Assignement - Airline Overbooking Issue

EMBA 2016, MSB, TUNISIA

Business Statistics

May 19th to 22sd

Personal Assignment

Prof. Kristín  Friðgeirsdóttir

Student: Nader Ben Sheikh Brahim

Problem 1: Airline Overbooking

WOW air: new low cost airline, with planes (most) having 200 seats

Target is to manage the overbooking strategy (like all airlines, WOW is selling more tickets on a flight than seats).

No-Show Probability: 5%

We will use binominal distribution to help WOW managers decide

Our two possible outcomes would be: Show up and does not show up

We will approximate the binominal distribution with a normal distribution (number of passengers that show up is normally distributed) where:

• Mean = n*p
• SD =   [pic 2]

1. If we sell 209 seats

N= 209

P= 0.95 (P to show)

(1-P) = 0.05 (P to not show)

What is the Probability to have an overbooking situation?

It means, what is the probability to have customers showing up, more then 200

•  P(X>=201)

Z =    where  [pic 3]

        X = 201

        Mean = n*p = 209 * 0.95

        SD = [pic 4]

We notice that                 n*p = 198.55                   

n*p*(1-p) = 9.9275

We notice that both of them is bigger then 5, which mean that we can continue approximating a binominal with a nominal.

We get then:  

Z = 0.78

P(Z>=0.78) = 0.218 (21.8%)

In another hand, we can just directly use excel with following function:

        Norm.Dist (201;198,55;3,15;TRUE)= 0,218 (21.8%)

1. If we sell 218 seats

N=218

Mean= 218*0.95= 207.1

SD= SD = =3.217[pic 5]

What is the probability of having empty seats?

 →   it means that showing customers number is below 200.

P(Z<=199) = 0.006

We obtain same result with excel: Norm.dist(199;207.1;3.217;TRUE) = 0.006

1. If the company target 2% probability of an overbooking situation, how many tickets should it sell?

• It means that the probability of getting customers showing up at the flight, must be 98%
• The probability of number of customer showing up is bigger then 200, is 2%

We can use the table and we will see that corresponding Z to 2% probability is: 2.06 with P= 0.197

Z=   [pic 6]

We can check, by considering different values for n and calculating the probability see below:

I think selling 203 tickets is the answer, as if we go to 204 we have a probability over 2%.

1. Missing data for a better understanding and forecasting:

• Exact number of planes the company owns? Exact number of seats in each one?
• More detailed historical data?
• The company overbooking policy: what happens when they have showing up people more than seats? What is the financial impact of that?
• Proportions of combined reservations? (sometimes we have 2, 3 or more people in one reservation)

Problem 2: Managing Subscriptions at London Today

• LT is giving trial subscriptions to potential customers.
• Target is to convert as much as possible trial subscriptions to regular one.
• Marketing department to forecast next month’s new regular subscriptions.
•  Group of managers, forecasting are looking for 2 to 3 months ne subscriptions data
• JG, newly hired, suggested to look for factors that are helpful in predicting
• Some forecast in some months were inaccurate, because of time spent by telemarketers in training
• JG suggested getting number of new subscriptions and number of hours spent on telemarketing.

1. I think it is useless to forecast based on 3 months only Data. The model would be for sure insignificant.

Besides logically speaking, we need sure more historical Data to better forecast.

1. If we do the regression model, using the 24 months data, we obtain:

[pic 7]

As we can see, the chosen variable (number of hours spent in telemarketing), explain 85% of our number of new subscriptions variability, which is already good, but also, It means somewhere that we have some wiggle room to improve our model.