Category Archives: Management Science

Solution to Management Science Series #211: Real-world example: Kabuto Drinks forecasting production capacity and launching a loyalty program

A soft-drink company called Kabuto plans to model the production capacity for the year 2026.

The forecasters determined that the annual soft-drink consumption with the respect to Kabuto’s brands is normally distributed with a mean of 160 liters per customer of Kabuto per year and a standard deviation of 40 liters per customer per year.

a)What is the median per person annual consumption?

b)What is the mode for the per person annual consumption?

c)What percentage of Kabuto consumers do consume more than 160 liters per year?

d)What percentage of Kabuto consumers do consume more than 200 liters per year?

e)What percentage of Kabuto consumers do consume more than 230 liters per year?

f)What percentage of Kabuto consumers do consume fewer than 120 liters per year?

g)Your marketing department is proposing a loyalty program for the consumers who lie within the top 5% of Kabuto-branded soft-drink consumption. Find the threshold value of annual Kabuto drink consumption for these top consumers in liters.

h)In an alternative scenario, Kabuto will have customers within the top 3% of consumption join the loyalty program. Find the threshold value of annual Kabuto drink consumption for these top consumers in liters.

Solution to Management Science Series #210: Real-world example: Famous hotel chain, Mushroom Kingdom, bent on improving customer satisfaction

Real-world example: Famous hotel chain, Mushroom Kingdom, bent on improving customer satisfaction

You are the owner of the famous hotel chains called Mushroom Kingdom (MK). Historically, 75% of all the customers claimed that they were ‘completely satisfied’ with the services and accommodation offered by the MK.

You hired an analytics company, named Gotham Analytics (GA), that would conduct analyses to determine whether this still holds true. GA conducted a survey, by randomly sampling 35 customers out of a total of chain’s 250 customers. The number of customers in the sample who claimed that they were ‘completely satisfied’ is 25.

1) Calculate the sample proportion.

2) Could you assume that the distribution of the sample proportion is normal?

3) What is the standard deviation of the sample proportion using the finite population correction factor?

4) What is the standard deviation of the sample proportion ignoring the finite population correction factor?

5) Recalculate 3) and 4) assuming the chain has 110 customers.

6) Recalculate 3) and 4) assuming the chain has 1500 customers.

7) Assume again that the firm has 250 customers. Using the finite population correction factor to calculate the standard deviation of the sample proportion, what is the likelihood of finding 25 or fewer “completely satisfied” customers in a sample of 35 customers?

The Value of Your Customers to Your Firm

The Value of Your Customers to Your Firm
Your company has only two types of customers. Segment 1 consists of customers who purchase less in absolute dollars. However, the retention rate of this segment is high.
Segment 2 consists of customers who purchase more in absolute dollars compared to the purchasing level of segment 1. However, these customers churn at higher rates.
Both segments have identical acquisition costs.
Which segment should your company target?
Impossible to answer! That is why for your marketing efforts to work efficiently, you need a quantitative and data-driven approach even though some inputs are prone to assumptions.
In this text, I will demonstrate why this question cannot be answered easily even if you have all the data measured and ready to be tinkered with. I will also provide some contingency scenarios in which both segments can be very significant or less significant to your firm.

Solution to Management Science Series #209: Mysterious Disease in a Tropical Island: Data Analytics & Medicine

Mysterious Disease in a Tropical Island: Data Analytics & Medicine

23% of males in the tropical island, Cappytopa, are known to carry a mysterious disease called ‘Dinosaur flu’.

A newly developed test correctly detects dinosaur flu 90% of the time for males, but incorrectly detects dinosaur flu in non-infected males 35% of the time (false positive).

1.A randomly selected male is tested for the dinosaur flu and the result is positive. What is the probability that this male is dinosaur flu positive?

2.What is the probability that this same male is dinosaur flu negative?

3.What is the probability that a randomly selected male has a positive test? Would you trust in this test?

Solution to Management Science Series #208: Zodd Japanese Manga trying to improve customer satisfaction

Selim Hasagasioglu Academy and Consulting Services was contacted by a very niche e-commerce platform called Zodd that markets and sells Japanese manga and relevant merchandise.

Zodd has been recently struggling with customer satisfaction issues. Furthermore, Zodd does not have the information on the historical customer satisfaction levels.

Selim’s firm carried out a survey, randomly sampling 50 customers out of the firm’s 1300 customers. The number of customers in the sample who claimed that they were ‘entirely satisfied’ was 35.

a) Do you need to use the finite population correction factor?

b) What is the sample proportion for the sample collected by Selim’s firm?

c)Is the distribution of the sample proportion normal or can it be used to conduct a confidence interval analysis?

d) What is the margin of error assuming a 95% confidence level?

e) What is the 95% confidence interval for the proportion of customers who are “entirely satisfied”? What is the 99% confidence interval? Are you 95% confident that customers are more than likely to be entirely satisfied with Zodd? Are you 99% confident that customers are more than likely to be entirely satisfied with Zodd?

f) How many customers should be sampled to ensure a margin of error of 0.12 with a 90% confidence level if you use p* = 0.5?

g) How many customers should be sampled to ensure a margin of error of 0.12 with a 90% confidence level if you use p* = 0.75?

h) Between the answers to f) and g), which is a more conservative approach and why is this difference important in the practice of data/business analytics?

On Management Consulting Practices: Turnaround Projects followed by Business Transformation, Brand Revitalization, and Sustainable Growth. Focusing on Lego, Nintendo, and Sega

Studying successful turnaround projects will provide you with great lessons.

Many consultants tasked with turning around a business focus mainly on cost reduction projects and deem the mission complete after a successful turnaround.

However, natural and subsequent steps after a turnaround are business transformation and brand revitalization.

Business may have survived after the turnaround but whether it will reach a sustainable and organic growth phase ever again depends on following transformation and revitalization.
In this article, I elaborate on what needs to follow after a turnaround project for a business to continue to thrive in the future. I share how successful business transformation and brand revitalization look like, analyzing the history of Lego, Nintendo, and Sega in greater detail.

Solution to Management Science Series #207: Marketing real-world example ‘Crenner Toys designing a promotion’

Marketing real-world example: Crenner Toys designing a promotion

Crenner Toys, famous for its toy vehicles transforming into attack vehicles and sold with complementary figures, is planning to roll out a promotion through which Crenner will send discount codes to its existing customers via emails.

Crenner will deem this promotion viable and subsequently implement it at national scale only if more than 15% of customers receiving the codes use them within 10 days. To assess the viability of this promotion, Crenner sent codes to a random sample of 150 customers and 23 of those receiving the code used it.

1.Construct the Null and Alternative hypotheses.

2.Should Crenner launch this promotion at national scale? Crenner believes that a significance level of 5% is appropriate for the hypothesis testing.

Solution to Management Science Series #206: Hanagawa’s Mailing Campaign

Producer of high-quality plastic model kits, Hanagawa, strategized a mailing campaign. Hanagawa will send informational and promotional emails to its customers. Through pilot tests, Hanagawa found out that 15% of these emails are considered spam by the customers’ emailing services.

Hanagawa knows that each such email goes through a spam filter and only if the filter clears the email, it goes to the inbox of the customers. Otherwise, it will wind up in the customer’s Spam folder. Hanagawa estimates that 45% of the spam messages and 95% of non-spam messages end up in customers’ inboxes.

1.What is the probability that the next email sent by Hanagawa winds up in a customer’s inbox?

2.What is the probability that Hanagawa’s next email is spam and ends up in a customer’s inbox?

3.What is the probability that Hanagawa’s next email is labelled as either spam or ends up in a customer’s inbox?

4.Suppose the next email sent by Hanagawa is labelled as spam. What is the probability that it ends up in a customer’s spam folder?

5.Suppose the next email sent by Hanagawa goes to a customer’s Spam folder. What is the probability that it is spam?

Solution to Management Science Series #205: Arkham high-end action figures (Pricing real-world example)

Arkham is a prominent action figure manufacturer known for its high-quality action figures and playsets commanding higher prices than is usual in this particular market.

Arkham is considering launching a new brand of action figures called BATS. The marketing department of Arkham is required to come up with an estimate of the average preferred price within the entire action figure market to price this brand new line viably.

The marketers randomly sampled 50 people in the action figure market. The population, i.e. the entire action figure market, is large enough and the finite population correction factor can be ignored. The standard deviation of the preferred price within the entire action figure market is estimated to be $200 (valid for questions from 1 to 6 below).

1. What is the distribution of sample means? Explain your rationale.
2. Are you required to know the distribution for the entire action figure market?
3. What is the expected value of x ̅ (x bar)?
4. Calculate the standard deviation of x ̅ (x bar).
5. The average preferred price for the sample you collected was $750. Construct the 95% confidence interval for the average preferred price for people in the entire action figure market. Similarly construct the 99% confidence interval. Why is one confidence interval bigger than the other?
6. Instead of a sample size of 50 people, you randomly sampled 130 people and the average preferred price of this sample stayed constant at $750. Construct the 95% and the 99% confidence intervals for the preferred price for people in the entire action figure market.

Now, for the questions asked below, assume that you do not know the standard deviation of the preferred price for people in the entire action figure market. The average preferred price for the sample collected remains to be the same at $750 and the standard deviation for this same sample is $200. The sample size is 50 people.

7. Estimate the distribution of the sample means.
8. Estimate the standard deviation of the preferred price for people in the entire action figure market.
9. Calculate the standard deviation of x ̅ (x bar).
10. Construct the 95% confidence interval for the average preferred price for people in the entire action figure market. Similarly construct the 99% confidence interval. Compare your findings here with those you calculated in question 5.
11. Instead of a sample size of 50 people, you randomly sampled 130 people and the average preferred price of this sample stayed constant at $750 and the standard deviation of this sample remains to be the same at $200. Construct the 95% and the 99% confidence intervals for the preferred price for people in the entire action figure market. Compare these values with those that were found in question 6.

On outdated measures concerning how big a country’s economy is and what this means for your purchasing power, i.e. your salary or income

Many national income measurement methods of today are misleading and hardly reflect the realities of the state of a national economy. 🧭

Quoting from Michal Hudson’s “The Bubble & Beyond”

“By rejecting the classical distinction between productive and unproductive labor and credit, today’s national income accounts classify rentier gains as “earnings” on a par with wages and profits, adding to national product rather than simply being transfer payments.

This approach treats all wealth as being earned as part of the production process, not extracted from the economy in the form of a free lunch (“economic rent”) by rentiers. ”

In this article, I will investigate why current measures related to how big the economies of countries are trick many. Although many countries tend to jack up their GDP evaluations by using favorable methods, the reality for the average citizen is generally fundamentally different from what all these numbers tell. I will also share some other measures that will be more helpful for citizens in gauging their purchasing power, together with some additional considerations assisting them in making more informed decisions informed decisions.