Mathematical Models for Engineering Science
Combining mathematical forecasting with intuitive techniques for better decision
making
R. Siriram
Abstract - Mathematical models are used to forecast
new product sales. Forecasting using mathematical
methods have been criticized by many researchers, as
the forecasts are often not sufficiently accurate to be
applied to business decisions. Forecasting new product
sales may be improved by using intuitive techniques. In
this paper intuitive techniques are applied to
mathematical forecasting models. A growth curve
predication model is developed; in addition a reference
data set is used to validate the outputs, providing
important lessons for managers.
Keywords - Mathematical
techniques, decision making.
1.
forecasting,
intuitive
INTRODUCTION
There are many factors affecting new product growth.
[15] refers to these factors as complementary assets.
Some of these factors include services like marketing,
competitive manufacturing, after sales support, etc.
These factors affect the perception of users and hence
affect product diffusion and growth. For a product to
diffuse the necessary complementary assets supporting
the diffusion needs to be in place. For example [7]
argues cellular phones were a great invention, but its
commercial success depended on the development of
switching software and equipment, service providers,
and forecasts of microwave towers. Only when these
complementary assets were in place could the product
diffuse. The growth of a particular product is affected
by at least two factors a) the perceived characteristics of
the product or innovation (PCI), [12] and b) the user’s
propensity profile i.e. (AC). adopter categories
(innovators, early adopters, early majority, late majority
and laggards) [8]. In this paper a growth curve
predication model is developed taking PCI and AC as
inputs. The results are then compared to a reference
data set of historical growth curves, interesting
comparisons are drawn, assisting managers in improving
forecasts for better decision making.
[17] argues the growth progress follows a regular
pattern, characteristically an S-Curve pattern. He argues
the S-Curve is similar to the product-life cycle i.e. we
observe a slow initial growth, followed by a rapid rise,
which slows down as it approaches asymptotically, an
upper limit set by the technology. Since progress occurs
with human investment, the actual path is one of a
family of such curves (see Fig. 1). Here growth rates can
be slow, medium and fast. [14] say the force driving a
generation of curves is the diffusion of information.
Since information is formed through networks, as firms
collaborate with themselves and other firms, both inside
and outside the firm information gives rise to both tacit
and explicit knowledge.
This tacit and explicit
knowledge about a particular product may influence user
perceptions of a particular product and hence affect
product growth. Researchers like [4] find the degree of
product innovativeness plays an important role in
understanding the benefits of intra-organisational
collaboration during new product development (NPD).
Such collaboration should occur both in and outside the
firm [2]. From these views, it seems that networks and
collaboration are likely to influence growth curves.
Fig.1 possible paths of progress, adapted from [17]
II.
LITERATURE SURVEY
The varied number of complementary assets that are
available and different tendencies in terms of the PCI
and AC makes the growth process in terms of
forecasting complex.
Manuscript received September 28, 2010. R. Siriram is with Dimension Data
Middle East Africa, Bryanston, Johannesburg, South Africa (Phone: +2711 575
6702; fax; +2711 576 6702; e-mail; raj.siriram@mea.dimensiondata.com
ISBN: 978-960-474-252-3
Given this backdrop firms introducing new products are
faced with different paths of progress and these paths
may pose different challenges in terms of predicating
growth. The question is which path do we follow in
new product sales?
The growth process is complex, subject to many supply
and demand influences. [16] question the goal of
forecasting. Is it to find the rate of technological or
market change (a number), to check the availability and
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Mathematical Models for Engineering Science
accuracy of information (an investigation) or to explore
the range of future possibilities (scenario development)?
Other researchers argue forecasting should be enhanced
through exploratory means like brainstorming, expert
opinion, Delphi, scenario planning and relevance trees,
although radically different scenarios may encourage a
wait and see or a big bang approach. Such techniques
may influence growth curves, assisting managers in
improving forecasting capabilities. Understanding could
lead to manipulating growth curves by factors that affect
growth. So a basic growth curve must be explored to
provide a basis for analysis. Much research has gone
into a better understanding of forecasting, [3], [6], [5]
and [10]. While findings vary, the message is for a
deeper understanding of forecasting models and their
associated parameters.
At least the following researchers have attempted to
develop more accurate forecasts by using mathematical
models viz. [10], [18], [20] and [13]. Other researchers
like [12] and [8] have attempted to use more intuitive
techniques to predict the growth of new products.
However, research incorporating both models is lacking.
[9] used the Bass model to forecast the adoption of EBooks. A list of coefficients of innovation and imitation
for various products was tabled so that they could be
used by analogy in the pursuit of estimating coefficients
for the adoption of E-Books. The main problem with
this method of estimating coefficients by analogy is the
method does not incorporate the PCI of the
product/innovation or the AC of the product/innovation.
To this end [12] five factors may allow one to consider
a) PC1 and b) [8] allow the incorporation of AC.
Little work has been done to incorporate mathematical
models like Bass and PCI and AC. In this paper, the PCI
and AC are used in conjunction with the Bass model.
The key benefit of this approach is that determining the
growth curve of an innovation, two important factors are
taken into consideration. The first one is to consider the
attributes of the innovation, the perceived characteristics
of an innovation (PCI) and the second factor is a
consideration of the users of that innovation, called the
adopter categories (AC). The profile of the users is
important in terms of the adoption of an innovation
because it is the user perception which will determine
the growth rate of an innovation. When forecasting new
product growth it is important that the PCI and the ACs
are incorporated into the model. There are several
benefits of using such a model, these benefits are next
discussed.
Firstly, the PCI together with the ACs of the users of the
innovation are considered. Managers can have a better
understanding of the key drivers of the attributes of the
innovation by using PCI and ACs. The growth curve of
ISBN: 978-960-474-252-3
an innovation is determined by considering the PCI and
AC as inputs which give rise to growth curve
predication model. Secondly the model can be used
before actual demand data for the innovation is
available, which means that a rough estimate of the
growth curve for an innovation can be determined (prelaunch).
This model thus provides prospective
information about the growth rate of a particular
innovation. Thirdly, when growth data is available
(post-launch) the model can be validated and future
projections made; or refuted if the recommended growth
curve does not link with the actual data, in which case,
corrective action can be taken to amend the model. The
PCI and AC are next discussed.
A.
Perceived Characteristics of an Innovation
(PCI)
[12] developed a model showing stages of the
innovation-decision process. This process incorporates:
knowledge, persuasion, decision, implementation and
confirmation. This paper focuses on the persuasion
stage. In this stage, [12] says “the individual becomes
more psychologically involved with the innovation;
he/she actively seeks information about the new idea,
what messages he/she receives, and how he/she
interprets the information that is received”. “It is at this
stage that a general perception of the innovation is
developed”. This stage includes attributes like relative
advantage, compatibility, complexity, trialability and
observebility. These attributes is what sets users
perceptions and these perceptions drive product
diffusion.
From research evidence, the perceived characteristics of
an innovation (PCI) have a major role in how a user
adopts an innovation. The five elements of the PCI have
been quantified by developing a scoring model, to
measure the PCI. A product can be classified as having a
certain PCI score. This is accomplished by surveying
user’s opinion (on a specified scale) for each of the five
PCI attributes (relative advantage, compatibility,
complexity, trialability and observebility). These results
are a measure for PCI, which may be used as an
indication of the user’s perception for a particular
product/innovation. The adopter categories (AC) are
next discussed.
B.
Adopter Categories (AC)
People adopt products and these people have adoption
propensities. These propensities are called the adopter
categories (AC). [12] and [8] describe five adopter
categories, namely, innovators, early adopters, early
majority, late majority and laggards. The characteristics
of the adopter categories (AC) determine the propensity
profile (tendency or preference to adopt a product) of
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Mathematical Models for Engineering Science
users who are adopting a product or innovation. Similar
to the PCI a scoring model is developed for the AC.
Similarly, we can have an AC score associated with a
particular user category. This is equivalent to the
personality profile of the users of a product or
innovation.
In our research we develop a 2 x 2 matrix of PCI and
AC’s, the matrix will give an indication of the
relationship between the PCI and the ACs. There will be
a high and a low score for the PCI as well as high and
low score for the AC. Each quadrant will represent a
different growth curve related to the relationship
between the PCI and the AC. The shapes of the
different growth curves are shown in Fig. 2. Each of the
quadrants is next discussed.
been substituted by another product that had a higher
score in terms of the five factors. i.e. another product
was able to meet consumer need.
Quadrant IV: In this case, the early adopters viewed the
product, had initial interest, thereafter interest
diminished before the late adopters could have a chance
to adopt the product. This is a classic case of a product
which failed to gain interest from early adopters. This
product scored low on five factors. Here again, the
product may have been substituted by another product
providing the same need i.e. having a higher five factors
score. In this case, the product was substituted before it
could reach the late adopters.
III.
RESEARCH METHODOLOGY
Using the PCI and AC scores obtained through survey
analysis a “Growth Curve Prediction Model” is
developed. Fig. 3 gives a graphical representation of
how the model works. The growth curve predication is
obtained from the 2x2 matrix shown in Fig. 2. Once the
inputs to the model are used to select the growth curve,
the growth curve is linked to a reference data set, Fig. 4
and Fig. 5. Using Fig. 4 and Fig. 5 the coefficients for
innovation and imitation may be selected from a
historical data set. There are two inputs to the model the
PCI and AC scores, and the outputs from the model, are
the shape of the growth curve and the associated
coefficients for imitation and adoption.
Fig.2 shapes of growth curves
Quadrant I: Products in this quadrant satisfy most of the
five factors, they have a high AC score. They are also
have a high PCI score and are accepted by a high
number of early adopters, who help to push the adoption
rate to be steep. By the time the late adopters catch up,
the product has diffused into the society. However, the
late adopters help to prolong the lifetime of the product.
The PCI and AC scores are generated by having a group
of target user’s fill-out survey questionnaires the
questions address users’ PCI and ACs. The aggregation
of the data gives the relevant PCI and AC scores. The
selection of the user group is extremely important, in
appendix D, an example is given on how two different
user groups yield two different growth curves.
Therefore is important that careful attention is given to
the selection of the user groups.
Quadrant II: Products in this quadrant also satisfy most
of the five factors, they have a high PCI score. However,
even though they are, by definition, rapidly accepted by
the early adopters, these adopters are fewer, therefore a
low AC score. It is the late adopters who help to push up
the adoption rate.
Quadrant III: In this quadrant, because of the low AC
score for the five factors, this product takes a while to be
adopted by the early adopters, as well as by the late
adopters. After takeoff, the product stability in the
market is quickly reduced. The fact that the five factors
score is also low, may indicate the product may have
ISBN: 978-960-474-252-3
Fig. 3 growth curve predication model
Furthermore adequate statistical analysis needs to be
performed in order to ensure the user groups are a
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Mathematical Models for Engineering Science
Coeff. of Innovation (p)
I
The reference data set is made up of two data sets for
consumable products and the electronics, electrical and
IT industries. In the appendixes only the results for
consumer products are given. Appendix A, B, C and D
show, the survey results, how the boundaries for the AC
may be determined, how the boundaries for the PCI may
be determined and how the shape of the growth curves
may be determined respectively.
The parameters
(coefficients of innovation and imitation) for the Bass
growth model have been generated from historically
available data, a) [19] for consumable products and b)
[13] for electronics, electrical and IT products. The data
set by [19] and [13] are treated separately as they belong
to two separate industry categories.
The data sets are grouped into four groups, as per the
four quadrants in Fig. 2. It is namely the high and low
values for the coefficient of innovation and high and low
values for the coefficient of imitation. The output is a 2
x 2 matrix, with one axis being the coefficient of
innovation and the other axis being the coefficient of
imitation, this results are shown in Fig. 4, consumable
products and Fig. 5, electronics and electrical and IT
products respectively.
The reference model could be made up of data for
different growth curves e.g. Logistic, Gompertz or any
other curve of interest. In this paper the Bass curve is
used. The output of the model is a growth curve and its
corresponding parameters. (Comment: the market size is
not an output by the model. The researcher will have to
obtain an estimate of that information by other means.)
In the case where the reference model is made up of
other growth curve models, for example, the Logistic or
Gompertz models, the output will include the
corresponding parameter for each model. For example,
for the Logistic model, the parameters are b and k, and
for the Gompertz model, the parameters will be a, k. The
upper limit (L) of each curve must be estimated
somewhere elsewhere.
The goal of the research was to incorporate more
intuitive thinking into mathematical forecasting
techniques.
ISBN: 978-960-474-252-3
III
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Having selected a growth curve from the growth curve
predication model, the next step is to select the
coefficient of innovation and imitation from reference
data set of coefficients. The reference data sets are
discussed next.
Reference Chart (Bass Model)
Products
p
q
Fig. 4 reference data set consumable products
Fig. 5 reference matrix electronics, electrical & IT
IV.
RESEARCH RESULTS
Firstly a growth curve was generated using a growth
curve predication model; this was obtained by selecting
the quadrant into which the respective product fell into.
Viz,:
Quadrant I – high coefficient of innovation and high
coefficient of imitation.
Quadrant II – low coefficient of innovation and high
coefficient of imitation.
Quadrant III – low coefficient of innovation and low
coefficient of imitation.
Quadrant IV – high coefficient of innovation and low
coefficient of imitation
Secondly the curve was validated against a set of
reference data, which was compiled from historical data
for consumable products as well as the electronics &
electrical and IT products.
Using the data sets
coefficients innovation and imitation could be obtained.
116
Coeff. of Imitation (q)
correct representation of the users and the necessary
tests for bias, validity and reliability are conducted.
Based on these inputs, a growth curve is selected from a
2 x 2 matrix. The growth curve can be used to predict
the growth of a particular product, Fig. 3.
Mathematical Models for Engineering Science
In order to ensure adequate sample representation three
user categories were used Group I, Group II and Group
III. The data was aggregated to ensure normalization.
The aggregate data refers to the aggregated data
calculated from the three groups. A comparison of the
growth curve predication model and the Bass model is
shown in Table 1.
TABLE 1
COMPARISON OF THE GROWTH CURVE PREDICATION MODEL AND
THE BASS MODEL
model as a reference) other factors could have
contributed to the differences. Factors that may have
contributed to the variance may include: a) other
mathematical models may provide better results, b)
inadequate user group representation and c) marketing
factors. In terms of a) more research needs to be done on
using other forecasting models as a basis, in terms of b)
more rigor needs to be emphasized in user group
selection and more robust statistical techniques need to
be incorporated into the model, in terms of c) marketing
factors need to be further investigated. A more detail
explanation of the marketing factors are next discussed.
i.
Price
Price plays a major role in the decisions that users make
regarding purchasing a product. New technologies
usually start out being expensive and most users cannot
afford these products. Consequently, the rate of adoption
is slow. When the price drops products become more
affordable.
ii.
Performance
Usually the performance of new products is inferior to
existing products. Combined with high prices, there is
little justification for purchasing such products; hence
the adoption rate is low. As the performance improves,
users are more attracted to the new product and should
the product meet user’s needs, users may be willing to
pay a higher price. However, the combination of higher
price and lower performance propels products to much
higher adoption requirements.
Usually the performance of new innovations is inferior.
In most cases, only the early adopters embrace the
innovation, because late adopters cannot deal with the
accompanying problems related to new products. As the
performance of the product improves and it becomes
more stable and reliable, the late adopters start
embracing the so called newer products. The extension
of the Bass model to include price and advertising is
next discussed.
iii.
From the above results, the growth curve prediction
model could predict a quadrant that an innovation
belongs to in eight out of 14 times. In other words in
eight out of 14 times an accurate growth curve with
associated coefficients for innovation and imitation
could be predicted.
In the cases where the prediction model could not
predict the correct quadrant (when compared to the Bass
ISBN: 978-960-474-252-3
Extension Of The Bass Model To Include Price
And Advertising
Further research has been done in order to address the
marketing factors. In the article “Why the Bass Model
Fits without Decision Variables”, [1] extended the Bass
Model to incorporate price and advertising. The model is
referred to as the Generalized Bass Model (GBM),
which reduces the Bass Model as a special case. They
claim that “with price, advertising and other marketing
variables the curve is shifted with different policies
(price, advertising policies), but the shape remains the
same”. The generalized Bass model could be utilized to
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Mathematical Models for Engineering Science
VI.
investigate different coefficients for innovation and
imitation.
A.
V.
CONCLUSION
Using the growth curve predication model we were able
to predict the growth curves in eight out of 14 cases
using the Bass model. Further research is required to
consider at least the following:
AC - Hi
AC - Lo
PCI -Hi
PCI - Lo
Average PCI
Aggregate
AC - Hi13.46
AC - Lo 3.17
PCI -Hi19.10
PCI - Lo11.39
Average PCI
16.67
APPENDIX
TABLE 2
SURVEY RESULTS
Group
Aggregate
1
Group 2GroupGroup
1 3GroupAggregate
2
Group 3 Group 1
8.29
13.46 AC
8.93
- Hi 8.29 9.30 8.93 13.46 9.30
8.29
2.713.17 AC
2.07
- Lo 2.71 1.70 2.07 3.17 1.70
2.71
18.00
19.10 PCI
19.57
-Hi 18.0019.45 19.57 19.10 19.45
18.00
13.14
11.39 PCI
13.07
- Lo 13.1412.35 13.07 11.39 12.35
13.14
15.88
16.67 Average
16.66PCI
15.8816.95 16.66 16.67 16.95
15.88
Grou
8.93
2.07
19.5
13.0
16.6
i.
Other mathematical models like logistics, GBM
or any other mathematical technique.
ii.
More rigor and research into the selection of
the target user groups required for selecting the
target user groups.
Air Conditioner
17.80
Air
17.71
Conditioner
17.80
17.00 17.71 18.40 17.00 17.80 18.40
17.71
17.0
iii.
Investigating the linkage to marketing factors
Cable TV
other than those in the GBM.
Calculators
Cable TV
17.46
Cable
15.71
17.46
TV
15.86 15.71 19.20 15.86 17.46 19.20
15.71
15.8
Calculators
19.10
Calculators
17.29
19.10
19.57 17.29 19.40 19.57 19.10 19.40
17.29
19.5
iv.
CD be
Player
More post implementation analysis needs to
conducted to verify test results
Cell Phone
CD Player
18.34
CD
15.86
Player
18.34
19.50 15.86 18.40 19.50 18.34 18.40
15.86
19.5
Cell Phone
18.68
Cell
16.57
18.68
Phone
18.64 16.57 19.45 18.64 18.68 19.45
16.57
18.6
Dishwasher
15.14
16.37
16.93 15.14 16.40 16.93 16.37 16.40
15.14
16.9
Home
18.00
17.98
PC
16.71 18.00 18.85 16.71 17.98 18.85
18.00
16.7
Microwave
16.29
16.71 Oven
16.00 16.29 17.35 16.00 16.71 17.35
16.29
16.0
Radio
17.43
17.24
17.50 17.43 17.00 17.50 17.24 17.00
17.43
17.5
Satellite
14.43
15.39Radio 14.64 14.43 16.25 14.64 15.39 16.25
14.43
14.6
Telephone
16.00
17.05 Answering
17.71 16.00
Device16.95 17.71 17.05 16.95
16.00
17.7
Video
13.29
14.85
Cassette15.36
Recorder
13.29 15.05 15.36 14.85 15.05
13.29
15.3
7 41
41
Product
Air Conditioner
Aggregate
Product
PCI Score
Dishwasher
16.37
In addition a larger repository of data needs toDishwasher
be
Home
Home PC
17.98
created in order to develop a data base, which could
bePC
more representative and in so doing be used to improve
Microwave Oven Microwave Oven 16.71
forecasting techniques. Much research has been done
Radioin
Radio
17.24
forecasting however this paper makes a contribution
to
Satellite Radio
Satellite Radio
15.39
knowledge in terms of combining mathematical and
Telephone AnsweringTelephone
Device Answering17.05
Device
intuitive techniques and opens up interesting avenues for
Video Cassette Recorder
Video Cassette Recorder
14.85
further research.
Clothes Dryer
Clothes Dryer
Aggregate
Ave PCI
PCI Score
14
7
20
14
20
41
Aggregate
Ave
Product
PCIAve PCI
Ave PCIAve PCI
Ave PCI Ave PCI
PCI Score
14
Ave P
11.39
Clothes
13.00
11.39Dryer 11.71 13.00 10.60 11.71 11.39 10.60
13.00
11.7
Black & White TV Black & White TV
18.93
Black
18.00
18.93
& White 18.21
TV 18.00 19.75 18.21 18.93 19.75
18.00
18.2
Colour TV
Colour TV
17.10
Colour
16.43
17.10
TV
16.64 16.43 17.65 16.64 17.10 17.65
16.43
16.6
Freezer
Freezer
17.05
Freezer
16.14
17.05
17.64 16.14 16.95 17.64 17.05 16.95
16.14
17.6
Office PC
Office PC
18.41
Office
17.71
18.41
PC
18.29 17.71 18.75 18.29 18.41 18.75
17.71
18.2
Refridgerator
Refridgerator
17.66
Refridgerator
16.14
17.66
18.07 16.14 17.90 18.07 17.66 17.90
16.14
18.0
Room Air ConditionerRoom Air Conditioner15.85
Room
14.86
15.85
Air Conditioner
15.64 14.86 16.35 15.64 15.85 16.35
14.86
15.6
Tractors
Tractors
13.90
Tractors
14.29
13.90
15.21 14.29 12.85 15.21 13.90 12.85
14.29
15.2
Ultrasound
Ultrasound
12.73
Ultrasound
13.14
12.73
13.07 13.14 12.35 13.07 12.73 12.35
13.14
13.0
B. Determine the boundaries for the Adopter
Category (AC)
That is, the AC High and Low boundaries
Using the aggregated respondents from survey data
The Range is:
([Highest “Yes” scores] - [Lowest “Yes” scores])
divided by 2
= (9.30 – 8.29)/2 = 0.51
The Midpoint is:
Lowest “Yes” scores + Range
= 8.29 + 0.51 = 8.80
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Mathematical Models for Engineering Science
Therefore: AC Low is defined as [Lowest “Yes” scores]
to Midpoint = 8.29 to 8.80
AC High is defined as Midpoint to [Highest “Yes”
scores] = 8.80 to 9.30
C. Determine the boundaries for the Perceived
Characteristics of an Innovation (PCI)
High and Low boundaries
Using the aggregated respondents from survey data
The Range is:
([Highest PCI Score] - [Lowest PCI Score]) divided by 2
= (19.10 – 11.39)/2 = 3.86
The Midpoint is:
Lowest PCI Score + Range
= 11.39 + 3.86 = 15.25
Therefore: PCI Low is defined as the Lowest PCI Score
to the Midpoint = 11.39 to 15.25
Therefore according to this user group, the cell phone
product could be predicted to grow according the shape
shown in quadrant II, Fig. 6. The next step is to look at
the reference matrix, which will give us the coefficients
of the Bass curve so that we can use these to predict the
future growth of the cell phone product.
Considering a different user group for the same cell
phone product, the results might be different. Taking the
third user groups, the average AC score is 9.30. The
average PCI score for the cell phone product as scored
by this group is 19.45
Mapping this information (AC = 9.30, PCI = 19.45) on
the selection matrix will give us a different growth
curve, Fig. 6. For this user group, the growth of the cell
phone would be expected to be steep (Quadrant I).
The growth curve prediction model could predict a
quadrant that an innovation belongs to (most of the
time). The quadrant specifies the shape of the growth
curve to be used for that innovation.
PCI High is defined as Midpoint to the Highest PCI
Score = 15.25 to 19.10
D. Determine the Shape of the Growth Curve for a
Target Product
Let us say we want to determine the shape of the growth
curve for the cell phone product. We will choose one
user group, say group one. The average AC score for
this group is 8.29. The average PCI score for the cell
phone product as scored by this group is 16.57
Fig. 7 growth rate for cell phone user’s group 3
It is therefore important that the user selection process
be correctly structured with adequate statistically rigor
and the data adequately normalized.
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Fig. 6 growth rate for cell phone user’s group 1
From the above information, the Cell Phone product
would lie in the second quadrant as indicated in the chart
below:
ISBN: 978-960-474-252-3
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ACKNOWLEDGEMENTS
[1] Malinable, M. D for preliminary work on obtaining
the PCI and AC scores for the consumable products
[2] Young, P. for supplying data sets for consumable
products.
R Siriram became a member (M) of IIE in 1995 and a senior
member (SM) in 2001. He has a PHD in Industrial
Engineering, University of Witwatersrand, School of
Mechanical Industrial and Aeronautical Engineering
Johannesburg, South Africa, 2004. The main field of study
was in the management of technology.
He is also a sessional lecturer at the University of
Witwatersrand in the School of Mechanical Industrial and
Aeronautical Engineering
He held previous positions as MD at Siemens Ltd SA. He is
currently Chief Information Officer at Dimension Data MEA.
He has published previously in Technovation as well as the
South African Journal of Industrial Engineering. He has also
presented at the IIE, SAIIE and IEEM conferences both locally
and internationally.
He is also a member of the technical program committee of
IEEM Singapore Chapter and has also appeared in Who’s Who
in the World 2009.
Dr. Siriram is a member of ECSA, ASQ, IPET, IOD and
SAIIE.
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technology and innovation, Mc Graw Hill, 1996, pp. 32 -48.
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