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Lecture 17 Revenue Management I – Overbooking

Lecture 17 Revenue Management I – Overbooking. What is the expected revenue of selling S tickets?. What is the expected profits of selling S tickets?. If S = 2. What is the expected costs of selling S tickets?. If S = 3. Summary. How does the profit when S=2 compares to the profit when S=3?

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Lecture 17 Revenue Management I – Overbooking

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  1. Lecture 17Revenue Management I – Overbooking

  2. What is the expected revenue of selling S tickets?

  3. What is the expected profits of selling S tickets? • If S = 2

  4. What is the expected costs of selling S tickets? • If S = 3

  5. 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?

  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 18Revenue 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 thebooking limitof 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. 1- q(CH) q(CH) CH Two-Segment Problem Distribution of high-price segment demand • Overprotection probability: Pr{XH £CH} denoted q(CH) • Underprotection probability: Pr{XH > 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, Pr{XH £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 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} ³1 – pL/pH

  17. 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)

  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 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 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 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 is 210 – 180 = 30 rooms

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

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