Lecture 17 Revenue Management I – Overbooking 1

What is the expected revenue of selling S tickets? NO shows Revenue # of tickets sold Revenue 2

What is the expected profits of selling S tickets? If S = 2 NO shows Chance Revenue Cost Profit 3

What is the expected costs of selling S tickets? If S = 3 NO shows 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 ________ 6

Lecture 18 Revenue Management II – Advance Selling 7

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 8

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 9

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 10

Two-Segment Problem Notation and terminology C H : 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 X H : high-price order demand random variable p H : price of high-price segment p L : price of low-price segment Question: How should C H be determined? 11

12 Two-Segment Problem Overprotection probability: Pr{X H  C H } denoted q(C H ) Underprotection probability: Pr{X H > C H } = 1 – q(C H ) q(CH)q(CH) q(CH)q(CH) 1- q(C H ) CHCH 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: p L – Expected marginal profit: the benefit if the unit capacity is later taken by a high-price buyer:p H  [1 – q(C H )] 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: –p L + p H [1 – q(C H )] = 0 or, q(C H ) = 1 – p L /p H or, Pr{X H  C H }= 1 – p L /p H 13

Hotel Example Hotel has 210 rooms available for March 29 th Now is the end of February and the hotel is taking reservations for March 29 th Leisure travelers pay $100 per night Business travelers pay $200 per night Therefore 1 – p L /p H = 1 – 100/200 = 0.5

15 Hotel Example Historical demand by business travelers: DemandCumulative Distribution…  … The protection level is 79 rooms and the discount booking limit is 210 – 79 = 131 rooms

Two-Segment Problem When X H is a continuous random variable we need to find the value for C H that satisfies the equality Pr{X H  C H } = 1 – p L /p H When X H is a discrete random variable we need to find the smallest value of C H that satisfies the inequality Pr{X H  C H }  1 – p L /p H 16

Two-Segment Problem with Uniform Demand Suppose X H is uniformly distributed between a and b Then the condition Pr{X H  C H }= 1 – p L /p H is equivalent to (C H – a)/(b – a) = 1 – p L /p H or C H = a + (1 – p L /p H )(b – a) 17

18 Hotel Example with Uniform Demand Suppose X H 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 C H = (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 company’s fare structure

20 Hotel Example with Uniform Demand Suppose X H 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 C H = (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 company’s fare structure

22 Hotel Example with Uniform Demand Suppose X H 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 C H = (1 – 1/3)(220 – 100) = 180 rooms Therefore the low-price booking limit is 210 – 180 = 30 rooms

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