Lecture 17 Revenue Management I – Overbooking

1

What is the expected revenue of selling S tickets?

NO shows

0 1 2 3

Revenue

# of tickets sold

0 1 2 3

Revenue

2

What is the expected profits of selling S tickets?

If S = 2

NO shows 0 1 2

Chance

Revenue

Cost

Profit

3

What is the expected costs of selling S tickets?

If S = 3

NO shows

0 1 2 3

Chance

Revenue

Cost

Profit

4

Summary

How does the profit when S=2 compares to the profit when S=3?

In this case does the airline want to overbook or not?

What are the factors that you think will influence the decision of overbooking?

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Important lessons for over-booking

The company should be more aggressive in over-booking when

The probability of no shows _______ The revenue from each paying traveler

________ The cost of dispensing over-booked

customers ________

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Lecture 18 Revenue Management II – Advance Selling

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Revenue Management for Multiple Customer Segments Two Fundamental Issues:

How to differentiate the segments? The firm must create barriers or fences such that

customers willing to pay more are not able to pay the lower price

Airline examples Saturday night stay Two-week advance reservation Nonrefundable tickets

How much demand from different segments should be accepted to maximize expected revenue?

The firm must limit the amount of capacity committed to lower price buyers, or the firm must save a certain amount of capacity for the higher price segment

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A two-segment problem (Littlewood model) Consider two customer segments

High-price buyers Low-price buyers

Basic trade-off Commit to an order from a low-price buyer or wait

for a high-price buyer to come Decision entails two sources of risk or uncertainty

Spoilage risk: capacity is spoiled when low-price orders are turned away but high-price orders do not materialize

Spill risk: revenue is spilled when high-price buyers have to be turned away because the capacity has been committed to low-price buyer

How should these risks be managed?

Revenue Management for Multiple Customer Segments

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Two-Segment Problem

Want to balance between Overprotection

Saving too much capacity for high-price buyers: lose guaranteed low-price segment revenue

Underprotection Accepting too many low-price buyers: forego later

high-price segment revenue

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Two-Segment Problem

Notation and terminology CH: capacity saved for high-price buyers

This is also called protection level, i.e., how much capacity is protected from being taken by low-price buyers

The available capacity minus the protection level is called the booking limit of low-price buyers

XH: high-price order demand random variable pH: price of high-price segment pL: price of low-price segment

Question: How should CH be determined?

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Two-Segment Problem

Overprotection probability: Pr{XH CH} denoted q(CH)

Underprotection probability: Pr{XH > CH} = 1 – q(CH) q(CH)q(CH)

1- q(CH)1- q(CH)

CHCH

• Consider a marginal increase of one unit of protection level for high-price segment.– Expected marginal cost: the opportunity cost of the wasted

unit capacity, which could have been certainly sold to a low-price buyer:

pL

– Expected marginal profit: the benefit if the unit capacity is later taken by a high-price buyer: pH [1 – q(CH)]

Distribution of high-price segment demand

Protection level of high-price segment

Two-Segment Problem At the optimal protection level, the net expected

marginal contribution should be equal to zero:–pL + pH [1 – q(CH)] = 0

or,q(CH) = 1 – pL/pH

or,Pr{XH CH}= 1 – pL/pH

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Hotel Example

Hotel has 210 rooms available for March 29th

Now is the end of February and the hotel is taking reservations for March 29th

Leisure travelers pay $100 per night Business travelers pay $200 per night Therefore 1 – pL/pH = 1 – 100/200 = 0.5

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Hotel Example

Historical demand by business travelers:

Demand Cumulative Distribution… …78 0.48879 0.501 80 0.517… …

The protection level is 79 rooms and the discount booking limit is 210 – 79 = 131 rooms

Two-Segment Problem

When XH is a continuous random variable we need to find the value for CH that satisfies the equality

Pr{XH CH} = 1 – pL/pH

When XH is a discrete random variable we need to find the smallest value of CH that satisfies the inequality

Pr{XH CH} 1 – pL/pH

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Two-Segment Problem with Uniform Demand

Suppose XH is uniformly distributed between a and b

Then the condition Pr{XH CH}= 1 – pL/pH is

equivalent to (CH – a)/(b – a) = 1 – pL/pH or

CH = a + (1 – pL/pH)(b – a)

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Hotel Example with Uniform Demand

Suppose XH is uniformly distributed with lower limit of 100 rooms and upper limit of 220 rooms

This means that a = 100 and b = 220

Consequently the protection level isCH = 100 + (1 – 1/2)(220 – 100) = 160 rooms

Therefore the low-price booking limit is210 – 160 = 50 rooms

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Revenue Management for Multiple Customer Segments

The discount booking limit depends on Capacity High-price demand probability distribution Fare ratio

The discount booking limit does not depend on the low-price demand distribution

The primary concern of capacity allocation is determining the capacity to save for high-price buyers

Need to think in terms of protection level Q – b not booking limit b

Protection level does not change when Q changes Analysis of booking limits gives insight into a company’s

fare structure

20

Hotel Example with Uniform Demand

Suppose XH is uniformly distributed with lower limit of 100 rooms and upper limit of 300 rooms

This means that a = 100 and b = 300

Consequently the protection level isCH = 100 + (1 – 1/2)(300 – 100) = 200 rooms

Therefore the low-price booking limit is210 – 200 = 10 rooms

21

Revenue Management for Multiple Customer Segments

The discount booking limit depends on Capacity High-price demand probability distribution Fare ratio

The discount booking limit does not depend on the low-price demand distribution

The primary concern of capacity allocation is determining the capacity to save for high-price buyers

Need to think in terms of protection level Q – b not booking limit b

Protection level does not change when Q changes Analysis of booking limits gives insight into a company’s

fare structure

22

Hotel Example with Uniform Demand

Suppose XH is uniformly distributed with lower limit of 100 rooms and upper limit of 220 rooms

This means that a = 100 and b = 220 Suppose Leisure travelers pay $100 per night Business travelers pay $300 per night Consequently the protection level is

CH = 100 + (1 – 1/3)(220 – 100) = 180 rooms

Therefore the low-price booking limit is210 – 180 = 30 rooms

Next Lecture Overview of Channel Management

(Guest Lecture by David Hardwicke)