Suppose that you are a consultant modeller focusing on the technology adoption habits of buyers, i.e., the buyer behaviour. Your client, VIKEA, a very popular chain consumer goods operation, has developed an app to facilitate in-store purchasesof customers and reduce the customer reliability on staff availability. They would like to introduce this new technology gently in their stores to test the potential buy-in from their customers, before launching it across all their branches and fullyadopting this new technology.
They have some concerns over how different demographics would respond to the new technology
and therefore they reached out to you to run some analyses. Specifically, they are interested in understanding the behaviour of two different groups. One group loves new technology and anything
shiny that comes with it, who are for the sake of argument going to be called theAdopters (A). The other group of interest displays behaviour, which is starkly different; they will resist the adoption of
the technology and refuse to use ti as much as they can, and these wil be called the Refusers. (R).
As a modeller, you know that you can represent the adoption of the technology similarly for both groups, A and R. In either group, some people will start using the technology and some will not. You can represent the number of customers who start downloading the app and start using it as Uand the number of customers who do not use it as N. Over the course of time (t), the natural expectation would be for Uto increase and Nto decrease. And this behaviour can be represented by the following equations:
wherei= AorR
U- WFUM- gU- 4U
aM- – WFUM t bM dt
wdenotes the likelihood of ‘word of mouth’ recommendation, i.e., the likelihood that acustomer wil download the app and start using it upon referral by another user. Since this isrepresented as a joint
probability, we would expect the value of w to be always less than 1,
f denotes the likelihood of the use of the ‘friendship circle’, i.e., the probability/likelihood of one user promoting it to several people they know, who are also customers of VIKEA,
g refers to the rate of peoplewho uninstall the app after giving it atry for afew times,
I refers to the rate of people taking their custom away from VIKEA to another brand after using this a few times,
and lastly brefers tothe rate of ‘newbies’, i.e., rate of switching custom from elsewhere to VIKEA.
When the app is newly launched (t ~ 0), there will be very few people who will use it, which can be represented by: Mi(t)~ Nio = constant. Naturally, we can expect Nio » Uio.
Suppose that for the groups Aand R, we have the following population characteristics summarised in Table 1:
Table 1Summaryof population characteristics
Nominal Value
Distribution parameters Distribution ARAR
α=5 B=2 1=3
0.65 0.25 Beta
5 3 Poisson 1=5 3 1 Poisson 1=3
1. Study the population characteristics assumed for the variable f for Aand R. Explain in your own words what the differences would represent for the problem statement introduced
above. Consider what these statistical parameters represent int h e problem setting described. [15 marks]
Determine the expanded uncertainty at a confidence level of 95% around U and N separately
for groups Aand Rusingthe Monte Carlo Method. Conduct the same analysis at 90% and 99% confidence levels. Use tables or plots as you see appropriate. Discuss all your findings, clearly
stating and justifying all the assumptions you have made in this analysis. [35 marks: 10 (for code and results) + 10 (for the assumptions) + 15 (for discussion)]
Calculatethe sensitivity indices forthe five factors described abovefor both AandR using the Elementary Effects Method. Use tables or plots as you see appropriate. Discuss all your
findings, clearly statingand justifying the decisions you have made in this analysis particularly in relation to the choice of arbitrary values of any kind, at any stage. Show that you have sufficiently covered the -dimensional space you are exploring in this analysis. Note that in this question, you are expected to make the assumption that all variables follow a uniform distribution.
[35 marks: 10 (for the codes and the sensitivity indices) + 10 (for theassumptions) + 15 (for showing that the n-dimensional grid is adequately covered)]
4. Your client VIKEA asks you tomake a recommendation on how to prioritise working. on the sensitivity associated with different types of human behaviour impacting the adoption of the new technology and present two reasonable strategies to approach groups Aand R. Provide a critical evaluation of the sensitivity indices you calculated and an interpretation of your results from Question 3. [15 marks]