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Seminar 2 Overbooking

1. The Family Inn is considering overbooking due to frequent no-shows leaving rooms empty. No-shows cost $69 per room while paying for an overbooked guest costs $119. The expected gain from overbooking per night would be $69 * 4 + $119 * 3 + $69 * 2 + $119 * 1 = $828 2. Surfside Hotel analyzes no-show data and finds costs are $40 per empty room and $100 per turned away guest. (a) Expected gain is $40 * probability of 0-8 no-shows. (b) Yes, the no-show policy should be revised if costs are $100 per empty room instead of $40.

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Ana Florea
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335 views2 pages

Seminar 2 Overbooking

1. The Family Inn is considering overbooking due to frequent no-shows leaving rooms empty. No-shows cost $69 per room while paying for an overbooked guest costs $119. The expected gain from overbooking per night would be $69 * 4 + $119 * 3 + $69 * 2 + $119 * 1 = $828 2. Surfside Hotel analyzes no-show data and finds costs are $40 per empty room and $100 per turned away guest. (a) Expected gain is $40 * probability of 0-8 no-shows. (b) Yes, the no-show policy should be revised if costs are $100 per empty room instead of $40.

Uploaded by

Ana Florea
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Overbooking Problem

1. Family Inn
Problem Statement
A family-run inn is considering the use of overbooking, because the frequency of no-
shows has left many rooms vacant during the past summer season. An empty room
represents an opportunity cost of $69, which is the average room rate.
Accommodating an overbooked guest is expensive. The inn must however, because
the nearby resort rooms average $119 and the inn must pay the difference.

No-shows 0 1 2 3
Frequency 4 3 2 1

Question
What would be the expected gain per night from overbooking?

2. Surfside Hotel
Problem Statement
During the past tourist season, Surfside Hotel did not achieve very high occupancy
despite a reservation to keep the hotel fully booked. Apparently, prospective guests
were making reservation that, for one reason or another, they failed to honour. A
review of front- desk records during the current peak period, when the hotel was fully
booked revealed the record of no-shows given in the Table 1.

No- Probability Reservation Cumulative Probability


shows d P(d) Overbooked x P(d < x)
0 .07 0 0
1 .19 1 0.7
2 .22 2 0.26
3 .16 3 0.48
4 .12 4 0.64
5 .10 5 0.76
6 .07 6 0.86
7 .04 7 0.93
8 .02 8 0.97
9 .01 9 0.99

Table 1. No-shows Experience


A room that remains vacant because of a no-show result in an opportunity loss of the
$40 room contribution. The unit cost of overbooking (the cost incurred in turning a
customer away) is $100.
Questions
a) What would be the expected gain per night from overbooking?
b) What if the unit cost of no-shows (the revenue is lost due to an empty room or
seat) is $100? Should Surfside Hotel revise its no-show policy?

3. The clinic
Problem Statement
An outpatient clinic has kept a record of walk-in patients during the past year. The
table below shows the expected number of walk-ins by day of the week:
Day Mon. Tues. Wed. Thurs. Fri.
Walk-ins 50 30 40 35 40
The clinic has a staff of five physicians, and each can examine 15 patients a day on
average.
a) What is the maximum number of appointments that should be scheduled for
each day if it is desirable to smooth out the demand for the week?
b) Why would you recommend against scheduling appointments at their
maximum level?
c) If most walk-ins arrive in the morning, when should the appointments be made
to avoid excessive waiting?

4. The airline company


Problem Statement
A commuter airline overbooks all its flights by one passenger (i.e. the ticket agent will
take seven reservations for an airplane that only has six seat). The no-shows
experience for the past 20 days is shown below:

No-shows 0 1 2 3 4
Percentage 30 25 20 15 10

Using the critical fractile 𝑃(𝑑<𝑥) = 𝐶𝑢 ⁄(𝐶𝑢 + 𝐶𝑜 ) find the maximum implied
overbooking opportunity loss Co if the revenue Cu from a passenger is $20.

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