Question 1. Hotel Bookings

During high season, it is common that hotels take on more bookings than the

number of rooms they have. The reason being that bookings are often cancelled last

minute. However, it can happen that everyone shows up and then there are not

enough rooms available. This overbooking situation can be costly for the hotel as

they need to send their possibly unhappy guests to another hotel.

Land Hotel is a new hotel close to Turkey's main shopping street. It has 196

rooms. The hotel is very busy on a particular weekend in the end of August when

Turkey's Cultural Day takes place with Turkey Marathon and numerous other

events going on. However, in the past Land hotel has had some guests cancelling last

minute.

Land Hotel is interested in understanding the implication of taking on more bookings

than there are rooms. They estimate the cancelling probability on this weekend to

be 5%.

The socalled binomial distribution can be used to describe uncertain situations of

this kind where there are two possible outcomes; a guest shows up or

not. Fortunately, the binomial distribution can be approximated by the

normal distribution such that the number of guests that show up is normally

distributed with

a mean of np and a standard deviation of n p ( 1 p) where n is the number of

rooms booked and p is the probability of showing up.

a) If the hotel books 205 rooms on the Cultural Day what is the probability that there

will be an overbooking situation?

b) If the hotel books 210 rooms on the Cultural Day what is the probability of having

empty rooms?

c) If the hotel wants only 2% probability of an overbooking situation on the Cultural

Day, how many rooms should it book?

d) You have been hired as a consultant for Land Hotel. You have understood the

probability structure of the overbooking problem and the next step is to advise

them on how many overbooked rooms to allow during peak season. Please make

a list of the data you would need to get from the hotel in order to make your

recommendation.

Question 2. Meal Kits

DDL is a highend grocery store that focuses on good quality products and an

extensive range. DDL 's managers have noticed an increasing demand for readymade

meals as many new fast food restaurants have been opening up nearby their stores.

In order to grasp that part of the market, they thought of offering a meal kit where

the vegetables would already be chopped, the meat or fish possibly

marinated, and the simple cooking would take only 1520 minutes.

Before developing this kind of a product they first need to understand whether their

customers are interested in the product and also how much the customers would be

willing to pay.

The newlyhired data scientist randomly asked 150 of the customers how much they

were willing to pay for a meal kit for two people. The average amount was 15.0 and

the standard deviation was 4.0.

a) Build a 95% confidence interval for the average price the customers are willing to

pay. Please comment on what the standard deviation of 4.0 measures.

b) The data scientist had in fact collected the 150 answers in two parts. The first 80

data points were collected between 2 and 3pm on a Tuesday. The rest

was collected between 6 and 7pm on the same day. The early group was willing to

pay on average 13.3 for the meal kit with a standard deviation of 3.2 and the

later group was willing to pay on average 17.0 with a standard deviation of 4.8.

Is there a difference between how much these two customer groups are willing to

pay? Please explain.

c) Instead of considering how much the 150 customers are willing to pay on average,

the data scientist went through the numbers and saw that 20 out of the 150 were

willing to pay 20 or more for the meal kit. Assuming that the meal kit is offered

at 20 and that there are 2000 customers visiting their store per day. What do you

expect DDL 's revenues from the meal kits would be per day?

d) The managers feel that they need a deeper understanding on their customers'

interest in meal kits and have asked the data scientist to provide some more

insights. Even though the data scientist is good with crunching the numbers, he

needs some help with understanding what kind of additional information would be

valuable for the managers. What additional data would you suggest the data

scientist should collect in a survey that he is planning to run? List five suggestions.

Question 3. Managing Subscriptions at London

London Today is a growing online newspaper that has been offering trial

subscriptions to potential customers. To ensure that as many trial subscriptions as

possible are converted to regular subscriptions, the London Today marketing department

dedicates many hours on marketing efforts geared towards these trial

subscribers.

A team consisting of managers from the marketing department wanted to develop a

better method of forecasting new subscriptions. Their current approach for

forecasting is such that, after examining new subscription data for the previous 2 or

3 months, the team would develop a consensus on what the final forecast should be.

A newly hired MBA, Oliver, suggested a more thorough approach and that the

department should look for factors that might be helpful in predicting new

subscriptions.

The team noted that the forecasts in the last year had been particularly inaccurate

because in some months much more time was spent on marketing than in other

months. In particular, in the last month, only 1,055 hours were completed since

many of the department's employees were busy during the first week of the month

attending training sessions. Oliver suggested that the data for the number of new

subscriptions and the number of hours spent on marketing effort (geared towards

the trial subscribers) for each month for the past 2 years be obtained from company

records.

a) What criticism can you make concerning the forecasting method the team of

managers has been using that involved taking the new subscriptions for the past 3

months as the basis for future projections?

b) What factors other than number of marketing hours spent might be useful in

predicting the number of new subscriptions? Explain.

c) Analyze the data in the file, Subscription data.xlsx, and develop a statistical model

to predict the average number of new subscriptions for a month based on the

number of marketing hours. Interpret the model and comment on its quality.

d) If there are expected to be 1,200 hours spent on marketing in the coming month,

estimate the average number of new subscriptions expected for the month.

Indicate the assumptions upon which this prediction is based. Do you think these

assumptions are valid? Explain.

e) Estimate the average number of new subscriptions for a month in which 2,000

hours were spent on marketing.

Question 4. Electricity Trading (25%)

You have been hired to explore opportunities in electricity trading in the SouthEast

European region. The first thing to understand is the volatility of wholesale prices in

an emerging market and their drivers, so as to assess your risk exposure. It has been

pointed out to you that hydrologic conditions must be a key factor in price

formation: When there is a shortage of water, electricity production from hydro

plants is limited and needs to be substituted by more expensive plant technologies

(oil and natural gas). Under these conditions, prices tend to escalate, reflecting

higher fuel costs. On the other hand, when water is abundant, cheap hydro

generation becomes substantial, implying lower market shares for oil and gas

generation, which brings prices down.

Before analyzing the most recent years, you have decided to analyze first daily

market prices from two consecutive years (2008 and 2009) of varying hydro

conditions: a dry one (2008) and a wet year (2009). These two years are interesting

not only from the hydro condition perspective but also based on new entries to the

market and an economic recession.

The data is provided in the file Electricity data.xlsx.

a) Plot the data and comment on their main features.

b) Develop, analyse, and interpret a regression model for the price - demand

relationship. Is it linear and does it stay the same over time?

c) Develop, analyse and interpret a regression model, to clarify how prices respond

to demand and hydro conditions.

d) A new plant started operating in October 2009. The competition authority would

like to check whether prices declined as a result, due to emerging competition, or

whether this plant may have colluded with existing players, retaining prices at

similar levels. Can you assist the competition authority in its preliminary

investigation?

e) How would you incorporate seasonality into the model you developed in part c)?

Describe.