Effect of repeat purchase and dynamic market size on diffusion of an innovative technological consumer product in a segmented market.
Aggarwal, Sugandha ; Gupta, Anshu ; Govindan, Kannan 等
Introduction
Research background
New product development is the locus of innovative potential of an
organization. The competitive success of a firm depends largely on its
capability to develop new products. Driven by the globalization of
markets, technological advances and ever changing customer needs;
continuous innovation and development of an ecosystem of whole range of
new products has become a vital part of an organization's business
practices (Schimmoeller 2010). The rate of technological changes has
largely accelerated the development of new product innovations based on
newer technologies and shortened the product life cycles in the last two
decades (Ismail et al. 2012). Organization dedicate huge amount of
human, material, technological and monetary resources on the development
of new products. Yet the new products continue to fail at an alarming
rate due to many reasons. The biggest problem identified behind the huge
new product failures is the lack of timely and adequate analysis and
preparedness to market the products (Schneider, Hall 2011). With the
quest for successful product introductions, organizations constantly
look for the methods and techniques for innovation, new product
development and marketing.
Innovation, new product development and their successful marketing
is a widely studied area in the literature. The academic and business
periodical literature is replete with detailed research on the various
aspects of this process. Some of the widely studied aspects in this area
include studies related to the market research on the requirement and
acceptance of new products in markets (Sawng et al. 2011; Foulquie et
al. 2004), consumer behaviour and new product development (Tolba, Mourad
2011; Sawng et al. 2011; Renko, Janakiraman 2008), innovation,
technologies and new product development (Kock et al. 2011; Shane et al.
2004; Kim et al. 2011), market performance (Schimmoeller 2010; Ismail et
al. 2012; Schneider, Hall 2011; Jayaram, Narasimhan 2007), marketing
products (Ozer, Cebeci 2010), product life cycle, and time factors (Jha
et al. 2006; Aggarwal et al. 2012; Bayus et al. 1997, Calantone,
Benedetto 2000), successive generations of technological products
(Danaher et al. 2001; Foulquie et al. 2004) and many more. The
requirement of closely analysing the market performance of new products,
that how the product acceptability grows in the potential market over
their product life cycle is a research area which has grown tremendously
(Meade, Islam 2006) and is continuously growing due to ever changing
markets, marketing paradigms and consumer empowerment. This study
concentrates on this particular aspect of new product development and
proposes new mathematical models for predicting and analysing the
adoption growth of a technological consumer product. The proposed models
are applicable for describing the adoption behaviour of technological
consumer products with respect to joint effect of mass and
differentiated market promotion in a segmented market over the product
life cycle considering two different marketing scenarios. First scenario
describes the adoption under the possibilities of repeat adoption
behaviour while second scenario analyses dynamic nature of market
potential over time. The marketing environments under consideration have
been looked for the first time in such a study to the best of our
knowledge.
The theory of diffusion of innovation has developed across many
fields of research over the past several decades (Rogers 1983). While
the study of diffusion originated in sociology and anthropology,
marketing and consumer behaviour theorists have adopted the general
paradigm for use in their fields to explain new product acceptability
and diffusion over time. One of the important factors which make a new
product successful in the market is building an understanding about how
an innovation diffuses (diffusion process) within its target population
and measuring it over its life cycle. A diffusion model describes the
adoption characteristics, explains the mechanism, and assists in
predicting how a new product will diffuse in market. Selection of an
appropriate diffusion model to determine the diffusion pattern and main
factors influencing the rate and timing of a successful adoption of
innovation is vital to business firms for developing optimal marketing
strategies that help them increase the competitiveness of product and
the firm itself. In spite of several innovation diffusion models
developed in the literature over the past several decades, no model can
be called as general, which could be used for any product and in any
marketing environment. The main reason for this fact is the ever
changing and growing marketing environment. The changing marketing
environment necessitates development of the new innovation diffusion
models that can well describe the adoption behaviour for the recent and
future marketing environments. The diffusion models proposed in this
study have been developed for a marketing environment faced by many of
today's business organizations and has been tested on real life
situation.
Most of the earlier literature on the diffusion of technological
consumer products describes the growth of product considering the market
as a whole. The product diffusion is captured either with respect to
time, or promotional efforts assuming that all consumers are alike and
product is marketed with a common promotional strategy. These models
describe the external influence due to mass media and internal influence
due to word of mouth. In current marketing scenario the market of the
product is often segmented based on differential profile of the
consumers so as to better position the product in the market.
Segmentation allows firms to target the product specifically to the
different consumer groups by adopting promotional strategies keeping in
mind the differential characteristic of the segments. Diffusion model
which ignores the effect of segmentation on the adoption growth are not
applicable to estimate and predict the adoption behaviour when the
market observes a differentiated external influence due to segmented
promotional strategies; as the results obtained using them can be very
far from the reality. Diffusion of innovation in segmented market is a
research area explored very limitedly in the literature. We propose here
some diffusion models in this area by extending the work done due to Jha
et al. (2014). The models are developed considering a marketing
environment, which is different from the previous study, and are
applicable to wider marketing situations. More discussion on this is
carried in the later sections after the literature review.
Literature review
Main focus of the diffusion models in marketing is on communication
channels by which the information about an innovation is transmitted in
passage of time to the social systems, considering two distinct
influences--internal influence resulting from word-of-mouth
communication and external influence represented by the mass media
(Mahajan et al. 1990). The literature on new product diffusion growth
modelling is large-spread. While the preliminary studies focused mainly
on modelling the adoption process with respect to communication channels
and found successful implementation in the real life cases (Bass 1969;
Easingwood et al. 1983; Horsky, Simon 1983). Later, as the marketing
paradigms and environment changed, the researches in the field studied
the diverse and changing aspects of the process. The studies attempted
to offer generalizations concerning models and incorporate decision
variables and their effects on diffusion patterns (Mahajan et al. 2000;
Meade, Islam 2006; Hauser et al. 2006; Chandrasekaran, Tellis 2007;
Krishnan, Suman 2009; Renana et al. 2010). Earlier studies developed
models which addressed either pure external influence or internal
influence. Bass (1969) model was the mixed influence model and was
widely accepted due to its flexible nature and ability to describe both
pure external and internal influence situations. The model categorized
the adopter population into two groups: innovators and imitators
respectively. Innovators population adopt through external influences,
whereas imitators adoption is influenced by the innovators opinion.
Succeedingly several studies focus on the development of mixed influence
innovation diffusion models under diverse marketing environment and
assumptions (Horsky, Simon 1983, 1990; Jain, Rao 1990; Jain 1990; Jones,
Ritz 1991; Kalish 1985; Mahajan, Peterson 1978, 1985). Some models
attempted to combine the effects with traditional economic variables
such as price and advertising in the diffusion modelling (Russell 1980).
Bass along with other researchers (Bass et al. 1994) developed a
Generalized Bass Model (GBM) to describe the adoption growth with
respect to current marketing efforts. Various other factors such as
diffusion channels (Jones, Ritz 1991; Rangaswamy, Gupta 2000),
competition (Kauffman, Techatassanasoontorn 2005; Van den Bulte,
Stremersch 2004), technology update (Bass, P., Bass, F. M. 2004; Kim et
al. 2000), repeat purchase (Steffens 2002), indirect network externality
(Gupta et al. 1999) were also added to Bass model for its improvement
and expansion. Consumers' different preferences on price (Bridges
et al. 1995), risk (Chatterjee, Eliashberg 1990), brand (Libai et al.
2009), etc. affecting diffusion of products were also studied.
Some scholars compared the new product diffusion caused by
technological update to innovation diffusion in single technology, they
considered that diffusion of technology updates can increase market
potential and reflect the impact of consumer heterogeneity (Goldenberg,
Oreg 2007; Mahajan, Muller 1996). Early studies only focused on word of
mouth, that is, communication between consumers, but exchanges between
consumers are also affected by its host network which was done through
the study of network externalities (Stremersch et al. 2001), network
information (Van den Bulte, Stremersch 2004), and network structure
(Kossinets, Watts 2006). Some research also considers the spatial
diffusion of innovation and not just diffusion over time. For example,
there is a research about cross product diffusion in different cultural
resources (Redmond 1994) or different economic resources (Desiraju et
al. 2004). Steffens (1998) investigated cross-country heterogeneity and
studied the intra-country variations using priori segmentation schemes,
namely geographic segmentation. Bohlmann et al. (2010) examined the
effects of various network structures and relational heterogeneity on
innovation diffusion within market networks.
Research motivation
Promotion is a very crucial component of the marketing mix that
attracts attention, stirs up interest, creates desire, assures belief,
and impels action; action to buy the product. Since promotion is a
dominant marketing mix variable, the effects of other marketing mix
variables can be assumed at a constant level. The pioneering model of
innovation diffusion, due to Bass (1969) and various later models,
describes the adoption growth with respect to time. Firms are rather
interested to capture the adoption growth with respect to promotional
efforts carried to market the product. Innovation diffusion models given
by Jha et al. (2006) describe the adoption behaviour focusing on the
internal and external influences with respect to promotional efforts
under different market environments. The model retained the mathematical
nature of the Bass model due to the property that it has a flexible form
and can describe different types of adoption growth curves but
simultaneously generalized the model by eliminating some of its limiting
assumptions (restricted to apply in the situation of only first time
purchase and constant market size). However, due to growing economies,
national as well as global markets and growing heterogeneity of consumer
groups, these models find limited application and are not suitable to
reflect the appropriate adoption behaviour when the product is marketed
in a segmented market. Market segmentation is an important marketing
strategy followed by most of the marketers of new products. Consumer is
the most powerful entity in the present market, segmentation of market
allows firms to serve its customers keeping in mind their differential
characteristics. By segmenting the market while marketing a product, the
product is positioned differentially in each segment so as to influence
each segment differently, according to the segment characteristics and
thereby generating higher product growth. As stated earlier, models of
innovation diffusion besides marketing variables focus mainly on the
communication channels, and the communication channel influences are
extremely different in case of segmented market as compared to the mass
market. The models due to Bass (Bass 1969; Bass et al. 1994) and its
generalizations considered the market as a whole and describe sales
growth considering the external influence due to mass media and internal
influence due to word of mouth. These models are not applicable
effectively to estimate and predict the adoption behaviour when the
market observes a differentiated external influence due to segmented
promotional strategies.
Different consumer segments have different behaviour towards the
new product and they respond distinctly for the promotional activities,
therefore, the rate of adoption vary across segments. Thus, it becomes
important to study how the new product diffuses in different market
segments under the effect of segmented promotional efforts. A segmented
market often observes two different forms of promotion viz. mass
promotion and differentiated promotion. Mass promotion addresses the
whole potential market assuming all customers alike. The mass promotion
strategy is implemented using the promotional vehicles for wider
awareness such as national television. Mass promotion targets larger
audiences in all segments of the market and creates a spectrum effect in
the market leading to wider product awareness and increased market
potential (Burrato et al. 2006). Differentiated promotion is carried out
by targeting individual segments through distinct promotional
strategies. Here, promotional planning is tailored according to the
consumer characteristics and promotional vehicle preferences for each
segment (Berry, Wilson 2001; Rao 2011; Egan 2007). Both forms of
promotions have their unique importance, the mass promotion along with
influencing diffusion, focuses on creating product awareness in a larger
market and influencing the total market potential size over time. On the
other hand, differentiated market promotion targets the respective
segments market potential towards adoption.
One of the recent studies Jha et al. (2014) caters to this
particular marketing environment with some major limitations. An
innovation diffusion model is developed by the authors for technological
consumer product assuming that the product diffuses in each segment due
to the combined influence of mass promotion and differentiated promotion
along with the internal influence factors. Although the model describes
the adoption growth with respect to the differential promotional effort
in segments along with mass promotion, but the model applicability is
constrained due to the assumptions that it captures only the first time
purchases and assumes that the eventual market potential is constant
(remains same throughout the product life cycle). However, in real
marketing scenario repeat purchasing is an important phenomenon and
can't be ignored. Traditionally, it is coined as one of the five
phases (last) of product adoption viz. awareness, interest evaluation,
trial, and adoption (Rogers 1983). The adoption phase incorporates
consumers' adoptability towards the product and his/ her propensity
to repurchase the product. Along with this market potential of a product
as determined in the initial phase of product launch doesn't remain
constant but grows as the product diffuses in the market due to various
factors such as widespread awareness of the product, increase in
purchasing power of the consumers, population growth and economic
reasons. Using an innovation diffusion model developed with these
restricted assumptions to predict the product adoption can provide
underestimated results and mayn't provide appropriate insight into
the product diffusion process. Decisions made using these results may
divert the firms from reality. It necessitates the development of
diffusion model which not only describes the adoption growth in the
segmented marketed under differentiated and mass promotion strategy, but
also associates the repeat purchase behaviour and dynamic nature of
market potential in the model. In this paper two generalized new
innovation diffusion models are proposed, by dropping the assumption of
only first time purchases and constant market size and developing
mathematical relationships to incorporate repeat purchase and dynamic
market size under the joint impact of differentiated promotion and
spectrum effect of mass promotion. The proposed models are applicable
for a wider marketing environment as compared to the previous study.
Distinguished features of the study
--The proposed models are developed for a marketing environment
which has been explored very rarely in the literature of the very
important study area of innovation diffusion in marketing.
--The model finds application for analysing how a new product
diffuses in a segmented market which observes two different forms of
promotion viz., mass and differentiated promotion. The impact of
external influence on adoption is captured under the joint influence of
both types of promotions.
--Earlier model in this category considered constant market size
throughout the planning period and only first time sales for describing
the adoption growth, which can give underestimated growth curves. The
proposed model first time analyses, the dynamic size of market potential
and repeat purchase behaviour in a segmented market.
--The model apart from the other known applications of diffusion
modelling in marketing such as promotion allocation, adopter
categorization, timing of new product introductions, etc. also finds
application for many other marketing decision making such as segment
wise effectiveness of mass and differentiated promotion, deciding on the
optimal resource distribution for mass and differentiated promotion,
segment wise market potential growth and repeat purchase parameters.
--The model is tested in a real life case.
The paper is organized as follows. Section 1 describes the
mathematical development of the proposed models. Section 2 presents the
validity of the model for a real marketing case and shows the estimation
of parameters for proposed models with results and discussion. The final
section concludes the paper.
1. Model development
Notations:
i Segment index; i=1,2,...K
[bar.N], [[bar.N].sub.i](t) Expected potential adopter population
in the ith segment of the market (at time t)
[p.sub.i] Parameter representing external influence in ith segment
[q.sub.i] Parameter representing internal influence in ith segment
[b.sub.i] Sum of coefficients of external influence and internal
influence in ith segment; ([b.sub.i] = [p.sub.i] + [q.sub.i])
[[beta].sub.i] Ratio of coefficient of internal influence to
external influence in ith segment; ([[beta].sub.i] = [q.sub.i] /
[p.sub.i])
[x.sub.i](t) Rate of promotional effort at time t in the ith
segment of the market; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII]
[X.sub.i] Promotional resources allocated for differentiated market
promotion in ith segment
X Promotional resources allocated for mass market promotion
Z Total promotional budget available
[N.sub.i](t) Expected number of adopters of the product in the ith
segment of the market by time t.
The proposed model uses basic mathematical structure of Jha et al.
(2014) sales growth model considering its flexible mathematical form and
applicability. The model describes external as well as internal
influence so that its mathematical structure becomes even more useful
for us to use it as a basic building block for the development of our
models.
Model assumptions:
1. The adoption process is binary.
2. The market can be segmented into k distinct segments.
3. Each purchaser buys a single unit of the product.
4. The size of the potential adopter population remains constant
throughout of the product life cycle as determined in the beginning of
the adoption process.
5. The adoption process grows over time due to both external and
internal influences.
6. The parameters of external and internal influences are fixed
over the diffusion process of the innovation.
7. The rate of adoption at any time t with respect to promotional
efforts is proportional to the remaining number of adopters in the
segment.
8. The adoption is influenced both due to mass and differentiated
promotional efforts. The differential equation of the Jha et al. (2014)
model for the ith segment is given as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)
Under the initial conditions [N.sub.i](t) = 0, [X.sub.i](t) = 0,
X(t) = 0 at t = 0 the model is described by the following equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
Equation (1) can be written alternately by changing the
mathematical form of the rate of adoption per remaining adopters denoted
by b(t) given as:
b(t) = b/(1 + [beta][e.sup.-bt]). (3)
The diffusion model (1) can be derived alternatively as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)
which can be solved under same initial conditions to give the form:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)
Sibstituting [[beta].sub.i] = [q.sub.i] / [p.sub.i] and [b.sub.i] =
[p.sub.i] + [q.sub.i] it can be observed that the Equation (5) is
identical to model (2). The alternative derivation (4) is necessary for
the development of the proposed model. Model generalization based on the
Equation (2) can't be solved for exact solution. However if the
model is derived using the differential Equation (4), exact solution can
be obtained for the proposed model maintaining the basic structure and
assumptions of the model (2).
1.1. Repeat purchase model
In this section, we develop a diffusion model for describing the
diffusion of a new technological consumer product due to both external
and internal influences in a segmented market considering repeat
purchase with respect to the joint effect of mass and differentiated
promotion. Repeat purchasing is an important real life phenomenon; the
existing adopters often repurchase the same product. Thus the increase
in sales of the product may not be alone through first purchase but it
also includes some proportion of repeat purchasers which a firm might
always be interested in knowing. Thus, here we relax the assumption that
each purchaser buys only a single unit of the product and generalize the
model (5) for the case when some adopters of the product adopt more than
one unit of the product.
The additional assumptions of the proposed repeat purchase model
excluding the assumption (3) above are:
1. The successive increase in the number of adopters may consist of
first time buyers as well as repeat buyers of an innovation.
2. At any given instant of time t, [g.sub.i](0 < [g.sub.1] <
1) proportion of total adoption is susceptible to repeat purchasing in
each segment.
3. Repeat purchasing is influenced by all factors (both internal
and external) affecting first purchase.
The differential equation for the rate of adoption of the product
in ith segment considering repeat purchase with respect to the
promotional effort (mass and differentiated) is formulated as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)
where: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The expected number of adopters in the interval (0, t] in the ith
egment after solving (6) under the initial conditions [N.sub.i](t) = 0,
[X.sub.i](t) = 0, X(t) = 0 at t = 0 is obtained as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (M1)
The model M1 can be used to illustrate the adoption growth in the
ith segment of the potential market.
1.2. Dynamic market potential model
This section shows the development of the diffusion model for a new
technological consumer product due to both external and internal
influences in a segmented market considering the dynamic nature of the
market potential for every segment with respect to the joint effect of
mass and differentiated promotion. It is an important point to note here
that the promotional activities not only influence the adoption
behaviour of the potential consumers, but also influence the size of the
market potential over time. In the beginning of the product life cycle,
i.e. at the time of introduction of the product, the estimated size of
the potential adopter population can be less, either due to unawareness
or poor estimation due to unavailability of actual adoption data. As the
product reaches the market, it is expected that with rise in product
awareness, promotion and internal influences a larger potential consumer
group will be created. Many other factors plays role here in influencing
the size of the market potential such as increase in the purchasing
power of the consumer. Assumption (4) of the Jha et al. (2014) model may
result in giving an underestimated diffusion of the product. Thus, it is
very important for a diffusion model to allow the market size to change
with time. Therefore, we drop the assumption (4) above and develop the
differential equation for the model under the assumption that the
expected cumulative market potential at any time t, in the product life
cycle is [[bar.N].sub.i](t), which is function of time. Further
discussion on the nature of [[bar N].sub.i]; (t) is carried after the
development of the model.
The adoption rate equation modifies as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)
We consider two different forms of [[bar.N].sub.i](t) according to
the nature of growth of the potential market size. Putting these forms
in Equation (7) and solving under the initial conditions [N.sub.i](t) =
0, [X.sub.i](t) = 0, X(t) = 0 at t = 0 we get solutions as given below
in Table 1.
The exact nature of [[bar.N].sub.i](t) depends upon the social
system and marketing environment.
2. Model validity and application
To test the validity and measure the performance of the proposed
models, we performed parameter estimation on data cited in Jha et al.
(2014) of a new hatchback car of an ABC automobile company evolved
through mass and differentiated promotion. The data cited in Jha et al.
(2014) is chosen primarily to compare the performance of the proposed
models with this model as the proposed models are generalizations for
their model. Using this data the parameters of the proposed models are
estimated and the estimates of adoption for the observed and future
period are obtained to test the models and measure their performance as
compared to the Jha et al. (2014) model (results taken from the study).
The mathematical structure of proposed as well as the model chosen for
comparative analysis are non-linear in nature. The method of non-linear
regression applies for the estimation of parameters of nonlinear
mathematical models. It is very difficult and time consuming to obtain
the estimates using non-linear regression manually. Various support
software are available, which can be used for the purpose that would
provide solution with high accuracy. Here we have used the non-linear
regression function of the software SPSS to estimate unknown parameters
of the model. SPSS is statistical software package widely used for
quantitative research and has gained popularity as it is easy to learn,
offers full range of data management system and editing tools, provides
full range of statistical capabilities and is widely tested for accuracy
of results. It allows exporting the data from many different types of
file formats.
A model's applicability is determined by its ability of
fitness on the data used for analysis. In the literature, various
methods and criteria are proposed to establish the goodness of fit of a
model depending on the type of model. The goodness of fit of the
proposed models is established using the criteria mean square error
(MSE) and coefficient of multiple determination ([R.sup.2]).
2.1. Data analysis
Unknown estimates of the proposed models (M1, M2 and M3) using the
24-period sales data in four distinct market segments are obtained using
the software support SPSS. The estimated parameter values for the
proposed and Jha et al. (2014) models are given in Table 2. Columns 8
and 9 of Table 2 list the MSE and [R.sup.2] values for all models in
each segment. The goodness of fit curves for all the four segments are
illustrated in Figures 1(a)-1(d), 2(a)-2(d) and 3(a)-3(d). The curves
also show the further projection of adoption for the next six months.
[FIGURE 1(a) OMITTED]
[FIGURE 1(b) OMITTED]
[FIGURE 1(c) OMITTED]
[FIGURE 1(d) OMITTED]
[FIGURE 2(a) OMITTED]
[FIGURE 2(b) OMITTED]
[FIGURE 2(c) OMITTED]
[FIGURE 2(d) OMITTED]
[FIGURE 3(a) OMITTED]
[FIGURE 3(b) OMITTED]
[FIGURE 3(c) OMITTED]
[FIGURE 3(d) OMITTED]
2.2. Results and discussion
Table 2 summarizes the results of parameter estimation. If we talk
in terms of the model which fits best to this data set from Table 2, it
can be seen that dynamic market size models best describe the adoption
growth for this product. Model M2 fits best in segments S1 and S2, while
model M3 fits best in segments S3 and S4 with lower value of MSE and
[R.sup.2]. Model M2 describes the growth in the adopter potential with
an exponential growth curve while the model M3 describes the market
potential growth as a linear function of promotional efforts. As
different segments have differential characteristics, so it is quite
expected that the nature of growth in market potential in the segments
can vary. We have explored only these two forms, however, one may also
use other growth curves for the purpose. In this case, the practitioner
can choose the model M2 for forecasting the adoption of product over its
life cycle for segments S1 and S2 and model M3 in case of segments S3
and S4.
As the segments are heterogeneous and consumer group of one segment
shows some unique characteristics as compared to other segments, hence,
not only the nature of growth in potential market size shows different
nature but also a product may assimilate quickly in one segment as
compared to other. Increase in potential segment size can also be
different as the time progresses; it can be high in one segment and
lower in another. It corresponds exactly to our analysis that different
forms of [[bar.N].sub.i](t) fit the data and the parameter of growth
([g.sub.i]) also varies between the segments. The product under
consideration is a high value product and in the analysis the parameter
[g.sub.i] takes value between 0.2 to 0.9 for the best fit segments.
Although the repeat purchase model (M1) is not among the best fit
but gives better fit than Jha et al. (2014) model. MSE obtained on
fitting the actual data on the proposed models comes out to be lower
than Jha et al. (2014) model. The data taken for analysis is for a
car's adoption behaviour, so very low repurchase behaviour (2-9%)
is observed for the product as expected. The repurchase behaviour is an
adoption characteristic more applicable to consumable product but it
can't be overlooked for the case of technological consumer durable
products. Firms always look for the loyal customers as they act as the
strong pillars for internal influence component of the product adoption.
Repurchase behaviour is important for technological consumer products
for one more and a very different reason, in case of technological
products new versions/regenerations hit the market at a faster rate and
often at the time of repurchase a consumer may find a newer version of
the product in the market. The decision to adopt the newer version from
the same marketer shows consumers' loyalty for the firm's
products. The measurement of loyal population helps the firm in
estimating the initial size of the potential segment for the new
products of the same firm.
The analysis brings forward a very important result. The column 3
of Table 2 lists the size of potential segment as estimated in the
beginning of the product life cycle. Jha et al. (2014) model gives the
highest value of potential population size in all the segments. These
estimates are nearest to the repeat purchase model. The difference
accounts for the repeater population in the segments. However, in case
of dynamic market size model the difference is quite wider, for example,
the initial market size for segments in case of model M2 as compared to
Jha et al. (2014) model is only 14.35%, 42.55%, 53.50% and 72.69%
respectively. The similar results are obtained in case of model M3 and
Jha et al. (2014) (34.18%, 60.30%, 47.33% and 69.35%) model. This is due
to the fact that in real marketing situations the size of the potential
segments is usually low in the early launch period which eventually
rises as the product awareness grows, by the means of both external and
internal influence. The estimation of the size of the potential
population is very useful in decisions related to promotional strategy.
An overestimated value may lead to inappropriate promotional policy
formulation and reduce the effectiveness of promotion.
The proposed models also give an estimate of contribution of the
mass promotion on the total adoption. For example, the mass promotion
accounts for 30% contribution in case of model M1 for segment S1. This
means 70% adoption in this segment is due to the differential
promotional strategy and 30% comes from the spectrum effect of mass
promotion.
The study and the results of analysis open a number of further
study areas in the field.
Here the developed models address repeat purchase and dynamic
market size separately. One may find the immediate need to develop a
model which can simultaneously capture both phenomena. However, an
attempt to develop such a model makes the differential equation very
complicated and difficult to solve for exact solution. It needs a
different structural formulation. Further scholars might look for how to
analyse the impact of price change, competition, older and newer
versions, etc. on the diffusions of the product under consideration.
Timing study for the new product version launch and similar study for
the consumable goods can also be performed for the marketing environment
under consideration.
Conclusions
Our study has developed diffusion models to describe the effect of
external-internal influences on adoption in marketing scenario when a
product is marketed in segmented market under the combined influence of
mass and differentiated promotion. Most of the existing models in the
literature assume absence of segmentation while developing the model and
if used for prediction the adoption behaviour for a product marketed in
segmented market mayn't provide appropriate results.
The proposed model also generalizes the assumptions of the existing
few studies in the marketing environment under consideration. An
important characteristic of the proposed models is their ability to
capture the repeat purchase behaviour and dynamic size of market
potential in the diffusion process. The model validity and performance
has been tested in a real life case which shows fair result and
improvement over the past studies. The model also provides some useful
results which help in making more appropriate promotional policy as
discussed in the result and discussion section of the paper.
There is much scope for further research, such as studies related
to the impact of price change, competition, technological generations,
etc. on the product diffusion. Timing studies related to new product
introduction, time lag models between diffusion and adoption, diffusion
of consumable goods and many more.
Caption: Fig. 1(a). Goodness of fit curve of segment 1 for M1
Caption: Fig. 1(b). Goodness of fit curve of segment 2 for M1
Caption: Fig. 1(c). Goodness of fit curve of segment 3 for M1
Caption: Fig. 1(d). Goodness of fit curve of segment 4 for M1
Caption: Fig. 2(a). Goodness of fit curve of segment 1 for M2
Caption: Fig. 2(b). Goodness of fit curve of segment 2 for M2
Caption: Fig. 2(c). Goodness of fit curve of segment 3 for M2
Caption: Fig. 2(d). Goodness of fit curve of segment 4 for M2
Caption: Fig. 3(a). Goodness of fit curve of segment 1 for M3
Caption: Fig. 3(b). Goodness of fit curve of segment 2 for M3
Caption: Fig. 3(c). Goodness of fit curve of segment 3 for M3
Caption: Fig. 3(d). Goodness of fit curve of segment 4 for M3
doi:10.3846/20294913.2014.885914
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Received 07 April 2013; accepted 30 June 2013
Sugandha AGGARWAL (a), Anshu GUPTA (a, b), Kannan GOVINDAN (c), P.
C. JHA (a), Ieva MEIDUTE (d)
(a) Department of Operational Research, University of Delhi, Delhi,
India
(b) SBPPSE, Dr. B. R. Ambedkar University, Delhi, India
(c) Department of Business and Economics, University of Southern
Denmark, Denmark
(d) Department of Business Management, Vilnius Gediminas Technical
University, Sauletekio al. 11, 10223 Vilnius, Lithuania
Corresponding author Kannan Govindan
E-mail: gov@sam.sdu.dk
Sugandha AGGARWAL obtained her MPhil and MSc degrees in the
Operational Research from University of Delhi, Delhi, India in 2011 and
2009 respectively. She is presently pursuing her PhD from University of
Delhi. Her research interests include modelling and optimization in
marketing and soft computing.
Anshu GUPTA obtained her PhD, MPhil and MSc degrees in Operational
Research from University of Delhi, Delhi, India in 2009, 2005 and 2003
respectively. She is currently working with School of Business, Public
Policy and Social Entrepreneurship, Dr Ambedkar University, Delhi,
India. She is a gold medallist in the Master's Degree, 2003. She
has published several papers in the area of Software Reliability and
Marketing. Her research interests include modelling and optimization in
software reliability and marketing.
Kannan GOVINDAN is currently an Associate Professor of Operations
and Supply Chain Management in the Department of Business and Economics,
University of Southern Denmark, Odense M, Denmark. He has published more
than 80 papers in refereed international journals and more than 70
papers in conferences. He received a gold medal for Best PhD Thesis. His
research interests include logistics, supply chain management, green and
sustainable supply chain management, reverse logistics and maritime
logistics.
P. C. JHA obtained his PhD, MPhil and MA degrees in Operational
Research from University of Delhi, Delhi, India in 2004, 1988 and 1986
respectively. He is an Associate Professor in the Department of
Operational Research, University of Delhi. He has also co-authored a
book Software Reliability Assessment with OR Applications, published by
Springer. He has published more than 45 research papers in the areas of
software reliability, marketing and optimization in Indian &
international journals and edited books. His research interests include
modelling and optimization in software reliability, marketing and supply
chain management.
Ieva MEIDUTE. Assoc. Prof., Dr of Technological Sciences (Transport
Engineering), Vilnius Gediminas Technical University, Faculty of
Business Management, Department of Business Technologies. Her research
interests are related with business processes management, logistics and
supply chain management.
Table 1. Different forms of [[bar.N].sub.i](t) d diffusion models
using these forms
Model [[bar.N].sub.i] (t) [N.sub.i] (t) Comments
M2 [MATHEMATICAL [MATHEMATICAL Market
EXPRESSION NOT EXPRESSION NOT size grows
REPRODUCIBLE IN ASCII] REPRODUCIBLE IN exponentially
ASCII]
Market
M3 [[bar.N].sub.i] [MATHEMATICAL size grows
(1 + [g.sub.i] EXPRESSION NOT as a linear
([X.sub.i] (t) + REPRODUCIBLE IN function of
[[alpha].sub.I] X (t))) ASCII] promotional
efforts
Table 2. Estimation results for the proposed models
Parameter estimates
Model Segments [[bar.N].sub.i] [b.sub.i] [[beta].sub.i]i
S1 279107 0.138370 179.63
M1 S2 152460 0.481736 414.08
S3 97581 0.541775 391.56
S4 215868 0.314169 571.61
S1 41330 0.123077 31.70
M2 S2 66633 0.428514 176.76
S3 57232 0.476789 220.09
S4 162318 0.336248 396.09
S1 98435 0.116946 58.51
M3 S2 94427 0.445413 259.51
S3 50631 0.481654 208.54
S4 154853 0.296856 399.71
Jha et al. S1 287962 0.132784 196.89
(2014) S2 156601 0.471786 417.25
S3 106977 0.56738 421.16
S4 223291 0.332286 534.08
Parameter estimates
Model Segments [g.sub.i] [[alpha].sub.i]
S1 0.0500 0.300
M1 S2 0.0265 0.190
S3 0.0878 0.189
S4 0.0476 0.321
S1 0.0453 0.339
M2 S2 0.0662 0.200
S3 0.0509 0.213
S4 0.0150 0.240
S1 0.0597 0.25
M3 S2 0.0500 0.20
S3 0.0964 0.20
S4 0.0202 0.33
Jha et al. S1 -- 0.373
(2014) S2 -- 0.198
S3 -- 0.166
S4 -- 0.264
Fit statistics
Model Segments MSE [R.sup.2]
S1 191467.00 0.98113
M1 S2 13753.13 0.98111
S3 11146.31 0.98332
S4 168077.37 0.97696
S1 1128.17 0.99864
M2 S2 5690.43 0.99989
S3 8144.91 0.98786
S4 143545.00 0.97876
S1 59571.97 0.99824
M3 S2 7242.82 0.98632
S3 5787.91 0.98734
S4 113393.58 0.97992
Jha et al. S1 196105.50 0.98513
(2014) S2 13832.28 0.99426
S3 11994.30 0.98225
S4 173423.70 0.98355
