Analyzing the Adoption Curve

The provided content appears to be a table of values for the number of imitators, innovators, and new adopters at different time intervals. The table shows the decrease in these numbers over time, with the probability of adoption also decreasing as the years go by. Additionally, there are appendix sections titled 'Appendix 2: Year' and 'Appendix 3: Graphical presentation of Imitators, Innovators and new adopters', which suggest that there may be additional information or graphs related to this data.

Decision support for
management

Table of Contents
INTRODUCTION......................................................................................................................2
TASK 1-System dynamics.........................................................................................................2
TASK 2-Identification of variables and formulation of constraints..........................................2
TASK 3-Simple analytical model..............................................................................................3
TASK 4- Analysis and solving the simple analytical model.....................................................4
TASK 5- Critical evaluation of simple analytical model...........................................................4
TASK 6- Construct the revised analytical model & solution....................................................4
TASK 7- Critical evaluation of revised analytical model..........................................................5
TASK 8- Constructing simulation model..................................................................................5
TASK 9-Critical evaluation of simulation model......................................................................6
TASK 10- CONCLUSION........................................................................................................6
REFERENCES...........................................................................................................................6
APPENDIX................................................................................................................................8
Appendix: 1............................................................................................................................8
Appendix 2.............................................................................................................................8
Appendix 3.............................................................................................................................8

INTRODUCTION
The Gorgeous Food Company Ltd is an existing private limited company with limited share
capital which was incorporated on 30th May 2008. It operates in retail
industry by offering food products in specialized stores and also is a non-
specialized wholesaler for the food & beverages & tobacco items. It is a
food and beverage supplier organization that is specializes in the 6 main
categories of foods that are confectionery, bakery, beverages, grocery,
World Foods and Crisp &Snacks. Its product portfolio consists of unique
items that are not easily available in the supermarkets (The Food
Gorgeous Company, n.d). It provides the best quality, flavour,
provenance food made up of sustainable sourced ingredients so as to
perfectly satisfy their client’s requirement. Honesty, integrity and quality services have created an
impressive image in the market and strengthen its position in UK, more importantly, for independent
delis, food halls and farm shops. In order to attract more audiences, it had recently launched a new
product, “Truffle Mustard”. The target of the firm is to grab a minimum market size of 60% but due to
volatile & uncertain market conditions, sales manager is not sure that what length of period, the
company will take to reach the target. Thus, this is the main issue faced by the firm which will be
resolved by applying suitable simulation & systematic dynamic modelling for anticipating the
probable market demand for the Truffle Mustard.
Although, the marketing manager of the firm is continuously putting great efforts for the purpose of
the sound promotion of the new product and thereby maximizes the yield, still, they have no idea
about the potential sales of the Truffle Mustard; as a result, they are facing market challenges. For
instance, the number of potential buyers, conversion into actual consumer, probability that a buyer will
not use the item because their purchasing preference is not affected by the word of mouth publicity
and many others are the unknown elements which cause several difficulties for the marketer of the
business unit (Stevens and et.al., 2015). Hence, to address the root problem, the report will construct a
systematic dynamic modelling and simulation model for examining the possible market dynamics that
will affect its success. Under the systematic dynamic modelling, stock flow diagram will clearly
present the system functioning and aware various interlinked components. Besides this, causal loop
diagram (CLD) gives a clear picture of the constituent’s elements along with the interrelationship.
However, on the other side, simulation will be modelled for identifying the possible buyers, actual
adopters, imitators, innovators and others.
TASK 1-System dynamics
The analytical models are providing mathematical equations and flow charts which are either
deterministic or stochastic .System dynamic is a mathematical modelling technique which helps in
examining complex system, structure and issues. Alternatively, it can be defined as a part of system
theory to develop sound understanding of the dynamic behaviour of the complicated system through
clearly presenting the links, interlocking and relationship among multiple of components. It was
initially developed in order to facilitate business managers to enhance their understanding of the
complex system & regular operational processes ((Barczak and Kahn, 2012). Now-a-days, the
modelling is used by all the private and publicly held enterprises for policy formulation. The system
reinforces the flow of stock & the significance of consistent via constructing a stock flow diagram
which is a quantitative model. However, on the other hand, CLDis qualitative representation which
clearly visualizes interrelationship among various components that is the part of new product sales in
2

the market. In this, Nodes are variables whilst edges present relations or connections between different
elements (Stevens, Lewis and Johnson, 2015).
TASK 2-Identification of variables and formulation of constraints
The procedure of systematic dynamic modelling (SDM) begins with the step of identifying variables
& constraints as well. It helps in clear, rigorous and transparent presentation. It helps to determine that
which elements can vary and affects the total sales of Truffle Mustard (consumer conversion rate etc.)
and the constraints market size). The key target of the firm is to maximize the actual buyers so as to
generate maximum yield and enjoy impressive & phenomenal growth in the market.
For the current issue of introducing new product, Truffle Mustard in the market, market size is a
constraint also called auxiliary variable, however, other are the variables i.e. consumer conversion
rate, actual buyers, WOM publicity that will encourage others individual too to buy the offering and
others. In the stock & flow diagram, product purchase is presented in the middle that influences the
conversion of potential customers into actual adopters. However, the arrows present relation pointing
at influenced element (Bennett and et.al., 2010). On the other hand, CLD model demonstrates
presented a clear picture to show linkage. Positive feedback loops tends to iterate the system away
from the equilibrium point which indicates instability whilst negative loops intends to dampen or hold
system in equilibrium state with high stability. The simple causal loop diagram helps to determine
unnecessary variables and other additional variables that are required to be added in Systematic
dynamic modelling.
TASK 3-Simple analytical model
Stock Flow diagram: In the illustration, stock presents the accumulation & depletion over time whilst
flow indicates the rate of conversion in the stock. Referring the below designed stock & flow diagram
of new product introduction project indicates that a portion of the market size will be potential buyer
of Truffle Mustard depicted on the left hand side, in the middle product purchase indicates flow means
conversion rate, in which, individual actually buy the item and become an actual adopter represented
on the right hand side (Ernst and et.al., 2011). Thus, in this way, maximizing the conversion rates
boost the actual number of consumers and benefits The Gorgeous Food Company with high sales &
yield or vice-versa.
Truffle Mustard Truffle Mustard Truffle Mustard
Market size
Causal loop analytical model: The designed CLD for the introduction of Truffle Mustard
reveals the clear structure through which firm can determine the user behaviour over a certain period
of time. In this, there are two loops can be seen. It clearly showcases qualitative interrelationship in
various components or constituents (Cui, Lui and Guo, 2012).
3
Potential
consumers
Actual
Adopters
Product
purchase
Potential buyers
of Truffle Mustard
Adoption rate Actual adopters
of Truffle Mustard
- +

Market saturation +
TASK 4- Analysis and solving the simple analytical model
The equations to solve both the stock, potential user and actual buyers are mentioned here as follows:
Potential consumers ∫
0
t
−adopters ( t ) dt
Here: X – Market size, 100,000 target audiences
Actual buyers: ∫
0
t
new adopters ( t ) dt
The equation clearly had presented the simultaneous relationship between both the two stocks and
indicates that rising trend of actual adopters of the new product will decrease the potential buyers or
vice-versa. It is because; new adopters through actual consumption convert an individual into actual
buyer and take out him or her from the list of prospective users (Kahn and et.al., 2012).
TASK 5- Critical evaluation of simple analytical model
Considering the above illustrated loop diagram, it can be seen that on the right hand side, the loop that
is labelled as “R” indicates that high number of buyers actually purchased or consumed the Truffle
Mustard due to high WOM popularity. It depicts the possibility of more number of buyers, high
reviews and actual adopters also prefer or suggest other to buy the item. As a result, The Gorgeous
Food Company will generate maximum sales and high yield. In contrast, loop in left labelled as B
(balancing) is a negative reinforcement which showcases that with the increase in actual number of
users, the rate of potential adopters will be decrease (Lavery and et.al., 2012). Thus, it becomes clear
that both the loops illustrated in the diagram acts simultaneously but with distinctive strength at
different time. Company often expects high sales during the initial period and declining sales in the
following years. However, there are number of other variables which affects the potential number of
buyers and actual adopters i.e. imitators who will buy the item due to WOM publicity etc.
TASK 6- Construct the revised analytical model & solution
+
Saturation point
+
New Adopters
+
Saturation point +
4
Early adopters(Innovatoers)
Potential
buyers
Adopters
-
+
+ Word of mouth (WOM)
+
WOM
Market
size
Likelihood that Imitators will
adopts the goods due to WOM
publicity

- +
Revised analytical model presents the influencing factors that affect the target outcome in the real-
business world. In the above designed simple analytical model, only few factors have been taken into
consideration that is potential buyers, conversion rate and actual consumer/adopters. However, in the
real business world, there are number of other influencing factors which are the constituents and play a
role in the introduction of new item, Truffle Mustard in the market. Therefore, the revised model with
several iterations considering additional factors has been developed (Meng and Kaxiras, 2010). The
earlier designed model in the simple model was not calculable. It is because, the potential buyer and
likelihood that they will actually buy means conversion rate is unknown. Without, solving these
variables, The Food Gorgeous Company will be unable to compute the amount of actual buyers of the
newly launched item. It requires some other variables too i.e. likelihood of buying, % of people who
suggests or recommend others to buy the goods through WOM publicity for the quantitative valuation
purpose.
TASK 7- Critical evaluation of revised analytical model
The above designed revised systematic dynamic model of stock flow depicts clearly the linkage
among all the variables. It depicts that, out of the potential market size that is expected by The Food
Gorgeous Company regarding the possible number of buyers who might be interested in actual
consumption of the offered good is known as potential buyer. In the designed stock & flow diagram
prospective buyers & actual adopter are the two stocks and there is one flow which is presented as new
adopters (Aronson and Angelakis, 2015). For every 1 new adopter that will actually purchase the item,
the potential users will be drop by 1 and actual user will be increase by the same number. Besides this,
there are several additional variables that have been included that are likelihood that imitators will buy
the item by influencing with the actual buyers word of mouth publicity and post-buying preference.
Thus, WOM plays an effective role in maximizing the number of buyers. It encourages the firm to use
a strong marketing and promotional campaign for bringing market awareness and thereby boost the
possibility of large user base (Pronk and et.al., 2013). However, at the same time, it is probable that
not all the imitators will influence by others hence, they might decide to not to purchase the item.
Thus, in this, an individual who will actually bought the item convert into new adopter otherwise,
potential buyer. Besides this, innovators are the users who first use the item and become actual users
of the recently launched item, Truffle Mustard.
Taking into account the total number of target market size which are the potential buyer at beginning
of the period is expected to be 100,000. It is taken considering The Gorgeous Food Company’s
consumer base in the UK market that is satisfied with the delivered services and always looks towards
using unique offerings to meet their own demand. Satisfied customer suggests it to their friends,
family members, colleagues and other persons too to purchase the item via WOM publicity. Taking
into account the above equations, the number of potential and actual consumers is determined in
Appendix 1. Finding the result of prospective consumers and actual adopters, it is clearly presented
that with the increase in actual user of the introduced product; expected number of potential buyers
came down because now, they are the actual adopters of Truffle Mustard. Over the period, the result
depicts growth in the actual adopters which clearly demonstrates that more buyers will use the offering
and as a result, the number of prospective buyer will come down. As reflected in the table, in 1st year,
actual users were reported to 3,000 grown up to 98,423 users at the end which is very close to the
5
Probability that consumers
Do not decide to purchase the item

target market size of 100,000. The outcome presents that at the end of year 15, The Food Gorgeous
Company had achieved 98% of their target market with sound competitiveness.
TASK 8- Constructing simulation model
Simulation is a technique applied for the forecasting purpose to ensure high yield for the business. In
today’s era, due to volatile & uncertain market situation, businesses often use different simulation
models to forecast prospective results and create plans and decisive actions accordingly to address
possible issues (Rubinstein and Kroese, 2016). Here, simulation is performed to determine the
potential number of consumers, actual adopters, imitators, innovators and new adopters as well at
different probability.
Probability that audience will contact will not yet adopted : Potentialbuyers/(Potential buyers+actual buyers)
I mitators :q∗actual buyers∗probability that buyer will not buy the item
Innovators : p∗potential adopters
New buyers: Imitators +Innovators
Potential adopters−¿ New buyers
Adopters+ New buyers
Assumptions: Probability: 0.03, q: 0.4 (see Appendix 2)
TASK 9-Critical evaluation of simulation model
According to the results of simulation constructed, it has been founded that in the 1st year, there will no imitator
because at this time, 3,000 early adopters/innovators will first time purchase Truffle Mustard and become actual
buyer (Figure attached in Appendix). Out of these, the satisfied users will popularize the item by recommending
it to others too to consume the product and satisfy their need & expectations effectively. Thus, since 2 nd year
onwards, imitators also will started demanding the newly launched product and buy it from the firm just
because they are influenced by word of mouth publicity in the market era. Looking to the outcome of 2nd year, it
is clearly presented that imitators will be expected to 1,164, innovators to 2,629 totalled to 4,074 at the actual
adopters of 7,074. The trend shows continuous increase in the imitators and new adopters till the end of 8th year
@ probabilityof 0.50 however, only the early adopters depict declining trend, After the year 2008, both the
imitators and adopters also demonstrates decreasing trend and came to 9,494 and 10,656. As said earlier, that in
the beginning years of new product introduction, it is often intended to generate maximum sales and afterwards
sales depicts a declining trend proven true. As reflected in the table, the number of imitators, innovators and
new adopters shows a declined trend in the 9th year and onwards. As The Gorgeous Food Company has targeted
to cover a minimum market share of 60% will be achieved in the 8th year (as highlighted) at total adopters of
61,250 means (61250/100,000) = 61.25%.
TASK 10- CONCLUSION
The results drawn from the systematic dynamic modelling identified that the actual adopters of the newly
launched product depends upon the variables i.e. effectiveness of WOM publicity and rate of innovators. The
revised systematic dynamic models stated that provided clear picture that how variables like imitators,
probability of purchase with WOM publicity, innovators influence the rate of actual adopters of Truffle
Mustard. The findings of simulation modelling reported that till 8th year, imitators and new adopters depicts a
growing trend, however, thereafter, the data reported a declining trend. It presents that in the following period,
new adopters who will purchase the item will be decrease due to declined WOM publicity and upcoming of
new product by competitor in the market. Thus, from the outcome, it becomes clear that the target of
accomplishing a minimum market share of 60% will be achieved in the end of 8th year in which actual adopters
have been reported to 61,250 at an actual market share of 61.25%. However, it must be noted that the
simulation results are based on forecasting, however, actual situation may be differ according to the market
situation and influence the actual adopters. Therefore, it must be suggested to the firm managers to must have a
look over market conditions to reinforce rationalized decisions.
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REFERENCES
Books and Journals
Barczak, G. and Kahn, K. B., 2012. Identifying new product development best practice. Business
horizons. 55(3). pp.293-305.
Bennett, E. J. and et.al., 2010. Dynamics of cullin-RING ubiquitin ligase network revealed by
systematic quantitative proteomics. 143(6). pp.951-965.
Cui, G., Lui, H. K. and Guo, X., 2012. The effect of online consumer reviews on new product
sales. International Journal of Electronic Commerce. 17(1). pp.39-58.
Ernst and et.al., 2011., Systematic analysis of chromatin state dynamics in nine human cell
types.Nature.473(7345).p.43.
Kahn, K. B. and et.al., 2012., An examination of new product development best practice. Journal of
product innovation management. 29(2). pp.180-192.
Lavery and et.al., 2012., A systematic molecular dynamics study of nearest-neighbor effects on base
pair and base pair step conformations and fluctuations in B-DNA. Nucleic acids
research.38(1). pp.299-313.
Meng, S. and Kaxiras, E., 2010. Electron and hole dynamics in dye-sensitized solar cells: influencing
factors and systematic trends. Nano letters. 10(4). pp.1238-1247.
Pronk and et.al., 2013., GROMACS 4.5: a high-throughput and highly parallel open source molecular
simulation toolkit. Bioinformatics.29(7).pp.845-854.
Rubinstein, R. Y. and Kroese, D. P., 2016., Simulation and the Monte Carlo method.(Vol. 10). John
Wiley & Sons.
Stevens and et.al., 2015., Aircraft control and simulation: dynamics, controls design, and autonomous
systems. John Wiley & Sons.
Stevens, B. L., Lewis, F. L. and Johnson, E. N., 2015. Aircraft control and simulation: dynamics,
controls design, and autonomous systems. John Wiley & Sons.
Online
Aronson, D. and Angelakis, D., 2015. Step by Step Stock and flows: Converting from Causal Loop
Diagram. [Online]. Available through: https://thesystemsthinker.com/step-by-step-stocks-
and-flows-converting-from-causal-loop-diagrams/. [Accessed on 5th August 2017].
The Food Gorgeous Company. n.d. [Online]. Available through:
https://www.gorgeousfoodcompany.co.uk/. [Accessed on 5th August 2017].
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APPENDIX
Appendix: 1
Year Probability Potential adopters Adopters
0 0 100,000 0
1 1.00 (100,000-3,000) = 97000 3000
2 0.97 (100,000-7,074) = 92926 7074
3 0.93 (100,000-12,491) = 87509 12491
4 0.88 (100,000-19,489) = 80511 19489
5 0.81 (100,000-28,180) = 71820 28180
6 0.72 (100,000-38,431) = 61569 38431
7 0.62 (100,000-49,742) = 50258 49742
8 0.50 (100,000-61,250) = 38750 61250
9 0.39 (100,000-71,906) = 28094 71906
10 0.28 (100,000-80,829) = 19171 80829
11 0.19 (100,000-87,603) = 12397 87603
12 0.12 (100,000-92,319) = 7681 92319
13 0.08 (100,000-95,386) = 4614 95386
14 0.05 (100,000-97,285) = 2715 97285
15 0.03 (100,000-98,423) = 1577 98423
Appendix 2
Year Probability Imitators Innovators New Adopters Potential adopters Adopters
0 0 0 0 0 100000 0
1 1.00 0 3000 3000 97000 3000
2 0.97 1164 2910 4074 92926 7074
3 0.93 2629 2788 5417 87509 12491
4 0.88 4372 2625 6998 80511 19489
5 0.81 6276 2415 8692 71820 28180
6 0.72 8096 2155 10250 61569 38431
7 0.62 9465 1847 11312 50258 49742
8 0.50 10000 1508 11507 38750 61250
9 0.39 9494 1163 10656 28094 71906
10 0.28 8080 843 8923 19171 80829
11 0.19 6198 575 6773 12397 87603
12 0.12 4344 372 4716 7681 92319
13 0.08 2836 230 3067 4614 95386
14 0.05 1761 138 1899 2715 97285
15 0.03 1057 81 1138 1577 98423
Appendix 3
Graphical presentation of Imitators, Innovators and new adopters
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
2000
4000
6000
8000
10000
12000
14000
Imitators
Innovators
New Adopters
Figure 1 Imitators, Innovators and new adopters
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