Models for Forecasting Waste Flows

Transcription

Diffusion, Obsolescence and Disposal of End-of-Life
Consumer Durables: Models for Forecasting Waste Flows
DISSERTATION
of the University of St. Gallen,
School of Management,
Economics, Law, Social Sciences
and International Affairs
to obtain the title of
Doctor Oeconomiae
submitted by
Deepali Sinha
from
India
Approved on the application of
Prof. Dr. Markus Schwaninger
and
Prof. Dr. Lorenz Hilty
Dissertation no. 4113
Gutenberg AG, Schaan, 2013
The University of St.Gallen, School of Management, Economics, Law, Social
Sciences and International Affairs hereby consents to the printing of the present
dissertation, without hereby expressing any opinion on the views herein expressed.
St. Gallen, October 23, 2012
The President:
Prof. Dr. Thomas Bieger
This dissertation is dedicated to my mum
Subhra Sinha
For her immense belief, encouragement and support
in embarking on and completing my doctoral studies.
Acknowledgement
This thesis was made possible only because of the support, encouragement and good
wishes of many wonderful people who have been with me on this interesting journey.
Firstly, I am very grateful to Prof. Markus Schwaninger for accepting me as a doctoral
student and guiding me with his prompt and powerful insights. I also owe many
thanks to Prof. Lorenz Hilty, who, as my co-supervisor, contributed greatly with his
incisive comments which helped to not only bring focus to the thesis but to also make
me a better researcher.
I owe a special debt of gratitude to Rolf Widmer for hand-holding me through the
journey – for his constant support, advice and encouragement and especially for
taking time out from his busy schedule to chat, comment, correct and coach on the
thesis as it evolved – his support has been instrumental and without it the thesis would
not have been realised.
I have my brother, Tanmoy Sinha to thank for his software wizardry which made the
modelling much simpler.
Furthermore, I would like to the many, many friends and colleagues from around the
world for their unflagging support – for cheering me up when I was low, for calming
me when I was in a panic and for being considerate when I was obnoxious!
I highly appreciate the support provided by EMPA and the TSL team towards my
doctoral studies, without which this research would never have been accomplished.
Most of all, I’d like to thank my parents, who whole-heartedly supported my doctoral
adventure and were always there for me, encouraging me and providing me with
invaluable moral support. And last, but not the least, my husband Rupesh, who was
patient when I was preoccupied, encouraging when I was unconfident and relieved
when it was over!
Deepali Sinha
London, 2012
Table of Contents
Table of Contents............................................................................................................ 5
List of Figures ................................................................................................................. 9
List of Tables ................................................................................................................ 10
List of Abbreviations .................................................................................................... 11
CHAPTER I
The Diffusion, Obsolescence and Disposal of Consumer Durables .............................. 1
1.
Introduction ................................................................................................... 1
1.1.
1.2.
1.3.
2.
Diffusion of Consumer Durables ............................................................................. 1
Obsolescence of Consumer Durables....................................................................... 2
Disposal of Consumer Durables............................................................................... 4
Existing Research .......................................................................................... 5
2.1.
2.2.
2.3.
Research in Waste Management .............................................................................. 5
Research on Innovation and Diffusion of Consumer Durables................................ 6
Research on Obsolescence, Replacement and Disposal of Consumer Durables...... 7
3.
4.
Research Gap ................................................................................................ 8
Research Goal ............................................................................................... 9
5.
Thesis Architecture ..................................................................................... 10
5.1.
5.2.
5.3.
5.4.
6.
Chapter I................................................................................................................. 10
Chapter II ............................................................................................................... 10
Chapter III .............................................................................................................. 11
Chapter IV .............................................................................................................. 13
Discussion and Conclusions........................................................................ 13
6.1.
6.2.
6.3.
Key Findings .......................................................................................................... 13
6.1.1.
Applicability of Diffusion Modelling in Waste Management Research ............ 13
6.1.2.
Improving Forecasting Models for Disposal of Consumer Durables ................. 14
6.1.3.
Importance of Consumer Behaviour: ................................................................. 15
Practical Implications ............................................................................................. 16
Conclusion ............................................................................................................. 17
References .................................................................................................................... 19
CHAPTER II
From Introduction to Obsolescence: Estimating Societal Stocks and Flows of
Consumer Durables ...................................................................................................... 24
1.
Introduction ................................................................................................. 25
2.
Literature Review ........................................................................................ 27
2.1.
2.2.
2.3.
Delay Models or Market Supply Models ............................................................... 27
Material Flow Analysis (MFA) Models ................................................................. 27
Diffusion Models ................................................................................................... 28
3.
Goal and Purpose ........................................................................................ 29
4.
Conceptual Model & Mathematical Framework ........................................ 30
5.
Model Parameters and Variables ................................................................ 30
5.1.
5.2.
5.3.
5.4.
5.5.
6.
Stocks ..................................................................................................................... 30
Inflows ................................................................................................................... 32
Outflows ................................................................................................................. 32
Disposal Distribution Function .............................................................................. 34
Technology Substitution ........................................................................................ 35
Experimental Frame .................................................................................... 36
6.1.
6.2.
Application to the Case of TVs in Switzerland ...................................................... 36
TVs in Switzerland –Background .......................................................................... 37
7.
Data ............................................................................................................. 37
8.
Extensions to the Specific Model................................................................ 38
8.1.
8.2.
Estimating the Development of Household Population ......................................... 39
Estimating Devices per Household - Multi-unit Ownership Sub-model ............... 39
8.2.1.
9.
Number of Devices per Swiss Household .......................................................... 41
Results ......................................................................................................... 42
9.1.
9.2.
Swiss TVs – Installed Base .................................................................................... 42
Swiss TVs – Sales and Disposals ........................................................................... 42
10.
Model Validation ........................................................................................ 44
11.
Discussion and Conclusion ......................................................................... 45
References .................................................................................................................... 48
CHAPTER III
Reverse Diffusion: Estimating Disposal of Consumer Durables through Application of
Diffusion Modelling ..................................................................................................... 52
1.
Introduction ................................................................................................. 53
2.
Literature Review ........................................................................................ 54
2.1.
2.2.
2.3.
3.
4.
Forecasting Adoption of Consumer Durables ........................................................ 54
Consumer Disposition Behaviour .......................................................................... 56
Waste Forecasting Models ..................................................................................... 57
Goal and Purpose ........................................................................................ 58
Conceptual Model and Mathematical Framework ...................................... 58
4.1.
Bass Diffusion Model ............................................................................................ 58
4.2.
4.3.
4.4.
5.
Application: Case Study – Consumer Durables in Switzerland ................. 63
5.1.
5.2.
5.3.
5.4.
6.
Data ........................................................................................................................ 64
Case Study 1: CRT Monitors in Switzerland ......................................................... 65
Case Study 2: CRT TVs in Switzerland ................................................................. 67
Case Study 3: LCD Monitors in Switzerland ......................................................... 68
Model Validation ........................................................................................ 70
6.1.
6.2.
6.3.
7.
Reverse Diffusion .................................................................................................. 60
Model Parameters .................................................................................................. 62
Assumptions ........................................................................................................... 62
CRT Monitors ........................................................................................................ 70
CRT TVs ................................................................................................................ 71
LCD Monitors ........................................................................................................ 71
Discussion & Conclusion ............................................................................ 72
References .................................................................................................................... 75
CHAPTER IV
Forecasting Consumer Durable Disposals: A Review and Comparison of Modelling
Approaches ................................................................................................................... 80
1.
Introduction ................................................................................................. 81
2.
Modelling Approaches to Estimate Consumer Durable Disposals ............. 83
2.1.
Terminology ........................................................................................................... 84
2.1.1.
2.1.2.
Inflows ............................................................................................................... 84
Stocks ................................................................................................................. 84
2.1.3.
2.1.4.
Delay Distribution .............................................................................................. 85
Product Mass ...................................................................................................... 85
3.
Goal and Purpose ........................................................................................ 86
4.
Delay Model Approach ............................................................................... 86
4.1.
4.2.
4.3.
Delay Model A: Example Reference – Oguchi et al., 2008 ................................... 87
Delay Model B: Example Reference – Gregory et al., 2009 .................................. 88
Delay Model C: Example Reference – Chapter II ................................................. 89
5.
Reverse Diffusion Model Approach ........................................................... 90
6.
Structural Comparison ................................................................................ 91
7.
Experimental Frame .................................................................................... 93
8.
Results ......................................................................................................... 93
8.1.
8.2.
8.3.
8.4.
Output Comparison ................................................................................................ 94
Predictive Validity ................................................................................................. 95
Fit Improvement ..................................................................................................... 96
Sensitivity Analysis................................................................................................ 98
8.4.1.
Sensitivity of Delay Model Parameters .............................................................. 98
8.4.2.
Sensitivity of Reverse Diffusion Parameters ..................................................... 98
9.
Discussion and Conclusion ......................................................................... 99
References .................................................................................................................. 103
Annexes ...................................................................................................................... 107
Annexe 1: CRT Monitor Sales in Switzerland ............................................................... 107
Annexe 2: CRT and FPD TV Sales in Switzerland ........................................................ 108
Annexe 3: CRT Glass Collection by SWICO Recycling ............................................... 109
Annexe 4: LCD Monitor Collection by SWICO Recycling ........................................... 109
Annexe 5: TV Permits in Switzerland ............................................................................ 110
Annexe 6: Household TV Ownership in Switzerland .................................................... 110
Annexe 7: Swiss population of households .................................................................... 110
List of Figures
Figure 1: Annual sales of electronic consumer durables .......................................... 2
Figure 2: Technological evolution of the television … ............................................ 3
Figure 3: Annual Sales of Televisions in Switzerland .............................................. 4
Figure 4: Thesis architecture ................................................................................... 12
Figure 5: Generic stock-flow model ....................................................................... 31
Figure 6: Stock and flow diagram for the delay model .......................................... 33
Figure 7: Technology Substitution - CRT TV to non-CRT TV in Switzerland ..... 37
Figure 8: Multi-unit Devices per Household (DPH)............................................... 41
Figure 9: Societal Stock – TVs (CRT and Non-CRT TVs) in Switzerland ............ 42
Figure 10: Societal Flows - Sales and Disposals of CRT TVs in Switzerland ....... 43
Figure 11: Disposal and Collection of CRT TVs.................................................... 44
Figure 12: Stock and flow diagram for the reverse diffusion model ...................... 61
Figure 13: Cumulative Disposal R(t)- CRT Monitor Glass .................................... 66
Figure 14: Disposal curve r(t) – CRT Monitor Glass ............................................. 66
Figure 15: Cumulative Disposal R(t) - CRT TVs ................................................... 67
Figure 16: Disposal Curve r(t) - CRT TVs ............................................................. 68
Figure 17: Disposal Curve - LCD Monitors ........................................................... 69
Figure 18: Delay Model Structure .......................................................................... 91
Figure 19: Reverse Diffusion Model Structure ....................................................... 91
Figure 20: Model Comparison - CRT Glass Disposal Estimates vs Observed ...... 94
Figure 21: Disposal Forecasts ................................................................................. 96
Figure 22: Fit improvement by introducing product mass function ....................... 97
Figure 23: Sensitivity of delay model parameters .................................................. 98
Figure 24: Sensitivity of reverse diffusion model parameters ................................ 99
List of Tables
Table 1: Primary data gathered and sources ........................................................... 38
Table 2: Parameters of multi-unit adoption - devices per household ..................... 42
Table 3: Parameters of the disposal function for CRT TVs ................................... 43
Table 4: Data collected ........................................................................................... 64
Table 5: Parameter values for CRT Monitor reverse disposal................................ 65
Table 6: Parameter values for CRT TVs reverse disposal ...................................... 68
Table 7: Parameter values and fit statistics ............................................................. 70
Table 8: Model forecast vs actual disposal – CRT PC Monitors............................ 71
Table 9: Model forecast vs actual disposal – CRT Glass from CRT TVs .............. 71
Table 10: Model forecast vs actual disposal - LCD Monitors ................................ 71
Table 11: Summary table of model characteristics ................................................. 92
Table 12: Parameter values and fit statistics ........................................................... 95
Table 13: Comparison of Predictive Power ............................................................ 96
Table 14: Fit improvement statistics ....................................................................... 97
Table 15: CRT and FPD Monitor Sales in Switzerland. ....................................... 107
Table 16: CRT and FPD TV Sales. ....................................................................... 108
Table 17: CRT Glass Collection by SWICO. ....................................................... 109
Table 18: LCD Monitor Collection by SWICO.................................................... 109
Table 19: TV licences issued by Billag. ............................................................... 110
Table 20: Household Ownership of TVs. ............................................................. 110
Table 21: Number of households. ......................................................................... 110
List of Abbreviations
2D – Two Dimensional
3D – Three Dimensional
BDM – Bass Diffusion Model
BfS – Swiss Federal Statistical Office (BfS)
CRT – Cathode Ray Tube
DPH – Devices per Household
EMPA – Swiss Federal Laboratories for Material Science and Technology
EOLE – End-of-Life Equipment
FPD – Flat Panel Displays
ICT – Information and Communications Technology
ITU – International Telecommunications Union
LCD – Liquid Crystal Display
MAE – Mean Absolute Error
MFA – Material Flow Analysis
OLED – Organic Light Emitting Diode
PC – Personal Computer
SCEA – Swiss Consumer Electronics Association
SFA – Substance Flow Analysis
TSL – Technology and Society Lab
TV – Television
UK – United Kingdom
UNEP – United Nations Environment Programme
WEEE – Waste Electrical and Electronic Equipment
Summary
Consumer durables pervade modern society. Technological innovation has brought a
plethora of products to market that are ever more accessible and affordable. The past
decades have seen the diffusion of consumer durables on a phenomenal scale globally.
The corollary to this widespread diffusion of consumer durables is that there are ever
greater numbers of products reaching the waste stream. The growing magnitude of
this waste stream raises both theoretical and practical questions, including how many
products will be disposed of and when.
My dissertation tackles the question of estimation and forecasting of end-of-life
consumer durables. Across three papers, I develop, apply and compare models to
estimate and forecast such disposals.
In my first paper, I develop a societal stock and flow model based on the delay
modelling approach which incorporates elements from diffusion models commonly
used in marketing. I propose a sub-model that extends the diffusion model to estimate
multiple-unit adoptions of consumer durables. The stock and flow model also
incorporates technological substitution, allowing the estimation and forecasting of
disposals in the light of scant or patchy data.
In my second paper, I propose a reverse diffusion model which extends the application
of diffusion models to the waste forecasting domain. Arguing that the dynamics of
disposal are not dissimilar to that of adoption of consumer durables, the model is
empirically validated through three case studies.
Finally, in the third paper, I critique the modelling approaches discussed in papers one
and two, namely the delay model and the diffusion model. Applying the same data set
to three variants of the delay model and the reverse diffusion model, the outputs and
predictive validity of the models are compared, and sensitivity of their parameters
discussed.
Through the three papers, the research identifies the advantages and limitations of
both modelling approaches and suggests improvements to enable better forecasts and
provide insights into consumer disposal behaviour.
Zusammenfassung
Die moderne Gesellschaft ist von langlebigen Gebrauchsgütern durchdrungen.
Technologische Fortschritte haben eine umfangreiche Palette von Konsumgütern auf
den Markt gebracht, die den Menschen immer zugänglicher und erschwinglicher
werden. In den letzten Jahrzehnten haben sich Gebrauchsgüter auf phänomenale
Weise weltweit verbreitet. Die logische Folge dieser umfassenden, globalen
Ausbreitung ist, dass eine immer größere Anzahl von Altgeräten in den Abfallstrom
gelangt. Das wachsende Ausmaß dieses Stroms wirft sowohl theoretische als auch
praktische Fragen auf, etwa wie viele und zu welchem Zeitpunkt Altgeräte entsorgt
werden. Diese Doktorarbeit geht die
Frage der
Mengenabschätzung
und
Prognostizierung von Altgeräten an. In drei Abhandlungen werde ich verschiedene
Modelle erarbeiten, anwenden und vergleichen, um die Entsorgungen von Altgeräten
zu bewerten und zu prognostizieren.
Im ersten Papier entwickle ich ein gesellschaftliches Stock-Flow-Modell, das auf dem
Modellierungsansatz einer Zeitverzögerung basiert und auch Elemente von
Diffusionsmodellen, die häufig im Marketing verwendet werden, berücksichtigt. Ich
schlage ein Teilmodell vor, welches das übliche Diffusionsmodell erweitert, um den
Mehrfachbesitz von Gebrauchsgütern zu bewerten. Das Stock-Flow-Modell bezieht
auch technologischen Ersatz ein und ermöglicht somit die Bewertung und Voraussage
von Entsorgungen angesichts karger oder lückenhafter Daten.
Im zweiten Papier schlage ich ein Umkehr-Diffusionsmodell vor, das die
Anwendbarkeit von Diffusionsmodellen auf das Gebiet der Abfallprognose ausweitet.
Mit der Argumentation, dass die Dynamik der Entsorgung nicht viel anders als die der
Einführung von Gebrauchsgütern ist, wird dieses Modell anhand von drei
Fallbeispielen empirisch bestätigt.
Im dritten Papier werden schliesslich die Modellierungsansätze, die in den ersten
zwei Papieren behandelt wurden, nämlich das Zeitverzögerungs-Modell und das
Umkehr-Diffusionsmodell, miteinander verglichen. Indem derselbe reale InputDatensatz an drei Varianten des Zeitverzögerungs-Modells und des UmkehrDiffusionsmodells angewendet wird, werden die Outputs und die Validität der
Modelle verglichen und die Sensitivitäten bezüglich der Modelparameter besprochen.
In den drei Abhandlungen identifiziert diese Forschungsarbeit die Vorteile und die
Einschränkungen beider Modellierungsansätze und macht Verbesserungsvorschläge,
um bessere Prognosen zu ermöglichen und Einsichten in das Entsorgungsverhalten der
Konsumenten zu gewinnen.
CHAPTER I
The Diffusion, Obsolescence and Disposal of Consumer
Durables
1. Introduction
1.1.
Diffusion of Consumer Durables
Innovation in the consumer durables industry has brought new products with new and
improved functions and at increasingly affordable prices. The spread of an innovation
in a market is termed “diffusion”. Schumpeter (1942) distinguishes three stages in the
process of adoption of a new technological innovation: invention - the development of
a scientifically or technically new idea; innovation – the incorporation of the idea in a
product made available on the market; and finally diffusion – the process by which the
product is available widely. The diffusion of consumer durables in modern society has
been not only rapid, but also widespread. Consumer durables such as mobile phones,
music players, personal computers and televisions are, to name a few, some of the
most commonly available, widely adopted and aspirational products globally. Since
their introduction in the early 20th century, consumer durables have become pervasive
in homes and offices and many are no longer considered a luxury, but rather a
necessity. In the past decades, electronic products have multiplied and become more
accessible, affordable and numerable. From simple calculators to the latest
smartphones and tablet computers, the price of electronic products has kept falling,
while their features and functionality has kept rising. Recent figures from the
International Telecommunications Union (ITU) indicate that global penetration of
mobile phone subscriptions in 2011 reached 87% of the world population (ITU, 2012).
Additionally, consumer durables are no longer limited to single-unit ownership per
household. Households often have multiple mobile phones, music players, laptop
computers and televisions.
Not surprisingly, the number of electronic consumer durables sold annually has nearly
tripled in the past decade as shown in Figure 1 (Euromonitor, 2011). Moreover, the
miniaturization of electronics, instead of reducing the physical mass flow of hardware
Chapter I – Introduction to Thesis
1
by providing the same function with less, has in fact not helped to reduce the demand
for products or total mass flow of products. In some cases it has in fact led to lower
per functional unit costs, thereby greater demand, overcompensating for the reduction
in material inputs (Hilty, 2005; Hilty et al., 2006).
Figure 1: Annual sales of electronic consumer durables
1.2.
Obsolescence of Consumer Durables
Technological change, and the rapid pace at which it is taking place, is making not
only products, but entire technologies obsolete. The personal computer-printer
combine made typewriters extinct; the compact disc player replaced the cassette
player and was itself replaced by MP3 players.
Sood and Tellis (2005) define technological change in terms of the intrinsic
characteristics of the technology, suggesting three types of technological change,
namely through platform innovation (eg. from magnetic tape cassettes to compact
disks), component innovation (eg. from magnetic tape to floppy disks), and design
innovation (eg. from 5.25 inch floppy disks to 2.5 inch floppy disks). However, what
is common to all three types of technological change is the emergence of a ‘dominant
design’, when the new entrants displace incumbent technologies (Christensen, Suárez
& Utterback, 1998; Srinivasan et al., 2006). Thus, technological change is understood
as a shift from the existing dominant design to a new dominant design. A dominant
design is a synthesis of fragmented technological innovations which may have been
2
introduced independently in prior products for specific user requirements. Thus, a
dominant design embodies the requirements of many classes of users of a particular
product and has the effect of enforcing industry standardisation (Suárez & Utterback,
1995). The emergence of a dominant design is a key event in the evolution of an
industry (Utterback and Abernathy, 1975; Anderson and Tushman, 1990). Such a
dominant design represents a milestone or transition point in the life of an industry as
the standardisation allows production economies and effective competition can then
take place on the basis of cost and product performance.
An example of such a technological change is the shift in the display industry’s
dominant design – from the Cathode Ray Tube (CRT) based displays, to the Flat
Panel Displays (FPD). As Utterback & Suárez (1993) have identified, the CRT
emerged as the dominant design for televisions in 1956, after which there have been
incremental improvements in performance, functionalities and production techniques.
This dominance continued for a long time, until recently, when the CRT was
challenged by various flat panel display technologies. The graphic below shows the
evolution of the television, starting as a CRT, with incremental improvements for 45
years until new display technologies came to the market in the late 1990s.
Figure 2: Technological evolution of the television (Source: Ahonen, 2011)
3
Technological substitution from one dominant design to another follows a classic
sigmoidal curve (Fisher and Pry, 1971; Norton and Bass, 1987). The seminal paper by
Fisher and Pry (1971) proposed a simple substitution model of technological change
and has since been referenced extensively in diffusion literature to forecast the sales of
new innovations. Figure 3 below illustrates this technological substitution with the
transition of the Swiss television market from CRT TVs to FPD TVs (Source of data:
see Annexe 2). Following the introduction of FPD TVs in 1998, CRT TVs start to
decline, and are completely substituted within ten years.
Figure 3: Annual Sales of Televisions in Switzerland
1.3.
Disposal of Consumer Durables
Rapid technological obsolescence is leading to growing quantities of consumer
durables reaching the waste stream. Ongondo et al., (2011), referencing a study by
Greenpeace, suggest an indicative range between 20 – 50 million tonnes of electric
and electronic consumer durables disposed of annually worldwide. According to
Huisman et al. (2008), the 27 European Union Member States alone generated
between 8.3 and 9.1 million tonnes in 2005, with the figure expected to rise annually
between 2.5% - 2.7% to reach 12.3 million tonnes by 2020.
While the advantages of consumer durable products are evident, there is growing
recognition of their environmental and social impacts given their mass production and
intensive use of increasingly scarce resources (Brett, 2009; UNEP, 2009), improper
4
disposal, especially in developing countries and overall greenhouse gas emissions
during their lifecycle (Erdmann and Hilty, 2010; Van Nes and Cramer, 2006; UNEP,
2009). The intensive use of scare resources in their mass production has raised also
raised worries about future disruptions to supply of scarce raw materials (Wäger et al.,
2010). For example, by some estimates, the global material supply of some critical
metals in the manufacture of electronics such as Indium might be exhausted soon
(UNEP, 2009).
The increasing quantities of consumer durables in the waste stream and their
associated environmental and social effects have led to legislation in many countries
specifically for the disposal of such products. It has also led to the establishment of
both formal and informal systems for their collection and a recycling. All this has
made it ever more important to estimate and forecast the existing stocks and future
flows of consumer durables. Such appraisals are useful for early recognition of
environmental problems, for investment planning in production and waste
management infrastructures, as also for government policy formulation, such as
environmental policy, R&D funding emphasis, or strategic stockpile objectives
(Müller, 2006). Better understanding and forecasting of this waste stream is therefore
critical for producers, waste managers and policy makers alike.
2. Existing Research
This thesis straddles two domains, namely waste management and consumer
behaviour. Waste management research on consumer durables has a fairly recent
history, with the majority of literature less than ten years old. In comparison,
researchers in the field of marketing have been studying consumer behaviour related
to the purchase for durable goods for over five decades.
2.1.
Research in Waste Management
Most waste management research has tended to focus on municipal solid waste, in
particular packaging. Early waste management models paid attention to the problems
in subsystems, e.g. routing of vehicles and location of treatment and disposal facilities,
with a strong focus on reducing costs, etc. More recently, waste management models
have incorporated demographic, social and economic dynamics (Beigl et al., 2008).
5
However, these models are for frequent, high volume municipal solid waste
comprising largely of organic matter, plastics, papers and packaging.
The most common modelling approach for estimating and forecasting post-consumer
end-of-life product flows is the “delay model approach” (Van der Voet, 2002), also
sometimes referred to as the market supply approach (Widmer et al., 2005), based on
combining sales data with average lifetime of the consumer durable. In its simplest
form, time-series of sales of consumer durables is time-shifted by the fixed average
lifetime. More recently, several researchers have improved upon this traditional model
by combining product sales with a lifetime distribution such as Weibull (Oguchi et al.,
2008) or a derived lifetime (Gregory et al., 2009). Such a delay model approach is also
used in Material and Substance Flow Analysis (MFA and SFA) models to estimate
flows of materials or substances through society, for example, cement (Müller, 2006;
Kapur et al., 2008), lead (Elshkaki et al., 2005), copper (Lifset et al., 2002; Spatari et
al., 2005) and zinc (Gordon et al., 2004).
Citing Lohse et al. (1998), Widmer et al. (2005) have also mentioned the
“consumption and use” and “market saturation” approaches for estimating end-of-life
consumer durables. The consumption and use method takes the average number of
consumer durables of a typical household as the basis for a prediction of the potential
amount of end-of-life products, while the market saturation approach is based on the
assumption that private households are already saturated with consumer durables, and
for each new product purchased, an old one reaches its end-of-life. However, in
literature, no applications of or further research on these approaches were found.
2.2.
Research on Innovation and Diffusion of Consumer Durables
The diffusion, or adoption, of new products in the market has been of much
managerial interest, and there is a wealth of research especially on the adoption of
consumer durables, popularised in the marketing literature with the seminal article by
Bass (1969). Numerous researchers have since extended the diffusion model further
incorporating consumer behaviour insights.
Diffusion models traditionally have been used in the context of forecasting, though
they may also have other objectives, being used for descriptive or normative purposes,
as pointed out by Mahajan and Wind (1985) and Kalish and Lilien (1986). Diffusion
6
models have been particularly useful in providing frameworks for understanding the
processes by which new products come into circulation and spread across populations
of adopters. The literature indicates that the predominant application of such models
has been for purposes of forecasting new product adoption to predict the trajectory
and ultimate market potential of the product. Mahajan et al. (1990), Mahajan et
al.(1995) and Lilien, Rangaswamy and Van den Bulte (2000) describe some generic
uses of diffusion modelling in marketing which include pre-launch forecasting;
business valuation and strategic decision analysis based on the product life cycle; and
the determination of optimal prices, etc.
2.3.
Research on Obsolescence, Replacement and Disposal of
Consumer Durables
Obsolescence, replacement and disposal of consumer durables are connected but
separate concepts. Replacement and disposal are consumer decision points with a time
gap between them ranging from seconds to decades. As Khetriwal and First (2011)
suggest, forced replacements (eg. broken appliances) are very likely to lead to
immediate disposal. Would forced replacement be the only disposal trigger, disposal
and replacement could, within waste management, be used interchangeably. However,
as many products are replaced before they fail, and/or subsequently often stored or
reused elsewhere, the disposal decision can be long after the replacement decision.
Khetriwal and First (2011) also differentiate replacement from obsolescence,
suggesting that while unforced replacement is a possible outcome of obsolescence,
obsolescence is a more inclusive situational factor which leads to disposal, regardless
of whether a replacement occurred or not. Once the consumer starts perceiving a
product as obsolete, the product might be either directly disposed of without being
replaced (e.g. once the lifestyle or trends changes), can be first replaced and then
disposed of (immediately or after a period of storage), or disposed and only later
replaced.
Research on disposal, or disposition (a term more commonly used in the consumer
research domain), of durable goods started in the late 70s as an offshoot of consumer
behaviour research. In their seminal article, Jacoby et al. (1977) concluded that
although consumption consists of three stages, namely acquisition, actual
consumption and disposition, the research focus had been largely on acquisition
7
phase, and almost non-existent on the disposition stage. Looking deeper at disposition
behaviour, Jacoby et al. (1977) showed that factors influencing disposal behaviour are
psychological characteristics of a decision maker, factors intrinsic to the product, and
situational factors extrinsic to the product. Disposition behaviour thus is a function of
disposition intention, social factors and situational factors (Hanson, 1980). Antonides
(1991) also notes that the lifetime of a durable good is determined by a consumer’s
decision which is in turn determined by economic, psychological and producttechnical factors. A more recent study by Cooper (2004) focussed on disposal of
consumer durables in UK households found similar results, with respondents echoing
similar reasons for disposing of their durables. Cooper states that the three main
reasons people dispose of their products are changes in consumer needs,
dissatisfaction with product functionality and product failure.
3. Research Gap
In the relatively recent literature in waste management focussing on the end-of-life
disposal of consumer durables, forecasting models most commonly used have tended
to base their forecasts only on available sales or shipment time series data, and
generally using the “delay modelling approach”, forecast the timing and quantity of
disposals. In case sales data was available for only a partial time period since the
introduction of the product, these models have tended to estimate disposals based on
only the available sales time-series. This neglects products in the waste stream from
sales that took place in time periods before the sales data was available for.
Surprisingly, none of the models estimating and forecasting end-of-life flows of
consumer durables until now have validated their forecasts against real-system data,
making it difficult to judge the accuracy or predictive validity of these models.
In comparison, there exists a rich body of knowledge on the diffusion of consumer
durables that analyses the timing of durable goods purchases by consumers. The
literature indicates that the predominant application of “diffusion models” has been
for purposes of forecasting new product adoption to predict the trajectory and ultimate
market potential of the product. As diffusion models have largely been used in the
marketing domain, the few authors that have incorporated replacements of consumer
durables in the model are more from a perspective of estimating replacement sales,
rather than estimating disposals. Thus, insights from the diffusion of consumer
8
durables have as yet not been incorporated into models for forecasting the timing of
disposal of consumer durables.
Additionally, there is as yet no research which provides a critique and comparison of
models for forecasting disposals of consumer durables proposed by different authors.
Comparing the outputs of the models to each other and against real-system data
provides useful information not only in terms of the predictive validity of the model,
but also enables a better understanding of the similarities and differences between the
models, and their applicability in a given case.
4. Research Goal
The research gaps identified above serve as a platform for this thesis. The main goal
of the research is to apply concepts and insights from consumer durable diffusion
to improve our understanding of, and forecasting models for, the obsolescence
and disposal of end-of-life consumer durables.
The overall research questions the thesis answers is whether and how forecasting
models for disposal of consumer durables can be improved by incorporating
insights from the extensive research on the adoption of consumer durables.
This overall goal is achieved through the cumulative contribution of three specific
parts:
In the first part, diffusion modelling concepts are used to recreate inflows in the case
of missing or patchy data. A diffusion model is proposed for multiple-unit adoptions
of consumer durables. Applied together with the technology substitution model, the
societal stock-flow model enables estimation and forecasting of disposal of consumer
durables by the “delay model” approach.
In the second part, insights from literature on consumer durable adoption and
diffusion models to forecast sales of such products provides the conceptual basis for
the “reverse diffusion” model for forecasting disposal of consumer durables.
9
In the third part, the performance, strengths and limitations of the delay model and the
reverse diffusion modelling approaches are compared and improvements to both
models are discussed based on insights from literature on consumer durable diffusion.
5. Thesis Architecture
Models are central to this thesis as they are simplified representations of real systems,
and can be used to explain, anticipate or design a real system (Schwaninger and
Groesser, 2009). This thesis presents two models for anticipating waste flows from
consumer durables, validating their results against real system data and finally
suggesting improvements. The thesis is structured into four chapters as illustrated in
Figure 4.
5.1.
Chapter I
This first part, the “Introduction”, provides the context for the research and establishes
its overall research purpose. Outlining the theoretical underpinnings of the following
parts, the introduction provides the red-thread running through the three independent,
yet interlinked papers presented in the thesis. It offers an overview of the related
research on the diffusion of consumer durable products and forecasting models
developed for the same, as well as disposal of end-of-life consumer durables and their
estimation models.
5.2.
Chapter II
Titled “From Introduction to Obsolescence: Estimating Societal Stocks and Flows of
Consumer Durables”, is the first of three papers. This paper presents a stock and flow
model to estimate the post-consumer flow of end-of-life consumer durables through
society. The model developed in the paper, hereafter referred to as a “delay model”,
both recreates and anticipates the stocks and flows of consumer durable inflows and
outflows as well as the delay between the stock and the outflow while also
incorporating aspects of technology substitution and multiple-unit product ownership.
The model is empirically validated using the diffusion and disposal of cathode ray
tube televisions in Switzerland as a case study.
10
5.3.
Chapter III
Titled “Reverse Diffusion: Estimating Disposal of Consumer Durables through
Application of Diffusion Modelling”, is the second of three papers. This paper
proposes that the dynamics of disposal of consumer durables are not dissimilar to the
adoption of new products. It proposes a new approach to forecasting disposals,
building on extant literature on demand forecasting of new products based on
diffusion models. A model operationalizing this approach is developed and
empirically tested using the diffusion and disposal of three consumer durables in
Switzerland as case studies.
11
CHAPTER I
Introduction
Existing Research
Research in waste management
Research on innovation and diffusion of consumer durables
Research on obsolescence, replacement and disposal of consumer durables
Research Gap
Research Goal
Thesis Architecture
Discussion and Conclusions
CHAPTER II
Introduction
Literature Review
Delay Models or Market supply models
Material Flow Analysis (MFA) models
Diffusion models
Goal and Purpose
Conceptual Model & Mathematical Framework
CHAPTER III
Introduction
Literature Review
Forecasting Adoption of Consumer Durables
Consumer Disposition Behaviour
Waste Forecasting Models
Goal and Purpose
Conceptual Model and Mathematical Framework
Stocks
Inflows
Outflows
Disposal Distribution Function
Technology substitution
Experimental Frame
Application: Case Study CRT TVs in Switzerland
Bass Diffusion Model
Reverse Diffusion
Model Parameters
Assumptions
Estimating Devices per household - Multi-unit
ownership sub-model
Results
Model Validation
Discussion & Conclusion
Case Study 3: LCD Monitors in Switzerland
Application: Case Study – Consumer Durables in
Switzerland
Extensions to the Specific Model
Case Study 1: CRT Monitors in Switzerland
Estimating the Development of Household Population Case Study 2: CRT TVs in Switzerland
Model Validation
Discussion & Conclusion
CHAPTER IV:
Introduction
Modelling approaches to estimate consumer durable disposals
Terminology
Goal and Purpose
Delay Model Approach
Delay Model A: Example Reference – Oguchi et al., 2008
Delay Model B: Example Reference – Gregory et al., 2009
Delay Model C: Example Reference – Chapter II
Reverse Diffusion Model Approach
Structural Comparison
Experimental Framework
Results
Output comparison
Predictive Validity
Fit Improvement
Sensitivity Analysis
Discussion and Conclusion
Figure 4: Thesis architecture
12
5.4.
Chapter IV
Titled “Estimating Consumer Durable Disposals: A Review and Comparison of
Modelling Approaches”, is the last of the three papers. This paper reviews two
modelling approaches to forecasting disposal of consumer durables, namely the “delay
model” approach and the “reverse diffusion model” approach. Applying the same
dataset on the disposal of cathode ray tube monitors in Switzerland to both the
approaches, the estimates and forecasts of the models are compared against real
system data, sensitivity of the model parameters examined and the assumptions,
strengths, limitations and applicability of both modelling approaches discussed. The
comparison also provides an opportunity to discuss further improvements to both
modelling approaches, especially the importance of developing models which
incorporate consumer disposal behaviour.
6. Discussion and Conclusions
6.1.
Key Findings
Key findings and their theoretical and practical implications of the thesis are
summarised below.
6.1.1. Applicability of Diffusion Modelling in Waste Management Research
Diffusion models have been successfully applied in the forecasting of the adoption of
consumer durables. This research has extended the applicability of diffusion
modelling in three ways – by proposing a multiple-unit adoption model, by
incorporating technology substitution into the stock-flow model and by developing the
reverse diffusion model.
Multiple-unit adoption model: Although multiple-unit adoptions for many durable
products (eg. televisions, mobile phones, gaming consoles, laptop computers) are
becoming common, they have remained largely ignored in diffusion models. In
Chapter II of the thesis, a multiple-unit adoption model based on the diffusion
modelling tradition is presented. The model indicates that the multiple-unit adoptions
take place in a phased approach. The first phase is given by the traditional diffusion
model which models the first unit adoption. The additional-unit adoptions thereafter
take place in the second stage, once first-unit market potential has been achieved, and
13
can also be characterised by a sigmoidal curve. By combining both phases, it is
possible to estimate multiple-unit adoptions. Such a model is not only useful for waste
forecasting, but for sales forecasting as well.
Technology substitution: One of the main reasons for the disposal of consumer
durables is obsolescence as a result of technological developments. Incorporating
technological substitution into the stock-flow model, it is possible to improve the
estimation and forecasting of stocks and flows of consumer durables. The Fisher-Pry
technology substitution model which has been well documented in diffusion literature
and empirically validated to fit across a range of technologies provides a useful model
to combine with stock-flow model.
Reverse diffusion model: The diffusion modelling framework provides the theoretical
underpinnings of the reverse diffusion model described in Chapter III. The empirical
results of the reverse diffusion model indicate that diffusion modelling concepts can
be applied to the de-adoption, or disposal, of consumer durables. It lays a basis for
further extensions to the reverse diffusion model, just as the diffusion model has been
extended and improved over time. The advantages of the reverse diffusion model as
compared to other models of estimating disposal of consumer durables are two-fold.
Firstly, the model is parsimonious as it is able to provide disposal estimates even in
the event of relatively sparse data on disposal. Secondly, the model makes it possible
to estimate disposal flows in the absence of average lifetime and sales data as required
by delay models.
6.1.2. Improving Forecasting Models for Disposal of Consumer Durables
A limitation of forecasting models for disposals of durable goods has been that it has
not been possible to assess their predictive validity, largely due to a lack of data on
disposals. An output comparison against real system data therefore provides a glimpse
into the performance and predictive power of the models. The results presented in
Chapter IV of the thesis indicate that societal stock-flow model and the reverse
diffusion model perform better than two other models compared. Thus, it is suggested
that the application of diffusion models can be used to improve models of forecasting
disposals of consumer durables.
Improving delay models: For delay models, time series data on inflows of consumer
durables is essential as is the lifetime distribution. The sensitivity analysis illustrates
14
the importance of parameter estimates, in particular the influence of average lifetime.
In the absence of accurate lifetime distribution data, it may be better to estimate the
parameters by linear optimisation within the model, as proposed in Chapter II to get
more accurate forecasts. Such an approach can be particularly useful in cases where
fragmented or incomplete data are available.
Improving reverse diffusion models: The early forecasting efficacy of the reverse
diffusion model is highly dependent on the upper limit of potential adoption of the
durable. Sales forecasting models have successfully based estimates of potential
adoption on the diffusion of analogous products. With the formalisation of the takeback and recycling system for end-of-life consumer durables, more data on disposal is
expected to become available, and with it the possibility to have a library of reverse
diffusion parameter estimates across product categories.
6.1.3. Importance of Consumer Behaviour:
The thesis sheds light on the importance of consumer behaviour on the disposal of
durables. Additionally, based on the parameter values of the reverse diffusion model,
it may be inferred that significantly smaller value of the coefficient of technical
disposal, as compared to the value of the coefficient of discretionary disposal,
indicates that the large majority of disposal of consumer durable products is driven by
consumer behaviour.
Influence of new technology: In Chapter II, the model overestimates sales of CRT TVs
as compared to actual sales soon after the introduction of new technology products.
This indicates that it is likely that consumers held back new TV purchases
immediately following the introduction of the new technology. This latent demand for
new TVs is then reflected in the sharp rise in the disposals of old technology CRT
TVs soon after.
Cultural influences: The research demonstrates the importance of the lifetime
distribution in generating accurate forecasts. Using lifetime distribution estimates
from Japan to estimate disposals in Switzerland resulted in significantly different
disposal estimates. The values suggested a more rapid disposal rate in Japan than in
Switzerland, suggesting that the timing of disposal of consumer durables may be
attributed to cultural influences. It is likely that the lifetimes of consumer durables in
15
Japan and Switzerland are significantly different due to different consumer usage
patterns, or that there was a difference in the storage time, or likely a combination of
both factors.
6.2.
Practical Implications
Multiple forecasting models: The research presents and compares several forecasting
models for disposal of consumer durables, based on two modelling approaches. The
comparison of the two approaches provides valuable insights for forecasting disposals
of consumer durables. Both modelling approaches are equally valid, each with its
strengths and weaknesses, and can provide reasonably accurate forecasts given
sufficient data. The choice of model used would therefore largely be dependent on the
quantity and quality of the data available.
The societal stock-flow model offers insights into the societal stocks and flows, from
its introduction to its obsolescence, including peaks of sales, disposals and installed
base of a consumer durable, especially with only limited data availability. Such a
model can provide collection and take-back systems as well as recycling companies
with better forecasts to help plan their capacities. For policy makers, it provides a
gauge of the collection efficiency of a formal take-back and collection system, and a
basis to check against potentially environmentally harmful or materially significant
leakages.
The reverse diffusion model provides a simple and parsimonious model as it is able to
provide disposal estimates even in the event of relatively sparse data on disposal.
Additionally, the model makes it possible to estimate disposals in the absence of data
on average lifetime and sales time series. Such a model can be particularly useful for
established take-back and collection systems. Moreover, its parameters can be updated
every year by fitting to the latest available data, thereby enabling ever more accurate
forecasts for the years ahead.
Estimating historic flows: In addition to providing estimates of future waste flows, the
societal stock-flow model presented in the thesis makes it possible to estimate historic
disposals. Such data can indicate the existence of anthropogenic stores of disposed
16
consumer durables which could pose a risk due to hazardous substances, but are also
increasingly being considered as urban mines containing precious and rare materials.
6.3.
Conclusion
This cumulative thesis on the disposal, obsolescence and disposal of consumer
durables sheds new light on the disposal of consumer durables and builds
interdisciplinary bridges between the sales forecasting and waste forecasting domains.
The research is however not without limitations, which provide directions for future
research.
Models for forecasting consumer durable disposals currently provide only statistical
estimates, without any explicit representation of the underlying consumer disposal
behaviour and the socio-economic factors which may play a role in the timing of
disposal of consumer durables. Future research can look at incorporating such aspects
into both the delay as well as reverse diffusion modelling approaches. The reverse
diffusion model could potentially be extended by disaggregating discretionary
disposal into various aspects to get better understanding of drivers of disposal. Further
research can look to incorporating variables such as competitive effects of new
technology, advertising, product quality, price and income effects into the model.
Another limitation of the models discussed in this research is that they do not
explicitly account for storage time between consumers replacing their consumer
durables and disposing them. In the delay model approach, the assumption is made
that consumer durables are either in active stock or disposed of, not accounting for
time spent in private storage. Consumer durables may be stored in attics or basements
or garages for months or even years before finally being disposed of. The models
presented in the thesis are, as yet, unable to provide insight into such behaviour.
Incorporating such aspects in a model could help give estimates regarding
“hibernating” stocks, which could be particularly helpful in understanding potential
anthropogenic stocks available for recycling and recovery, especially in the light of
material scarcity. The delay model is well suited to disaggregation into stages such as
reuse and storage. Such a “nested-delay” model has been presented by Widmer et al.
(2005) for disposals of personal computers, albeit using a fixed (dirac) lifetime
distribution. Further research on consumer behaviour will not only be able to provide
17
better parameter estimates for the delay functions at every stage, but also inform
model design in terms of stages an end-of-life consumer durable.
Furthermore, neither of the models incorporates the time-varying nature of consumer
behaviour. Given the fairly long societal existence of consumer durables compared to
the rapidly changing consumer preferences and perceptions of obsolescence, it is
likely that the residence time of a consumer durable changes between its introduction
and decline. Anecdotal evidence for PCs and mobile phones has shown that average
lifetime of these products has reduced over time, with more frequent replacements and
disposals taking place. In the delay models, the disposal function is time-invariant,
while in the reverse diffusion model, the coefficients p (coefficient of technical
disposal) and q (coefficient of discretionary disposal) are constant over the time
horizon of the model application. In both cases changing consumer behaviour due to
newer products, lower prices of newer products, more convenient disposal
opportunities, etc. (which all may lead to disposals), are not explicitly considered.
Moreover, it would also provide an opportunity to examine whether the disposal of
consumer durables accelerates between technology generations.
Further research into consumer behaviour to get insights into why, when and how
consumers dispose their durable products, will provide useful information that could
lead not only to better, more accurate forecasting models, but also inform consumer
education and awareness programs directed towards improving consumer attitudes
towards disposal of durable products.
18
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23
CHAPTER II
From Introduction to Obsolescence: Estimating Societal
Stocks and Flows of Consumer Durables
Deepali Sinha, University of St.Gallen
Abstract
The long residence time of consumer durables in households makes it important to
estimate their entire anthropogenic stocks and flows, both from a waste management
as well as a material management perspective. This paper presents a stock and flow
model to estimate the post-consumer flow of end-of-life consumer durables through
society. The descriptive model developed in the paper both recreates and anticipates
the stocks and flows. The model incorporates the aspects of technology substitution as
well as multiple-unit product ownership. The model is empirically validated using the
diffusion and disposal of cathode ray tube televisions in Switzerland as a case study.
Chapter II – From Introduction to Obsolescence:
Estimating Societal Stocks and Flows of Consumer Durables
24
1. Introduction
Electrical and electronic consumer durables have become entrenched in modern
society since their first appearance in the early 19th century. The success of the
electronics industry over the last several decades in developing a mass consumer
market for personal electronic equipment has been phenomenal. Not only have
electrical and electronic products proliferated, they have also been the focus of intense
technological innovation that has been both incremental and disruptive. This
technological progress is making not only products, but entire technologies extinct.
The intense competition in the industry has meant an ever increasing pace of
technological change, making the time interval between successive generations of
products and technologies relatively small in comparison with the time interval
between replacing technologies using historical norms (Norton and Bass, 1987). The
personal computer-printer combine made typewriters extinct; the compact disc
replaced cassette players and was itself replaced by even more compact solid state
storage music players; cathode ray tube televisions are being replaced by liquid crystal
displays which in turn will be made obsolete by Organic Light Emitting Diode
(OLED) televisions in the near future, also taking a leap from two dimensional (2D) to
three dimensional (3D).
Additionally, the rise in the number of consumer durables is because many products
are no longer limited to single-unit ownership per household. Households often have
multiple mobile phones, music players, laptops and televisions. Multiple-unit
adoptions are a major component of sales for many consumer durable product
categories, and authors from the marketing domain such as Steffens (2003) have
identified the importance of including multiple-unit adoptions in sales forecasting
models.
Moreover, as Hilty (2005) suggests, the continued miniaturisation of consumer
durables, especially electronics, has resulted in the price per functional unit falling,
triggering greater demand which compensates, or sometime even overcompensating
for the miniaturisation effect in terms of mass flow. Based on data for Switzerland,
Hilty et al. (2006) show the considerable reduction in the average physical mass of a
mobile phone from over 350 g in 1990 to about 80 g in 2005, which corresponds to a
reduction by a factor of 4.4, was accompanied by an increase in the number of
25
subscribers, which in turn led to a rise of the total mass flow by a factor of 8.0 in that
period.
Thus, the increasing number of consumer durables, combined with increasing
affordability and multiple-unit ownership further compounded by shorter time periods
between technological generations has meant an increasing volume of end-of-life
consumer durables being disposed.
The long residence time of consumer durables in households makes it important to
estimate their entire anthropogenic stock and flows, both from a waste management as
well as a material management perspective. Estimation and quantification of this
growing volume of end-of-life equipment (EOLE) commonly known as e-waste, has
drawn the attention of several scholars. Various models of forecasting EOLE flows
have been presented, the most common being the delay modelling approach. A
drawback of these models is that their forecasts are highly dependent on the sales data
and average lifetime, and are unable to estimate or forecast the entire stock and flow
of the consumer durable over its societal lifetime, from its introduction to its
obsolescence.
The goal of this paper is to present an approach to estimate the stocks and flows of a
product through society, especially in light of incomplete and patchy data over the
entire time period. The model developed in the paper both recreates and anticipates
the stocks and flows (Schwaninger, 2010). The paper makes a contribution in two
ways: firstly, the model incorporates multiple-unit ownership of consumer durables in
a dynamic model to estimate inflows, outflows and stocks of a product. Secondly, the
model provides an estimate of stocks and outflows of a consumer durable, given
patchy data on sales, disposals and installed base.
Societal stocks and flows of consumer durables, especially those in the midst of a
technological shift, are of particular interest to producers, policy makers and waste
managers in understanding the quantity and timing of the outflow of these durables
into the waste stream. This model will therefore be useful as a tool for managerial
decision making.
The paper is organised as follows. In the next section, a review of relevant literature is
presented followed by the purpose and objectives of the research. Section 4 describes
26
the conceptual and analytical bases of the model, followed by a description of the
model parameters and variables in Section 5, the experimental frame in Section 6 and
the data in Section 7. Section 8 presents the sub-model for multiple-unit adoption. In
Section 9, the model formulation is empirically examined with data for televisions in
Switzerland following which model validity is discussed. Section 11 concludes the
paper with a summary of the contributions, limitations and suggests areas for future
research.
2. Literature Review
A number of studies have been conducted on the estimated product flow of consumer
durables, both sales to households and disposals from households. In this section, a
literature review of previous research on existing models of estimation and forecasting
of end-of-life products is presented. Three main modelling approaches which have
been applied to consumer durables are reviewed, namely market supply models,
material flow analysis models and diffusion models.
2.1.
Delay Models or Market Supply Models
Market supply models are perhaps the most common approach used for forecasting
post-consumer end-of-life product flows. Waste estimates (outflows) can be made by
modelling discards as a function of sales (inflows), distributed over time given by a
lifetime distribution function or a derived lifetime distribution.
The most basic market supply models combine sales data with a fixed average lifetime
or residence time to forecast waste flows of end-of-life consumer durables (Widmer et
al., 2005; Kang and Schoenung, 2006). More sophisticated market supply models
combine product sales with a lifetime distribution such as Weibull (Oguchi et al.,
2008), a derived lifetime distribution (Gregory et al., 2010; Yu et al., 2010) or a
likelihood of failure in the shape of a bath-tub curve (Linton et al., 2002). While this
method provides estimates of outflows, a pre-requisite for these models is data on
inflows, i.e. sales or shipments data.
2.2.
Material Flow Analysis (MFA) Models
Material and substance flow analysis models have been commonly used to estimate
societal stocks and flows of materials such as cement (Mueller, 2006; Kapur et al.,
27
2008), lead (Elshkaki et al., 2005), copper (Lifset et al., 2002; Spatari et al., 2005) and
zinc (Gordon et al., 2004). Most previous MFA models focussed only on flows,
however, recently researchers have realised that stocks may be equally or sometimes
even more important, especially in the prediction of future emissions and waste flows
of products with a long life span (Kleijn et al., 2000). Recent material flow analysis
models have been used to forecast waste material flows, especially for construction
and demolition waste (Bergsdal et al., 2007; Hu et al., 2010) as well as e-waste
(Streicher-Porte et al., 2005) who applied MFA to assess obsolete PC processing in
the informal sector in Delhi, India.
However, most material flow analysis models have system boundaries which include
material flows from production to disposal, including mining, fabrication and
manufacture before the consumption phase as they look at materials rather than
products, which are a composite of many materials.
2.3.
Diffusion Models
Forecasting the sales of consumer durables has been the focus of a significant body of
research, ever since the 1960’s. The seminal article by Bass (1969) elaborating the
application of a logistic-curve based model to forecast the diffusion of innovations
into a market was the starting point for a wave of models which since further extended
and improved upon the original Bass Diffusion Model (BDM). While BDMs have
been applied to all sorts of products, one of the most common applications is the
forecasting of consumer durables sales. A comprehensive review of the literature on
diffusion of new products can be found in Mahajan et al. (1990), Meade and Islam
(2006), and most recently Peres et al. (2010).
Three especially relevant extensions of the BDM in the context of obsolescence of
consumer durables are the inclusion of replacement sales (Kamakura and
Balasubramanian, 1987; Bayus, 1991; Mahajan and Mueller, 1996), technology
substitution (Fisher and Pry, 1971), and multi-generation product models (Norton and
Bass, 1987).
Walk (2009) is one of the very few authors to utilise diffusion modelling from the
marketing domain for the estimation and forecasting of end-of-life consumer durables.
He presents a three-step forecasting model for CRT appliances (television sets and
28
monitors) for a region in Germany which includes modelling product life time,
extrapolation of stocks and modelling technology change based on the Fisher-Pry
substitution model.
More recently, Yu et al. (2010) have also used a diffusion model together with
material flow analysis to forecast the global generation of obsolete Personal
Computers (PCs). They apply the diffusion model to estimate historic and future sales
of PCs, combining with an average lifetime distribution to provide scenarios of
generation of obsolete PCs.
This paper utilises approaches presented in papers by Walk (2009) and Yu et al.
(2010), as well as that of material flow analysis, combining and extending their
concepts to present a model of societal stocks and flows of consumer durables.
3. Goal and Purpose
From the above discussion of the existing models of forecasting flows, it is clear that
considerable work has been done in the estimation and forecasting of end-of-life
consumer durables. However, the drawbacks of the models discussed above is that
they can be used only given sufficient sales data, and are unable to estimate the flows
of consumer durables with multiple-unit ownership, or are limited to only a part of the
period since the introduction to the obsolescence of the product, rather than looking at
the entire societal flow.
Hence, the goal of this paper is to develop a model to estimate the stocks and flows of
a consumer durable product through society from its introduction to its obsolescence,
incorporating the substitution effect of changing technology, which includes the
possibility of multiple-unit ownership of the durable good. The purpose of the model
is to provide a forecast for the end-of-life waste flows of a consumer durable product,
providing estimates to waste managers, policy makers and recyclers on existing stock
and expected waste volumes.
The contribution of the paper is twofold: Firstly, it provides a model to estimate the
total societal stock and flow of a consumer durable product category over its lifetime
in the market, from its introduction to withdrawal. Secondly, in the course of
29
developing this stock-flow model, a sub-model for estimation of stock for durables of
which households may have multiple-unit ownership is also presented.
4. Conceptual Model & Mathematical Framework
Societal models to estimate the stocks and flows of consumer durables can be thought
to be similar to population models, with a stock or installed base equivalent to total
population and sales (inflows) = births and disposals (outflows) = deaths. They can
also be considered to be analogous to models of epidemics, with the rise and fall in the
number of infected persons equivalent to the sales and disposals of a product
(Sterman, 2000). Though population models have relatively long time horizons,
typically decades or centuries and epidemics relatively shorter time horizons typically
from a few weeks to a few years, with consumer durables somewhere in between, the
underlying dynamics of stocks and flows are similar. Not surprisingly, the logistic
model of diffusion of consumer durables has its roots in ecology in modelling
population growth (Yu et al., 2010).
In this paper, a stock-flow model is presented, combining concepts of MFA models,
waste flow estimation based on distributed residence time as well as diffusion models
of consumer durable adoption and substitution.
In MFA, time step changes in stock are determined by tracking flows into and out
from the stock. In the context of consumer durables, for this model, the installed base
of a product in households is the stock, with flows in being the equivalent of sales or
shipments and flows out being disposals of the product.
5. Model Parameters and Variables
5.1.
Stocks
A stock is the integral of inflows and outflows over time – stocks grow when the
inflows exceed the outflows of a system, and vice versa. Kleijn et al. (2000)
distinguish between two types of relations between stocks and flows: stocks as a size
buffer and stocks as a time buffer. A stock acts like a size buffer when the outflow is
proportional to the magnitude of the stock and independent of the time of inflow into
the system. In contrast, when outflow is dependent on the time of inflow, stocks act
30
as a time buffer. Consumer durable stocks are time buffers because the timing of
disposal of a product is linked to when it entered into use, as it is more likely for older
devices to be disposed of than newer devices.
The stock-flow diagram below graphically illustrates the relationship between inflows,
stocks and outflows.
Stock (t) =
In (t)
�[𝐼𝐼𝐼𝐼(𝑡𝑡) − 𝑂𝑂𝑂𝑂𝑂𝑂(𝑡𝑡)]𝑑𝑑𝑑𝑑
Out (t)
Figure 5: Graphical illustration of generic stock-flow model
The relationship between stocks and flows is represented by:
In differential form:
𝑑𝑑𝑆(𝑡𝑡 ) = 𝐼𝐼𝐼𝐼(𝑡𝑡 )𝑑𝑑𝑡𝑡 − 𝑂𝑂𝑂𝑂𝑡𝑡 (𝑡𝑡 )𝑑𝑑𝑡𝑡
In integral form:
𝑡
(1)
(2)
𝑆(𝑡𝑡 ) = ��𝐼𝐼𝐼𝐼(𝜏) − 𝑂𝑂𝑂𝑂𝑡𝑡 (𝜏)�𝑑𝑑𝜏
𝑡0
In difference form :
(3)
∆𝑆𝑡+1 = 𝑆𝑡+1 − 𝑆𝑡 = (𝐼𝐼𝐼𝐼𝑡 − 𝑂𝑂𝑂𝑂𝑡𝑡𝑡 )∆𝑡𝑡
As a recurrence relation (to numerically integrate the differential equation
(1)):
𝑆𝑡+1 = 𝑆𝑡 + (𝐼𝐼𝐼𝐼𝑡 − 𝑂𝑂𝑂𝑂𝑡𝑡𝑡 )∆𝑡𝑡
(4)
where 𝑆(𝑡𝑡 ), 𝑆𝑡 represent the stock, 𝐼𝐼𝐼𝐼(𝑡𝑡 ), 𝐼𝐼𝐼𝐼(𝜏), 𝐼𝐼𝐼𝐼𝑡 represent the inflow and
𝑂𝑂𝑂𝑂𝑡𝑡 (𝑡𝑡 ), 𝑂𝑂𝑂𝑂𝑡𝑡 (𝜏), 𝑂𝑂𝑂𝑂𝑡𝑡𝑡 represent the outflow.
31
The stock of a consumer durable in households at any time t can be considered as the
number of all households 𝐻𝐻𝑡 multiplied by the number of devices of the consumer
durable 𝐷𝑃𝐻𝑡 each household owns on average at the time t.
𝑆𝑡 = 𝐻𝐻𝑡 ∙ 𝐷𝑃𝐻𝑡
(5)
𝑆𝑡𝑜𝑡𝑎𝑙 = � 𝑆𝑘
(6)
In the event of technological change, several technologies compete to render the same
service, thus, the total installed base is a sum of all stocks of all technologies.
𝑘
where 𝑆𝑡𝑜𝑡𝑎𝑙 is the total stock of all devices of all technologies 𝑘 at any time.
Initially, when there is only one type of technology to render the same service, change
in the stock of technology type 1 is equal to the change in total stock, 𝑆𝑡𝑜𝑡𝑎𝑙 . However,
with the advent of new technology and saturated 𝑆𝑡𝑜𝑡𝑎𝑙 = 𝑐𝑜𝐼𝐼𝑠𝑡𝑡, as technology type 1
is substituted by type 2, stock of technology type 1, 𝑆1 , decreases as stock of
technology type 2, 𝑆2 , increases. Therefore, ∆𝑆1 is positive initially, becoming
negative following the introduction and diffusion of technology type 2. Technological
substitution is discussed separately further in the paper
5.2.
Inflows
Previous authors have used sales or shipment data from market research to get inflow
values. However, in the absence of existing sales data, especially historic sales data
going back to the introduction of the consumer durable, the inflow can be constructed
by using data on change in stock and disposals. From equation (3),
𝐼𝐼𝐼𝐼𝑡 = Δ𝑆𝑡+1 + 𝑂𝑂𝑂𝑂𝑡𝑡𝑡
5.3.
(7)
Outflows
Outflows, or disposals, of consumer durables are a function of inflow (sales) and of
the residence time (given as a survival or reliability function R(t)) of the product in a
32
household. As this model assumes that all products are disposed of at end of life the
lifetime distribution function
𝐹 (𝑡𝑡 ) = 1 − 𝑅 (𝑡𝑡 )
is also the disposal distribution D(t) and its derivative, the disposal density function
d(t), describes the rate of disposals.
In (t)
disposal
d(t)In(t)*d(t)
Out (t)
� 𝑑𝑑𝑑𝑑
Stock (t)
Figure 6: Stock and flow diagram for the delay model ('*' represents a convolution)
The outflows (disposals) at time t are then expressed as a convolution of the inflows
In and the disposal density d,
In discrete form the convolution writes:
∞
(𝑓 ∗ 𝑔)[𝑘 ] = � 𝑓 [𝑖] ⋅ 𝑔[𝑘 − 𝑖]
(8)
𝑖= −∞
Thus,
∞
𝑂𝑂𝑂𝑂𝑡𝑡𝑡 = � 𝑑𝑑𝑖 ⋅ 𝐼𝐼𝐼𝐼𝑡 − 𝑖
(9)
𝑖=−∞
where 𝑂𝑂𝑂𝑂𝑡𝑡𝑡 is the number of products disposed and 𝑑𝑑𝑡 (𝑖) the disposal function.
33
If both 𝐼𝐼𝐼𝐼𝑡 and 𝑂𝑂𝑂𝑂𝑡𝑡𝑡 are zero outside a time window 𝑇𝑚𝑖𝑛 < 𝑖, 𝑡𝑡 < 𝑇𝑚𝑎𝑥 then the
integration interval can be limited to [2𝑇𝑚𝑖𝑛 , 2𝑇𝑚𝑎𝑥 ].
Combining equations
(4) and (9) and taking care of the required integration interval e.g.
𝑇𝑚𝑖𝑛 = 0, 𝑇𝑚𝑎𝑥 = 𝑇𝑙𝑎𝑠𝑡_𝑠𝑎𝑙𝑒 + 𝑇𝑙𝑎𝑠𝑡_𝑓𝑎𝑖𝑙𝑢𝑟𝑒 :
𝑡
(10)
𝑆𝑡+1 = 𝑆𝑡 + �𝐼𝐼𝐼𝐼𝑡 − � 𝑑𝑑𝑖 ⋅ 𝐼𝐼𝐼𝐼𝑡 − 𝑖 � ∆𝑡𝑡
𝑖=0
5.4.
Disposal Distribution Function
The outflow in the delay model is solely determined by the inflow and the residence
time of the product in a household. The latter is defined as the probability that the time
of obsolescence is later than some specified time t.
𝐹 (𝑡𝑡 ) = 𝐷 (𝑡𝑡 ) = 1 − 𝑅(𝑡𝑡 )
(11)
and
𝑡
𝐷 (𝑡𝑡 ) = � 𝑑𝑑(𝜏)𝑑𝑑𝜏
(12)
0
in discretized form:
𝑡
𝐷𝑡 = � 𝑑𝑑𝑖
(13)
𝑖=0
where 𝑑𝑑𝑖 is the discrete disposal density of the consumer durable.
As consumer durables are often reused, resold and stored by consumers before finally
being disposed of (Widmer et al., 2005), it is important to specify the point at which
the product is considered as waste and included in outflow. As Yu et al., (2010) note,
different definitions of lifetime are possible which could be limited only to the length
of time a household uses a device or could be inclusive of time in storage after the
device has left the active stock. Spatari et. al., (2005) and Yu et. al., (2010) consider
34
lifetime as limited to only products in use, not including time spent “hibernating”, i.e.
products that have been retired but remain in households unused. In contrast, Kang &
Schoenung (2006) and Oguchi et al.,(2008) among other consider their stocks to
include all products in households, whether being used or stored. They explicitly state
that hibernating or out-of-use products stored in households are not considered as
waste, and hence form part of the consumption stock.
In this model, the definition of residence time used is similar to Spatari et. al., (2005)
and Yu et. al., (2010) whereby the disposal function does not consider stored or
hibernating products in stocks, but rather includes them in the outflows once they are
not part of the active stock.
The shape of the disposal density function is also important. While some models use a
Dirac distribution, or a fixed average lifetime, distributed lifetimes are more common
because some individual products will be discarded earlier than others. The rate of
disposal of a consumer durable device can be described by many probability densities
in an analogous way to product failure. This is a reasonable assumption given that
disposals are either due to technical failure or discretionary obsolescence, both of
which are correlated with the product’s age (Steffens, 2003). Following its acceptance
in failure analysis, the Weibull distribution is the most commonly used distribution to
model the lifetime distribution (Oguchi et al., 2008; Walk, 2009; Yu et al., 2010).
Therefore, in this model, a Weibull distribution is used for the disposal distribution
function; it's discrete density is given by the equation:
𝛾 𝑖 𝛾−1 −� 𝑖 �𝛾
� �
𝑑𝑑𝑖 =
𝑒 𝛼
𝛼 𝛼
(14)
where 𝛾 is the shape parameter and 𝛼 the scale parameter of the disposal function.
5.5.
Technology Substitution
Technological advances and the emergence of a new dominant design (Utterback and
Abernathy, 1975) signal the substitution of an old technology with a new one.
Research on technology substitution has shown that substitution follows a classic
35
logistic curve (Fisher and Pry, 1971). The Fisher-Pry substitution model of
technological change is incorporated in the model to estimate the inflow curve of the
new technology product, and its rate of substitution of the old technology product.
The Fisher-Pry substitution model is given by:
𝑠(𝑡𝑡) =
1
[1 + tanh 𝛼(𝑡𝑡 − 𝑡𝑡ℎ )]
2
(15)
where s(t) is the fraction of the sales substituted by the new technology, 𝑡𝑡ℎ is the time
at which the new technology has substituted 50% of the market share, and 𝛼 is
interpreted as a parameter indicating half the annual fractional growth rate in the early
years of the new technology product. As sales of the new technology devices
increases, their stock or installed base also increases, reducing the share of the stock of
old technology devices and change in stock of old technology devices becomes
negative as new technology devices gain 50% of market share.
6. Experimental Frame
The generic model presented above is applicable to all types of consumer durable
goods which can be characterised as high value purchases used over extended periods
of time. As there is a significant time and monetary commitment involved in
purchasing such a product (Steffens, 2003), the adopting and disposing unit is
assumed to be the household rather than an individual. However, theoretically, it is
possible to apply the model for individuals as well. An important assumption the
model makes is that the disposal function remains the same over the entire time period
of the technology.
6.1.
Application to the Case of TVs in Switzerland
The generic model described above is now applied to a specific case of TVs, in
particular the Cathode Ray Tube TV (CRT TV), in Switzerland. The data available on
this case provides the opportunity to empirically test and validate the model. Not only
is the television a widely adopted consumer durable, it is also one that has seen both
incremental and disruptive technological innovation over its societal lifetime from the
time it was introduced in the early 1950s. The dominant design in TV technology
since then had been the CRT TV, until the late nineties when the first Flat Panel
Display TVs (FPD TV) were introduced in the market. The rapid technological
36
substitution meant that in a span of 10 years, CRT TVs were made completely
obsolete in Switzerland. Thus, the specific case of CRT TVs in Switzerland from 1950
– 2010 provides a suitable case to estimate stocks and flows of a consumer durable
through society from introduction to obsolescence.
6.2.
TVs in Switzerland –Background
The TV market in Switzerland has seen a rapid change, as shown below, in Figure 7,
with the sharp drop in sales of CRT TVs matched by the steep rise in sales of nonCRT TVs, reflecting a classic substitution. In the space of 7 years since its
introduction in 1998, the sale of non-CRT TVs has overtaken sale of CRT TVs in
Switzerland, with CRT TVs completely phased out of the market from 2009.
Figure 7: Technology Substitution - CRT TV to non-CRT TV in Switzerland (Data
source: see Table 1)
7. Data
Data for the model was obtained from numerous sources, as it was fragmented and
incomplete. Confidence in figures presented here was developed using cross-checks,
parallel sources of information and expert discussions. Some data can be referenced to
literature, with others collected through primary research.
The data on number of households and household ownership of TVs in Switzerland
was obtained from the Swiss Federal Statistical Office (BfS). The Swiss Consumer
Electronics Association (SCEA) provided sales data for TVs in Switzerland from
1995 onwards. For the period before 1995 on early TV ownership, data from the TV
37
licencing authority in Switzerland, Billag, was gathered. The table below provides a
summary of the data gathered and their sources (See also annexes for data values).
Available
data (for
Switzerland)
Household
Population
Measurement Time period Comment
unit
Source
No. of
households
Swiss Federal
Statistical
Office (BfS)
Household
TV
Ownership
% of TV
households
TV Licenses
No. of
licenses
issued
TV Sales
No. of TVs
1950 – 2009 Data for every 10
(intermittent) years as per census;
linear interpolation
for continuous
series.
1990 – 2005 Relatively short
(intermittent) and intermittent
time series; Survey
in 2005 gathered
data on households
with multiple-unit
TV ownership.
1954 – 2008 Patchy data on
(intermittent) early TV
ownership, i.e. not
for all years. For
recent years, no. of
TV licenses issued
does not fully
reflect no. of
households with
TVs as not all
households pay
license fees due to
exemptions; also
does not capture
multiple TV
ownership.
1995 – 2009 Industry sales data
(continuous) with categorization
of type (i.e. CRT /
non-CRT) and size
of TV (in ranges).
Table 1: Primary data gathered and sources
Swiss Federal
Statistical
Office (BfS)
Billag AG (is
the
government
organisation
that collects
TV license fees
applicable to
all Swiss
households by
law, unless
exempt.
SCEA (the
Association of
Swiss
Consumer
Electronics
Manufacturers)
8. Extensions to the Specific Model
Two elements have to be added to adapt the model to the empirical case:
38
• Due to the long time horizon, change in household population is included in the
model.
• Because data from the Swiss Federal Statistical Office confirms multi-unit
ownership of TVs by many households, a sub-model to estimate the number of
devices per household is included.
8.1.
Estimating the Development of Household Population
Census data is used to estimate the development of the number of households in
Switzerland between 1950 and 2010. As the census data is only available for 10 year
intervals, the household population in the intervening years is estimated by linear
interpolation.
8.2.
Estimating Devices per Household - Multi-unit Ownership Submodel
Ownership or adoption of consumer durables by households is often also known as the
market penetration of the consumer durable. In markets with all households owning
the durable product, diffusion of the product is complete, and market is considered
saturated, with market penetration considered 100%. However, for many consumer
durable products such as televisions to mobile phones and even automobiles,
households may often own more than one device. Therefore, it is important to
establish the evolution of number of devices per household over time. Surprisingly
little attention has been given to multiple-unit ownership in diffusion modelling
literature. Of the few models developed for multiple-unit adoptions, the majority, with
the exception of Steffens (2003) who considered automobiles, have been for fast
moving consumer goods with short life cycles rather than durable consumer goods
with longer-term ownership patterns.
Multiple-unit adoption is a long-term process, and existing diffusion models do not
include the saturation effect for multiple-unit adoptions. To overcome this, a solution
is presented based on the Bass model which reconceptualises multiple-unit adoptions
as a two-step diffusion-based process. The logistic function displays an S-shaped
behaviour and has been found to empirically describe the diffusion of a range of
technologies ranging from mobile phone, home electric appliances to computers.
39
Following Walk (2009), it is assumed that the number of devices owned per
household follows an S-shaped logistic curve, given by the equation:
𝐷𝑃𝐻 (𝑡𝑡 ) = 𝑠 ×
exp (𝛼 × [𝑡𝑡 − 𝑡𝑡ℎ ])
1 + exp (𝛼 × [𝑡𝑡 − 𝑡𝑡ℎ ])
(16)
where DPH (t) is the number of devices per household at time t, s is market potential,
i.e. the number of devices per household at which market saturation occurs, 𝛼 is the
shape parameter and 𝑡𝑡ℎ is the time at which half the households own the device, or in
other words, 50% of market potential is reached.
For first-unit adoptions, the market saturation is assumed to be 100%, that is to say
that the first-unit diffusion of the device complete when all households own the
product. This is given by the following equation:
𝐷𝑃𝐻1 (𝑡𝑡 ) = 𝑠1 ×
exp (𝛼 × [ 𝑡𝑡 − 𝑡𝑡ℎ1 ])
1 + exp (𝛼 × [ 𝑡𝑡 − 𝑡𝑡ℎ1 ])
(17)
where 𝐷𝑃𝐻1 (𝑡𝑡) is the number of first-unit devices, 𝑠1 is the market potential of the
first-unit diffusion and 𝑡𝑡ℎ1 is the time at which 50% of the market potential of the first
phase has been achieved.
The second phase of additional-unit adoptions are given by a similar equation, with
the second phase starting once first-unit market potential has been achieved.
Therefore,
𝐷𝑃𝐻2 (𝑡𝑡 ) = 𝑠1 + �𝑠2 ×
exp (𝛽 × [ 𝑡𝑡 − 𝑡𝑡ℎ2 ])
�
1 + exp ( 𝛽 × [ 𝑡𝑡 − 𝑡𝑡ℎ2 ])
(18)
where 𝐷𝑃𝐻2 (𝑡𝑡 ) is the number of additional devices, 𝑠2 is the market potential for
additional unit adoptions and 𝑡𝑡ℎ2 is the time at which half of the additional-unit
adoption is attained.
The overall diffusion of multiple-unit ownership, 𝐷𝑃𝐻𝑀 (𝑡𝑡), is given by combining
both phases. Therefore,
40
𝐷𝑃𝐻𝑀 (𝑡𝑡) = 𝐷𝑃𝐻1 (𝑡𝑡 ) ∙ 𝐷𝑃𝐻2 (𝑡𝑡 )
(19)
8.2.1. Number of Devices per Swiss Household
Applying the multi-unit ownership model to historical penetration rates on TV
ownership available from Billag and BfS data results in the devices per household for
the period 1950 – 2010. The first-unit adoption curve is fitted to the data on TV
licences issued by Billag, with the market potential 𝑠1 set to 1. The total market
potential for the Swiss TV market is estimated to be 2.24 TVs per household, based on
one TV per person as per official statistics on the average number of persons per
household. Therefore, for the multi-unit adoption curve, the total market potential 𝑠2 is
set at the difference between the average no. of persons per household and 𝑠1 . The
parameters are fitted to the data by minimising the sum of squared residuals.
Figure 8: Multi-unit Devices per Household (DPH)
A good fit of the diffusion curve to the available data for both the first unit adoption
and the multi-unit adoption was found using the parameters given in Table 2. The data
show that the first TV adoption was quite rapid, and reached 50% market saturation in
just 18 years from introduction, reaching 100% market saturation by 1988. In
comparison, multi-unit adoption diffuses more slowly, with 50% of households
having multiple units only in 2021, nearly 40 years after the start of multiple unit
adoptions. This is reflected in the values of shape parameters
α, which has a value of 0.4, and β which has a value of any 0.12.
41
First-unit adoption
Multi-unit adoption
1
1.24
𝒔𝟏
𝒔𝟐
0.4
0.12
𝜶
𝜷
1968
2021
𝒕𝒉𝟏
𝒕𝒉𝟐
Table 2: Parameters of multi-unit adoption - devices per household
9. Results
9.1.
Swiss TVs – Installed Base
Combining data on number of households per year and the discretised total TV
devices per household per year results in the total installed base of TVs in Swiss
households from 1950 – 2010. Figure 9 below shows the development of Swiss
societal stocks of TVs through time. Following the introduction of FPD TVs, the fall
in the stocks of CRT TVs is estimated by subtracting non-CRT TV stock, estimated
using the Fisher-Pry model substitution (15), from total stocks. The stock of CRT TVs
reached a peak of nearly 4.2 million TVs in 2003, after which substitution by nonCRT TVs rapidly depletes the stock, with only a little over a third remaining in
households in 2010.
Figure 9: Societal Stock – TVs (CRT and Non-CRT TVs) in Switzerland
9.2.
Swiss TVs – Sales and Disposals
Equation (10) above is used to estimate sales and disposals of CRT TVs over its
societal existence. The parameters of the disposal function are iteratively determined
by fitting the model data to the sales data from SCEA for the period 1995 – 2009 by
42
minimising the sum of squared residuals. The scale parameter is interpreted as the
average lifetime of CRT TVs and the shape parameter the deviation from the mean.
As it is not possible to solve the convolution in equation (8) analytically, it is
discretised and integrated numerically, as given by (9).
Parameter
Description
Value
Shape parameter
2.79
𝜸
Scale parameter
10.27
𝜶
Table 3: Parameters of the disposal function for CRT TVs
Figure 4 below shows the societal flows – both sales and disposals – of CRT TVs
through Swiss society from 1950, the time of introduction of the product, to 2020 by
when it is almost fully disposed.
Figure 10: Societal Flows - Sales and Disposals of CRT TVs in Switzerland
The results show that nearly 15 million CRT TVs were sold between 1950 and 2008.
According to the model, CRT TV sales peaked in the year 2001 at 487,000 units, and
then rapidly declined to be completely substituted by non-CRT TVs in 2008.
In 2011, as per model estimates, over a million CRT TVs still remained in Swiss
households. However, rapid disposal would see the large majority of CRT TVs
disposed of from Swiss households by 2016, with only a fraction, just a little over
200,000 TVs, remaining to be disposed of. The model shows that the peak disposal of
CRT TVs took place in 2010, with nearly 600,000 CRT TVs estimated to have been
disposed in the year. The model results show that disposals of old technology devices
43
shoot up sharply following the take-off and mass adoption of new technology devices.
This is also reflected in the data of actual disposals, which also show a large increase
from 2009 to 2010.
10. Model Validation
Validity, or the model’s property of adequately reflecting the system modelled, is the
primary measure of model quality (Schwaninger and Groesser, 2009). From a model
validation perspective, Switzerland provides an exceptional source of data on the
disposal of CRT TVs through the organised collection and recycling operated by
SWICO Recycling, allowing validation of the model against real system data which is
entirely separate from the data used for parameter estimation (as described in the
“Data” section above). SWICO Recycling started collecting CRT TVs only in 2002,
and has over time built consumer awareness regarding the possibility of disposing
their CRT TVs through its take-back channels. As consumer awareness has grown, the
collection efficiency of the system has also increased, with few CRT TVs leaking out
of the system or disposed of in other waste streams. The take-back and recycling
system currently has a collection efficiency of 90%, as confirmed by SWICO
Recycling experts. Data specifically on number of CRT TVs disposed is available
from 2006 from SWICO Recycling annual reports. Although this dataset is only
recent, with only a short time series available, it provides a basis to assess the
predictive validity of the model, i.e. the extent to which the model actually predicts
the outcome that it is intended to model.
Figure 11: Disposal and Collection of CRT TVs
44
It is seen that both model estimates and the data on actual collection of CRT TVs
show the same underlying trend with the correlation coefficient between the two a
high 0.89. However, in the period 2006 - 2009, there is a significant difference
between the actual collection by SWICO Recycling and the model estimates. This
may be attributed to two reasons:
• The assumption of collection efficiency of 90% in the early years of the takeback and collection system. It is plausible that the collection efficiency of the
system has grown over time – it was likely not as high in the initial years as it
is currently. In such a case, the actual disposals including both those collected
and not collected by the system, would have been closer to the model estimated
disposals.
• The balance discrepancy may be explained by the stored unused or
“hibernating” CRT TVs in households which have not as yet reached the waste
stream.
11. Discussion and Conclusion
The model offers insights into the societal stocks and flows, from its introduction to
its obsolescence, including peaks of sales, disposals and installed base of a consumer
durable, especially with only limited data availability. Such a model can provide
collection and take-back systems as well as recycling companies with better forecasts
to help plan their capacities. For policy makers, it provides a gauge of the collection
efficiency of a formal take-back and collection system, and a basis to check against
potentially environmentally harmful or materially significant leakages.
In addition to providing estimates of future waste flows, it also provides an insight
into historic disposals which have taken place before the advent of formal and
organised collection and take-back systems. Such data can indicate the existence of
anthropogenic stores of disposed consumer durables which could pose a risk due to
hazardous substances, but are also increasingly being considered as urban mines
containing precious and rare materials.
The overestimation of modelled sales as compared to actual sales soon after the
introduction of new technology products indicates that it is likely that consumers held
back new TV purchases immediately following the introduction of the new
45
technology. This latent demand for new TVs is possibly also contributing to the sharp
rise in the disposals of old technology CRT TVs soon after. This insight could also be
useful to predict similar phenomena occurring with other high-value consumer
durables which are subject to radical technology changes.
The multi-unit adoption sub-model developed to estimate the devices per household is
an addition to the extensive literature on diffusion of consumer durable products, and
provides a useful model especially as multi-unit ownership of consumer durables is
increasing.
The current model is not without limitations which can, however provide directions
for future research.
Firstly, the model provides only statistical estimates of stocks and flows; it
incorporates no explicit representation of the underlying consumer disposal behaviour
and the socio-economic factors which may play a role in the timing of disposal of
consumer durables.
Secondly, the assumption that consumer durables are either in active stock or disposed
does not account for time spent in private storage. Consumer durables may be stored
in attics or basements or garages for months or even years before finally being
disposed of. The model presented above is so far unable to provide insight into such
behaviour.
Thirdly, the time-invariant disposal function has much scope for improvement. Given
the fairly long societal existence of consumer durables compared to the rapidly
changing consumer preferences and perceptions of obsolescence, it is likely that the
residence time of a consumer durable changes between its introduction and decline.
Anecdotal evidence for PCs and mobile phones has shown that average lifetime of
these products has reduced over time, with more frequent replacement taking place.
Fourthly, the model assumes there are only two competing technologies which render
the same service – the existing dominant technology and the challenger. However, it is
possible to have more than one technology challenging the dominant technology.
Currently, the model is unable to incorporate such multiple technology substitution.
46
As the model is applied only to a single case study of a consumer durable product in a
specific geography, further empirical work is required to substantiate the
generalizability of the model.
47
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51
CHAPTER III
Reverse Diffusion: Estimating Disposal of Consumer
Durables through Application of Diffusion Modelling
Abstract
The diffusion of consumer durables has been extensively modelled, in particular by
the Bass Diffusion Model which has been empirically validated across a range of
products. This paper proposes that the dynamics of disposal of consumer durables are
not dissimilar to the adoption of new products. Building on the extant literature on
demand forecasting of new products in the diffusion modelling tradition, a model for
forecasting the disposal, or “reverse diffusion”, of consumer durables is developed
and validated using three case studies. The results show that the model provides a
simple, yet effective method of estimation and forecasting of waste flows from endof-life consumer durables.
Chapter III – Reverse Diffusion:
Estimating Disposal of Consumer Durables through Application of Diffusion Modelling
52
1. Introduction
Consumer durables pervade modern lifestyles and their usage is growing rapidly
around the world. Innovation and intense competition in the consumer durables
industry has brought new products with new and improved functions and at
increasingly affordable prices. In the past decades, electrical and electronic consumer
durables have multiplied and become more accessible and numerable, becoming
standard items for the vast majority of households.
On the flip side, newer products and improved functionalities are resulting in greater
obsolescence of consumer durables, with large quantities of these products being
replaced and disposed. Given the rapid growth and affordability of consumer durables,
the large majority of consumer durables are scrapped before they are technically
broken (Bayus, 1988). Increasingly, the obsolescence of consumer durable products is
often discretionary in nature rather than technical.
The pervasiveness of gadgets in modern lifestyles and their rapid obsolescence makes
end-of-life consumer durables ranging from televisions to computers to washing
machines, commonly known as Waste Electrical and Electronic Equipment (WEEE),
one of the fastest growing waste streams not only in developed countries but around
the world. This waste stream has been recognised for its hazard potential and the need
to ensure it is disposed of properly. Growing concern regarding the importance of
managing this waste has led many countries to implement legislation designed to
reduce the volume of this waste, remove its hazardous components, encourage
recycling and minimize the environmental and health risks of unsound waste disposal.
The WEEE Directive of the European Union, which came into force in August 2004,
is the most prominent legislation focussing on the end-of-life management of disposed
consumer durables. The Directive, which places the responsibility of the end-of-life
management of WEEE on producers of consumer durable products, has led to the
development of recycling and take-back systems in European Union Member States
since it came into force. Similar legislation in many other countries is also in place or
upcoming, and with it more formalised systems to take-back end-of-life consumer
durables.
Forecasts of waste flows are as essential to waste planners as estimated potential sales
and the timing of sales are to marketers. While sales forecasting models of consumer
53
durables are dominated by diffusion models, waste forecasting models are more
commonly based on delay modelling, with the emphasis on Material Flow Analysis
(MFA).
Consumer behaviour, for both purchase and disposal of durables, is a result of
interacting social and market driven factors. However, there is little interdisciplinary
research between the two, despite the fact that both domains share a significant
overlap regarding consumer behaviour. This research builds on the extant literature on
demand forecasting of new products based on well documented diffusion models
which form the conceptual basis of this research. It proposes that the dynamics of
disposal of consumer durables are not dissimilar to the diffusion of new products. A
“reverse diffusion” model to forecast the disposal of consumer durables is developed
and validated using three case studies, thereby extending the application of diffusion
models from the classical questions of forecasting the timing and rate of adoption of
consumer durables to the forecasting of timing and rate of disposal of these products.
The paper is organised as follows: In the next section, a review of relevant literature is
presented, followed by the purpose and objectives of the research. Section 4 describes
the conceptual and analytical bases of the model. In the following sections, the model
is empirically examined, applied to three case studies of disposal of consumer durable
products in Switzerland, and validated against real system data. The final section
concludes the paper with a summary of the contribution, limitations and suggests
areas for future research.
2. Literature Review
For this paper, two streams of literature are reviewed – firstly research from the
marketing domain on consumer behaviour, including models for forecasting adoption
of durable products and secondly research from the waste management domain
regarding models of forecasting waste flows of consumer durables.
2.1.
Forecasting Adoption of Consumer Durables
The adoption of consumer durables is extensively researched in diffusion models,
popularised in the marketing literature with the seminal article by Bass (1969). The
Bass Diffusion Model (BDM) is the most widely known model of diffusion of
54
consumer durables, with the diffusion framework developed by Bass providing the
basis for the large body of diffusion research that has followed. Diffusion research
seeks to understand the spread of innovations by modelling their entire life cycle from
the perspective of communication and consumer interactions. Diffusion models have
been particularly useful in providing frameworks for understanding the processes by
which new products come into circulation and spread across populations of adopters.
In his paper, Bass presented a growth model for the timing of initial purchases of new
products, suggesting that new technologies are not adopted immediately by all the
potential buyers, but rather a diffusion process is set in motion in which there are
largely two groups of adopters – the innovators and the imitators. The innovators are
uninfluenced by the other members of the social system in their adoption behaviour.
The imitators, on the other hand, are those who are influenced in the timing of the
adoption by the decisions of other members of the social system. This model assumes
that the trajectory of cumulative adoptions of a new product follows a function whose
growth rate depends on two parameters. One parameter captures a consumer’s
intrinsic tendency to purchase and is independent of the number of previous adopters,
and is called the coefficient of innovation. The other parameter captures the influence
of previous adopters, being called the coefficient of imitation. It is analogous to the
spread of an epidemic, which is spread quickly by contact between the infected and
non-infected, and once the large majority of the population has been affected, the
infection growth slows down.
Essentially, the BDM attempts to predict how many customers will eventually adopt
the new product, but most importantly, when they will adopt it. The great appeal of
the BDM is that it is parsimonious, has been shown to fit data, and provides
parameters that have an intuitive behavioural interpretation. Many variations and
extensions to the BDM have since been proposed, extending the original model to
include marketing mix variables such as effect of price (Jain and Rao, 1990;
Kamakura and Balasubramanian, 1988), placement (Jones and Ritz, 1991), and
advertising (Horsky and Simon, 1983; Simon and Sebastian, 1987). Others have
proposed models to include multi-generation products (Norton and Bass, 1987),
replacement sales (Bayus, 1991), the influence of technology substitution (Fisher and
Pry, 1971) and multiple product ownership (Steffens, 2003).
55
Diffusion models are employed in two basic ways: to develop a better general
understanding of diffusion phenomena (descriptive), and to predict diffusion paths for
new technologies (predictive) before there is significant amount of data available
(Peres et al., 2010). Mahajan et al. (1990), Mahajan et al.(1995) and Lilien,
Rangaswamy and Van den Bulte (2000) describe some generic uses of diffusion
modelling in marketing which include pre-launch forecasting, business valuation and
strategic decision analysis based on the product life cycle, and the determination of
optimal prices, etc.
A comprehensive review of the literature on diffusion of new products can be found in
Mahajan et al. (1990), Meade and Islam (2006), and most recently Peres et al. (2010).
2.2.
Consumer Disposition Behaviour
Research on disposal of durable goods started in the late 70s as an offshoot of
consumer behaviour research, following a broader research thrust on consumer
behaviour. Jacoby et al. (1977) identified three stages of consumption of consumer
durables – namely acquisition, consumption and disposition or disposal. Hanson
(1980) further suggests that the evaluation process for disposition involves concepts
similar to those in the acquisition evaluation process. More recent studies of consumer
acquisition behaviour have looked at replacement of consumer durables, given that the
large majority of sales of many durables, especially in industrialised economies, are
replacement purchases. However, the focus of this research is more inclined towards
consumer behaviour regarding purchase of new products to replace existing ones,
rather than the disposition of existing products. Though both replacement and
disposition are closely related, there is a distinction between replacement and
disposition, especially with regards to the timing, and there are only a few studies
dealing specifically with the topic of consumer disposition behaviour.
Antonides (1991) notes that the lifetime of a durable good is determined by a
consumer’s decision which is in turn determined by economic, psychological and
product-technical factors. According to Hanson (1980), the decision to dispose of
consumer durables is aroused by some triggering cues such as product damage or
obsolescence which could be in terms of product function, psychological or style
obsolescence. Disposition or disposal behaviour thus is a function of disposal
intention, social factors and situational factors (Hanson, 1980).
56
Consumer motivation for replacement of consumer durables is in many ways similar
to disposal. Consumers replace durable products for a variety of reasons including
product failure, likely due to wear and tear or defects due to improper use or breakage
(Cooper, 2004; Islam and Meade, 2000), change in consumer needs perhaps due to
socio-economic reasons such as higher income (Pickering, 1981; Cooper, 2004; Bayus
and Gupta, 1992), dissatisfaction with product functionality or style preferences,
largely arising as a result of the availability of new technology (Cooper, 2004; Islam
and Meade, 2000; DeBell and Dardis, 1979; Hoffer and Reilly 1984; Sherman and
Hoffer 1971). Some authors (Bayus, 1991; Kamakura and Balasubramanian, 1987)
include replacement sales in their forecasting models, however, there are surprisingly
few sales forecasting models explicitly incorporating replacement sales.
2.3.
Waste Forecasting Models
Models to estimate and forecast consumer durable disposals are part of a growing
literature on waste forecasting. The most commonly used model for forecasting postconsumer end-of-life product flows is based on combining sales data with a fixed
average lifetime or residence time to forecast waste flows of end-of-life consumer
durables (Widmer et al., 2005; Kang and Schoenung, 2006). More recently, several
researchers have improved upon this traditional model by combining product sales
with a lifetime distribution such as Weibull (Oguchi et al., 2008) or a derived lifetime
(Gregory et al., 2009, Yu et al., 2010).
Material and substance flow analysis (MFA and SFA) have also been commonly used
to estimate societal stocks and flows of materials often used in durable products such
as lead in TVs (Elshkaki et al., 2005) and copper in electrical and electronic
equipment (Lifset et al., 2002; Spatari et al., 2005). Hilty et al. (2006a) have used a
macro-level System Dynamics model of ICT (Information and Communications
Technology) use to predict e-waste flows and other ICT impacts. Dynamic material
flow analysis models have been used to forecast waste material flows, especially for
construction and demolition waste (Bergsdal et al., 2007; Hu et al., 2010) as well as
electronic waste (Streicher-Porte, 2005).
Common to existing models of waste forecasting is that they are based on sales and
average lifetime data, rather than disposal data. The proposed model applies concepts
57
from diffusion models of consumer durable acquisition to estimate and forecast
disposition, based instead on disposal data.
3. Goal and Purpose
From the above discussion of the existing models of forecasting adoption and disposal
of consumer durables, it is clear that there are distinctions between sales forecasting
models, which focus on consumer behaviour, and waste forecasting models, which are
focussed on material flows. The model put forth in this paper derives from prior work
in the areas of diffusion modelling, building upon knowledge gained in those studies
to inform and improve waste forecasting models.
Hence, the goal of this paper is to develop a model to estimate the disposals of a
consumer durable product, applying the diffusion modelling framework. The purpose
of the model is to forecast disposals of a consumer durable product, providing
estimates to waste managers, policy makers and recyclers on expected waste volumes.
The contribution of the paper is twofold: Firstly, it makes a unique contribution by
extending the applicability of the diffusion modelling framework, bringing the
insights from the sales forecasting domain to the waste forecasting domain in a
relatively simple and parsimonious form. Secondly, it provides an alternative model
for estimation of the disposal of consumer durables without requiring estimates of
average product lifetime and time series sales data.
4. Conceptual Model and Mathematical Framework
4.1.
Bass Diffusion Model
Diffusion models have been particularly useful in providing frameworks for
understanding the processes by which new products come into circulation and spread
across populations of adopters. The literature indicates that the predominant
application of diffusion models has been for purposes of forecasting the trajectory of
new product adoption – for newly introduced products as well as for products to be
introduced that are similar in some way to existing products whose diffusion history is
known (Lilien, Rangaswamy and Van der Bulte, 1999).
58
The Bass Diffusion Model (BDM) has a behavioural rationale that is consistent with
studies in social science literature on the adoption and diffusion of innovations
(Norton and Bass, 1987). Over a large number of new products and technological
innovations, the BDM describes the empirical adoption curve quite well. Therefore,
because of its simplicity and generality, the BDM forms the conceptual basis for this
research.
In the BDM, the cumulative adoption of a consumer durable follows sigmoid function,
as sales of a product are driven initially by innovative demand followed by imitative
demand until the market potential, or saturation is reached.
This behaviour can be described by the nonlinear Bass differential equation (a Riccati
equation):
𝑆̇ = 𝑝 + (𝑞 − 𝑝)𝑆−𝑞𝑆 2
(20)
Where 𝑆̇ is the change in stock, p is the coefficient of innovation and q is the
coefficient of imitation.
which can be rewritten as:
𝑆̇ = 𝑝 ∙ (1 − 𝑆) + 𝑞𝑆 ∙ (1 − 𝑆)
(21)
which for:
q=0 becomes 𝑆̇ = Innovators = p ∙ (1 − S) which results in an exponential decay
function
for p=0 becomes 𝑆̇ = 𝐼𝐼𝑚𝑖𝑡𝑡𝑎𝑡𝑡𝑜𝑟𝑠 = 𝑞𝑆 ∙ (1 − 𝑆) which results in a logistic function
The dynamics of the stock 𝑆 is thus solely dependent on the stock and is a
superposition of an exponential decay and a logistic function. The equation is solved
by the following cumulative distribution function S(t) and the respective probability
density function s(t):
𝑆(𝑡𝑡 ) =
1 − 𝑒 −(𝑝+𝑞)𝑡
𝑞
1 + 𝑒 −(𝑝+𝑞)𝑡
𝑝
(22)
59
𝑠(𝑡𝑡 ) =
(𝑝 + 𝑞)2
𝑝
𝑒 −(𝑝+𝑞)𝑡
2
𝑞
�1 + 𝑒 −(𝑝+𝑞)𝑡 �
𝑝
(23)
where parameters p and q are interpreted as the ‘coefficient of innovation’ and the
‘coefficient of imitation’ respectively. The coefficient p captures the influence on
potential adopters’ decisions that is independent of the existing number of adopters,
i.e., the influence that is not obtained through interpersonal (word-of-mouth)
communication with existing adopters. The coefficient q expresses the influence of
existing number of adopters on purchase decisions of other people yet to adopt the
new product.
Sales are given by the equation:
𝑠𝑎𝑙𝑒𝑠(𝑡𝑡 ) = 𝑚 ∙ 𝑓(𝑡𝑡)
(24)
where 𝑚 is the total market potential. Total market potential in the BDM is specified
as total number of adoptions of a product, thus equation (24) gives the adoption rate,
or in other words, sales of a product.
4.2.
Reverse Diffusion
With the BDM as the conceptual basis, the model is applied to forecast the disposal,
rather than adoption, of a consumer durable – a ‘reverse diffusion’. We use the term
‘reverse diffusion’ to refer to the opposite of diffusion: while diffusion is about how
products enter the market, reverse diffusion is about how they exit the market. Thus,
reverse diffusion is defined as the process of de-adoption and outflow of a product
from society which may be driven by technical and social influences. The outflow
feeds a disposal stock which determines, together with the parameters p and q the
dynamics of the outflow. The total stock in the market which is to be depleted to the
disposal stock scales the outflow.
60
p
In (t)
Market (t)
q
Out (t)
Disposal (t)
Figure 12: Stock and flow diagram for the reverse diffusion model
In many ways, reverse diffusion is similar to innovation diffusion, in that it follows an
S-curve, the shape and the trajectory of which are influenced by consumer behaviour,
until market depletion is reached, with the decay in the number of potential
consumers.
For the reverse diffusion process, two types of ‘disposers’ are suggested - namely
those who dispose of products for technical reasons, and those who choose to dispose
of products for discretionary reasons. Technical disposals take place due to product
not functioning, or reaching their end-of-technical life. Such disposals are analogous
to the innovator adoptions in the BDM. On the other hand, consumer durables
disposed of for discretionary reasons are much like the imitator adoptions in the BDM.
These are influenced due to socio-economic factors, such as perception of
obsolescence of existing products, network or complementarity effects, aesthetics,
social status etc., much like word-of-mouth effects in product diffusion. Thus, the
discretionary disposers, like the imitative adopters create a reinforcing loop – as more
households dispose of a product, the more obsolete it is perceived, and the more
households want to dispose of it. In the reverse diffusion model, we consider the total
quantity sold over the product lifetime as the market potential. In other words, the
reverse diffusion is complete when the cumulative sum of products sold over time
(adoption) is equal to the cumulative disposal of products (deadoption). If product
mass is known, reverse diffusion is complete with the cumulative disposal of the total
material inflow.
61
4.3.
Model Parameters
Similar to innovation diffusion, the reverse diffusion distribution function can be
characterised by the parameters p and q, where p is considered the coefficient of
technical disposal, influenced by factors such as breakdown and wear and tear; and q
is considered the coefficient of discretionary disposal, influenced by social and
functional signals such as status, new product technologies, etc.
Operating under assumptions as described below, the reverse diffusion equation
results in:
𝑅(𝑡𝑡 ) =
𝑟(𝑡𝑡 ) =
1 − 𝑒 −(𝑝+𝑞)𝑡
𝑞
1 + 𝑒 −(𝑝+𝑞)𝑡
𝑝
(𝑝 + 𝑞 ) 2
𝑝
2
𝑞
�1 + 𝑒 −(𝑝+𝑞)𝑡 �
𝑝
(25)
(26)
where 𝑅 (𝑡𝑡 ) is the cumulative disposal function, 𝑟(𝑡𝑡 ) is the disposal density function,
i.e. the specific disposal rate.
The absolute disposal rate, d(t) is given by:
𝑑𝑑 (𝑡𝑡 ) = 𝑚 ∙ 𝑟(𝑡𝑡)
(27)
where 𝑚 is the total number of the durable products in the market stock which is to be
depleted to the disposal stock.
4.4.
Assumptions
The following assumptions characterise the reverse diffusion model:
1. The reverse diffusion model is a model of disposal, accounting for products
that have entered into the waste stream. Similar to one of the limiting
assumptions of the Bass model, it is assumed that consumers either use or
dispose of a consumer durable, without accounting for an intermediate stage of
storage.
62
2. The model is time invariant, in that parameters p and q do not change over
time. This in turn implies that consumer disposal behaviour remains the same
over time. (However, as consumer durable products tend to be used over longer
periods of time, it is possible that consumer behaviour changes over time).
3. The average mass and composition of a product is also considered constant.
While this is done in the interest of model parsimony, it may provide inaccurate
estimates of the mass flow which experience shows is not the same over time.
For example, there was a considerable reduction in the average physical mass
of a mobile phone from over 350 g in 1990 to about 80 g in 2005 (Hilty, et al.,
2006b). By assuming an average mass, the model could underestimate the mass
flow in the earlier years and overestimate it in the latter.
4. The model assumes there are no other factors that can influence disposal of
consumer durable products such as the awareness and convenience of disposal
options. While the discretionary disposal coefficient captures the overall
influence of all non-technical factors leading to disposal, it is unable to
distinguish between different drivers of discretionary disposal.
5. Application: Case Study – Consumer Durables in
Switzerland
Three empirical case studies applying the reverse diffusion model to disposed
consumer durables in Switzerland are presented. Switzerland has an established
collection system for consumer durables since 1994, giving time series data over 15
years. This not only provides us with disposal data to estimate parameters, but also
importantly, from a model validation perspective, it enables the comparison of the
model forecasts with real system data.
In this paper, the reverse diffusion model is used to estimate the disposal paths of
three consumer durable products namely Cathode Ray Tube (CRT) monitors, CRT
TVs and Flat Panel Display (FPD) Monitors. In the FPD monitor category, of the two
technologies, namely Liquid Crystal Display (LCD) and plasma display, plasma
displays form a miniscule share of the market and are therefore not considered.
63
5.1.
Data
Diffusion models are normally estimated with data from ownership surveys, or early
sales data. For the reverse diffusion model, data on disposals was obtained from the
SWICO Recycling annual reports and EMPA, who do the monitoring and control of
material flows of the take-back system. Sales data on the three products were also
collected. The table below shows the data collected, the time period over which data
was available and the relevant sources. (See also the Annexes).
Consumer Durable
Product
CRT Monitors
Data Type
Time Series
Source
Sales of CRT
Monitors (in
units)
Disposal of CRT
Glass (in tonnes)
1983 – 2005
Robert Weiss
Consulting
1994 – 2010
CRT TVs
Sales of CRT
TVs (in units)
1998 – 2007
CRT TVs
Disposal of CRT
Glass (in tonnes)
2002 – 2010
LCD Monitor
Sales of LCD
Monitors (in
units)
Disposal of LCD
Monitors (in
units)
1999 – 2009
SWICO
Recycling Annual
Reports; EMPA
SCEA (the
Association of
Swiss Consumer
Electronics
Manufacturers)
SWICO
Recycling Annual
Reports; EMPA
Robert Weiss
Consulting
CRT Monitors
LCD Monitors
Table 4: Data collected
2006 – 2010
SWICO
Recycling Annual
Reports; EMPA
Data on units of CRT Monitors and CRT TVs collected by SWICO Recycling is
available only from 2006 onwards, however, data on CRT glass collected by the
system is available for the entire period, from 1994 – 2010. Where necessary, data is
converted from tonnes of CRT glass to number of units, based on a fixed average
mass of leaded CRT glass per TV or monitor.
64
5.2.
Case Study 1: CRT Monitors in Switzerland
CRT monitors were sold in Switzerland between 1983 and 2005, reaching peak sales
in 1998 before being made obsolete by LCD monitors. While initially limited to
business users, as the personal computer became more affordable, CRT monitors
diffused into households as well, becoming a consumer durable just as TVs and
radios. With the advent of LCD monitors, however, their adoption rate declined, with
no further CRT monitor sales after 2005.
With data on both the annual sales and disposals of CRT monitors in Switzerland for
over 15 years, the CRT monitor presents an excellent case study to validate the
conceptual and predictive validity of the reverse diffusion model. Switzerland
provides an exceptional source of data on the disposal of CRT monitors through the
organised collection and recycling operated by SWICO Recycling, allowing validation
of the model against real system data. SWICO Recycling started collecting Personal
Computer (PC) monitors in 1994, and has over time built consumer awareness
regarding the disposal of PC monitors through its take-back channels. As consumer
awareness has grown, the collection efficiency of the system has also increased, with
few monitors leaking out of the system or disposed of in other waste streams. The
take-back and recycling system currently has a collection efficiency of 90%, as
confirmed by SWICO Recycling experts. Although it has taken time for the SWICO
Recycling system to achieve such high collection efficiency, with clearly lower
collection efficiency in the early days of the system, for simplicity, 90% collection
efficiency is assumed throughout the time period.
From Figure 13Figure 13: Cumulative Disposal R(t)- CRT Monitor Glass below, it
can be seen that the disposal of CRT monitors follows an S-shaped curve, terminating
when maximum potential CRT monitor inflow (m) has been depleted. The fit statistics
are given in Table 5.
0.0001
p
0.3400
q
61,735 [tonnes CRT Glass]
m
2
0.98
R
Table 5: Parameter values for CRT Monitor reverse disposal
65
Figure 13: Cumulative Disposal R(t)- CRT Monitor Glass
Figure 14 below shows the timing of the peak disposals, which occurred in 2005, by
when half the stock of CRT monitors were disposed of.
5000
4000
Actual CRT Monitor Glass Disposal [tonnes]
Model Estimated CRT Monitor Glass Disposal
[tonnes]
3000
2000
1000
0
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
CRT Monitor Glass [t/a]
6000
Figure 14: Disposal curve r(t) – CRT Monitor Glass
The parameter values for p and q, the maximum potential ownership, m, and the
coefficient of determination, R2, are given in the table below:
Interpreting the parameters, given the low value of p and much higher value of q, it
can be inferred that technical failures trigger only a small number of disposals, with
the large majority of disposals driven by discretionary factors.
66
5.3.
Case Study 2: CRT TVs in Switzerland
CRT TVs have been sold in Switzerland since the 1950’s, and until 1998 when LCD
TVs were introduced, all TVs sold were CRT TVs. Although the take-back of CRT
monitors started in 1994, TVs were included in the SWICO Recycling system only in
2002. With SWICO Recycling collection data available from 2002 onwards, sales data
for the period 1995-2009 are considered, on the basis of the assumption that TVs have
a minimum lifetime of seven years. Cumulative sales of CRT TVs in Switzerland in
the period are considered as m.
Figure 15 below shows the cumulative disposal of CRT TV glass from CRT TVs sold
since 1995. As per the model, it is estimated that 97% of CRT TVs will be disposed of
by 2020. The parameter values and fit statistics are given in Table 6Table 7.
Figure 15: Cumulative Disposal R(t) - CRT TVs
Figure 16 below shows that the peak disposal of CRT TVs is expected to take place in
2012.
67
Figure 16: Disposal Curve r(t) - CRT TVs
The parameter values for p and q, the maximum potential ownership, m, and the
coefficient of determination, R2, are given in the table below:
p
q
m
0.0004
0.3933
95,337 [tonnes CRT Glass]
R2
0.98
Table 6: Parameter values for CRT TVs reverse disposal
Similar to parameters for CRT monitors, the low parameter value of p as compared to
q suggests that the driver of disposal for CRT TVs is greater due to discretionary
rather than technical factors.
5.4.
Case Study 3: LCD Monitors in Switzerland
LCD monitors were introduced into the Swiss market in 1999, and within 6 years had
made CRT monitors completely obsolete. LCD monitors were already being seen in
the waste stream within 5-6 years, and SWICO data on LCD monitors disposed is
available from 2006. Technology trends indicate that LCD monitors may themselves
be made probably obsolete by newer OLED monitors in the coming years. However,
currently, LCD monitors continue to be sold. This poses a challenge in terms of
estimating the maximum cumulative sales, which is an important factor affecting the
model’s predictive value (Yu et al., 2010).
68
This challenge is addressed through a bounding analysis, similar to Yu et al., (2010),
who consider three scenarios for their model, namely upper, baseline, as well as lower
value of maximum carrying capacity for diffusion of PCs. Similarly, for this analysis,
three scenarios of the maximum potential inflow of LCD monitors in Switzerland are
considered.
Cumulative sales of monitors in Switzerland from 1999 to 2009 are taken as the basis
for the three scenarios. From the example of CRT monitors for which sales declined
once a new technology was introduced, a similar substitution is expected to take place
for LCD monitors as they are replaced by newer technologies. Therefore, the
continued sales of LCD monitors are to an extent contingent on the speed of diffusion
of next generation monitors. In the first scenario, in the event of a rapid substitution of
LCD monitors, it is assumed that 75% of total potential inflow of LCD monitor has
been achieved by 2009, with only a quarter of the cumulative sales remaining to be
achieved thereafter. In the second scenario, at a slower substitution rate of LCD
monitors, it is assumed that 65% of maximum potential inflows of LCD monitors
have been achieved until 2009. In the third scenario, the slowest substitution rate of
the three scenarios is assumed, with only 55% of LCD monitors expected to have been
sold until 2009. Fitting the parameter estimates with SWICO collection data for LCD
monitors from 2006 -2010 for each of the years, the peak disposal of LCD monitors
will be in 2013 in case of rapid substitution, and in 2014 in the medium and slow
substitution scenarios.
Figure 17: Disposal Curve - LCD Monitors
69
For each of the three scenarios, the parameter values for p and q, the maximum
potential ownership, m, and the coefficient of determination, R2, are given in the table
below:
Scenario 1
Scenario 2
p
0.0001
0.0001
q
0.5791
0.5643
m
5,510,013
6,357,708
2
R
0.98
0.98
Table 7: Parameter values and fit statistics
Scenario 3
0.0001
0.5494
7,513,655
0.97
6. Model Validation
Validity is a model’s property of adequately reflecting the system modelled and a
primary measure of model quality (Schwaninger and Groesser, 2009). As the reverse
diffusion model attempts to predict when consumers will eventually dispose of their
consumer durable product, the predictive validity of the model is demonstrated by
comparing the model forecast to the actual disposals. Bass, Krishnan and Jain (1994),
have compared predictive qualities of their two diffusion models using step-ahead
forecasting. First fitting the model for n periods, a forecast is made for the n+1th
period. Re-estimating the model for n+1 periods, a forecast is made for the n+2th
period and so on. In this paper, following Bass et al., (1994) a one-year ahead forecast
is made for the year 2011 by using data until 2010 for parameterising the model to test
the forecasting performance of the reverse diffusion model. The Mean Absolute Error
is calculated to test the forecasting efficacy of the model.
6.1.
CRT Monitors
The results indicate the reverse diffusion model underestimates actual disposals of
CRT glass from PC monitors by 16%. The table below shows the model forecast and
actual values for CRT monitors for 2011 as well as the Mean Absolute Error (MAE).
A potential reason for the under-estimation could be that the monitors coming into the
waste stream are bigger, with greater CRT glass mass, as compared to the fixed
average mass of glass per PC used for in the model.
70
CRT Glass Disposal from CRT PC Monitors – 2011
Model Forecast
Actual Disposal
MAE
% Difference
[tonnes]
[tonnes]
[tonnes]
2,142
2,559
417
- 16%
Table 8: Model forecast vs actual disposal – CRT PC Monitors
6.2.
CRT TVs
The reverse diffusion model forecast for CRT glass from CRT TVs also
underestimates the actual disposal by approximately 19%. The table below shows the
model forecast and actual values for CRT glass from CRT TVs for 2011 as well as the
Mean Absolute Error (MAE). As in the case of PC monitors, the difference may be
explained by the underestimation of the mass of CRT glass per TV. As larger screen
CRT TVs, containing greater mass of glass per TV, were more popular, it is likely that
the average mass of glass of the disposed TVs is higher than the average mass used in
the model.
CRT Glass Disposal from CRT TVs – 2011
Model Forecast
Actual Disposal
MAE
% Difference
[tonnes]
[tonnes]
[tonnes]
9,805
12,031
2226
- 19%
Table 9: Model forecast vs actual disposal – CRT Glass from CRT TVs
6.3.
LCD Monitors
Contrary to the CRT monitor and CRT TV forecasts, the reverse diffusion model
overestimates the disposal of LCD monitors between 55% - 61% in the three scenarios
described above. Counterintuitively, the disposal of LCD monitors in 2011 was
fractionally lower than in 2010. A possible reason is the influence of uncertainty and
volatility in macro-economic conditions which make consumers more conservative in
their replacement and disposal of consumer durables.
LCD Monitors Disposal – 2011
Scenario 1 Scenario 2 Scenario 3
Actual Disposal [units]
375,519
375,519
375,519
Model Forecast [units]
587, 648
603,564
583,116
MAE
212,129
228,045
207,597
% Difference
56%
61%
55%
Table 10: Model forecast vs actual disposal - LCD Monitors
71
7. Discussion & Conclusion
The three case studies presented above validate the model based on three consumer
durable products collected by the SWICO Recycling take-back system. In each case,
the parameter estimates are realistic and provide a reasonable fit to each product’s
disposal path. The p values (the coefficient of technical disposal) in all cases are
significantly smaller than the q values (the coefficient of discretionary disposal),
indicating that the large majority of disposal of consumer durable products is driven
by consumer behaviour. This is in keeping with evidence from Cripps and Meyer
(1994) and Grewal et al. (2004) which indicates that discretionary replacements are
more likely to occur when the motivation is perceived technological obsolescence
than in the case of technical deterioration.
The advantages of the reverse diffusion model as compared to other models of
estimating disposal of consumer durables are two-fold. Firstly, the proposed model is
parsimonious as it is able to provide disposal estimates even in the event of relatively
sparse data on disposal. Secondly, the model makes it possible to estimate disposal
flows in the absence of any sales data as required by previous models.
To forecast the disposal path of a consumer durable by means of the reverse diffusion
model, it is necessary to have some initial values to estimate the model parameters.
Lilien, Rangaswamy and Van der Bulte (2000) suggest that with data for usually four
or more periods it is possible to obtain the p and q parameters of the Bass model. With
the formalisation of the take-back and recycling system for end-of-life consumer
durables, as more data on disposal becomes available, the reverse diffusion model can
similarly be used for forecasting the disposal trajectory with initial data from four to
five periods as shown in the LCD monitor case study. The early forecasting efficacy
of the model in such a case is highly dependent upon generating accurate estimates of
the upper limit of potential adoption which can be estimated based on analogy with
similar products or bounding analyses of expert opinions.
For durable products or regions for which disposal data is as yet unavailable, it is
possible to gain insights from the reverse diffusion history of analogous products or
regions. This may be specially relevant when projections regarding the disposal must
be made during the early stages of the product penetration, and may be typically be
based on using reverse diffusion parameters from previous generations as analogy.
72
Lilien, Rangaswamy and Van der Bulte (2000) have suggested that analogies based on
similarities in expected consumer behaviour are preferable to analogies based on
product similarities alone, as well as a weighted average of p and q values of multiple
analogues. It would be interesting for future research to explore how applicable
analogies are for reverse diffusion models.
However, the model is not without limitations. These limitations, however, could
provide directions for future research. The case studies presented in this paper are only
three products among a vast array of consumer durables. Generally, empirical data
indicates that disposal of consumer durables follows the classic logistic curve. A more
robust test would be required across product categories and across geographies to test
the model. Future research should test the generalizability of this model for other
durable goods such as, laptop computers, refrigerators, automobiles, etc.
Another limitation, similar to Bass Diffusion Models, is the assumption that the
coefficients p and q are constant over the time horizon of the model application, which
implies that time-varying factors, such as changing consumer behaviour due to newer
products, lower prices of newer products, more convenient disposal opportunities, etc.
(which all may lead to disposals), are not explicitly considered. Several authors have
indicated that the major reasons for replacement of consumer durables are change in
consumer needs, socio-economic reasons such as higher income (Cooper, 2004; Bayus
and Gupta, 1992) or dissatisfaction with production functionality, largely arising as a
result of the availability of new technology (Cooper, 2004; Islam and Meade, 2000).
The underestimated model values as compared to the actual values for the disposal of
CRT TVs in 2010 when there was a sharp jump in the disposals of CRT TVs is likely
due to changing consumer disposal behaviour. The sudden rise in disposals may be
largely attributed to discretionary disposals by consumers who replaced their old CRT
TVs for newer technology TVs such as LCD and Plasma TVs became more affordable
as well as promotional deals offered during the year.
The reverse diffusion model also does not shed light on the reasons for discretionary
disposal, or the number of products disposed for technical or discretionary reasons.
Therefore, it would be interesting to extend the model by explicitly including
consumer behaviour aspects which can provide greater understanding of the drivers
for disposal, especially discretionary disposals. Further research can look to
73
incorporating variables such as competitive effects of new technology, advertising,
product quality, price and income effects into the model.
Several authors (Mahajan and Muller, 1996; Norton and Bass, 1987) have examined
the issue of whether diffusion accelerates between technology generations. Similarly,
this could also be true for disposals, and it would be an area for further research
whether reverse diffusion accelerates between technology generations.
74
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CHAPTER IV
Forecasting Consumer Durable Disposals: A Review and
Comparison of Modelling Approaches
Abstract
This paper reviews two modelling approaches to forecasting disposal of consumer
durables, namely the “delay model” approach and the “reverse diffusion model”
approach. Applying the same dataset on the disposal of cathode ray tube monitors in
Switzerland to both the approaches, the estimates and forecasts of the models are
compared against real system data, sensitivity of the model parameters examined and
the assumptions, strengths, limitations and applicability of both modelling approaches
discussed. The comparison also provides an opportunity to discuss further
improvements to both modelling approaches, especially the importance of developing
models which incorporate consumer disposal behaviour.
Chapter IV – Forecasting Consumer Durable Disposals:
A Review and Comparison of Modelling Approaches
80
1. Introduction
Consumer durable goods – from household appliances such as refrigerators and
vacuum cleaners to entertainment electronics such as televisions and music players to
information technology products such as computers and printers – have proliferated
over the last fifty years. Not only have the number and types of products multiplied,
their increased affordability has seen sales of consumer durables skyrocket. Estimates
by Euromonitor (2011) suggest that global sales of consumer electronics were to the
tune of 3 billion units in 2010.
The flip side to increasing consumption of durable goods is the growing volumes
reaching their end-of-life. The disposal of these end-of-life products has gained
importance over the past decades because not only do they contain toxins which can
be harmful to human health and the environment, but they also contain valuable
precious metals and rare earths which are critical for the manufacture of new
generation consumer durables. For example, by some estimates, the global material
supply of critical metals in the manufacture of electronics such as Indium might be
exhausted before the end of the decade (UNEP, 2009). The reservoirs of end-of-life
products are therefore increasingly seen as valuable “mines” to recover scarce
elements from.
Over the past decade, these social, environmental and economic drivers have
necessitated better management of end-of-life consumer durables, spurring legislation
such as the European Union’s Waste Electrical and Electronic Equipment (WEEE)
Directive, the Japanese Specified Home Appliances Recycling Law (SHAR) and the
Swiss Ordinance on the Return, Taking back and Disposal of Electrical and Electronic
Equipment (ORDEE), among others, which are specifically aimed at end-of-life
consumer durables.
Essential for sustainable and efficient management of end-of-life consumer durables is
an accurate estimation of the timing and quantity of disposed consumer durables
(Kang and Schoenung, 2006). Models, as simplified representations of real systems,
can both reproduce or recreate ( “portrait”) and anticipate (“paragon”) and are crucial
in providing an understanding of the real system (Schwaninger, 2010). Modelling endof-life consumer durables to quantify the waste stream has drawn the attention of
81
several scholars with the aim of improving decision making efforts for policy makers
(for example in setting targets), recyclers (for estimating availability of supply) or
take-back systems (to estimate logistical and cost implications).
Research so far on modelling disposals of consumer durables has tended to focus
more on the sales and marketing of consumer durables rather than their disposal. In
part, this is likely due to the fairly recent emergence of the problems associated with
disposal of consumer durables. The main challenges however of modelling end-of-life
consumer durables are:
1. Insufficient, or at best fragmented, time-series data regarding sales, existing
products in use, and average product mass.
2. Insufficient understanding of consumer disposal behaviour, especially how and
when end-of-life durables are disposed of by the consumer.
Nevertheless, several authors have proposed models to forecast the waste flow of
durable goods, with some focussing on a product, quantifying the number or weight of
one or many consumer durable product(s) (Widmer et al., 2005; Oguchi, et al., 2008;
Yang, et al., 2008), while others study flows of materials from consumer durables,
quantifying flows at the material level, such as lead, plastics, copper and glass
(Elshkaki et al., 2005; Macauley, et al., 2003; Spatari et al., 2005, Gregory et al.,
2009; Krivtsov et al., 2004).
However, as yet, there has been no validation of the disposal forecasts of the models
against observed data from a real system. As Schwaninger (2010) advises, it is not
enough to build insightful models; they must also be valid. Although validity is not
the only criterion of model quality, with other criteria including parsimony, ease-ofuse, and practicality also important, model validity is considered the primary measure
of model quality (Schwaninger and Groesser, 2009). Bolstering the argument for
validation is a recent global review of the management of electrical and electronic
waste management by Ongondo et al. (2011) who conclude that reported global
quantities of WEEE are grossly underestimated.
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Additionally, there is as yet no study that compares the structural properties,
assumptions, strengths and limitations of the various models which differ from one to
another. This paper aims to provide such a comparison between models, focussing on
two generic modelling approaches, namely the delay model approach and the
diffusion model approach. The paper also compares their predictive validity by
applying each model to the case of the disposal of Cathode Ray Tube monitors (CRT
monitors) in Switzerland.
The paper is organised as follows: The next section provides a brief overview of the
two modelling approaches and a summary of the terminology and definitions,
followed by the purpose and objectives of the research. In Sections 4 and 5, both
modelling approaches are described in detail, including three variants of the delay
model approach, with a structural comparison and a summary table comparing their
main characteristics in Section 6. In the following section, the forecasting results of
four models are compared against real system data on cathode ray tube monitors
disposed of in Switzerland. A fit improvement and sensitivity analysis is also
conducted to compare the performance of the models. The final section discusses the
advantages and limitations and suggests areas for future research in improving the
models.
2. Modelling Approaches to Estimate Consumer Durable
Disposals
The most commonly used modelling approach to estimate disposals of consumer
durable product is the “delay model” approach, also sometimes referred to as the
market supply approach (Widmer et al., 2005). Citing Lohse et al. (1998), Widmer et
al. (2005) have also mentioned the “consumption and use” and “market saturation”
approaches for estimating end-of-life consumer durables. The consumption and use
method takes the average consumer durables of a typical household as the basis for a
prediction of the potential amount of end-of-life products, while the market saturation
approach is based on the assumption that private households are already saturated with
consumer durables, and for each new product purchased, an old one reaches its endof-life. However, in literature, no applications of or further research on these
approaches were found, and therefore are not considered in this paper.
83
The second modelling approach discussed and compared in this paper is the “reverse
diffusion” approach. Diffusion models are extensively used in the forecasting of sales
of new consumer durables. Chapter III of this thesis, suggests that similar to sales of
new products which follow a sigmoid curve, the cumulative disposal of old consumer
durables also tends to follow a sigmoid curve and have applied the diffusion
modelling approach to disposal of consumer durables.
Both the delay model and the reverse diffusion model approach are discussed further
in detail in the next section.
2.1.
Terminology
One of the challenges in comparing models is to find a common terminology,
especially with the aim of understanding both implicit and explicit assumptions. The
main variables, and various terms used for these in delay and diffusion models are
discussed briefly in the section below.
2.1.1. Inflows
“Sales” and “shipments” are often synonymously used for inflows of consumer
durables into the consumption stock, even though there can be significant time gaps
between shipments of products from manufacturers to distributers before being finally
sold to a consumer. However, some authors (e.g. Oguchi et al., 2008) argue that given
lean inventory management, the delay between shipment and sales is insignificant,
making it a close approximation of sales data and therefore used for inflow data. An
implicit assumption that all models make regarding inflows is that all sales are of new
products within geographic boundaries, not accounting for second-hand sales or
imports of second-hand consumer durables.
2.1.2. Stocks
The stock of consumer durables has been conceptualised differently by different
authors. As consumer durables are often reused, resold and stored by consumers
before finally being disposed of (Widmer et al., 2005), differences in the definition of
“stock” can have significant implications in the magnitude of the stock. Spatari et. al.,
(2005) consider stocks in their model to include only those products in use, not
including “hibernating” products comprising those that have been retired and remain
84
in households unused. In contrast, Oguchi et al.,(2008) consider their stocks to include
all products in households, whether being used or stored. They explicitly state that
hibernating or out-of-use products stored in households are not considered as waste,
and hence form part of the consumption stock. Kang & Schoenung (2006) take a
similar approach, defining stock in the consumer phase as the sum of the amount
being used by the first user, any following users and stored products that are not in
active. Consequently, Spatari et al.(2005) calculate the discard rate of WEEE without
distinguishing between discarded electronics, i.e. those which are disposed of, and
‘hibernating’ electronics, i.e. those which remain in households unused. In contrast,
(Oguchi et al., 2008) define WEEE flows only as those out-of-use products that are
disposed of.
2.1.3. Delay Distribution
The lifetime of a consumer durable is an essential piece of information in modelling
waste flows at end-of-life in the delay model approach. Various terms are used in
literature by authors to describe the time a durable product is considered as part of a
stock, between inflow and outflow. Commonly used terms are “average lifetime”,
“residence time”, “survival function”, “disposal distribution function”, “product
lifetime function”, “disposal function”, “domestic service lifetime”, “total lifetime”,
and “possession time”. Though very similar, the terms may likely include or exclude
one or several intermediate stages (e.g. reuse or storage) between purchase and
disposal by a consumer. Additionally, some authors consider lifetime as a fixed value
(or Dirac distribution) while others use parametric or non-parametric distributions in
their models. Oguchi et al., (2010) provide a comprehensive review of the different
types of lifetime distribution and as well as distribution estimation methodologies.
2.1.4. Product Mass
Estimating units of disposed consumer durables, while useful, may often not be
sufficient for decision making. In such cases, the total estimated physical mass or the
composition of the waste stream in terms of specific materials is required. Most
authors use a constant average product mass throughout the entire time horizon of the
model. However some authors caution against a constant value, especially given that
the size and material composition of products change over time. The reduction in the
average physical mass of a mobile phone from over 350 g in 1990 to about 80 g in
85
2005 (Hilty, et al., 2006a) demonstrates the benefits of product mass function that
reflects the changes to the product mass over time over a constant value.
3. Goal and Purpose
The goal of the paper is to review and compare two modelling approaches used to
estimate and forecast disposals of consumer durables. Applying the same dataset to
the different models, the paper examines their differences and compares the
performance of outputs of the models against a real system. Through such a
comparison, the paper aims to provide a summary of strengths, limitations,
applicability and acuity of two modelling approaches as well as discuss research gaps
and areas for improvement in consumer durable disposal modelling. Thus, the paper
will enable policy makers, recyclers and other stakeholders to make better and more
informed forecasts of consumer durable disposals by using the most appropriate
modelling approach in view of available data.
4. Delay Model Approach
Modelling waste streams from durable products using the delay model is well
established and has been used to forecast waste such as concrete from buildings
(Müller, 2006), automobiles (Steffens, 2001) as well as consumer durables. In the
delay model approach, the outflow of products (disposals) is dependent on the inflow
of products (sales) and the time spent as stock, given by the delay function (lifetime).
The outflow therefore is independent of the stock, which acts as time buffer, with the
timing of disposal of a product linked to when the product entered into stock, as it is
more likely for older devices to be disposed of than newer devices.
The outflow is determined by the inflow and the average delay time. The outflows
(disposals) at time t are expressed as a convolution of the inflows In and the disposal
density d:
Thus,
∞
𝑂𝑂𝑂𝑂𝑡𝑡𝑡 = � 𝑑𝑑𝑖 ⋅ 𝐼𝐼𝐼𝐼𝑡 − 𝑖
(28)
𝑖=−∞
86
Most authors use the delay model approach with variations in the delay time
distribution for average life. In its simplest form, the average delay time has a Dirac
distribution (Streicher-Porte et al., 2005; Kang & Schoenung, 2006) with disposals
following exactly the same curve as sales, only shifted in time by the fixed delay.
Although authors have previously used a fixed delay distribution, it is increasingly
common to use distributed delays which are more realistic, as products from a cohort
are not all disposed at the same time, with some disposed of earlier than others.
Three variants of the delay model approach are discussed below:
1. A delay model with the Weibull distribution, the most commonly used lifetime
distribution for estimation of disposals of end-of-life consumer durables. The
model by Oguchi et al. (2008) is used an example.
2. The second delay model uses a derived lifetime distribution, as well as a
product mass function. The model by Gregory et al. (2009) is used as an
example.
3. The third delay model, presented in Chapter II of this thesis also uses a Weibull
lifetime distribution, albeit coupled with a technology substitution model, and
estimates the parameters of the Weibull within the model, as opposed to
externally.
4.1.
Delay Model A: Example Reference – Oguchi et al., 2008
In this model, the mass of disposed consumer durables is expressed as a product sum
of the shipments or sales, the lifetime distribution and a fixed average mass per unit.
Oguchi et al. (2008), Elshkaki et al. (2005), Steffens (2001), Mueller et al. (2006)
among others use a Weibull distribution function for the lifetime.
The model specification is as follows:
∞
𝑂𝑂𝑂𝑂𝑡𝑡𝑡 = � 𝑑𝑑𝑖 ⋅ 𝐼𝐼𝐼𝐼𝑡 − 𝑖 ⋅ 𝑚
(29)
𝑖=−∞
87
where 𝐼𝐼𝐼𝐼 is the shipments or sales into the market, 𝑑𝑑𝑖 is the lifetime distribution and
𝑚 is the mass of the product which is considered to remain constant over time.
The two parameters of the Weibull distribution are interpreted as the average lifetime
and the deviation. These parameter values are estimated separately, in most cases
either through a sample survey of the age of disposed products at the point of disposal
(eg. recycling facilities) or through a questionnaire survey of consumers regarding age
of owned products at time of disposal.
Oguchi et al., (2008) have modelled waste flows for a diverse range of consumer
durables ranging from large household appliances such as washing machines and
refrigerators to consumer electronics equipment such as televisions and radios to
information and communication technology products such as personal computers and
printers.
4.2.
Delay Model B: Example Reference – Gregory et al., 2009
Gregory et al. (2009), Yang et al. (2008), Yu et al. (2010) have modelled the disposal
of consumer durables by specifying their delay models using non-parametric
distributions. Oguchi et al. (2010) suggest that with sufficient data, a non-parametric
approach can derive a more precise distribution. In the case of Gregory et al. (2009),
the retirement probability or lifetime distribution was derived from information based
on data from a collection trial.
In addition, Gregory et al. (2009) have also included in their model a product mass
function that incorporates the changing weight of TVs and PC Monitors as heavier,
larger screen size products are sold.
∞
𝑂𝑂𝑂𝑂𝑡𝑡𝑡 = � 𝑑𝑑𝑖 ⋅ 𝐼𝐼𝐼𝐼𝑡 − 𝑖 ⋅ 𝑚𝑖
(30)
𝑖=−∞
where 𝐼𝐼𝐼𝐼 is the shipments or sales into the market, 𝑑𝑑𝑖 is the derived lifetime
distribution and 𝑚𝑖 is sales-weighted product mass.
88
4.3.
Delay Model C: Example Reference – Chapter II
The model presented in Chapter II of this thesis adopts the delay model approach to
estimate the societal stocks and flows of consumer durables. The model incorporates
the Fisher-Pry technology substitution model (Fisher and Pry, 1971) to estimate sales
of a durable product.
The Fisher-Pry substitution model is given by:
𝑠(𝑡𝑡) =
1
[1 + tanh 𝛼(𝑡𝑡 − 𝑡𝑡ℎ )]
2
(31)
where s(t) is the fraction of the sales substituted by the new technology, 𝑡𝑡ℎ is the time
at which the new technology has substituted 50% of the market share, and 𝛼 is
interpreted as a parameter indicating half the annual fractional growth rate in the early
years of the new technology product.
Disposals are expressed as a product sum of the sales, the lifetime (a Weibull
distribution) and a fixed average mass per unit.
∞
𝑂𝑂𝑂𝑂𝑡𝑡𝑡 = � 𝑑𝑑𝑖 ⋅ 𝐼𝐼𝐼𝐼𝑡 − 𝑖 ⋅ 𝑚
(32)
𝑖=−∞
where 𝐼𝐼𝐼𝐼 is the sales into the market, 𝑑𝑑𝑖 is the lifetime distribution and 𝑚 is the mass
of the product which is considered to remain constant over time. The difference
between the delay models A and C is in the estimation of the Weibull parameters.
Whereas in delay model A the Weibull parameters values are externally estimated, in
delay model C, the values are estimated iteratively by optimisation, setting the
objective function to minimize the sum of squared residuals.
89
5. Reverse Diffusion Model Approach
The diffusion model, which has its origins in ecology, was first applied as a model to
forecast sales of consumer durables by Bass in 1969. It has since become one of the
most widely researched models in marketing, with several extensions and
modifications to the original Bass Diffusion Model. In the reverse diffusion model
proposed in Chapter III, the market depletion of a durable is driven by technical
disposals and discretionary disposals, characterised by the parameters p and q, where
p is considered the coefficient of technical disposal, influenced by factors such as
breakdown and wear and tear; and q is considered the coefficient of discretionary
disposal, influenced by social and functional signals such as status, new product
technologies, etc.
The reverse diffusion differential equation is given as:
𝑆̇ = 𝑝 ∙ (1 − 𝑆) + 𝑞𝑆 ∙ (1 − 𝑆)
(33)
Where 𝑆̇ is the change in stock, p is the coefficient of innovation and q is the
coefficient of imitation and has the following solutions.
𝑅(𝑡𝑡 ) =
𝑟(𝑡𝑡 ) =
1 − 𝑒 −(𝑝+𝑞)𝑡
𝑞
1 + 𝑒 −(𝑝+𝑞)𝑡
𝑝
(𝑝 + 𝑞 ) 2
𝑝
2
𝑞
�1 + 𝑒 −(𝑝+𝑞)𝑡 �
𝑝
(34)
(35)
where R(t) is the cumulative disposal function, r(t) is the disposal density function,
i.e. the specific disposal rate.
The absolute disposal rate, d(t) is given by:
d(t) = m ∙ r(t)
(36)
90
where m is the total number of the durable products in the market stock which is
to be depleted to the disposal stock.
6. Structural Comparison
The underlying structure of the delay and the reverse diffusion models, as discussed in
Chapters II and III respectively, are illustrated in the diagrams below.
disposal d(t)
In (t)
Out (t)
� 𝑑𝑑𝑡𝑡
Stock (t)
Figure 18: Delay Model Structure
p
In (t)
Market (t)
q
Out (t)
Disposal (t)
Figure 19: Reverse Diffusion Model Structure
From the diagrams, it can be seen that both models are structurally different. In the
delay model, the outflows (disposals) are expressed as a convolution of the inflows In
and the disposal density d, and entirely independent of the stock. In comparison, in the
case of the reverse diffusion model, the outflow is independent of the inflow. The
outflow feeds a disposal stock which determines, together with the parameters p and q
91
the dynamics of the outflow. The total stock in the market which is to be depleted to
the disposal stock scales the outflow.
The table below provides a summary of the characteristics of the four models being
compared.
Example
Reference
Model
Independent
Variables
Delay
distribution
Model
Parameters
Lifetime
distribution
estimation
methodology
Terminology Point of
“disposal”
Model 1 - Delay Model 2 - Delay Model 3 - Delay Model 4 Model A
Model B
Model C
Diffusion
Model
Oguchi et al.
Gregory et al.
Chapter II
Chapter III
(2008)
(2009)
Inflows of
Inflows of
Stock of product; Disposal timeproduct
product;
Inflow of new
series
technology
Product mass
function (time
variant)
Weibull
Derived nonWeibull
n/a
parametric
lifetime
distribution
Fixed average
n/a
Fixed average
p (coefficient
mass of product
mass of product of technical
(time invariant)
(time invariant) disposal)
Weibull
Weibull
q (coefficient
parameters alpha
parameters alpha of
and beta
and beta
discretionary
disposal)
Based on a user Based on survey Parameters
n/a
survey
at disposal point estimated within
model
Does not
Does not
Does not
consider storage consider storage consider storage
time – if not part time – if not part time – if not part
of active stock, of active stock, of active stock,
considered as
considered as
considered as
disposed
disposed
disposed
Table 11: Summary table of model characteristics [n/a = not applicable]
Storage time
implicitly
included –
only counted
if actually
disposed
92
7. Experimental Frame
The models discussed above are compared to each other by applying them to the case
of the disposal of Cathode Ray Tube (CRT) monitors in Switzerland. CRTs had been
the dominant display technology for both televisions and Personal Computer (PC)
monitors until they were rendered obsolete with the advent of new flat panel display
technologies.
Personal computers were introduced to the Swiss market in the early 1980s. Disposals
of these products followed soon after, and by 1994, there was a formal collection and
take-back system to ensure sound disposal of end-of-life PCs. With reliable data on
sales, stocks and specially disposals, estimating and forecasting flows of CRT
monitors makes an excellent case study to compare and validate the models discussed
above.
Data on the stock and inflow (sales) of PC monitors was obtained from Robert Weiss
Consulting (www.weissbuch.ch), while data on outflows (disposals) was acquired
from SWICO Recycling, the Swiss producer responsibility organisation that manages
the collection and take-back system for several consumer durables, including IT
equipment such as PC monitors and EMPA, who provide the monitoring and control
for the SWICO system.
8. Results
Applying the data on CRT monitors to all four models discussed above, annual CRT
glass disposal in Switzerland is estimated and compared with collection data from the
SWICO Recycling system.
Several assumptions are made in order to compare the model outputs.
1. Given the long experience and high consumer awareness of the SWICO
Recycling take-back and collection system, currently the collection efficiency
of the system is very high, at 90%, as confirmed by SWICO Recycling experts,
with only a small fraction of end-of-life product disposals not captured by the
system. For simplicity, a collection efficiency of 90% is assumed throughout
93
the time period modelled, although it is likely that collection efficiency in
earlier years was not as high.
2. The value of the average mass of glass in CRT monitors, 9.5 kgs/monitor is
taken as the average of 10.5 kgs/monitor from a study by Monchamp et al.
(2001) and 8.5 from a study by Huisman et al. (2008).
3. It is assumed that the parameter values of the Weibull distribution in Delay
Model A are the same for Switzerland as they are for Japan as estimated by
Oguchi et al. (2008), given that both are highly developed economies with
likely similar consumption and disposal patterns.
4. The derived lifetime distribution as also the sales-weighted product mass
function has been estimated for the United States of America by Gregory et al.
(2009). It is assumed that the same distribution and product mass function are
applicable to Switzerland, given that both are developed, industrialised
economies with similar consumption and disposal patterns.
8.1.
Output Comparison
In Figure 20 below, the disposal curve of the four models is plotted alongside the
observed data from the SWICO Recycling collection system. The reverse diffusion
model performs the best, followed by Delay Models C, A and B.
Figure 20: Model Comparison - CRT Glass Disposal Estimates vs Observed
94
Parameter and fit statistics for all four models is given in the table below. 𝛼 and 𝛾 are
the scale and shape parameters of the Weibull distribution respectively, and p and q
are parameters of the reverse diffusion model. 𝛼 is interpreted as the average lifetime
of the product, with 𝛾 the deviation from average lifetime.
Delay
Model A
Delay
Model B
Delay
Model C
Reverse
Diffusion
Model
0.0001
0.3490
6.70
n/a
8.72
𝜶 OR p*
4.80
n/a
2.83
𝜸 OR q*
m (crt glass
kgs/monitor) OR m
9.5
7.7 – 11.3
9.5
61,735
(total tonnes)*
2
0.05
-0.01
0.81
0.99
R
Table 12: Parameter values and fit statistics (* indicates parameters of reverse
diffusion model)
From Figure 20, it is clear that the delay models A and B are predicting earlier
disposals than actually observed. Delay model A forecasts the quickest disposal of
CRT monitors, with the disposal nearly complete by 2011. Model C performs the best
of the three delay models, with the highest R2 of 0.81 of the three delay models. This
is likely due to the higher average age of Model C as compared to Model A, indicating
that the average age of CRT PC monitors in Switzerland at the time of disposal was
closer to 9 years than 7 years. Sampling by SWICO Recycling has shown that the
average age of PCs collected by the take-back system is approximately 9 years
(Widmer et al., 2005) which explains the better fit of Model C as compared to Model
A and B. The influence of the Weibull parameters in forecasting disposals is
investigated further as part of the sensitivity analysis of the parameters.
8.2.
Predictive Validity
The predictive ability of a model is demonstrated by comparing the model forecast to
the observed values of the real system. To validate and compare the predictive power
of the four models, truncated data until 2005 is used for fitting the models and
forecasts produced for the balance time periods (2005-2011) by extrapolating the
fitted models (Figure 21). The mean absolute error (MAE) is used to measure how
95
close forecasts are to the eventual outcomes. The lower the MAE, the better the
predictive performance. The mean absolute error is highest for delay model B, which
is 6.89 times higher than the lowest mean absolute error for the reverse diffusion
model. The results are reported in Table 13: Comparison of Predictive Power below.
Delay
Model A
Delay
Model B
1872.68
2014.29
Mean Absolute Error
Table 13: Comparison of Predictive Power
Delay
Model C
700.45
Reverse
Diffusion
Model
292.35
Figure 21: Disposal Forecasts
8.3.
Fit Improvement
To test if the fit of delay models A and C can be improved by changing the mass from
a fixed value to a variable function, the sales-weighted product function from model B
is applied to models A and C. The Modified Models A and C are recalculated with the
weight of CRT Glass mass per monitor varying from 7.7 to 11.3 kgs/ monitor
depending on the year of sale.
96
Figure 22: Fit improvement by introducing product mass function
Both models show an improved fit as a result, as shown in Table 14. This reflects the
increased sales over time of monitors with larger screen sizes, thereby containing
more glass per monitor. For the Modified Delay Model A, the coefficient of
determination, the R2, improves substantially by 0.17 to become 0.22. Delay Model C
also sees an improvement in the fit, increasing marginally by 0.09. However, it must
be noted that this improvement is at the cost of simplicity as it introduces an
additional variable and data requirements.
Model
Weibull
Coefficients
𝜶
𝜸
CRT Glass
Mass
[kgs/monitor]
Modified
Sales-weighted
6.70
4.80
Delay
7.7 – 11.3
Model A
Modified
Sales-weighted
8.72
2.83
Delay
7.7 – 11.3
Model C
Table 14: Fit improvement statistics
R2
𝚫R2
0.22
0.17
0.90
0.09
97
8.4.
Sensitivity Analysis
A sensitivity analysis of the model parameters is performed to determine which
parameters exert the most influence on model results. For delay models, sensitivity of
Weibull parameters is tested, while for the reverse diffusion model, sensitivity of the
coefficients, p and q, is analysed. Delay model A is used as a representative for the
delay models as it is expected that the parameter sensitivity of delay models is similar.
8.4.1. Sensitivity of Delay Model Parameters
A sensitivity analysis is performed by testing the fit of model by a change of 30%,
both positive and negative for both Weibull parameters (𝛼, 𝛾) of the delay model A.
As seen in Figure 23, the model is far more sensitive to the change in average lifetime
(𝛼) than the change in the deviation (𝛾). As lifetime parameter, 𝛼, is increased, the fit
of the model, indicated by R2 plotted on the Y-axis, improves significantly. In
comparison, even a large change in the deviation of the distribution parameter, 𝛾,
affects only a very small change in the fit.
Figure 23: Sensitivity of delay model parameters
8.4.2. Sensitivity of Reverse Diffusion Parameters
A sensitivity analysis of the reverse diffusion model parameters shows that the fitted
parameters were at the optima, maximising R2. The model is sensitive to changes in
both p and q parameters, with the q parameter having a greater influence on the model
98
fit than the p parameter. Importantly, it indicates that any change in the coefficient of
discretionary disposal can reduce the fit of the model significantly. In case of
changing consumer disposal behaviour, with greater or lesser discretionary disposal,
the model fit might be reduced.
Figure 24: Sensitivity of reverse diffusion model parameters
9. Discussion and Conclusion
A comparison of the two modelling approaches namely the delay modelling approach
and the reverse diffusion approach provides valuable insights for forecasting disposals
of consumer durables. Both modelling approaches are equally valid, and can provide
reasonably accurate forecasts given sufficient data. The choice of model would largely
be dependent on the quantity and quality of the data available.
For delay models, time series data on inflows of consumer durables is essential as is
the lifetime distribution. The sensitivity analysis illustrates the importance of
parameter estimates, in particular regarding the alpha parameter (interpreted as the
average lifetime), as a 20% change in the parameter results in the fit improving by
330%. In the absence of accurate lifetime distribution data, it may be better to estimate
the parameters within the model, as in Model C to get more accurate forecasts. Such
99
an approach can be particularly useful in cases where fragmented or incomplete data
are available.
As seen above, the lifetime distribution is crucial in providing accurate estimates of
the timing of disposals of consumer durables. Parameters from Japan did not provide
such a good fit to Swiss data, potentially indicating that either the lifetime in Japan
and Switzerland are significantly different due to different consumer usage patterns, or
that there was a long period of storage between the time the products were considered
obsolete and their physical disposal, or likely a combination of both factors. In every
case, it is important to understand consumer behaviour.
In comparison, data requirements for the reverse diffusion model are very different –
namely that it requires data on outflows, rather than inflows. This simple and
parsimonious model can be particularly useful for established take-back and collection
systems with data over several years. Additionally, its parameters can be updated
every year by fitting to the latest available data, thereby enabling ever more accurate
forecasts for the years ahead. However, a limitation of the reverse diffusion model is
that it needs data for at least a minimum of 3 years, and preferably more, ideally until
the reverse diffusion reaches the mid-way point, to be able to provide forecasts with
greater accuracy. Additionally, it is likely that the collection efficiency of the system
biases the disposal results, as collection data would not reflect the true disposals
especially in the case of any leakages from the system. End-of-life consumer durables
such as TVs and PCs are often shipped from developed countries to developing
countries illegally, thereby are not accounted for in the formal collection system. A
model fitted to only collection data from legal, formal systems risks underestimating
actual disposals.
Disposals of consumer durable products are governed by socio-economic factors that
we are barely beginning to understand. Several authors (Elshkaki, 2004; Oguchi,
2008) have hinted that technological advancement and social acceptability may also
be factors that influence disposal. However, as yet there is little or no research
regarding the timing and fate of end-of-life consumer durables. In a pilot research
exploring the consumer motivations behind disposal of consumer durables, Khetriwal
and First (2011) propose that disposals are dependent on “triggers” and “influencers”.
100
In their study on the disposal of TVs, they found evidence that the price of new
products, new product features and promotions of new products, as well as changes in
the technological landscape trigger product obsolescence. Furthermore, they also
found social, price and technology sensitivity of consumers influencing the effect of
the aforementioned obsolescence triggers. The preliminary results of their research
showed that consumer disposal decisions on why, when, and how to dispose of a
durable product are not as much based on the product life as based on technical
failure, but more so on subjective reasons and consumer perceptions which lead to
discretionary obsolescence of consumer durables.
One of the major drawbacks of both models is that neither incorporates the timevarying nature of consumer behaviour. Anecdotal evidence for PCs and mobile
phones has shown that average lifetime of these products has reduced over time, with
more frequent replacements and disposals taking place.
Another drawback in all four models discussed above is that they do not account for
storage time between consumers displacing their old products and disposing them.
Though consumers may replace their old products, they rarely dispose of these
immediately. For policy makers and waste managers, it is essential to bear in mind
that even in saturated markets, with most sales being replacement sales, they may not
find as many products disposed of due to extensive storage periods as well as the
importance of second hand market, especially for some consumer durables.
Incorporating such aspects in a model can help give estimates regarding “hibernating”
stocks, which can be particularly helpful in understanding potential anthropogenic
stocks available for recycling and recovery, especially in the light of material scarcity.
The delay model is well suited to disaggregation into stages such as reuse and storage.
Such a “nested-delay” model has been presented by Widmer et al. (2005) for PC
disposals, albeit using a fixed (dirac) lifetime distribution. Further research on
consumer behaviour will not only be able to provide better parameter estimates for the
delay functions at every stage, but also inform model design in terms of stages an endof-life consumer durable.
For the reverse diffusion model, future research should be aimed at disaggregating
discretionary disposal into various aspects to get better understanding of drivers of
101
disposal. Such insights will be especially relevant given that the large majority of
consumer products are replaced not because they stop functioning, but for reasons
motivated by consumer decisions. Additionally, this would also help overcome
another assumption the model makes – in that all consumers are homogeneous. Given
that several consumer durables are dual-use products, widely used in homes and in
business and commercial environments, it would provide insights into the different
drivers and disposal options preferred by different user groups.
The models presented above do not shed any light on why and how consumers
dispose of their durable goods, especially when they are still functional. Neither model
provides any insight into the factors that influence disposal decisions or the
alternatives to disposal that consumers may consider. This calls for interdisciplinary
behavioural research efforts to understand consumer disposal behaviour which can be
incorporated into forecasting models. Using system dynamics models is one possible
approach in this direction. Hilty et al., (2006b) have previously used system dynamics
modelling in their simulation of the environmental sustainability of information and
communication technologies, which includes a sub-model on waste generated from
electronics. Such models can be expanded to include consumer dynamics, as has been
explored by Ulli-Beer (2006) in her model for solid waste management at the local
level which incorporates consumer recycling behaviour.
Further research into consumer behaviour to get insights into why, when and how
consumers dispose their durable products, will provide useful information that could
lead not only to better, more accurate forecasting models, but also inform consumer
education and awareness programs directed towards improving consumer attitudes
towards disposal of durable products.
102
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Annexes
Annexe 1: CRT Monitor Sales in Switzerland
Year
CRT Monitor Sales [units] FPD Monitor Sales [units]
1983
10,000
1984
18,500
1985
38,000
1986
67,000
1987
110,000
1988
160,000
1989
235,000
1990
274,000
1991
297,000
1992
320,000
1993
377,000
1994
449,000
1995
519,000
1996
538,000
1997
632,000
1998
717,250
1999
618,540
4,020
2000
584,000
13,250
2001
326,800
59,400
2002
124,380
128,800
2003
55,760
210,000
2004
15,780
310,800
2005
8,340
597,800
2006
755,440
2007
695,000
2008
726,000
2009
632,000
2010
564,000
Table 15: CRT and FPD Monitor Sales in Switzerland.
Source: Robert Weiss Consulting
Annexe
107
Annexe 2: CRT and FPD TV Sales in Switzerland
Year
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2009
Sale - CRT TV Sales - FPD
[units]
TVs [units]
439,000
455,000
455,000
458,900
100
467,000
1,000
471,500
3,500
415,000
5,200
373,350
22,300
307,950
65,500
268,000
107,000
174,000
262,500
75,000
414,000
17,500
553,000
10,000
680,000
3,000
747,000
865,000
Table 16: CRT and FPD TV Sales.
Source – SCEA
Annexe
108
Annexe 3: CRT Glass Collection by SWICO Recycling
Year
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
CRT Glass [tonnes]
CRT Monitors
CRT TVs
60
655
836
910
1,522
1,927
2,397
2,840
3,585
896
4,395
1,465
4,804
2,059
5,032
3,354
4,804
3,925
4,633
4,436
3,088
4,279
3,453
6,440
2,375
10,021
2,304
10,937
Table 17: CRT Glass Collection by SWICO.
Source: SWICO Annual Reports/ EMPA
Annexe 4: LCD Monitor Collection by SWICO Recycling
Year
SWICO Collection - LCD
Monitors [units]
2006
79,000
2007
85,283
2008
140,125
2009
312,844
2010
348,759
2011
375,520
Table 18: LCD Monitor Collection by SWICO.
Source: SWICO Annual Reports/ EMPA
Annexe
109
Annexe 5: TV Permits in Switzerland
Year
# TV Permits ['000]
1954
4
1968
1,011
1973
1,627
1987
2,289
1993
2,560
2000
2,650
2005
2,885
2006
2,885
2007
2,928
2008
2,972
Table 19: TV licences issued by Billag.
Source: Billag
Annexe 6: Household TV Ownership in Switzerland
Year
% Households with at
least 1 TV
1990
85.77%
1998
91.72%
2000
92.52%
2001
93.33%
2002
93.60%
2003
94.30%
2004
93.70%
2005
94.20%
Table 20: Household Ownership of TVs.
Source: BfS
Annexe 7: Swiss population of households
Year
# Households ['000]
1960
1,594.0
1970
2,062.4
1980
2,459.3
1990
2,859.8
2000
3,181.6
Table 21: Number of households. Source: BfS
Annexe
110
Deepali Sinha Khetriwal
11, St.Peter’s Court, NW4 2HG,
London, United Kingdom
Academic Background
10/ 2005 –
07/2012
University of St.Gallen, St.Gallen, Switzerland
Doctoral Program in International Management
Dissertation Diffusion, Obsolescence and Disposal of End-of-Life
Consumer Durables: Models for Forecasting Waste Flows
10/ 2002 –
10/ 2004
University of St.Gallen, St.Gallen, Switzerland
Master of International Management
Master thesis: The Management of Electronic Waste: A Comparative
Study on India And Switzerland
08/ 2003 –
12/ 2003
Indiana University, Bloomington, IN, USA
Exchange Semester - Kelly School of Business
07/ 1998 –
05/ 2000
University of Pune, Pune, India
Master of Arts in Economics - Department of Economics, University of
Pune
07/ 1995 –
05/1998
University of Pune, Pune, India
Bachelor of Arts in Economics - Nowrosjee Wadia College, Pune
Publications
Journal Articles
Khetriwal, D.S., (with R. Widmer, R. Kuehr, J. Huisman) (2011). “One WEEE, many
species: Lessons from the European Experience” in Waste Management and Research
in Waste Management and Research., Volume 29, Issue 9, Pages 954-962.
Khetriwal, D.S., (with I. First) (2010) “Exploring the Relationship Between
Environmental Orientation and Brand Value: Is There Fire or Only Smoke?” in
Business Strategy and the Environment, Volume 19, Issue 2, Pages 90-103.
Khetriwal, D.S., (with R. Widmer, P.Kraeuchi) (2009) “Producer Responsibility for
E-Waste Management: Key Issues for Consideration - Learning from the Swiss
Experience” in Journal of Environmental Management, Volume 90, Issue 1, Pages
153 – 165.
Khetriwal, D.S., (with P.Krauechi, M. Schwaninger) (2005) “A comparison of
electronic waste recycling in Switzerland and in India” in Environmental Impact
Assessment Review, Volume 25, Issue 5, Pages 492-504.
Curriculum Vitae
111
Khetriwal, D.S., (with R. Widmer, H.Oswald-Krapf, M. Schnellmann, H. Boeni)
(2005) “Global perspectives on e-waste” in Environmental Impact Assessment Review,
Volume 25, Issue 5, Pages 436-458.
Refereed Conference Papers
Khetriwal, D.S (with R. Widmer, L. Hilty, M. Schwaninger) (2012) “Application of
System Dynamics to Assess Mass Flows of Waste Electrical and Electronic
Equipment (WEEE)” presented at the 30th International Conference of the System
Dynamics Society, July 2012, St.Gallen, Switzerland.
Khetriwal, D.S (with I. First) (2011) “Enabling Closed Resource Loops In
Electronics: Understanding Consumer Disposal Behaviour Using Insights From
Diffusion Models” presented at the 22nd Cromar Congress, October 2011, Pula,
Croatia.
Khetriwal, D.S (2011) “Consumption and Obsolescence: The Consumer Link to
Sustainable Global Electronic Product Chains” presented at the 17th Annual
International Sustainable Development Research Conference, May 2011, New York,
USA.
Khetriwal, D.S (with R. Widmer, R. Kuehr, J. Huisman) (2008) “One WEEE, Many
Species” – Lessons from Europe” presented at ISWA Congress, September 2008,
Singapore.
Khetriwal, D.S “Technological Substitution and its End-of-Life Impact: A Case of
the Television” presented at the Electronics Goes Green 2008+, September 2008,
Berlin, Germany.
Khetriwal, D.S (with I. First) (2007) “The Influence of Environmental Orientation on
Brand Value: a Case of the Electronic & Electrical Equipment Industry presented at
the 2nd IIMA Conference on Research in Marketing, Ahmedabad, India, 2007.
Others
Khetriwal, D.S (with K. Wankhede, S.Sinha) (2007) “Mumbai: Choking on E-Waste
- A study on the status of e-waste in Mumbai” by Toxics Link, New Delhi
Curriculum Vitae
112
Professional Experience
03/ 2009 – United Nations University, Bonn, Germany
Research Associate, London
Ongoing

Conceptual and strategic inputs to capacity building programs
under the aegis of the StEP Initiative

Lead the development of the summer school concept, structure and
programme
09/ 2010 – SOFIES Consulting, Geneva, Switzerland
Ongoing
Associate Consultant, London

Overview of legislative and regulatory institutional setup and
stakeholder analysis for e-waste management in India

Identification of relevant environmental legislation and impact
analysis of compliance requirement on producer

Ongoing tracking and assessment of developments regarding Ewaste legislation and stakeholder actions
01/ 2006 – UNEP (United Nations Environment Programme), Paris, France
Project Consultant, E-waste in India, Mumbai
06/ 2006

Liaised with international & local experts, government officials
and other stakeholders in e-waste area

Identified potential local implementation partners and developed
Terms of Reference
02/ 2005 – EMPA (Swiss Federal Laboratories for Material Testing &
12/ 2008
Research), St.Gallen, Switzerland
Consultant, Mumbai/ London

Knowledge transfer and capacity building through web and
academic publishing

Conducted rapid market assessment studies on e-waste generation
and recycling, especially in Mumbai

Provided support for evidence based policy and supported
development of e-waste related legislation

Initiated and maintained relationships with government, industry
and other stakeholders for assessments, pilot case study, trainings,
factory visits etc.
Professional Qualifications and Memberships


Certified EMS Auditor – IEMA Approved Advanced Environmental
Management
AIEMA – Associate Member Institute of Environmental Management and
Assessment Systems Auditor
Curriculum Vitae
113

Models for Forecasting Waste Flows

Transcription

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