1. Demand and Revenue Management
Anton J. Kleywegt
April 2, 2008

2. Revenue Management What is Revenue Management
Why do Revenue Management
Pricing Optimization
Demand Modeling and Forecasting

3. What is Revenue Management
Management of inventory, distribution channels and prices to maximize profit over the long run
Selling the right product to the right customer at the right time at the right price

4. What is Revenue Management
Revenue Management involves the following activities
Demand data collection
Demand modeling
Demand forecasting
Pricing optimization
System implementation and distribution

5. What is Revenue Management
Airline industry
How many seats to make available at each of the listed fares, depending on the OD pair, time of year, time of week, remaining seats available, remaining time until departure
What contracts and prices to provide to corporations
How many seats to make available to consolidators and travel agents (if at all), and at what prices
How much capacity to make available to cargo shippers and freight forwarders, and at what prices

6. What is Revenue Management
Hotel industry
How much to charge for a room depending on the location, type of room, time of year, time of week, duration of stay

7. What is Revenue Management
Ocean cargo industry
Which types of contracts to enter into with shippers
How much capacity to commit to each shipper
Which contract prices to have for each shipper
How to vary prices as a function of direction of trade, commodity, and time of year

8. What is Revenue Management
Car rental industry
How much to charge for a rental car depending on the class of car, time of year, time of week, duration of rent
Restaurant industry
How much to charge for lunch vs dinner

9. What is Revenue Management
Manufacturing industry
Make-to-stock: dynamic pricing of inventory
Make-to-order: dynamic pricing of orders, how much discount to give for orders in advance
Make-to-stock and make-to-order: prices of advance orders vs prices of inventory

10. What is Revenue Management
Retail industry
Example: fashion apparel industry
Products in fashion for a single season
Retailer wants to sell available inventory for maximum profit
Prices higher at start of season
Retailer has to decide when to mark prices down, and by how much

11. What is Revenue Management
Entertainment ticket pricing
Example: opera houses let their ticket prices depend on
The performance
The reviews received so far
Location of seat in opera house
Day of the week of the performance
Time of the day of the performance
Time of performance in the season
Remaining time until the performance
Number of remaining seats available

12. What is Revenue Management
Golf courses
Variable pricing: Choose prices to vary by
time of day
day of week
season of year
Round duration control
control tee-time interval
control uncertainty in arrival time
control uncertainty in duration

13. Hospital Contract Case Study
Major customers of hospitals
Insurance companies
Medicare
Medicaid
Individuals
Hospital contracts with major customers
Discount-off-listed-charges contracts
Per-diem contracts
Case-rate contracts
Capitation contracts

14. Hospital Contract Case Study
Example of setting per-diem rates

15. Hospital Contract Case Study
Example of setting per-diem rates
Observe that most patients stay for only a few days, although a few patients make the average length of stay quite high
Stratified per-diem rates
Charge more per day to patients who stay for only a few days
Results
Higher average revenue
Lower standard deviation of revenue

16. Hospital Contract Case Study
Higher average revenue clearly beneficial to the hospital
Lower standard deviation of revenue
Beneficial to the hospital?
Yes. More predictable revenue
Beneficial to the insurance company?
Yes. More predictable costs

17. What is Revenue Management
Overbooking may be part of revenue management
Overbooking important practice in many industries that use reservations, and where cancellations or no-shows may occur
airlines
hotels
car rental
cruise lines
restaurants
contractors (construction etc)

18. What is Revenue Management
Overbooking
Important trade-off between opportunity cost of unused resources if cancellations or no-shows cause resources to be wasted, and cost of oversales
In 1960’s, Simon and Vickrey proposed the use of auctions to allocate airline seats in case of oversales
Airlines rejected idea for many years
Nowadays, reverse Dutch auctions are widely used to allocate airline seats in case of oversales, and seem to be widely accepted

19. What is Revenue Management
Dynamic pricing and the bullwhip effect
Dynamic pricing can increase demand variability
The case of Campbell Soup
Wild swings in demand and in shipments of chicken noodle soup from the manufacturer to distributors and retail stores
Increase in production, storage and logistics costs
Frequent stockouts resulting in lost sales
The culprit: Trade promotions!

20. What is Revenue Management
Dynamic pricing and the bullwhip effect
Dynamic pricing can be used to decrease demand variability
Peak load pricing: lower prices during off-peak times, higher prices during peak times
Airlines
Hotels
Golf courses
Electricity wholesale market
Oil/gasoline?

21. What is Revenue Management
Revenue Management may involve price discrimination, but it does not have to
130
Consumer surplus=1800
P=130-Q
Unit cost = 10
Firm’s profits
under single price:
(130-Q-10)Q 60 70 P
Firm profits=3600
Deadweight loss=1800
MC=10 q
130

22. Price Discrimination (continued)
P=130-Q
Unit cost = 10
What if the firm
could segment
the market and charge two
different prices?
130
Consumer surplus=1600 90 P
Firm profits=4800 50
Deadweight loss=800
MC=10 q 40 80
130

23. Price Discrimination (continued)
130
110
Consumer surplus=1000 90 P 70
Firm profits=6000 50
Deadweight loss=200 30
MC=10 q 20 40 60 80
100
130

24. Price Discrimination (continued)
Perfect price
discrimination
130
Consumer surplus=0
Deadweight loss=0
Firm profits=7200 P
MC=10 q
130

25. What is Revenue Management
The same product sold at different times for different prices is not necessarily price discrimination, because at different times...
the production or distribution costs may be different
inventory costs were incurred to keep the product in stock until a later time
the product value may change over time, such as perishable or maturing or seasonal products, fashion goods, antiques.
the remaining inventory may be different
interest is earned if product is sold at an earlier time
consumers value products differently at different points in time
locking sales in early reduces uncertainty

26. What is Revenue Management
It is not spam

27. Fairness and Legal Issues
Depending on the industry, there may be legal obstacles to revenue management
Examples
Regulated prices of utilities (this is changing)
Prices in airline industry were regulated until price and quantity changes had to be approved by CAB
Pricing in ocean cargo industry was regulated until carriers had to provide all shippers with the same essential contract terms
Spot market pricing in ocean cargo industry is still regulated - 30 days notice required for price increases

28. Fairness and Legal Issues
Golf course examples
Kimes and Wirtz survey results (1 = extremely fair, 7 = extremely unfair)
Time-of-day pricing: 3.41
Varying price (for example, as function of bookings on hand): 6.16
Two-for-one coupons for off-peak use: 1.80
Time-of-booking pricing: 5.12
Reservation fee/Charge for no-shows: 3.19
Tee-time interval pricing: 3.95

29. Fairness and Legal Issues
Amazon.com example
Fall 2000, Amazon conducted experiment to try to determine price sensitivity of demand for DVDs
Discounts between 20% and 40% offered randomly
Customers who visited amazon.com multiple times noticed changing prices
Furious response by customers and press, suspecting Amazon varied price by demographics
Why are varying airline prices accepted by most, and not varying DVD prices?

30. Why do Revenue Management
Success stories
American Airlines increased annual revenue with $500 million through revenue management
Delta Airlines increased annual revenue with $300 million through revenue management
Marriott hotels increased annual revenue with $100 million through revenue management
National Car Rental was saved from liquidation with revenue management
Canadian Broadcasting Corporation increased revenue with $1 million per week

31. Why do Revenue Management
Increasing competition
Fewer restriction on international trade
More efficient international transportation
Low cost foreign competitors
Competitors use revenue management
Use revenue management to stay on top

32. Why do Revenue Management
At many companies, little cost-cutting juice can easily be extracted from operations. Pricing is therefore one of the few untapped levers to boost earnings, and companies that start now will be in a good position to profit fully from the next upturn. – McKinsey Quarterly, 2003

33. Revenue Management Optimization
Control Methods
Resource Bucket Control Methods
Bid Price Control Methods
Dynamic Programming
Software

34. Revenue Management Optimization
Control Methods/Optimization Methods
OD based
Stochastic
Leg Based
Deterministic
Static
Dynamic

35. Revenue Management Optimization
Resource Bucket Control Methods
If supply of different products are related, for example if different products use shared resources or capacity, then revenue management should not be done separately for the different products
Also if demand for products are related, for example complementary goods or substitutes
Examples
Airlines: Itineraries with different origin-destination pairs share the same flight legs (resource)
Hotels and rental cars: Multiple day bookings share capacity

36. Revenue Management Optimization
Bid price methods
Simple single-stage deterministic LP model
Input:
Lines of flight (LOF)
The flights (legs/segments) each LOF traverses (flight-LOF incidence matrix A)
Fares f1,f2,…,fk for each LOF
Demand Dj for each LOF-fare combination j (not well-defined notion)
Capacity Qi of each flight (leg/segment) i
Primal decision variables:
xj = number of seats allocated to LOF-fare combination j

37. Revenue Management Optimization
Dynamic programming
State of process: current bookings/seats available for each flight, competitor information
Transitions: take place through bookings and cancellations
Decisions: which prices/fares are quoted when booking requests are received
Policy: decision for each state x and time t
Objective: determine optimal policy
Value function: expected value V(x,t) as function of state x and time t
Solving problem involves computing optimal value function V*(x,t)
Another benefit: Optimal policy very simple:
accept booking request if fare > V*(x,t) - V*(x-1,t)

38. Revenue Management Optimization
Optimization Software Surveys
Fourer, R., “Linear Programming”, OR/MS Today, volume 32, number 3, pp , June 2005, < survey.html>.
Nash, S. G., “Nonlinear Programming”, OR/MS Today, volume 25, number 3, pp , June 1998, < html>.
Grossman, T.A., “Spreadsheet Add-Ins for OR/MS”, OR/MS Today, volume 29, number 4, pp , August 2002, < html>.

39. Revenue Management Optimization
Decision Support Software Surveys
Aksoy, Y. and Derbez, A., “Software Survey: Supply Chain Management”, OR/MS Today, volume 30, number 3, pp , June 2003, <
Buede, D., “Decision Analysis Software Survey: Aiding Insight IV”, OR/MS Today, volume 25, number 4, pp , August 1998.
Hall, R., “Vehicle Routing Software Survey: On the Road to Recovery”, OR/MS Today, volume 31, number 3, pp , June 2004, < .html>.
Maxwell, D.T., “Decision Analysis: Aiding Insight VII”, OR/MS Today, volume 31, number 5, pp , October 2004, <
Swain, J. J., “'Gaming' Reality: Biennial survey of discrete-event simulation software tools”, OR/MS Today, volume 32, number 6, pp , December 2005, < n.html>.
Swain, J. J., “Power Tools for Visualization and Decision-Making”, OR/MS Today, volume 28, number 1, pp , February 2001.

40. Demand Forecasting
The first law of forecasting: The forecast is always wrong
Sources of forecast error:
Modeling error
Parameter error
Measurement error

41. Demand Forecasting Modeling error
The basic form of the demand model is wrong
Example
Suppose we want to forecast demand d as a function of price p
The true demand function is d = exp(3-2p) / (1 + exp(3-2p))
We try to estimate a linear demand model d = a – bp, with parameters a and b that are estimated with data
No matter what values we estimate for a and b, the estimated model is wrong – modeling error

42. Demand Forecasting Parameter error
The basic form of the demand model is correct, but we do not know the correct values of the parameters
Example
The true demand function is d = exp(3-2p) / (1 + exp(3-2p))
We try to estimate a demand model d = exp(a-bp) / (1 + exp(a-bp)), with parameters a and b that are estimated with data
If we estimate a=3 and b=2 (for example, with good data and a good statistical technique), then the estimated model is correct

43. Demand Forecasting Measurement error
The basic form of the demand model is correct, but we do not know the correct values of the parameters, and data errors make it impossible to use statistical techniques to estimate the parameter values
Example
The true demand function is d = exp(3-2p) / (1 + exp(3-2p))
We try to estimate a demand model d = exp(a-bp) / (1 + exp(a-bp)), with parameters a and b that are estimated with data
Because of bad data, we estimate a=4 and b=-1

44. Demand Modeling
It is very important to understand and model customer behavior accurately
Incorrect models of customer behavior can lead not only to suboptimal prices, but can lead to the systematic deterioration of models, prices, and profits over time – the spiral-down effect

45. Demand Modeling Spiral-down effect in airline revenue management
For many years, airlines have used following simple model of customer behavior
Some time before departure, customer requests a ticket in a particular fare class
Airline accepts or rejects the request
Above model describes the way airline reservations systems work
However, it does not accurately describe the way customers behave

46. Demand Modeling Spiral-down effect in airline revenue management
Low fare tickets and high fare tickets
Airlines set aside chosen number of seats for high fare tickets
Airlines use observed sales to estimate the supposed “demand for high fare tickets”

47. Demand Modeling Spiral-down effect in airline revenue management
Airline allows some low fare sales
Some flexible customers (not modeled by the airlines) willing to buy high fare if that is the only option, now buy low fare tickets
Airlines observe more low fare sales and less high fare sales – decrease their estimate of “high fare demand”
Airlines set aside fewer seats for high fare tickets, and allow more low fare sales
More customers buy low fare tickets, and the spiral down continues
Spiral-down effect is the consequence of an incorrect model of customer behavior

48. Demand Forecasting Forecasting methods Judgmental methods
Statistical forecasting methods

49. Demand Forecasting Judgmental forecasting methods “Expert” opinion
Questionable: See the articles
Armstrong, J.S., “How Expert Are the Experts?”, Inc, pp.15-16, 1981
Armstrong, J.S., “The Seer-Sucker Theory: The Value of Experts in Forecasting”, Technology Review, pp.16-24, 1980
Consensus methods, such as Delphi technique

50. Demand Forecasting Statistical forecasting methods Non-causal methods
Exponential smoothing
Time series methods
Causal methods
Linear regression
Nonlinear regression
Discrete choice models (logit, probit, etc)
Whatever the method, the basic approach is to find systematic behavior in data that one has reason to believe will continue in the future

51. Demand Forecasting Forecasting software surveys:
Yurkiewicz, J., “Forecasting: Predicting Your Needs”, OR/MS Today, volume 31, number 6, pp , December 2004, < fr.html>.
Swain, J. J., “Desktop Statistics Software: Serious Tools for Decision Making”, OR/MS Today, volume 26, number 5, pp , October 1999.
Swain, J. J., “Looking for Meaning in an Uncertain World”, OR/MS Today, volume 28, number 5, pp , October 2001.
Swain, J. J., “2005 Statistical Software Products Survey: Essential Tools of the Trade”, OR/MS Today, volume 32, number 1, pp , February 2005, < survey.html>.

52. Revenue Management Implementation
Business case: assessment of
Revenue opportunity
Development and support personnel needs
Development cost
Maintenance cost
Hardware
Software
DBMS
Forecasting
Optimization
Interfaces

53. Revenue Management Implementation
Distribution system
Communication network hardware
Interfaces with revenue managers
Interfaces with customers
Management of customer awareness and customer perceptions
Management of organizational change

54. Questions?