Lecture 17 Revenue Management I

1
Lecture 17 Revenue Management I Overbooking
2
What is the expected revenue of selling S tickets?
NO shows 0 1 2 3
Revenue
of tickets sold 0 1 2 3
Revenue
3
What is the expected profits of selling S tickets?

• If S 2

NO shows 0 1 2
Chance
Revenue
Cost
Profit
4
What is the expected costs of selling S tickets?

• If S 3

NO shows 0 1 2 3
Chance
Revenue
Cost
Profit
5
Summary

• How does the profit when S2 compares to the
  profit when S3?
• In this case does the airline want to overbook or
  not?
• What are the factors that you think will
  influence the decision of overbooking?

6
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
  ________

7
Lecture 18 Revenue Management II Advance
Selling
8
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

9
Revenue Management for Multiple Customer Segments

• 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?

10
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

11
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?

12
Two-Segment Problem
Distribution of high-price segment demand

• Overprotection probability PrXH CH denoted
  q(CH)
• Underprotection probability PrXH gt CH 1
  q(CH)

Protection level of high-price segment

• 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)

13
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,
• PrXH CH 1 pL/pH

14
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

15
Hotel Example

• Historical demand by business travelers
• Demand Cumulative Distribution
• 78 0.488
• 79 0.501 ³ 0.5
• 80 0.517
• The protection level is 79 rooms and the discount
  booking limit is 210 79 131 rooms

16
Two-Segment Problem

• When XH is a continuous random variable we need
  to find the value for CH that satisfies the
  equality
• PrXH CH 1 pL/pH
• When XH is a discrete random variable we need to
  find the smallest value of CH that satisfies the
  inequality
• PrXH CH ³ 1 pL/pH

17
Two-Segment Problem with Uniform Demand

• Suppose XH is uniformly distributed between a and
  b
• Then the condition PrXH CH 1 pL/pH is
• equivalent to (CH a)/(b a) 1 pL/pH or
• CH a (1 pL/pH)(b a)

18
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 is
• CH 100 (1 1/2)(220 100) 160 rooms
• Therefore the low-price booking limit is
• 210 160 50 rooms

19
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
  companys 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 is
• CH 100 (1 1/2)(300 100) 200 rooms
• Therefore the low-price booking limit is
• 210 200 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
  companys 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 is
• 210 180 30 rooms

23

• Next Lecture
• Overview of Channel Management
• (Guest Lecture by David Hardwicke)