = Warranty Time lag = 0
BE-l -18.0 -7.01 7.67
0.286 0.749 0.727
BE-2 -46.6 -42.5 -6.74
<0.001 <0.001 0.720
BE-3 -32.8 -27.6 8.17
<0.001 <0.001 0.674
TE-l -l8.1 -l7.7 -16.2
<0.001 <0.001 0.001
TE-2 ~17.l -l6.6 -15.5
<0.001 <0.001 0.001
TE-3 -20.8 -20.1 -l9.8
<0.001 <0.001 <0.001
TE-4 -l l .6 -10.2 -10.8
0.013 0.039 0.024
TE-S -18.1 -18.2 -20.1
<0.001 <0.001 <0.001
TE-6 -l3.3 -13.3 -16.2
0.004 0.004 <0.001
TE-7 -l3.2 -l3.3 -15.8
0.004 0.004 <0.001
TE-8 -3.92 -3.49 -4.62
0.367 0.428 0.273
TE-9 -10.8 -1 1.8 -10.8
0.025 0.020 0.024
TE- 1 0 -9.30 -9.46 10.3
0.042 0.041 0.021
TE-ll ~10.4 ~10.4 -10.1
0.032 0.033 0.029
I 76.0 71.1 61.5
ntercept
<0.001 <0.001 <0.001
Sm trl /uni t -0.0005 -0.0006 -0.0004
0.487 0.404 0.535
-0.0003 -0.0002 -0.0007
sales vol
0.771 0.808 0.472
# prod avail 0.037 0.257
0.437 0.038
. 2 -0.00]
# prod avarl 0.054
% update -5.26 -l 1.7 -29.5
0.81 0.620 0.223
% diversified -93.5 -89.4 -69.5
0.040 0.053 0.1 16
R2 0.967 0.968 0.972
E = Fixed effect for brand B term
TE = Fixed effect for time p-value

84

 

 

 

 

Table 9

Model 4a — Delta Warranty - no lag

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 4a
DV = Delta Warranty Time lag = 0
BE] -3.57 -2.80 0.800
0.283 0.403 0.818
BE-2 -l.85 -3.54 0.394
0.504 0.253 0.906
BE-3 -l .24 -l .56 0.906
0.632 0.547 0.732
2.72 3.01 3.16
Intercept
0.176 0.135 0.097
delta $mtr1/unit 0.0004 0.0004 0.0005
0.062 0.088 0.038
0.0001 0.0001 0.0001
delta sales vol
0.006 0.005 0.054
%prod add -11.5 6.55
0.227 0.574
2 ' -116.2
(% prod add) 0 021
. 0.750 3.01 -l.11
% updates entermg
0.832 0.450 0.787
R2 0.306 0.334 0.429
E = Fixed effect for brand B term
E = Fixed effect for time p-value

 

 

 

85

Table 10
Model 4a — Delta Warranty - lag 1

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 4a -
DV = Delta Warranty Time lag = 1
BE-l -2.28 -3.90 -6.29
0.550 0.324 0.121
BE-2 -1.57 0.584 -2.69
0.632 0.871 0.488
BE-3 -l .22 -1.07 -2.98
0.688 0.720 0.332
Intercept 2.33 2.1 1 1.92
0.317 0.358 0.386
delta $mtrl/unit -0.00007 -0.00003 -0.00005
0.706 0.916 0.831
0.0002 0.0001 0.0001
delta sales vol
0.006 0.007 0.021
%prod add 15.8 0.190
0.168 0.989
2 99.6
(% prod add) 0 067
% updates entering ‘1'73 4'56 .138
0.668 0.310 0.765
R2 0.237 0.282 0.357
E = Fixed effect for brand B term
E = Fixed effect for time p-value

 

 

 

86

Table l 1

Model 5a — Delta Warranty — no lag

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 5a ,
DV = Delta Warranty Time lag = 0
TE-l -7.43 -7.40 -7.14
0.036 0.042 0.035
TE-Z -8.55 -8.49 -6.83
0.019 0.025 0.056
TE-3 0.269 0.279 1.04
0.938 0.936 0.749
TE-4 -15.9 -15.8 -l6.3
0.003 0.004 0.002
TE-5 -5.28 -5.26 -5.00
0.120 0.128 0.121
TE-6 -8.47 -8.44 -8.43
0.016 0.019 0.013
TE-7 1.05 0.990 4.11
0.756 0.779 0.252
TE-8 -15.5 -15.4 -l6.2
0.001 0.002 <0.001
TE-9 -11.7 -11.8 -10.9
0.001 0.002 0.002
TE-10 -7.24 -7.19 -7.04
0.045 0.055 0.045
TE-ll 8.53 8.50 8.86
0.002 0.003 <0.001
-0.0002 -0.0002 -0.0003
Intercept
0.522 0.538 0.314
delta $mtrl/unit 0.00008 0.000008 -0.0002
0.894 0.887 0.675
Port Growth .0351 .495
0.943 0.327
P G h 2 -25.1
( ort rowt ) 0.026
. -0.973 -0.923 -O.810
% updates enterrng
0.662 0.697 0.714
R2 0.659 0.659 0.715
E = Fixed effect for brand B term
E = Fixed effect for time p-value

 

 

87

Table 12
Model 5a — Delta Warranty — lag 2

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 5a
DV = Delta Warranty Time lag = 2
TE] -0.446 0.718 0.722
0.901 0.834 0.837
TE-2 -l 3.3 -11.5 -11.5
0.003 0.007 0.009
TE-3 -5.30 -4.31 -4.31
0.145 0.210 0.221
"FE-4 -8.17 -6.20 -6.21
0.061 0.137 0.145
TE-S 0.706 1.76 1.77
0.842 0.603 0.610
TE- 6 -13.6 -12.5 -12.5
0.002 0.002 0.003
TE-7 -11.9 -13.0 -13.1
0.002 <0.001 0.001
TE-8 -6.43 -5.15 -5.15
0.116 0.184 0.195
8.04 7.10 7.09
Intercept
0.004 0.008 0.010
. 0.000004 0.00001 0.00001
delta $mtrl/unrt
0.989 0.963 0.962
0.00004 0.00004 0.00004
delta sales vol
0.456 0.469 0.478
Port Growth -10.00 -9.90
0.052 0.090
P G wth 2 0.488
( ort r0 ) 0.966
. -0.459 1.14 1.14
% updates entering
0.853 0.644 0.653
R2 0.679 0.728 0.729
E = Fixed effect for brand B term
E = Fixed effect for time p-value

88

 

 

 

 

Model 1a uses the number of products available as the operationalization of multiplicity
whereas model 4a uses the percentage of products added to the portfolio and model 5a
uses the percentage of portfolio growth. All three models use second order polynomials

to test the relationship between multiplicity and warranty cost.

Model 1a

The hierarchical regressions for model 1a reveal the coefficients for the linear and non-
linear multiplicity variables are significant at the 0.05 level for the no lag scenario, the
linear being positive and the nonlinear negative. The result when plotted over the range
of data is an inverted U shaped curve (see Figure 6). While the overall model explains

97.2% of the variance in warranty cost the fixed effects and controls account for 96.7%.

89

Figure 6
Hypothesis 1 Model 1a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

predicted warranty - lag O
80
J XII-K
60 “’7 r:
z
z 40
fi-
20
0 l I fir l l
0 50 100 150 200 250 300
# available
Brandl&2 * *— and3 —'1
¢——— Brand4 —————b

 

 

To confirm the validity of the shape of the curve each brand was plotted. If each brand
manifests the same general pattern, then the confidence can be placed in the curve.
However, if plots of the individual brands manifest different patterns, then the result is an
interaction of brand effects. In this case, the brand level plots reveal two distinct
populations; two that increase linearly and thus provide partial support for the hypothesis,

and two that decline exponentially.

Because the individual plots discussed above are likely errant due to their creation using
the coefficient from the regression equation that had interacting brand effects adversely
impacting it, separate regressions were performed on each brand using just the
complexity variables. The reduced number of variables was required due to the small

number of data points for each brand. The result is that brands x and p do not have any

90

statistically significant relationships with warranty cost. However, Brand 4 shows a
linear increase (B = 0.571, p=0.095) in warranty cost with an increase in complexity and
Brand 2manifests a nonlinear increase (Bl,-n = 18.4, p=0.036 and BM = 0.99,p=0.037).

Thus the partial support of the hypothesis is confirmed.

In the process of addressing the counter intuitive finding shown in Figure 6 a logarithmic
function form was investigated. The outcome is that the logarithmic form of the
complexity variables explain a greater amount of variance than the polynomial form
(18.7% vs. 15.5%). Furthermore, the logarithmic form does not suffer from the
interaction of fixed effects as evidence by each plot manifesting the same general shape.

The significance of the logarithmic relationship fully supports the hypothesis.

Model 4a

The hierarchical regressions for model 4a reveal the coefficients for the non-linear
multiplicity variables are significant at the 0.05 level for the no lag and one period lag
scenarios. The coefficient is negative in the no lag scenario and positive for one period
lag. The result of plotting the no lag scenario over the range of data is a curve which
decreases at an increasing rate (see Figure 7) and the result of plotting the one period lag
scenario is a curve which increases at an increasing rate (see Figure 8). The multiplicity
variables in Model 4a explain an additional approximately 12% of the variance in the
change in warranty cost beyond the fixed effects and controls; the no lag scenario

increasing from 30.6% to 42.9% and the one period lag scenario from 23.7% to 35.7%.

91

Figure 7
Hypothesis 1 Model 4a — no lag

 

 

predicted delta Indirect Cost - lag 0

 

 

 

 

 

 

 

 

 

 

 

92

40 _
%add
7 7 7 7 7 7 ‘7. 7 7 7 7 7 J
Figure8
Hypothesis 1 Model 4a - lag I
predicted delta Warranty-1391
40
30 .. 777 .7777. 2. _ - _.-..J
2
Z 20 ~»~ 77 — — —~ — — -- ~
* .
10 7 . ——-_ —~ — — — 7 .
0 T i 1 7 I r
0.00 0.10 0.20 0.30 0.40 0.50 0.60
%add

 

 

Model 5a

The hierarchical regressions for model 5a reveal the coefficient for the non-linear
multiplicity variable is negative and significant at the 0.05 level for the no lag scenario.
and the coefficient for the linear multiplicity term is negative and significant at the 0.05
level in the two period lag scenario. The result of plotting the significant multiplicity
variables over the range of data in the no lag scenario is an inverted U shaped curve (see
Figure 9). The total variance in change in warranty cost explained by the model for the
no lag scenario is 71.5% with the controls and fixed effects explaining 65.9% and two
period lag scenario shows 72.9% of variance explained with 67.9% coming from controls

and fixed effects.

Figure 9
Hypothesis 1 Model 5a

 

 

 

| predicted delta Warranty - lag 0

 

1n
1U T

/ 1,\

. T . o
-0.80 /(60 -0.40 0.20 ofo 0.20 0.40 0.50

c-
‘3

% portfolio growth

U11

 

$MM

 

 

 

 

 

 

93

Summary

Support for the hypothesis is found with the static model in the no lag scenario. Partial
support is found with model 4a with one period lag and model 5a in the no lag scenario.
Model 4a in the no lag scenario and model Sa in the two period lag scenario present

relationships opposite to that hypothesized.

5.2 Hypothesis 2

Hypothesis 2 states that inventory investment will increase at an increasing rate with
increasing levels of multiplicity. Three Operationalizations of multiplicity were used to
create models describing the impact of multiplicity on warranty cost: 1) the number of
products in the portfolio, 2) the percentage of products added to the portfolio in a given
period, and 3) percentage of portfolio growth. Inventory and change in inventory
investment wer regressed upon the independent and control variables with and without
lagged effects. Tables 13 — 15 display the hierarchical regression results for the models

with significant coefficients for the multiplicity variables.

94

Table 13

Model 4a — Delta Inventory - lag 2

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 4a
DV = Delta Inventory Time lag = 2
BE] -10.1 -17.7 -7.99
0.663 0.471 0.747
BE-2 -16.7 -7.29 7.32
0.41 1 0.744 0.760
BE-3 -12.1 -13.0 -6.12
0.515 0.488 0.745
Intercept 6.23 5.69 7.88
0.659 0.687 0.571
delta $mtrl/unit -0.002 -0.002 -0.002
0.117 0.150 0.157
-0.0002 -0.0001 -0.0001
delta sales vol
0.564 0.749 0.739
%prod add 71.0 151.5
0.325 0.096
2 '462.6
(% prod add) 0 148
% updates entering 23'0 9'54 .533
0.342 0.730 0.841
R2 0.143 0.208
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

95

 

 

 

 

 

 

Table 14
Model 5a - Delta Inventory — no lag

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 5a .
DV = Delta Inventory Time lag = 0
TE-l 62.3 63.0 61.6
0.005 0.005 0.004
TE-2 63.2 64.6 55.8
0.005 0.006 0.013
TE-3 36.9 37.2 33.1
0.082 0.086 0.108
TE-4 56.4 58.8 61.7
0.062 0.065 0.044
TE-S 34.4 34.8 33.4
0.095 0.097 0.094
TE-6 55.4 56.1 56.1
0.010 0.011 0.008
TE-7 0.615 -0.871 -17.4
0.976 0.967 0.429
TE-8 61.5 63.2 67.7
0.027 0.028 0.015
TE-9 66.8 66.4 61.8
0.002 0.003 0.004
TE-10 66.8 70.2 69.4
0.003 0.003 0.002
-45.5 -46.2 -48.l
Intercept
0.005 0.006 0.003
delta $mtrl/unit -0.001 -0.001 -0.0007
0.442 0.475 0.664
0.0002 0.0002 0.0004
delta sales vol
0.489 0.470 0.225
Port Growth -8.70 15.60
0.770 0.613
P G h 2 132.7
( ort rowt ) 0.052
% updates entering -7'39 6'15 ‘6'75
0.583 0.667 0.620
R2 0.546 0.548 0.606
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

96

 

 

 

Table 15
Model 5a — Delta Inventory — lag 2

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 5A .
DV = Delta Inventory Time lag = 2
TE] 31.3 24.8 24.9
0.167 0.256 0.265
TE-2 74.3 64.2 63.9
0.006 0.015 0.018
TE-3 32.6 27.1 27.1
0.146 0.209 0.219
TE-4 60.4 49.4 49.3
0.027 0.062 0.069
TE-S -l.55 -7.39 -7.29
0.943 -727 0.737
TE- 6 75.9 69.9 70.1
0.004 0.005 0.007
TE-7 65.3 71.6 71.1
0.006 0.002 0.004
TE-8 76.3 69.2 69.3
0.005 0.008 0.009
-49.3 -44.1 -44.3
Intercept
0.005 0.009 0.011
delta $mtrl/uni t 0.0003 0.0003 0.0003
0.833 0.847 0.847
0.0004 0.0005 0.0005
delta sales vol
0.177 0.143 0.151
Port Growth 556 569
0.082 0.118
6.02
2
(Port Growth) 0993
% updates entering 2.94 -5.96 -6.02
0.848 0.700 0.704
R2 0.537 0.595 0.595
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

 

 

 

97

Model 1a uses the number of products available as the operationalization of multiplicity
whereas model 4a uses the percentage of products added to the portfolio and model 5a
uses the percentage of portfolio growth. All three models use second order polynomials

to test the relationship between multiplicity and inventory investment.

Model 1a

The hierarchical regressions using model 1a failed to detect a significant (<0.10)
relationship between multiplicity and inventory investment. Low power is the likely
source of the null result since it is only approximately 0.55 for the nonlinear term and

nearly zero for the linear term.

Model 4a

The hierarchical regressions for model 4a reveal the coefficient for the linear multiplicity
variable is positive and significant at the 0.10 level for the no lag scenario. Thus the
indication is an increase in inventory investment with increasing levels of multiplicity.
The fixed effects and controls explain 11.2% of the variance in the change in inventory
investment and the multiplicity variable adds another 9.6% to bring the total variance

explained by the model to 20.8%.

Model 5a
The hierarchical regressions for model 5a reveal the coefficient for the non-linear

multiplicity variable is significant and positive at the 0.05 level for the no lag scenario

98

and the coefficient for the linear multiplicity term is positive and significant at the 0.10
level in the two period lag scenario. The result of plotting the significant multiplicity
variable over the range of data for the no lag scenario is a U shaped curve (see Figure

10). The total variance in the change in inventory investment explained by the model for
the no lag scenario is 60.6% with the controls and fixed effects explaining 54.6% and the
two period lag scenario shows 59.5% of variance explained with 53.7% coming from

controls and fixed effects.

To confirm the validity of the shape of the curve each brand was checked. If each brand
manifests the same general pattern, then the confidence can be placed in the curve.
However, if plots of the individual brands manifest different patterns, then the result is an
interaction of brand effects. In this case, the shape of the curves for each brand are

consistent with the curve shown in Figure 10.

Figure 10
Hypothesis 2 Model 5a

 

 

predicted delta Inventory - lag 0 i
|

 

 

 

 

   

 

23..
1
F._ \l l l G 1-- ‘i -1
z -0.80 oesNAo -0.20 0.00 0.20 0.40 0.50
z -20
'fl'

 

 

 

 

 

 

:11
TU

‘ % portfolio growth

 

 

99

Summa_ry

There is no support for the hypothesis from the static models. Partial support for the
hypothesis is found with model 4a in the two period lag scenario and model 5a in the no

lag and two period lag scenarios.

5.3 Hypothesis 3

Hypothesis 3 states that direct cost will increase at an increasing rate with increasing
levels of multiplicity. Three Operationalizations of multiplicity were used to create
models describing the impact of multiplicity on warranty cost: 1) the number of products
in the portfolio, 2) the percentage of products added to the portfolio in a given period, and
3) percentage of portfolio growth. Direct cost and change in direct cost were regressed
on the independent and control variables with and without lagged effects. Tables 16 — 18
display the hierarchical regression results for the models with significant coefficients for

the multiplicity variables.

100

Table 16
Model 4a - Delta Direct Cost — no lag

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 4a.
DV = Delta Direct Cost Time lag = 0
BE-l 24.1 34.4 35.2
0.294 0.120 0.156
BE-2 17.6 -5.01 -4.12
0.360 0.803 0.860
BE-3 16.0 11.7 12.3
0.377 0.489 0.51 1
-6.95 -2.99 -2.96
Intercept
0.614 0.818 0.822
delta Smtrl/unit 0.010 0.009 0.009
<0.001 <0.001 <0.001
0.002 0.002 0.002
delta sales vol
<0.001 <0.001 <0.001
% prod add -153.T -149.7
0.016 0.074
-26.2
(% prod add)2 0 939
% updates entering -16'0 14'3 133
0.515 0.582 0.645
R2 0.724 0.766 0.766
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

101

 

 

 

 

Table 17
Model 5a — Delta Direct Cost — no lag

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 5a
DV = Delta Direct Cost _ Time lag = 0
TE-l -42.2 -34.2 -32.7
0.188 0.252 0.263
TE-2 -32.5 -15.6 -6.4
0.315 0.611 0.835
TE-3 -14.3 -11.5 -7.3
0.652 0.696 0.802
TE-4 -17.9 9.45 6.39
0.690 0.827 0.880
TE-S -30.6 -25.4 -24.0
0.324 0.377 0.696
TE- 6 49.4 -41.5 -41.4
0.119 0.159 0.152
TE-7 -20.6 -37.6 -20.3
0.510 0.212 0.520
TE-8 -44.2 -25.5 -30.2
0.283 0.570 0.429
TE-9 -51.5 -56.8 -52.0
0.101 0.055 0.074
TE-10 -21.7 -6.07‘ -5.25
0.502 0.843 0.861
36.7 28.8 30.8
Intercept
0.122 0.193 0.158
delta $mtrl/unit 0.009 0.010 0.009
<0.001 <0.001 0.004
delta sales vol 0.002 0.002 0.002
<0.001 <0.001 <0.001
Port Growth ‘993 -125°4
0.022 <0.001
2 -139.3
(Port Growth) 0 151
% updates entering 1'20 ISA 16'0
0.953 0.442 0.415
R2 0.759 0.800 0.814
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

102

 

 

 

Table 18
Model 5a — Delta Direct Cost — lag 1

Hierarchical Regression:
Model 5a
DV = Delta Direct Cost ' Time lag = 1

TE-l ' °
0.183 0 l7

TE-2 '
0.888 .930

TE-3 '
0.450 0.060

TE-4 '
0.109

TE-S ' '
.166 0.207

TE-6 ° '
0.671 0.748

TE-7
0.051
TE-8
TE-9
Intercept
delta $mtrl/unit
delta sales vol
Port Growth

(Port Growth)2

% updates entering 1

R 0.693 0.717 0.750

 

 

 

BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

 

 

 

103

Model 1a uses the number of products available as the operationalization of multiplicity
whereas model 4a uses the percentage of products added to the portfolio and model 5a
uses the percentage of portfolio growth. All three models use second order polynomials

to test the relationship between multiplicity and direct cost.

Model 1a
The hierarchical regressions using model 1a failed to detect a significant (<0.10)

relationship between multiplicity and direct cost; power is greater than 0.90.

Model 4a

The hierarchical regressions for model 4a reveal the coefficient for the linear multiplicity
variable is negative and significant at the 0.05 level for the no lag scenario. Thus the
indication is a decrease in direct cost with increasing levels of multiplicity. The fixed
effects and controls explain 72.4% of the variance in the change in direct cost and adding

the multiplicity variable brings the total variance explained by the model to 76.6%.

Model 5a

The hierarchical regressions for model 5a reveal the coefficient for the linear multiplicity
variable is negative and significant at the 0.05 level for the no lag scenario. The total
variance in the change in direct cost explained by the model is 81.4% with the controls
and fixed effects explaining 75.9%. For the one period lag scenario the linear term is

positive and significant at 0.05 and the non-linear is positive and significant at 0.10.

104

Graphing this fimction over the range of the data reveals a U shaped curve (see Figure
11). The variance explained by the controls and fixed effects is 69.3%. The multiplicity
variables explain an additional 5.7% bringing the total variance explained by the model to

75.0%.

To confirm the validity of the shape of the curve each brand was checked. In this case,

the shape of the curves for each brand are consistent with the curve shown in Figure 11.

Figure 11
Hypothesis 3 Model 5a

‘ predicted delta Direct Cost - lag 1

* ,3 /
\ 50/

1

1

u . , 1

-0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
% portfolio growth .

 

 

1
I

$MM

 

 

 

 

D

 

Summary
No support for the hypothesis is found using the static model. The dynamic models, 4a

and 5a, provide mixed results. Models 43 and 5a find, contrary to that hypothesized, that

105

direct cost decreases in the no lag scenario. However, model 5a finds complete support

for the hypothesis in the one period lag scenario.

5.4 Hypothesis 4

Hypothesis 4 states that indirect cost will increase at a decreasing rate with increasing
levels of multiplicity. Three Operationalizations of multiplicity were used to create
models describing the impact of multiplicity on warranty cost: 1) the number of products
in the portfolio, 2) the percentage of products added to the portfolio in a given period, and
3) percentage of portfolio growth. Indirect cost and change in indirect cost were
regressed on the independent and control variables with and without lagged effects.
Tables 19 — 24 display the hierarchical regression results for the models with significant

coefficients for the multiplicity variables.

106

Table 19

Model 1a — Indirect cost — prior 1

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 1a
DV = Indirect Cost Time lag = -1
BE-l -16.8 -24.9 -15.7
0.505 0.351 0.549
BE-2 14.2 8.46 20.1
0.536 0.720 0.402
BE-3 56.0 41.9 19.2
0.020 0.129 0.514
TE-l 4.45 4.55 3.64
0.283 0.273 0.366
TE-2 -0.979 -0.655 -0.275
0.844 0.894 0.955
TE-3 4.95 11.3 1 1.5
0.082 0.057 0.046
TE-4 1.30 0.773 -1.02
0.775 0.866 0.822
TE-S 0.008 -0.081 -2.38
0.999 0.986 0.601
TE-6 3.93 4.05 1.4
0.377 0.364 0.751
TE-7 12.2 13.1 13.2
0.023 0.018 0.014
TE-8 8.84 7.11 6.97
0.368 0.166 0.160
TE-9 7.58 7.59 7.5
0.097 0.097 0.088
TE-l 0 12.63 11.93 10.9
0.010 0.015 0.022
56.9 64.0 73.2
Intercept
0.002 0.002 0.001
Smtrl/unit 0.0001 0.0002 0.0002
0.488 0.346 0.329
0.0003 0.00006 0.00003
sales vol
0.222 0.635 0.801
# prod avail 0.052 0.268
0.332 0.067
0.0004
. 2
# prod avarl 0.1 10
% update -1.80 -10.5 -21.4
0.933 0.651 0.363
% diversified -104.0 -96.0 ~57.2
0.041 0.061 0.287
R2 0.977 0.978 0.980
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

107

 

 

Table 20

Model la — Indirect cost — no lag

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model In.
DV = Indirect Cost Time lag = 0
42.2 -25.8 -1.96
BE" 0.061 0.367 0.942
-73.3 457.2 .402
BE'2 <0.001 <0.001 0.693
.44.5 -36.7 21.5
B -
E 3 <0.001 0.002 0.374
TE-l 48.0 47.5 44.9
0.006 0.008 0.012
43.5 42.7 41.0
"113-2
0.025 0.037 0.045
48.8 47.8 47.3
"3'3 0.005 0.008 0.005
40.8 -8.73 -957
TE-4
0.067 0.166 0.094
49.0 49.2 -22.3
TE-5
0.005 0.005 <0.001
47.2 47.3 -22.0
TE-6
0.004 0.004 <0.001
43.3 43.4 47.6
TE-7
0.020 0.020 <0.001
-3.58 -2.94 -4.78
"3'8 0.525 0.606 0.356
-6.04 -744 . -5.87
“3'9 0.317 0.236 0.248
-7.04 -7.28 -8.60
TE‘IO 0.225 0.212 0.105
-374 -3.77 .327
TE'” 0.535 0.534 0.547
[meme 1 127.5 120.2 104.7
p <0.001 <0.001 <0.001
Smtrl/unit -000001 -0.0001 0.0002
0.990 0.912 0.825
sales «31 0.00008 0.000008 -0.0006
0.379 0.950 0.580
. 0.055 0.414
# d 1
pm 3“" 0.372 0.009
-0.002
- 2
# prod avail 0.013
-26.7 —36.2 -65.3
0
/° update 0.352 0.241 0.034
. . 453.3 447.1 414.8
°/ d 1' d
° 'Vcrs' '6 0.012 0.016 0.039
R2 0.974 0.975 0.981
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

108

 

 

 

Table 21

Model 4a — Delta Indirect Cost - no lag

 

Hierarchical Regression:
Model 4a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DV = Delta Indirect Cost Time lag = 0
TE-l -0.601 -0.578 -2.34
0.906 0.910 0.620
TE-Z -5.06 -4.01 -2.51
0.331 0.450 0.607
TE-3 3.36 3.76 0.912
0.511 0.465 0.850
TE-4 -15.5 -13.7 33.8
0.038 0.075 0.052
TE-S -4.50 -4.34 -4.48
0.366 0.384 0.327
TE-6 -I.14 -0.809 -0.635
0.819 0.872 0.890
TE-7 4.74 5.12 4.42
0.347 0.313 0.342
TE-8 -9.26 -8.28 -10.4
0.165 0.219 0.010
TE-9 -10.5 -10.0 -7.87
0.040 0.052 0.098
TE-IO 0.760 1.72 1.56
0.884 0.745 0.747
S .15 4.49 7.91
Intercept
0.175 0.243 0.041
delta $mtrl/unit -0.0001 -0.0001 -0.000F
0.758 0.839 0.796
0.00004 0.00005 0.00001
delta sales vol
0.606 0.485 0.905
% prod add -8.80 7.64
0.343 0.473
-137.1
0 2
(/o prod add) -0.015
% updates entering -0.062 1.92 1.42
0.985 0.624 0.692
R2 0.539 0.553 0.639
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

109

 

 

 

 

 

Table 22
Model 4a — Delta Indirect Cost — lag 1

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 4a
DV = Delta Indirect Cost. Time lag = 1
BE-l -2.05 -4.28 -8.22
0.675 0.395 0.100
BE-2 -1.97 1.01 -4.37
0.641 0.826 0.357
BE-3 -1.25 -1.05 31719
0.748 0.783 0.267
2.55 2.25 1.94
Intercept
0.391 0.442 0.475
delta $mtr1/unit 0.0003 0.0004 0.0003
0.354 0.270 0.293
0.0002 0.0002 0.0001
delta sales vol
0.010 0.012 0.040
% prod add 21.8 -3.90
0.138 0.816
163.9
0 2
(A) prod add) 0.016
% updates entering -1.09 -4.99 0.252
0.834 0.384. 0.964
R2 0.208 0.262 0.389
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

110

 

 

 

 

Table 23

Model 5a - Delta Indirect Cost — lag l

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 5A
DV = Delta Indirect Cost, Time lag = 1
TE-l -5.70 —4.83 -4.83
0.263 0.312 0.319
TE-2 2.96 2.57 2.13
0.558 0.586 0.659
TE-3 -18.0 -16.7 -17.2
0.006 0.007 0.007
TE-4 -1.69 -2.26 -2.29
0.755 0.658 0.658
TE-S -2.20 -1.15 -1.03
0.663 0.808 0.829
TE- 6 4.48 5.24 5 .5 T
0.372 0.268 0.252
TE-7 408 -6.41 -7.79
0.063 0.263 0.213
TE-8 -8.84 .8739 823—.
0.097 0.043 0.104
TE-9 -0.687 1.92 1.70
0.894 0.699 0.737
Intercept 5.78 4.63 4.54
0.116 0.182 0.198
delta Smtrl/unit 0.0005 0.0005 0.0005
0.207 0.214 0.196
0.000005 0.00001 0.000004
delta sales vol
0.950 0.875 0.962
Port Growth ”'7 16'6
0.038 0.036
9.96
2
(Port Growth) 0. 5 4 6
% updates entering 0.954 -1.39 ~1.33
0.779 0.680 0.696
R2 0.569 0.636 0.642
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

111

 

 

 

 

 

Table 24

Insert Sa-delta indirect cost-2

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 5a
DV = Delta Indirect Cost Time lag = 2
TE-l 2.05 3.55 3.61
0.691 0.479 0.481
TE-2 -15.6 -13.3 -l3.6
0.012 0.028 0.029
TE-3 -4.39 -3.10 -3.04
0.392 0.570 0.546
TE-4 -4.29 -1.67 -1.78
0.484 0.777 0.768
TE-5 4.65 6.01 6.13
0.363 0.228 0.229
TE- 6 -8.86 -7.48 -7.26
0.118 0.169 0.192
TE-7 —11.1 -12.5 -13.1
0.037 0.017 0.018
TE-8 -1.53 0.128 0.213
0.789 0.982 0.970
5.70 4.49 4.28
Intercept
0.133 0.220 0.255
delta Smtrl/unit -0.0004 -0.0004 -0.0004
0.312 0.304 0.325
0.00005 0.00004 0.00004
delta sales vol
0.540 0.562 0.548
Port Growth -123 -11'4
0.082 0.173
2 6.89
(Port Growth) 0 678
. 2.47 4.53 4.46
% updates entermg
0.490 0.214 0.231
R2 0.586 0.638 0.641
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

112

 

 

 

Model 1a uses the number of products available as the operationalization of multiplicity
whereas model 4a uses the percentage of products added to the portfolio and model 5a
uses the percentage of portfolio growth. All three models use second order polynomials

to test the relationship between multiplicity and indirect cost.

Model 1a

The hierarchical regressions for model la reveal the coefficient for the linear multiplicity
variable is positive and significant at the 0.10 level for the one period prior scenario. The
total variance in indirect cost explained by the model is 98.0% with the controls and fixed
effects explaining 97.7%. For the no lag scenario both the linear and non-linear terms are
positive and significant at the 0.05 level. Graphing this function over the range of the
data reveals an inverted U shaped curve (see Figure 12). The variance explained by the
controls and fixed effects is 97.4%. The multiplicity variables explain an additional

0.7%.

113

Figure 12

 

 

 

 

 

 

 

 

 

 

 

Hypothesis 4 Model 111
predicted indirect cost - lag 0
150 . L

z 100
E
n- 50

0

0 50 1 0 150 200 250 300
:3 Available
Brandl&2 _’ 4——— Brand3 _’
+——— Brand 4 —.

 

 

 

 

To confirm the validity of the shape of the curve each brand was plotted. In this case, the
brand level plots revealed two distinct populations; two that increase linearly and thus

provide partial support for the hypothesis, and two that decline exponentially.

Because the individual plots are likely errant due to their creation using the coefficient
from the regression equation that had interacting brand effects, separate regressions were
performed on each brand using just the complexity variables. The reduced number of
variables was required due to the small number of data points for each brand. The result

is that brands 1, 2, and 4 do not have any statistically significant relationships with

114

indirect cost. However, Brand 25hows a nonlinear increase (B1,n = 21.6, p=0.046 and Bnl

= 0.12,p=0.049).

In the process of addressing the counter intuitive finding shown in Figure 12 a
logarithmic fimction form was investigated. The outcome is that the logarithmic form of
the complexity variables explains less variance than the polynomial form (20.9% vs.
24.4%). However, the logarithmic form does not suffer from the interaction of fixed
effects. As such it is a superior model. Thus the significance of the logarithmic

relationship provides full support for the hypothesis.

Model 4a

The hierarchical regressions for model 4a reveal the coefficient for the non-linear
multiplicity variable is negative and significant at the 0.05 level for the no lag scenario.
Graphing the function over the range of available data reveals a curve that monotonically
decreases at an increasing rate (see Figure 13). The fixed effects and controls explain
53.9% of the variance in the change in indirect cost and adding the multiplicity variable

increases the total variance explained by 10.0% to 63.9%.

115

Figure 13
Hypothesis 4 Model 4a — no lag

 

 

 

 

 

 

 

 

The non-linear coefficient for the one period lag scenario is positive and significant at the
0.05 level resulting in a curve that increases at an increasing rate monotonically (see
Figure 14). The total variance explained by the multiplicity variables is 3.9% whereas

the controls and fixed effects explain 20.8%.

116

Figure 14
Hypothesis 4 Model 4a — lag 1

 

 

 

 

 

 

 

 

 

 

 

 

predicted delta Indirect Cost - lag 1 j
50 1
40 ~-~ L
l _ _ #5, m- - __,-,,A-,,,_.__ ,_m_,______ _______- .-
I 1
1 or 20 “ ~—*1
I O 1 . + 1
1 0.00 0.10 0.20 0.30 0.40 0.50 0.60
|

 

°/o add

 

 

 

Model Sa

The hierarchical regressions for model 5a reveal the coefficient for the linear multiplicity
variable is positive and significant at the 0.05 level for the one period lag scenario and
negative and significant at the 0.10 level in the two period scenario. The model explains
similar amounts of variance in each case with the multiplicity variables explaining 7.3%
of variance beyond the controls in the one period lag scenario and 5.5% in the two period

lag scenario. The total variance explained is 64.2% and 64.1% respectively.

Summa_ry

The static model, model 1a, provides partial support for the hypothesis in the no lag and
one period prior scenarios. The dynamic models, 4a and 5a, provide mixed results. In

the one period lag scenario they provide partial support. However, model 4a indicates a

117

decline in the no lag scenario where an increase is hypothesized and model 5a indicates

the same in the two period lag scenario.

5.5 Hypothesis 5

Hypothesis 5 states that direct cost will decrease at a decreasing rate with increasing
levels of similarity. Three Operationalizations of similarity were used to create models
describing the impact of multiplicity on warranty cost: 1) the percentage of updated
products in the portfolio, 2) the degree of age diversification of products, and 3)
percentage of products entering the portfolio in a given period that are updates. Direct
cost and the change in direct cost were regressed upon the independent and control

variables with and without lagged effects.

Model 2a uses the percentage of updated products in the portfolio as the
operationalization of similarity whereas model 3a uses the degree of age diversification
of products in the portfolio and model 63 uses the percentage of products entering the
portfolio that are updates. Models 2a and 3a use second order polynomials to test the
relationship between similarity and direct cost whereas model 6a uses only a linear term.

The lack of a second order term for model 6a is attributable to collinearity constraints.

None of the models revealed a relationship between similarity and direct cost or changes
in direct cost. In the case of model 6a, which uses the percentage of updated products
entering the portfolio as the operationalization of similarity, power is nearly zero. This

could be the reason why a relationship was not detected.

118

Summagy

No significant relationships were identified using either the static or dynamic models.

5.6 Hypothesis 6

Hypothesis 6 states that sales volume will increase at a decreasing rate with increasing
levels of multiplicity. Three Operationalizations of multiplicity were used to create
models describing the impact of multiplicity on volume: 1) the number of products in the
portfolio, 2) the percentage of products added to the portfolio in a given period, and 3)
percentage of portfolio growth. Sales volume and change in sales volume were regressed
on the independent and control variables with and without lagged effects. Tables 25 —— 28
display the hierarchical regression results for the models with significant coefficients for

the multiplicity variables.

119

Table 25
Model 1b — Sales Volume — no lag

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 1b
DV = Sales Volume Time lag = 0
BE] 232736 230648 236556
<0.001 <0.001 <0.001
BE-2 -24911 26767 75559
0.020 0.039 0.029
BE-3 -16206 35720 37047
0.219 0.014 0.019
30704 9968 311.9
Intercept
<0.001 0.150 0.973
$mtrl/unit 0.805 0.849 0.562
0.635 0.513 0.662
# prod avail 357.1 645.1
<0.001 0.002
. 2 -1.85
# prod avail 0.123
% update -89672 -113594 -123726
0.183 0.031 0.018
% diversified -65011 -39865 9956
0.587 0.663 0.917
R2 0.973 0.985 0.986
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

120

 

 

 

 

Table 26
Model 1b — Sales Volume — lag 1

 

Hierarchical Regression:
Model 1b
DV = Sales Volume Time lag = 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

BE-l 228303 22954 239101
<0.001 <0.001 <0.001
BE-2 -22837 9850 42489
0.009 0.546 0.302
BE-3 -15162 23755 56408
0.655 0.190 0.180
I 34542 19412 13763.0
ntercept
<0.001 0.031 0.210
$mtrl/unit 0.235 0.155 0.142
0.884 0.915 0.923
# prod avail 268.8 450.7
0.006 0.055
-1 40
. 2 .
# prod avail 0.385
% update -17319 -37473 -50954
0.770 0.488 0.368
% diversified -24022 -19765 -10316
0.828 0.843 0.919
R2 0.978 0.983 0.983
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

 

 

 

121

Table 27
Model 4b — Delta Sales Volume — no lag

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 4b
DV = Delta Sales Volume Time lag = 0
TE—l -4653 4520 -6463
0.691 0.698 0.577
TE-2 -8750 -11176 -8639
0.460 0.352 0.471
TE-3 11414 9872 5714
0.328 0.398 0.631
TE-4 -54149 57763 -53520
<0.001 <0.001 <0.001
TE-5 2036 1522 1258
0.858 0.893 0.911
TE- 6 -4177 -4883 -4376
0.716 0.670 0.699
TE-7 5067 3840 2733
0.660 0.739 0.810
”PE-8 -44771—"75489——35383_
0.001 0.001 0.001
TE-9' 2730 1233 3862.0
0.811 0.914 0.736
TE-l 0 -14903 -16844 -16046
0.206 0.157 0.173
TE-l 1 12680 13982 17350
0.134 0.103 0.052
-2.47 -2.48 -2.4
Intercept
0.005 0.005 0.007
% prod add 23481 42686
0.261 0.095
-171685
0 2
(A) prod add) 0.187
% updates entering 2383 -3007 -3455
0.754 0.737 0.696
R2 0.555 0.574 0.599
BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

 

 

 

122

Table 28
Model 5b — Delta Sales Volume — lag 1

 

Hierarchical Regression:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 5b
DV = Delta Sales Volume Time lag = 1
TE-l -5685 -5912 -5283
0.652 0.646 0.671
TE-2 6230 6324 2618
0.621 0.622 0.835
TE-3 -40928 -41227 -40624.0

0.004 0.004 0.004
TE-4 11023 11157 9782
0.415 0.418 0.463

TE-S -3534 -3813 -2611
0.779 0.768 0.834
TE- 6 5295 5077 6434
0.671 0.690 0.601

TE-7 -32953 -34100 -40177
0.014 0.020 0.007
TE- 8 7261 7123 7460
0.576 0.590 0.559

TE-9 -12328 -13016 -13234
0.335 0.332 0.308
Intercept 9664 9961 8243
0.279 0.279 0.355
delta $mtrl/unit 1'46 1°47 1'53
0.117 0.122 0.099

Port Growth -3989 10319
0.829 0.601

P G wth 2 69300
( on m ) 0.095
% updates entering 7048 7674 7279
0.406 0.400 0.408

R2 0.505 0.506 0.557

BE = Fixed effect for brand B term
TE = Fixed effect for time p-value

123

 

 

 

Model la uses the number of products available as the operationalization of multiplicity
whereas model 4a uses the percentage of products added to the portfolio and model 5 a
uses the percentage of portfolio growth. All three models use second order polynomials

to test the relationship between multiplicity and sales volume.

Model lb

The hierarchical regressions for model 1b reveal the coefficient for the linear multiplicity
variable to be positive and significant at the 0.05 level for the no lag and one period lag
scenarios. Thus the indication is an increase in units sold with increasing levels of
multiplicity. The fixed effects and controls explain 97.3% of the variance in the volume
for the no lag scenario and 97.8% for the one period lag scenario. Adding the
multiplicity variable brings the total variance explained by: the model to 98.6% and

98.3% respectively.

Model 4b

The hierarchical regressions for model 4b reveal the coefficient for the linear multiplicity
variable to be positive and significant at the 0.10 level for the no lag scenario. Thus the
indication is an increase in units sold with increasing levels of multiplicity. The fixed
effects and controls explain 55.5% of the variance and adding the multiplicity variable

brings the total variance explained by the model to 59.8%.

124

Model 5b

The hierarchical regressions for model 5b reveal the coefficient for the non-linear
multiplicity variable to be significant and positive at the 0.10 level for the one period lag
scenario. The total variance in the change in volume explained by the model is 55.7%
with the controls and fixed effects explaining 50.5%. Graphing the significant

multiplicity variable over the range of the data reveals a U shaped curve (see Figure 15).

To confirm the validity of the shape of the curve each brand was checked. If each brand
manifests the same general pattern, then the confidence can be placed in the curve.
However, if plots of the individual brands manifest different patterns, then the result is an
interaction of brand effects. In this case, the shape of the curves for each brand are

consistent with the curve shown in Figure 15.

Figure 15
Hypothesis 6 Model 5b

 

 

 

predicted delta Volume - lag 1

 

 

 

 

 

 

 

1 -0.40 '0.20 0.00 0.20 0.40 0.60
’ °/o portfolio growth

 

 

125

Summary

Model lb provides partial support for the hypothesis in the no lag and one period lag
scenarios. Models 4a and 53 provide partial support in the no lag and one period lag

scenarios respectively.

5.7 Hypothesis 7

Hypothesis 7 states that sales volume will not be impacted by similarity. Three
Operationalizations of similarity were used to create models describing the impact of
multiplicity on warranty cost: 1) the percentage of updated products in the portfolio, 2)
the degree of age diversification of products, and 3) percentage of products entering the
portfolio in a given period that are updates. Sales volume and the change in sales volume
were regressed on the independent and control variables with and without lagged effects.
Table 29 displays the hierarchical regression results for the model with a significant

coefficient for a similarity variable.

Model 2a uses the percentage of updated products in the portfolio as the
operationalization of similarity whereas model 3a uses the degree of age diversification
of products in the portfolio and model 6a uses the percentage of products entering the
portfolio that are updates. Models 2a and 3a use second order polynomials to test the
relationship between similarity and direct cost whereas model 6a uses only a linear term.

The lack of a second order term for model 6a is attributable to collinearity constraints.

126

Table 29
Model 2b — Sales Volume — no lag

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hierarchical Regression:
Model 2b
DV = Volume Time lag = 0
BE-l 215236 224044 223208
<0.001 <0.001 <0.001
BE-2 20217 24693 17792
0.097 0.037 0.094
BE-3 34413 35260 28106
0.022 0.014 0.029
1 5589 11045 22066
Intercept
0.017 0.086 0.002
$mtr1/unit 0.227 0.878 0.923
0.862 0.494 0.418
. 340.2 358.7 330.2
# prod avail
<0.001 <0.001 <0.001
% update -104432 31796
0.028 0.582
-1334775
2
% update _ 0.002
R2 0.982 0.985 0.988
BE = Fixed effect for brand B term
TE = Fixed effect for time P-Value

 

 

 

Model 2b
The hierarchical regressions for model 2b reveal the coefficient for the non-linear
multiplicity variable to be negative and significant the 0.05 level for the no lag scenario.

The total variance in the change in volume explained by the model is 98.8% with the

127

controls and fixed effects explaining 98.2%. Graphing this function over the range of the

data reveals a monotonic curve that decreases at an increasing rate (see Figure 16).

Figure 16
Hypothesis 7 Model 2b

 

predicted volume - lag 0 ’

 

 

 

1 percentage of updated products in portfolio

 

Models 3b and 6b

 

The hierarchical regressions using models 3b and 6b failed to detect a significant (<0.10)
relationship between similarity and volume or change in volume; model 3b has sufficient

power (>080), but model 6b has virtually no power.

Summa_ry

The hypothesis is supported with both the static and dynamic models in all scenarios

except the no lag scenario of model 2b where a declining relationship was found.

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6.0 Discussion

6.1 Introduction

This chapter discusses and interprets the findings highlighted in the prior chapters. It
provides an overview of the hypotheses and whether they are supported as well as an

interpretation of the findings on both a global level and by hypothesis.

Table 30 provides an overview of the hypothesized relationships studied and whether
support for them was found. A review of the table reveals that there is at least partial
support for six of the seven hypotheses. In some cases there is conflicting support;
findings that are both consistent and counter to the hypothesized relationship. These
findings are discussed below in hypothesis specific sections. A review of the table also
reveals that dynamic models explain more instances of complexity’s impact on supply
chain outcomes (warranty, inventory, etc.) than static models. Within the dynamic
models, the percentage of growth in the portfolio appears to have more explanatory
power than the percentage of the portfolio comprised of recent additions. These

observations are elaborated upon below.

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Table 30
Summary of Findings

.—
r

O '-‘ N

Variables Warranty - H1

 

N = No Support
P = Partial Support
O = Opposite

6.2 Interpretations and explanations

6.21 High level interpretations

There are two categories of models that were created to test the hypotheses set forth in

this research project: static and dynamic. Between these two types of models, the

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complexity variables in the dynamic models have more explanatory power. They predict
a greater number of outcomes and they provide a greater increase in explained variance
over the control variables (about 10% on average compared to about 5% for the static
models). This implies that the study company has systems in place that readily adapt to
increases in product portfolio complexity and that these systems effectively mitigate the
longer term impacts. Stated another way, the study company reacts to changes in
complexity levels and begins to manage it effectively, rather than having in place a

system which accommodates complexity changes.

This implication is interesting in that contacts at the study firm do not believe complexity
is well managed. This perspective may be a result of the business planning process used
at the study company. The study company has for decades performed more business
planning and monitoring of progress toward realizing the plan than most other firms.
This planning process exposes costs and managers are encouraged to address those that
rise unexpectedly or too rapidly. The planning process also creates an informal reward
system by providing visibility of managers who effectively manage / reduce costs under
their purview to senior management. This planning process may be what is driving the
response to changes in product portfolio complexity and these responses may include the

creation and evolution of systems to effectively manage the change.

An alternative explanation for why static models do not have as much explanatory power
is that the study firm simply may have large amounts of untapped capacity in production,

production support, and development. While capacity utilization was not provided, the

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study company continually monitors headcount and willingly reduces it to ensure it is at
appropriate levels as evidenced by articles in the popular press. Hence it seems unlikely
that spare capacity is the source of the capability of adapting to changing levels of

product portfolio complexity overtime.

The multiplicity models within the set of dynamic models use two different
operationalizations of product portfolio complexity; percentage of portfolio growth and
percentage of the portfolio added in the period. The firndamental difference between the
two models being that the ‘percent growth’ variable accounts for the products that exit
the portfolio. A review of Table 30 reveals that the growth measure explains significant
amounts of variance in a greater number of outcome variables. Additionally, it results in
relationships consistent with those hypothesized more often than the ‘percent add’
measure. Each model explains about the same amount of variance beyond the control
variables. Thus the models based upon net portfolio growth are better than those based
upon portfolio additions and the model focused on net portfolio growth is better than the

model focused on portfolio additions.

This finding makes logical sense. The outcomes that are considered in this study (e. g.
warranty cost) are more dependent on the net portfolio size. Additions to the portfolio
have impacts, but reductions also have impacts that when accounted for provide
meaningful information. Possibly, the information that the net portfolio growth captures

is utilization changes.

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6.22 Hypothesis 1

 

The static model for predicting warranty, which uses the number of products available in
the portfolio as the operationalization of multiplicity, shows a decrease in warranty cost
at an increasing rate. However, this initial result must be set aside as it is an artifact of an
interaction of brand effects; this is discussed in greater detail in section 5.2. As a result
of discovering the interaction of brand effects, additional analyses were performed.

These analyses included investigating a logarithmic relationship between the number of
products in the portfolio and warranty cost. It is the significance of the coefficient for the
logarithmic multiplicity variable that provides support for the hypothesis that warranty

costs will grow at a decreasing rate.

The presence of a curtailment on the rate of increase in warranty cost may be attributable
to increases in learning; learning being reflected in better quality as measured by
warranty cost. The results, in conjunction with a post hoc. regression of warranty cost on
similarity (similarity variables were nonsignificant), suggest that greater learning occurs
with greater variety rather than greater focus. Thus, it is better to expose a worker to a
variety of assembly operations rather than let her perfect a single operation for the
purpose of maximizing quality improvement. This finding is consistent with the
principle of absorptive capacity (Cohen & Levinthal, 1990) which indicates that exposing
a worker to greater variety leads to more situations where learning can take place and

more contexts into which the principles learned can be applied and refined.

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Given that the increase in multiplicity accentuates socialization (Linderman, Schroeder,
Zaheer, Leidtke, & Choo, 2004), Nonaka’s (1994) spiral of knowledge creation offers
insight into the mechanism by which greater multiplicity can curtail warranty cost.
Nonaka states that the spiral containes four steps: socialization, combination,
extemalization, and internalization. Exposing the worker to a larger number of products
provides more reasons to communicate with other workers. At the factory floor level,
working on several products may lift the worker’s focus from a very narrow task to
something more general and hence may be the catalyst for conversations leading to
embarkation upon the knowledge spiral. In the context of engineering design, increases
in multiplicity may be the catalyst for pushing an engineer out of a silo mentality.
Interacting with peers from other product lines increases opportunities to pick up new
concepts and combine them with their existing knowledge base. Hence increasing
multiplicity facilitates the spiral of knowledge creation, which in turn accelerates

learning, which leads to improved quality as reflected by a decrease in warranty cost.

This finding may initially appear contrary to TPF, which suggests that learning is the
result of better utilization through scale. However, learning through increases in scope
may actually be the best way to increase resource utilization. Considering resources to
include the human capital of the firm, accessing it — utilizing it — leads to improved

performance. It may even lead to improved utilization of the physical assets.

The dynamic models tell a slightly different story than the static model. Model 4a, which

uses the percentage of the portfolio added in the period as the operationalization of

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multiplicity, shows a nonlinear decline in warranty costs in period zero followed by a
nonlinear increase the next quarter. The decrease in period zero may be an artifact since
an analysis of the product release dates revealed that most often products are introduced.
toward the end of the quarter. Since the focus of the model is change in warranty cost,
there may not be enough time for changes in multiplicity to impact the dependent
variable. Thus the one period lag scenario lagged effect is probably more reliable as
there is full quarter where each product has the chance to accrue a warranty claim. The
increase found in the one period lag scenario is consistent with the finding of the static

model and partially supports the hypothesis.

6.23 Hypothesis 2

 

Three models were used to test hypothesis two; 1a, 4a, and 5a. Respectively they use the
number of products available in the portfolio, the percentage of the portfolio added in the
period, and the percentage growth of the portfolio as the operationalizations of
multiplicity. The models constructed to test hypothesis two generally show support for
the hypothesis. The results of the models constructed in this study reveal that inventory
investment grows with increased multiplicity thereby providing support to Fisher et al.
(1999). Further more this growth follows the polynomial relationship put forward by
Manne (1958) and Wagner & Whitin (1958) and conforms to the variance pooling
properties suggested by the Theory of Performance Frontiers (Schmenner & Swink,

1998).

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Model 1a, the static model, did not detect a significant relationship with inventory
investment. There are a couple potential explanations for this phenomenon. This finding
could result if several products are constructed of the same set of components in a build
or assemble to order environment since these environments typically result in less
inventory build up than make to stock environments. However, this would be partially
controlled for by the similarity variable which in the model. The study company operates
in a quasi build / assemble to order environment. Their objective is to build to order, but
at times finished goods inventory is created proactively or partial units constructed and
then finished to order by adding various options after an order is received. Thus there
will be changes across time and these should be detected. The quasi nature of the
environment suggests that there may be other variables that are masking the relationship
between multiplicity and inventory; potential variables include presence of marketing
campaigns or the influence of incentive systems. However, even though masked, if there
were sufficient power, the effect might be detected. Low power, which is nearly zero in

this case, is the most likely explanation for the finding.

However, the dynamic models did detect and explain changes to inventory investment.
The model that operationalizes multiplicity using the portfolio growth finds an increasing
rate of increase in the period in which the portfolio size is changed. This may be
attributable to a build up to ensure high fill rates in case demand takes off faster than
expected. Two periods later inventory increases linearly with portfolio growth. This
relationship provides partial support for the hypotheses in that the data could be from a

location on the growth curve that is relatively flat and hence detected by the model as a

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linear term. A similar relationship is found using the percentage of products added to the
portfolio in the same two period lag scenario. However, in this instance, if the criterion
for significance is relaxed, the nonlinear term becomes meaningful and suggests a
declining rate of increase as hypothesized. Alternatively, inventory grth could be
curtailed as forecasting improves with increased amounts of historical information and
component lead times shorten. Together these will have the effect of straightening the

growth curve.

6.24 Hypothesis 3

 

The same three models that were used to test hypothesis two were also used to test

hypothesis three; la, 4a, and 5a.

Model 1a, the static model, did not detect a significant relationship between multiplicity
and direct cost. Besides being attributable to a genuinely null result, the result could be
attributable to low power, bad data, or a bad measure. Insufficient power results in the
inability to detect statistically significant relationships. However, power is not an issue in
this case since a check of power tables (Cohen et al., 2003) reveals that power is greater
than 0.90. The likelihood that the null is an artifact of the cost accounting used by the
study firm is low since contacts at the firm indicate the costs are actual and not

applications.

The most likely explanation is that the number of products available in the portfolio may

not measure multiplicity as effectively as desired. There is a positive correlation (r=.306,

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p=.04) between the number of products available in the portfolio and the percentage that
are updates of prior products that provides evidence for the conclusion that the measure
may explain little additional information. The initial conceptualization of the measure
assumed that there would be less correlation between the number of updated products and
the total number of products, thus providing a cleaner representation of portfolio breadth.
For example the ‘updated’ products may be only nominally different and hence offer
little differences in assembly or fabrication. Thus the measure of the number of items
available in the portfolio is contaminated by the number of products that are similar to
others in the portfolio thus impacting the prediction of direct cost. A better measure may

be the number of new products in the portfolio.

The two dynamic models, those using percent add and percent growth as
operationalizations of multiplicity show a linear decrease in direct cost in the period that
changes are made to the portfolio which is counter to the hypothesis. There is a very
practical reason that explains this phenomenon. Contacts at the study company confirm
that the direct cost of new products is typically lower than older ones. The implication is
that replacing older products with newer simply changes the cost structure. This
continual cost reduction is consistent with the reductions seen generally in the technology
sector. Since the cost of materials is controlled, this implies there is something else

driving the cost reductions.

A different relationship is manifested in the one period lag scenario though. The model

using percent growth reveals an increase in direct cost at an increasing rate, thereby

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providing support for the hypothesis. The growth in cost may be related to requirements

for additional learning.

Exposure to an increased number and variety of scenarios increases the capacity to learn.
Cohen and Levinthal (1990) refer to this as absorptive capacity. In the context of a
manufacturing plant, the knowledge gain associated with an increase in absorptive
capacity is translated into increased productivity. However, as additions to the portfolio
increase, the capacity to apply this knowledge or even firnction at a steady state level
becomes overwhelmed, productivity diminishes, and a rapid increase in direct cost
results. Direct costs rise because the manufacturing infi'astructure is being required to
perform at a level beyond that which the process or operators and managers can handle.
The result is manifested as inventory shortages and forecasting limitations, increased
material handling requirements, increased work in process, and an increased number of

defects and hence scrap or rework.

The interesting implication is that exceeding the capacity of the human capital leads to
declines in the utilization of the physical capital. This leads to the question as to whether
TPF is properly specified. The theory as initially proposed focuses on the physical assets.
It may be that there are latent and antecedent relationships to people, policies, and other
such soft / intangible assets that should be incorporated into the theory. Alternatively,
these sofi / intangible assets may be simply subject to the same forces causing similar

outcomes as those seen in the physical assets of production.

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The conclusion that increased multiplicity will lead to increased direct cost supports the
application of TPF to this context. TPF suggests that decreased utilization will increase
costs. Increases in multiplicity will decrease utilization for reasons discussed in chapter
three. Thus the increase in multiplicity leading to increased direct cost provides

empirical support for TPF.

The conclusion of this research, that increased multiplicity will lead to increases in direct
cost, is also consistent with the scenarios alluded to by Skinner (1974b) and Collins and
Schmenner (1993). Skinner (1974b) and Collins and Schmenner (1993) hypothesized
that increased focus, be it in manufacturing objectives or processes, is an effective means
for improving performance. They assert that when a production process is required to do
too many things it bogs down and the overall performance diminishes. This increase in
focus is analogous to reduced multiplicity. A survey of the financial performance of
commercial laboratories provides additional evidence supporting the benefit of reducing
multiplicity (Miller & McConneghy, 1997). The survey reports that laboratories more
narrowly focused, those offering a lesser number of services to fewer market segments,
have the best financial performance. Thus this research provides empirical support for

the work of Skinner (1974a) and Collins and Schmenner (1993).

6.25 Hypothesis 4

 

The static model, which uses number of products available as the operationalization of
multiplicity shows a linear increase in indirect cost in the period prior to products

becoming available. However, this finding is suspect due to a brand effect interaction.

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Using a natural log function is another means of arriving at the hypothesized relationship.
It offers the benefit of not being conformable to an increasing rate of decline. Hence an
alternate model using a logarithmic relationship instead of a polynomial was constructed
as a part of the additional analyses discussed in section 5.5. This revised model shows a
logarithmically increasing cost with increasing multiplicity. The significance of the
logarithmic relationship in period zero and the one period lag scenario supports the

hypothesis.

Both of the dynamic models, 4a and 5a, show a decline in indirect cost. Model 4a shows
a decrease at an increasing rate in period zero where model 5a shows a linear decline in
the two period lag scenario. These declines in indirect cost might be attributable to

business process transformations or unique aspects of the business models for each brand.

If business process transformation initiatives were carried out they would likely be
reflected most dramatically in the category of indirect cost. For example, the installation
of an e-procurement system should reduce the purchasing effort required to support a
product line. Another example would be the implementation of a product data
management or product lifecycle management system reducing engineering costs.
However, contacts at the study firm indicated there were no such initiatives during the

study period.

If the brands were behaving differently in regards to indirect cost, it would be seen in a

brand level analysis. This analysis was carried out and established that each brand

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manifests the same relationship between multiplicity and indirect cost. Thus this is not

an issue in this instance.

The explanation that seems most plausible is that the indirect cost is increased in quarters
prior to those examined in this research as engineering and other support staff design and
make ready for introduction the forthcoming products. It is entirely reasonable to assume
that the time required to perform these activities is greater than the 90 days used in the
analysis. Hence these costs are already at an elevated level when the analysis begins and
what is detected is a return to normal operational levels. Since the study firm has a six
month pattern to their planning process, the elevated level of indirect cost may have
caught the attention of managers. The result is that managers then take corrective action
by reducing headcount or other means of cost curtailment. This rationale is tentatively

supported by articles that appear in the popular press.

6.26 Hypothesis 5

 

None of the models used to test the hypothesis that increased levels of similarity result in
increasingly lower direct costs found any statistically significant relationship. Nor were

any of the controls for similarity significant in the models testing multiplicity hypotheses.

There are a couple potential rationales why no relationship was found. The first pertains

to power. Insufficient power results in the inability to detect statistically significant

relationships. However, power is not an issue in this case. A check of power tables

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(Cohen et al., 2003) reveals that power is greater than 0.90 and as such is not likely to be

the reason for the null result.

The second rationale is that similarity just does not impact direct cost. However, this
logic goes against a long standing widely held and empirically validated belief that
increased similarity will impact direct cost. Hence this rationale is not likely valid. In a
similar vein, it is possible that the benefit to increased similarity is delayed until some
point after the two period lag that this analysis is able to accommodate. This too seems

implausible as scale benefits tend to be recognized immediately.

A third rationale is that the similarity measures created do not effectively capture the
construct. While this may eventually be proven to be true, the logic used to create them
is sound. Furthermore, one of the measures is anchored in the literature and has been

empirically validated in other settings (Hitt, Hoskisson, & Kim, 1997).

A fourth rationale is that the null result is an artifact of the cost accounting used by the
study firm. For example, if the study firm used an allocation factor rather than collecting
actual costs. However, this is unlikely since contacts at the firm have indicated the costs

are actuals.

Since none of these explanations can be fully embraced, additional research into the

measurement of similarity is required.

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6.27 Hypothesis 6

 

The three models used to test the relationship between multiplicity and volume found
positive linear relationships in period zero and the one period lag scenarios. This
provides partial support of the hypothesis. Full support requires significance of the
nonlinear coefficient for the multiplicity variable. The significance of the nonlinear term
may have gone undetected due to reduced power (~ 0.55) in the case of models 1b and 4b

which use the number of products available as the operationalizations of multiplicity.

The one period lag scenario for model 5b, which uses the percentage of portfolio growth,
reveals a different functional form; a U shaped curve. Hence, as the portfolio either
contracts or expands, the number of units sold increases. At first blush this seems
counter intuitive. However, given the assumption that the products trimmed from the
portfolio are not strong market performers, this relationship makes sense. Sales volume
increases as new products are entered into the portfolio, as expected. The explanation for

the increase in sales from portfolio reductions requires some additional explanation.

Quelch and Kenny (1994) offer a couple reasons why removing poor performers could
also result in increased sales volume: customer confusion, brand dilution, and
cannibalization. The excess of choice in one brand can confuse a customer and lead to
the selection of a safer ‘one size fits all’ product offered by a competitor. Another
potential reason for increased demand with decreased multiplicity is an improvement in
the ability of the sales force to explain the merits of each product to either buyers or

channel partners resulting in a focusing of the marketing message. Quelch and Kenny

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(1994) indicate that line extensions, which are thematically similar to the updated
products in this research, rarely expand category demand. Often they carmibalize the
flagship product leading eventually to a reduced brand image and a reduction in the

ability to draw customers to the brand.

Quelch and Kenny’s explanation that a reduction in portfolio size enables the sales staff
to better articulate the merits of the product leads to the variance pooling benefits of TPF.
The sales staff are more focused on comparatively fewer products; their efforts are
concentrated — their efforts are pooled. It could be argued too that their utilization is
improved since there is a greater sales volume for their efforts. Both of these arguments

support the application of TPF to the intangible asset of the sales forece.

One insight gained from a review of the models used to test hypothesis six pertains to
material cost. The coefficient for material cost per sales unit is significant and positive in
model 5b. Since higher materials costs are generally associated with higher sales prices
this finding appears to be incongruent with the economic principle that lower prices
increase sales volume. However, considering the nature of the product, the variable may
serve as a proxy for technological advancement or customer perception of performance.
This desire for the latest technology or highest performance is a strong inducement for
purchase and is reflected in the positive correlation between materials cost and sales
volume. Thus customers assign value to technological or performance superiority and
use it as a purchasing guideline. The result is that products perceived as superior achieve

greater market success.

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6.28 Hypothesis 7

 

Two models were used to test the hypothesis in the static setting, 2b and 3b. Model 2b
uses the percentage of the portfolio comprised of updated products as the
operationalization of similarity. This model finds no relationship between similarity and
volume in the one and two period lag scenarios. However, it finds that volume declines
at an increasing rate with increasing levels of similarity in period 0. There are several

rationales that might explain this result.

It may be that buyers are skeptical about the value of products that are perceived as minor
variations of older products. Alternatively the buyer may be expecting differences
between products and not finding them becomes confused causing the buyer to select a
competitor’s product. Thus as reported in section 6.26, buyers may be seeking notable

technological advances and distinguishable value propositions.

Model 3b uses the degree of diversification as the operationalization of similarity. This
model found no relationship to sales volume. Since this model has sufficient power
(>080), this finding is plausible. However, it is possible that the measure does not
effectively measure the similarity construct. While this may eventually be proven to be
true, the logic used to create it is sound. Furthermore, the measure is anchored in the

literature and has been empirically validated in other settings (Hitt et al., 1997).

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The model used to test the hypothesis in the dynamic setting, 6b, uses the percentage of
products entering the portfolio that are updates as the operationalization of similarity.
Consistent with the hypothesis, there were no significant relationships found. However,

power is virtually zero and as such no conclusion should be drawn from the analyses.

Considered in conjunction with the insights reported in section 6.26, the findings in this
section point to the importance of the portfolio size and complexion. The regression
models indicate that too many products and products too similar to one another are each
detrimental to sales volume. Therefore, the most successful portfolio must cover the
price and performance points of the market parsimoniously and in a manner that allows
differentiation of the products from each other. Conventional wisdom is that there are
cost benefits to increased standardization. However, the regression models used to test
Hypotheses 7 indicate that sales volume is at risk of curtailment from employing
increased levels of standardization. This leads to the conclusion that standardization
should be on aspects of the product not discemable to the customer e. g. a windshield
wiper motor or vent fan. Hence this research provides some empirical validation of
comments made by Closs et a1. (2007) about the merits of focusing on customer
discemable component commonality and is consistent with Kim and Chhajed’s (Kim &
Chhaj ed, 2001) finding that customer perceptions of similarity impact the price the

customer is willing to pay.

There are several practical implications related to this finding including the use of

product platforms and modularity. Since product platforms are a type of strategy to

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reduce the multiplicity and most often are beyond consumer perception, they may be very
effective strategies for cost effective growth. This research provides some empirical
support for incorporating platforms into a portfolio when practical. Product modularity
requires more attention to the impact of the module on customer perception. While cost
improvements can be captured from increased similarity, sales volume growth may be
more difficult to recognize since the modules are often feature oriented or evident to the

consumer.

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7.0 Conclusion

7.1 Introduction

This chapter addresses the contributions this research project has made to the academic
and practitioner communities. It highlights implications that are the result of the
contributions and includes a discussion of limitations to ensure that there is full
disclosure around the research and to guide any researchers building on the work. A
section on lessons learned is included and the research agenda spawned fiom this

research is articulated. The chapter concludes with a synopsis of the research.

7.2 Contributions

This research was executed with the intent of advancing theory for the purpose of
impacting the practice of management. This objective was realized by demonstrating the
appropriateness of a theoretical perspective and the extension thereof, the establishment
of a definition and typology of complexity, and the creation and validation of variables
that could be used in decision support tools to aid managers in determining the optimal

level of complexity for a portfolio of products.

7.21 Research

 

This research provides a definition for product and portfolio complexity grounded in the
literature of multiple disciplines. This definition and the associated typology that was
also developed in this research formally establish that product and portfolio complexity

are multidimensional constructs. This research empirically establishes the validity of the

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multidimensional aspect by demonstrating that two separate dimensions of complexity

have differential impacts on various costs and demand.

A significant contribution to the academic community is the demonstration that the
Theory of Performance Frontiers (Schmenner and Swink, 1998) is an appropriate
theoretical lens through which to view issues pertaining to product portfolio complexity.
It is this theoretical perspective that provides the rationale for the formulation of the
models developed to explain the various cost and demand outcomes. This leads directly
to the identification of the functional form of the relationship between each dimension of
complexity investigated over the course of this research project and the various cost and

demand outcomes examined.

This research also expanded TPF by demonstrating its relevance to capabilities. These
capabilities may construed as intangible assets. They are treated as such in the resource
based view of the firm and protected as such by firms such as 3M which have unique
manufacturing capabilities. One aspect of capabilities is that they may not be smooth;

they may be discontinuous or irregular in shape and yet TPF still seems to be usefirl.

The nature of the nonlinear relationship between complexity and cost and complexity and
demand reveals that an optimum level of complexity exists. This is a contribution in its
own right, but is facilitated by another contribution; the operationalizations of similarity

and multiplicity.

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7.22 Managerial

 

This research demonstrates that an optimal level of product portfolio complexity does
exist and provides to firms an approach for quantifying the most profitable levels
considering their own portfolios. Specifically, regression equations established to
substantiate the hypotheses above can be combined to form a multilevel model predictive
of profitability. This model can be incorporated into a decision support tool to aid
managers in making decisions about the portfolio that move the organization closer to
maximum profitability. A side benefit of this research is the explication of the relative
impacts of design reuse and part count reduction initiatives. Hence the manager receives
guidance on where to place engineering emphasis. The overall impact being better

managed companies using resources more efficiently.

A further contribution to managers is the identification of factors that influence the profit-
complexity curve. Factors that can guide the strategic design of the portfolio were
identified and validated. Thus armed with the knowledge provided by this research,

managers can design their portfolios for either profit or market share.

7.3 Implications

7.31 Theory

The demonstration of the Theory of Performance Frontiers (Schmenner and Swink, 1998)
as an appropriate theoretical lens through which to view issues pertaining to product
portfolio complexity is a significant implication. Extending T PF into the realm of

intangibles is another. This was accomplished through establishing the impact of

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similarity on sales volume and the various costs examined in this study. The ‘percentage
of updated products in the portfolio’ and ‘percentage of diversification’ serve as proxies
for design reuse; product designs being intangible assets. Thus this research has
demonstrated that, consistent with the predictions of TPF, better utilization of these
intangible assets results in improved performance. Thus this research has extended the

scope of TPF and has by definition been theory building.

Another implication of the validation of TPF as an appropriate theoretical lens through
which to view issues pertaining to product portfolio complexity is an improved tie
between product and portfolio complexity and the discipline of economics. TPF has its
foundations in the neoclassical school of economics and to the extent that it describes
microeconomic activity, it is an economic theory. This research established the
diminishing returns to investment that TPF predicts. Keynesian economics also predicts
a decreasing return to investment. Therefore, a bridge is built to prominent economic

theory.

This research provides and empirically validates a new definition of complexity. This
allows researchers to re-characterize prior research as examining either multiplicity or
similarity and constrain the findings to these discrete dimensions. This will create greater
harmony within the existing literature and resolve apparent paradoxes. It will also guide

future research in a similar manner when adopted by other researchers.

7.32 Operationalizations

 

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The determination of the means by which product portfolio complexity can be quantified
is another significant outcome of this research project. The implications of the
operationalizations of product portfolio complexity include the ability to incorporate
them in decision support models. These models would use the operationalizations of
product portfolio complexity to guide managerial decision making; the ramification being

more profitable levels of complexity represented in the portfolio.

F irms that embrace the use of the complexity factors validated in this research for the
purposes of improving decision making will necessarily reduce wasted effort. Finding
the optimal level of complexity will result in higher levels of performance given the
inputs. This occurs through the enhanced utilization of resources, as highlighted by TPF.
Since resources are more fully and effectively utilized, the result is the consumption of
fewer resources. These resources, if they are human, can be redirected to other firms or
locations of the economy where the marginal return for their use is higher. Alternatively,
they could be redeployed within the organization to focus on activities that lead to a
stronger competitive position within the industry. Examples of these activities could be
the design of novel features or the improvement of manufacturing processes. If the
resources are physical, then green initiatives are forwarded and the overall environment

improved by reducing natural resource consumption and producing less pollution.

The validation of the operationalizations of product portfolio complexity leads to tools by
which future researchers can study the topic. The operationalizations may provide

insight to other researchers for additional ways to conceptualize or operationalize the

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construct, or may prove useful when employed in other settings by researchers from other
disciplines. For example social researchers may use the similarity and multiplicity
dichotomy to study the transformation process that occurs in the classrooms of primary
schools. They may find that class size does not impact the educational outcome to the

extent that homogeneity of student ability does.

7.4 Managerial Implications

The managerial implications of this research may be quite broad reaching, but the
discussion herein will be constrained to those pertaining to marketing, operations, and
procurement. These are the areas where the most immediate implications arise and where

application of the insights could most readily be made.

Marketing

The research of Closs et. al. (2008) suggests that the propensity of marketing functions to
add products and variants to the portfolio can be detrimental to the organization. The
findings of this research confirm that there are deleterious impacts to both operational
costs and sales volume to increasing the portfolio size too greatly. There is an inverted U
shaped curve with product size on the x-axis and sales volume on the y-axis. For each
company there will be a unique optimal size of the portfolio. Since the costs are
nonlinear as well, there will be a similar relationship with profit. However, the profit
maximum may not be at the same point as volume maximum. Therefore market share
strategies may be detrimental to the financial health of the firm. Hence top management

needs to understand the role of portfolio breadth in determining market share and

154

profitability since it should play a critical role in maintaining the proper size of the

portfolio.

There are also implications for portfolio mix. If this research proves to be generalizable
beyond the firm from which the data was drawn, the instruction to marketers is to
maintain the portfolio in a perpetual state of ‘newness’ since new products outperform
existing products in terms of sales volume. New products should be regularly introduced
in replacement of older products. Cosmetic changes of products from time to time will
not be effective in growing sales since the consumers will fail to find differences between
products with the result being a decline in sales volume. Hence the portfolio manager
needs to ensure that there is an appropriate level of differentiation between products in

the portfolio.

Operations

This research calls attention to the need for operations managers to effectively manage
capacity. The critical issue is not whether capacity is available, but whether utilization is
at the right level. Hence the organization could benefit from incorporating asset
utilization choices at the time of design. This is the next step beyond design for
manufacture in that it additionally considers the existing asset constraints of the

organization.

This research suggests that mangers could view their assets as a portfolio. This means

that the firm should consider the mix of assets and how well suited it is to the needs of

155

the organization. Assets that are more multi-purpose are likely to be superior to those
dedicated to a particular product. Multi-purpose assets can handle a wider assortment of
needs and as such utilization should increase. However, at the point where setups begin
to constrain the utilization, tooling dedicated to the process should be secured and the
multi-purpose asset redeployed. Conversely, this research also suggests that there is little

benefit to having several highly similar assets performing the same task.

Procurement

 

There are decisions that are made by managers regularly about whether to internalize or
extemalize production (an asset). This research indicates there are ramifications to cost,
quality, and possibly market share that must be considered. While outsourcing may
expose the organization to a different set of performance frontiers which are superior
their own, there is the risk that the outsourcing firm will take on too many projects. The

ultimate result will be a decline in performance.

The insource / outsource question leads to the matter of supplier selection and evaluation.
The contracting firm needs to carefully evaluate the types of products produced and
processes employed by the contractor and set limits on contractor growth. Consideration
should be given to the quality of the production assets relative to peers and that of the
contractor. This is critical since gains in performance will only accrue to better

utilization of assets, which is in turn limited by the total amount of assets.

156

There are implications in this research for employee training. This research suggests it is
better to expose employees to a broad array of scenarios than to focus the training on the
details of a single scenario. Hence human resources departments should re-craft
employee development programs to move employees out of silos. There should be a
continual churn of employees from one functional area to another. This continual
exposure to new situations leads to better overall performance. Extending this concept to
the insource / outsource decision for labor suggests the benefit from exposing employees
to a wide variety of settings is a compelling argument for using contract labor. Using
workers who are continually exposed to other firms and practices offers the potential to
make the greatest progress toward performance goals. The caveat being that the

contracting company can protect its own intellectual property.

7.5 Limitations

The findings of this research should be interpreted in light of its limitations. The first
limitation is the power of the study. Although power is generally greater than 0.80, there
are a couple instances where it is lacking that impacted the interpretation of the results.
The impact of this is that with greater power the nonsignificant coefficients of the
nonlinear terms may have been found to be statistically significant and thereby offer
greater support to the hypotheses put forward. More significantly, some of the
operationalizations which were not found to be related to the performance outcomes
examined in this research may actually be good predictors. This lack of power thus limits
the empirical validation of these additional conceptualizations of product portfolio

complexity and as such their validity remains unknown.

157

The data set is from a single firm. Many researchers would characterize this as a
limitation due to the inability to be generalized beyond the study company. However, the
generalizability of the coefficients is not the primary focus of this research but rather the
principles revealed in the results. These principles may be generalizable to firms
providing competing products to the same markets, which is a significant market
globally. Additionally, the principles might be generalizable to portfolios of similar
products; multi-system durable electronic goods. Examples include audio equipment,
televisions, imaging and diagnostic equipment, many types of medical devices,
telecommunications switches, and the like which collectively represent a significant
portion of the global economy. However, whether the findings are generalizable is
reserved for future studies. Using this research design is appropriate since a new
theoretical perspective and operationalizations were tested and the single firm focus

prevents confounds exogenous of the study company from masking the findings.

The use of longitudinal data is a particular strength of this study. The ability to detect
changes over time greatly improves the ability to claim causality. However, the three
year duration of the study is a limitation. Some of the products represented within the
portfolio have life spans beyond three years and as such the impacts on outcomes such as
warranty cost my not be fully revealed. There is a possibility that the failure frequency
could escalate at a point beyond what is supported by the data. Thus lagged effects may

not be firlly explicated in this study.

158

7.6 Future research

This dissertation is a portion of a multi-stage research agenda investigating the impact of
product and product portfolio complexity on supply chain performance outcomes. Figure
1 provides a graphical overview of the dimensions of product complexity which will,
over time, be addressed by fully executing the research agenda. Through the exhaustive
execution of this comprehensive research agenda, the limitations and remaining gaps in
knowledge will be ameliorated and filled. Mitigations for the limitations and remaining
gaps in knowledge are mentioned below. These mitigations should be assumed to be
incorporated in the research designs of studies spawned by the research agenda discussed

further below.

7.61 Address limitations

There are three notable limitations to the research presented in this dissertation: power,
external validity, and longitudinal duration. These can be mitigated by incorporating
larger sample sizes, greater variety of subjects, and longer time windows respectively.

These mitigations will be employed as appropriate in the studies discussed below.

7.62 Address remaining gaps

 

Gaps in the academic community’s knowledge about product portfolio complexity
remain. One is the issue of whether the typology of complexity offered in this research is
comprehensive. Although two dimensions were empirically validated, there may be

more. Thus establishing or refirting the existence of additional dimensions of product and

159

portfolio complexity remains to be accomplished as does determining how to measure

these dimensions should they exist.

Gaps remain in the area of operationalizations. In addition to operationalizing
dimensions of complexity not studied in this research, there is a need to find improved
measures of complexity. For example, finding a measure better that can capture
similarity better than percentage diversified or multiplicity more cleanly than number of

products in the portfolio.

There is another gap that is more implicit; the nomological net. Missing in the literature
is the relationship between product portfolio complexity and other constructs relating to
product design and supply chain management; constructs such as flexibility, agility,
design effort, supplier collaboration, customer perception of value, market value of the
firm, firm growth, etc. Additionally, the existence and influence of moderating or

mediating relationships remains to be established and quantified.

Beyond the more general gaps mentioned above, there are some specific gaps that this
research has identified. One pertains to the phenomenon found in the analysis carried out
in the evaluation of hypotheses one and four. The phenomenon is the different
relationships between multiplicity and warranty or indirect cost. Additional exploration
is warranted to uncover reasons for this difference. Are there differences in the supply

chains, incentive plans, tools to manage complexity, some aspect of the business model?

160

Common wisdom is that costs in the high tech sector decline because increased volume
amortizes development costs over a larger number of products; once recovered the
development cost can be removed from the price of an item. However, this research
shows that there are reasons beyond the cost of materials. There is an opportunity to

identify these forces and quantify their impact.

A rationale was put forward in chapter six that when knowledge acquisition / application

is required that exceeds a threshold point, performance degrades. How to identify that

point has not been articulated in the literature of operations management.

7.63 Extensions

 

There are three extensions to this research that could be undertaken. One is to add
portfolios of similar types of products such as those fi‘om HP, Sun, and Dell. Beyond that
is the analysis of other products that are similar; highly engineered, durable, electronic.
Medical and laboratory instrumentation are two examples of similar products, but from
different markets. Looking more microscopically, another extension is to explore a more
detailed level of the data. Research could be undertaken to explore complexity at the
component or option level. Lastly, the principles elucidated in this research could be

tested in a services environment.

7.64 Additional research questions emerging from this study
0 What is the relationship between complexity management competencies and

supply chain design?

161

o What is the role of fit between product and supply chain design?

a Does supplier involvement moderate the impact of complexity on product cost?

0 What is the role of fit between tangible and intangible assets?

0 What factors moderate the relationship between tangible and intangible assets?

0 What causes the decline in cost, beyond that explained by volume and materials,
in high tech products?

0 What is the point of diminishing performance of the human capital?

0 What is the role of fit in regards to employee capability and product portfolio
complexity?

«1 What is the best way to operationalize similarity?

- What is the best way to operationalize multiplicity?

o What aspects of a business model are the most critical to enabling the effective

management of complexity?

7.7 Summation of dissertation

This study enhances the understanding of the relationship between product portfolio
complexity and various costs and sales volume by clearly defining the construct,
developing a typology, applying the theoretical framework of Theory of Performance
Frontiers, developing measures or complexity factors descriptive of the construct, and

testing several hypotheses informed by the definition and theoretical perspective.

From a thorough grounding in the literature, product portfolio complexity was defined as

the state of possessing a multiplicity of, and relatedness among, products within the

162

portfolio. Product portfolio complexity was empirically established as possessing two
dimensions, multiplicity and relatedness, by demonstrating their differential impacts on

various costs and demand.

Several measures of multiplicity and similarity, informed by the definition and theoretical
perspective, were created. The measures include: the number of products available in the
portfolio, the number of products added to the portfolio, number of products exiting the
portfolio, revenue per product, products per model, age differential, maximum age, the
variance of age among products, age entropy, percentage of the portfolio composed of
updates to prior products, the amount of churn for products. Hypotheses which relate
these measures to various costs and sales volume were tested by analyzing longitudinal
product portfolio and cost data provided by a designer and manufacturer of data

processing equipment using panel data regression.

Thus this research fills a portion of the gap in understanding that exists about the
relationship between product portfolio complexity and firm performance by providing a
theoretically grounded understanding of product portfolio complexity’s relationship to
cost and sales volume. Further, a typology of complexity is developed, two of its
dimensions operationalized, and the Theory of Performance Frontiers extended to
intangible assets. Beyond the contributions to the research community is the benefit
offered to the business community. Specifically, this research provides a quantitative
approach to identifying the most profitable configuration of a product portfolio. Thus the

research both advances theory and offers benefit to the practitioner community.

163

Appendix

164

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