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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?
5
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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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