1. Copyright Robert L. Phillips. 2006. All Rights Reserved. Copyright Robert L. Phillips 2006. All Rights Reserved A Decision Analytic Approach to Revenue Management Robert L. Phillips Nomis Solutions Stanford University March 13, 2006

2. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 2 Agenda Introduction to Revenue Management Elements of Revenue Management Capacity Control Overbooking Network Management An RM System Example

3. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 3 What is Revenue Management? The allocation of fixed capacity to different customer classes with different fares in order to maximize profitability. A special case of Pricing and Revenue Optimization, applicable in situations with: Fixed and perishable capacity (and therefore opportunity costs) Advanced bookings Fixed fare classes Uncertain demand and customer behavior (no-show, cancellation)

4. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 4 Basic Revenue Management Business Assumptions Fixed, immediately perishable capacity -- airline seat, hotel room night, gas pipeline capacity, etc. Units of capacity are identical - “a seat is a seat” Reservations (bookings) for future capacity accepted prior to its use Marginal costs per unit sale are fixed and small relative to price per unit A finite number of fixed prices are set ahead of time. The seller can control the number of units that he will provide for sale at each price at each time before departure. The seller has opportunities to change availabilities at intervals prior to departure based on bookings received. The goal of the seller is to control availability by fare class in each time before departure in order to maximize revenue (= contribution) This is the “basic revenue management” business problem. Each of the assumptions can be relaxed to create a variation.

5. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 5 History of Revenue (Yield) Management Early 60’s - Overbooking Analysis, News-vendor Problem Late 70’s - Airline deregulation 1981 - Rise of Peoples Express (Discount Airline) 1982 - Adoption of Controlled Super-Saver fares (American Airlines) 1983 - 1990 Development of first leg-based Airline Revenue Management Systems by major airlines. Development of Commercial Revenue Management Systems (Aeronomics, DFI, PROS, SABRE) 1985 - 1990 Development of early hotel (Marriott, Hyatt) Systems. Commercial hotel RM systems (Aeronomics, DFI, OPUS) 1989 First O&D Airline Revenue Management System (SAS) 1990 First Rental Car System (Hertz) 1990’s E-Commerce, distribution control, lifetime customer value issues 1995 - today. Pricing and Revenue Optimization Systems (Talus, Manugistics, Khimetrics, ProfitLogic, …)

6. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 6 Revenue Management Industries

7. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 7 The Basic Revenue Management Question A supplier (airline, hotel, made-to-order manufacturer) takes reservation for some stock of fixed capacity. A customer is “on the phone” requesting a particular fare. Do we say “yes” and sell him at the requested fare or do we say “no”? Why we would say yes: To get his revenue Why we might say no: Because we don't have sufficient capacity to accommodate him Because he might displace a future, more profitable booking

8. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 8 Revenue Management Elements Capacity Control: How to allocate limited capacity to different classes of customer? Overbooking: How many total bookings to accept? Network Management: How to manage bookings across a complex service network? Additional Topics: Customer value management; group management; integration with pricing, scheduling, etc We will discuss capacity control, overbooking, and network management.

9. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 9 Agenda Introduction to Revenue Management Elements of Revenue Management Capacity Control Overbooking Network Management An RM System Example

10. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 10 Basic Airline Segmentation Leisure Travelers Price Sensitive Book Early Schedule Insensitive f d = Discount Fare Business Travelers Price Insensitive Book Later Schedule Sensitive f f = Full fare

11. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 11 Two-Class Capacity Management Problem Fixed capacity C Two fare classes (full-fare and discount) with fares f f > f d > 0. Marginal costs are 0. Discount fares book first. All seats not sold at discount are available for sale at full fare. No cancellations or no-shows. The demands at each fare are random variables, d d and d f.. F f (x) = Probability that d f < x. How many seats should we save for late-booking full-fare customers?

12. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 12 Capacity Control Problem Tradeoffs Cannibalization - Seats were sold at f d, but some full-fare customers were turned away due to lack of seats. Cost = f d - f f for each full-fare customer turned away. Spoilage - Discount passengers were turned away but the plane left with empty seats. Cost = f d for each “spoiled” seat. How do we set b -- the first period booking limit -- to optimally balance cannibalization and spoilage and maximize expected total revenue?

13. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 13 Capacity Control Problem: Marginal Analysis Relative Impact Hold b Constant 0 f d - f f fdfd 0 b  b+1 d d < b d d > b d f > C - b d f < C - b 1-F d (b) 1- F f (C-b) F f (C-b) F d (b)

14. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 14 Optimality Condition for Two-Class Problem The optimal booking limit b* solves F f (C-b*) = 1 - f d /f f. This is known as Littlewood’s Rule. Littlewood's Rule is a simple variation on the standard critical fractile solution to the newsvendor problem.

15. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 15 Two ways to implement Littlewood's rule Set booking limit b* and hold Use Littlewood's rule as the basis a dynamic decision rule: Accept discount bookings as long as f d > [1-F f (C-x d )]f f, where x d is the number of discount bookings already accepted.

16. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 16 Interpreting Littlewood's Rule Acceptance Criterion: f d > [1-F f (C-x d )]f f This is expected opportunity cost! fdfd Expected Opportunity Cost

17. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 17 Total Revenue Expected DB Cost Expected Net Revenue Net revenue as a function of booking limit

18. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 18 Time Period: n n-1 321 … Fare: First Booking Departure fnfn f n-1 f3f3 f2f2 f1f1 Bookings: xnxn x3x3 x2x2 x1x1 x n-1 Low Fare BookingsHigh Fare Bookings Standard Structure for Multi-Class Problem The basic assumption -- bookings occur in order of fare, that is: low to high.

19. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 19 Nesting -- a Three-Class Example x 1 = seats reserved for 3 x 2 = seats reserved for 2 and 3 b 2 = Booking Limit for 2 b 1 = Booking Limit for 1 We assume three classes 1,2, and 3, booking in order, with f 1 < f 2 < f 3 Aircraft Seating Capacity

20. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 20 Relative Impact Hold b 3 Constant 0 p 3 – p 1 p3p3 0 b 3  b 3 +1 d 3 < b 3 d d > b 3 Displace Class 1 Booking 1-F 3 (b 3 ) No Displacement F 3 (b 3 ) Displace Class 2 Booking p 3 – p 2 q1q1 q2q2 1-q 1 -q 2 Capacity Control with three fare classes

21. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 21 Solving the multi-class problem In general, the capacity allocation problem with more than two classes does not have a closed-form solution. Two solution alternatives: Solve by dynamic programming -- generally too computationally intensive. EMSR heuristics -- formulate as a series of two-class problems and approximate the solution.

22. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 22 Introduction to Revenue Management Elements of Revenue Management Capacity Control Overbooking Network Management An RM System Example Agenda

23. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 23 Overbooking Airlines and other industries historically allowed passengers to cancel or no- show without penalty. Airlines book more passengers than their capacity in order to hedge against this uncovered call, Airlines need to balance two risks when overbooking: Spoilage: Seats leave empty when a booking request was received. Lose a potential fare. Denied Boarding Risk: Accepting an additional booking leads to an additional denied-boarding.

24. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 24 Denied Boarding Cost Consists of four elements: 1. Provision Cost of meals or lodging provided 2. Reaccom Cost of putting a bumped passenger on another flight 3. Direct Cost of direct compensation to the passenger -- usually a discount certificate for future travel 4. Ill-will Cost for involuntary denied boarding. Voluntary denied boardings have a higher cost than involuntary denied boardings.

25. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 25 Denied Boarding Rates Denied Boarding Rates per 100,000 Boardings Source: US DOT. Large US domestic Carriers

26. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 26 Marginal Analysis: Overbooking D < b 0 f-d f 0 s does not increase s  s+1 (s|b) > C (s|b) < C b  b+1 Relative Impact D > b F(b) p (1-p)

27. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 27 Overbooking Problem Solution We want to find the smallest b* such that: F(b*)p[Pr{(s|b*)>C}(f-d) + Pr{(s|b*)<C}f] = 0 or: Pr{(s|b*) > C}(f-d) +[1- Pr{(s|b*) > C}]f = 0 Pr{(s|b*) > C} = f/d

28. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 28 Overbooking Revenue $8,000 $9,000 $10,000 $11,000 90100110120 Booking Limit Revenue C b* Passenger Revenue Overbooking Cost Net Revenue

29. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 29 Departure Capacity Time Bookings Booking Limit Bookings No-show “Pad” AB Overbooking Dynamics

30. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 30 Introduction to Revenue Management Elements of Revenue Management Capacity Control Overbooking Network Management An RM System Example Agenda

31. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 31

32. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 32... MondayTuesdayWednesdayThursdayFriday Resources: Monday 3-Night Stay Tuesday 2-Night Stay Wednesday 3-Night Stay Products:... Hotel Network Friday 1-Night

33. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 33 SFO SAC RNO SLC GSC DEN OMA CHI Passenger Train Capacity and Load

34. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 34 Hotel Example Capacity Unconstrained Occupancy Day of Week

35. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 35 San Francisco (SFO) Denver (DIA) St. Louis (STL) Flight 1Flight 2 Why the Problem is Hard SFO – STL Fare = $400 SFO – DIA Fare = $200 DIA – STL Fare = $250 Which passengers we want to accept depends upon expected demands for all products. Sometimes we prefer SFO-STL pax, sometimes we prefer SFO-DIA or DIA-STL pax.

36. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 36 San Francisco (SFO) Denver (DIA) St. Louis (STL) Flight 1Flight 2 When the Problem Really gets Interesting... MarketY-ClassM-ClassB-ClassG-Class SFO-STL$600$400$300$250 SFO-DIA$280$200$150$140 DIA-STL$350$250$180$110

37. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 37 San Francisco (SFO) Denver (DIA) St. Louis (STL) Flight 1Flight 2 Bid Pricing MarketY-ClassM-ClassB-ClassG-Class SFO-STL$600$400$350$250 SFO-DIA$280$200$150$140 DIA-STL$350$250$180$110 BP = $190 BP = $230 Set a bid price equal to the opportunity cost (λ) on each leg.

38. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 38 MonTueWedThurFriSatSun 31 d=85 b=$84.34 1 d=93 b=$92.07 2 d=112 b=$153.12 3 d=108 b=$112.34 4 d=99 b=$92.57 5 d=65 b=$54.30 6 d=80 b=$62.33 7 d=91 b=$88.47 8 d=102 b=$122.00 9 d=135 b=$172.15 10 d=120 b=$142.34 11 d=92 b=$95.67 12 d=53 b=$42.34 13 d=44 b=32.34 14 d=67 b=$54.37 15 d=85 b=$72.48 16 d=110 b=$122.47 17 d=97 b=$99.97 18 d=93 b=$92.34 19 d=72 b=$55.18 20 d=66 b=$54.54 21 d=86 b=$89.11 22 d=104 b=$130.02 23 d=157 b=$199.93 24 d=140 b=$178.25 25 d=122 b=$122.20 26 d=95 b=100.69 27 d=85 b=$85.18 28 d=84 b=$84.33 29 d=92 b=$93.44 30 d=114 b=$155.67 31 d=100 b=$101.01 1 d=82 b=$78.77 2 d=60 b=$53.92 3 d=75 b=$62.74 Hotel Bid Price Calendar

39. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 39 Agenda Introduction to Revenue Management Elements of Revenue Management Capacity Control Overbooking Network Management An RM System Example

40. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 40 Sporting Event Revenue Management A classic Revenue Management opportunity: Fixed, immediately perishable inventory Seating sections in stadiums are similar to cabins in airplanes Section prices are fixed prior to season starting Season tickets are offered first; all other seats are free-sell Bookings come in over time…from a year out to the day of the game Most baseball teams have a range of discounts that apply to a seating sections - market segments Jnr, Snr, 4H, buy-one-get-one-free

41. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 41 EventRM – Challenges Industry resistant to change - Very risk averse -- like quick sell-outs (especially concerts) Fear public perception of venue trying to “gouge” the fans with higher prices -- want to increase revenue without increasing price Bookings do not follow traditional industry approach of lowest value books first, highest value books last value of ticket is not correlated to time of booking Availability denials not currently captured Data can be sparse

42. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 42 EventRM – What it Does Forecasts demand for each market segment historical data enables market segmentation Maximizes expected revenue from forecasted remaining demand into remaining capacity Recommends which market segments to sell to venue sets rate structure for market segments event manager determines which market segments are always open event manager has final say on which segments to keep open for sale or to close DOES NOT recommend changes in price

43. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 43 Event Overview

44. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 44 Pricing Screen

45. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 45 Booking Pace

46. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 46 Demand Forecast

47. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 47 Optimization Parameters

48. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 48 Re-Optimize

49. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 49 Optimization

50. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 50 Availability Controls

51. Copyright Robert L. Phillips. 2006. All Rights Reserved. Property of Nomis Solutions Inc. - Confidential Material Page 51 Summary Revenue management is the science of setting availabilities for multiple fare classes in the case in which capacity is constrained and perishable. The decision analytic approach gives lots of insight and some useable answers to basic revenue management problems without lots of annoying multiple integrals! Many dynamic revenue management implementations involve calculating the opportunity cost of a unit of remaining capacity and accepting only those requests whose fare exceeds the opportunity cost.