Dynamic Pricing and Yield Management

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Dynamic Pricing and Yield
Management

• Yossi Sheffi
• Professor, MIT

MIT Executive Course January 7th, 2003
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Outline

• Airline revenue management
• An analytical model of seat reservation
• The essence of price discrimination
• Revenue management in TL trucking

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Yield/Revenue Management

• Objective maximize revenue (minimize lost
  revenue / opportunity costs)
• Science of squeezing every possible dollar from
  customers

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Revenue Management Example
R25,000
50
500
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Revenue Management Example
of Seats
Lost Revenue Affordability
100
Lost Revenue M.O.T.T
50
1,000
500
Price
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Revenue Management Example
of Seats
100
R31,250
50
25
750
1,000
500
Price
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Revenue Management Example
of Seats
100
R37,500
75
50
25
750
1,000
500
250
Price
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Revenue Management Example
of Seats
Maximum Revenue (area under the curve) 50,000
100
1,000
Price
Note willingness to pay ? happiness to pay
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Two Challenges

• How do we make sure that the people who are
  willing to pay 750 will not buy the 250 ticket?
• How do we make sure that we have enough seats for
  those willing to pay 750?

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Two Answers

• Create artificial hurdles
• Advance purchase 21 days, 14 days, 7days
• Use limitations Saturday night stay,
  non-refundable tickets
• Restrict the number of seats sold at the low
  price
• This requires a forecast of future booking by
  higher-paying customers and the discipline to
  forgo a bird-in-hand.
• Note 1 airlines do not change prices
  dynamically they actually change capacity
  (classes) dynamically
• Note 2 freight can also displace passengers when
  RM is really optimized

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Why is This Important?

• American Airlines saved over 1.4B between
  1989-1992
• I believe that yield management is the single
  most important technical development in
  transportation management . . .
• Robert Crandall, CEO AMR

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Setting Multiple Prices Under Uncertainty An
Analytical Framework
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The Framework

• Scenario
• A flight with T seats
• The airline can sell as many leisure seats as it
  designates at a price of L (/seat)
• The airline reserves Q seats for business
  passengers.
• Each business seat can be sold for H (/seat)
• The demand for business seats is a random
  variable, D
• Any unsold business seat is lost.
• Problem
• How many business seats to reserve for a
  particular flight?

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Demand Data
Demand data for business seats for the same
flight for the last 52 weeks is the following

• Total business seat demand 4023 seats
• Average 77.4 seats
• Standard Deviation 15.4 seats
• Lowest 51 seats
• Highest 113 seats

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Bin Accumulation
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Optimal Seat Reservation
H 800 L 300 S 100
Reserve 90 but 70 show up 70?800(220-90)?30095,
000
Reserve 90 but 100 show up 90?800(220-90)?30011
1,000
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Slope (H-L)
Slope (-L)
Note the slopes
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Optimal of Reserved Seats

• The optimal order size, Q, will be at a point
  where the expected revenue from an additional
  seat reserved will be approximately zero, --
  turning extra revenue into lost revenue
• The expected revenue from reserving the (Q1)st
  business seat is H if it is sold and 0 for if it
  is unsold.
• The probability of selling the (Q1)st business
  seat is the probability that the demand will be
  higher than Q, Pr(X ? Q), and the probability
  of not selling it is Pr(X ? Q).
• The expected revenue from reserving the (Q1)st
  business seat is H ? Pr(X ? Q) 0
  ? Pr(X ? Q).
• Optimality conditions

• Solving for optimality

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Example

• H 800
• L 300
• Critical ratio (H-L)/H 0.625

Q 80 seats
Business Passengers would be turned away 37.5 of
the time.
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Normal Distribution

• Normal density function
• Average using original data 77.37
• Standard Deviation using original data15.38
• Use NORMDIST(x,?,?,T/F)

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Sensitivity Analysis
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Effect of Short Term Sale
H 800 L 300 S 100
Using the Internet or Bucket shops
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Optimal of Reserved Seats

• The optimal order size, Q, will be at a point
  where the expected revenue from an additional
  seat reserved will be approximately zero, --
  turning expected positive revenue into lost
  revenue
• The expected revenue from reserving the (Q1)st
  business seat is H if it is sold and S for if it
  is unsold at full fare but dumped using the
  Internet.
• The probability of selling the (Q1)st business
  seat is the probability that the demand will be
  higher than Q, Pr(X ? Q), and the probability
  of not selling it is Pr(X ? Q).
• The expected revenue from reserving the (Q1)st
  business seat is H ? Pr(X ? Q) S
  ? Pr(X ? Q).
• Optimality conditions

• Solving for optimality

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Example

• H 800
• L 300
• S 100
• Critical ratio (H-L)/H 0.71

Q 84 seats
Business Passengers would be turned away 29 of
the time.
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Back to General Price Discrimination
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Price Discrimination

• First degree willingness to pay (rare)
• RR in late 1800-s, asking shippers for their
  income statement so they could determine their
  ability to pay
• College financial aid
• Taxes
• Second degree artificial hurdles but open
• Buying process (coupons, advance purchase)
• Cost to serve (volume discounts, risk
  adjustments, store P/U, set up costs in travel
  industry)
• Distribution channels (Internet, outlets, etc.)
• Markdowns (timing of purchase, product age,
  selection, etc.)
• Value of product (in many rail movements
  regeltarifklassen)
• Commodity type (part of tariffs in many rail
  movements)
• Use limitations (e.g., final sale)
• Bundling (menu vs. a-la-cart)
• Time of use (e.g., peak hour, congestion pricing)

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Price Discrimination

• First degree willingness to pay (rare)
• Second degree artificial hurdles but open

• Third degree based on external factors
• Geography (neighborhood, state)
• Gender (womens clothing)
• Age (senior/student discounts)
• Profession/affiliation (small/large business
  business educational, medical)

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3rd Degree Discrimination
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Specific Example
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Price Discrimination

• Most schemes are based on 2nd degree
  discrimination seems more fair

• Principle of fairness discounts are more
  acceptable than price increases, even if the
  result is the same
• Principle of fairness profiteering is not
  acceptable

Fed Up With Airlines Business Travelers Start To
Fight Back WSJ 8/28/01
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Price Discrimination

• Most schemes are based on 2nd degree
  discrimination seems more fair

• Principle of fairness discounts are more
  acceptable than price increases, even if the
  result is the same
• Principle of fairness profiteering is not
  acceptable

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Price Discrimination

• Most schemes are based on 2nd degree
  discrimination seems more fair

• Principle of fairness discounts are more
  acceptable than price increases, even if the
  result is the same
• Principle of fairness profiteering is not
  acceptable

• Some forms of 3rd degree discrimination are
  illegal, but many are acceptable
• student/senior citizen discounts
• profession/use (Dell)
• Secretive schemes are not (Amazon)

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When Does RM Work?

• Requirements
• Long term pricing power
• Monopoly
• Oligopoly with signaling and/or government
  blessing
• Airlines, ocean conferences

Best of all, there is no Saturday night stay
required.
Boston Globe 10/16/01
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When Does RM Work?

• Requirements
• Long term pricing power
• Monopoly
• Oligopoly with signaling and/or government
  blessing
• Airlines, ocean conferences

• Temporary pricing power
• Limited capacity
• Demand spike
• Incentives
• Perishable product/service
• High fixed costs and low variable costs
• Ability to adjust prices easily (consider
  administration, relationships, etc.)

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Carrier Portfolio of Pricing
Dynamic pricing with spot market shippers
Dynamic pricing with contracted shippers
Long-term fixed-rate contracts
LT fixed rate contracts with capacity commitments
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Rev. Management in TL Trucking

• Little opportunity during bid response
• No monopoly power
• Exceptions good service history coupled with
  client strategy geared towards service
• Value-added services
• Only opportunity in real-time (spot) market
• There are limited opportunities for
  local/temporary monopolies
• Responses to shipper dialing for diesels
• Requests along power lanes

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Rev. Management in TL Trucking

• Remember the twin challenges
• How do we make sure that the people who are
  willing to pay 750 will not buy the 250 ticket?
• How do we make sure that we have enough seats for
  those willing to pay 750?
• Comes down to one question Should
  we take this load?
• Should capacity be committed to a particular
  load/shipper/contract?, or should we wait for a
  better-paying load?
• Depends on the forecast

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System Contribution of a Load

• Regional potential the expected contribution of
  a truck in a region.
• P(A) - Potential of region A
• D(A-B) - Direct cost for moving a truck from A to
  B
• R(A-B) - Revenue for the move from A to B

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System Contribution of a Load
S(A-B) R(A-B) - D(A-B) P(B) - P(A)
P(B) - the value of one more truck at region
B P(A) - the value of one less truck at region A
Order acceptance - Take a load only if S(A-B)
gt 0 - Take the load with the highest S(A-B)
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Analysis of Movements
Head haul
S(A-B) R(A-B) - D(A-B) P(B) - P(A)
Back haul
S(A-B) R(A-B) - D(A-B) P(B) - P(A)
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YM in Manufacturing

• Reserve capacity to the highest paying customer
• Tie the pricing to the capacity commitment
• Use pricing to manage component supply (in BTO)

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Final Observations

• RM involves the entire enterprise
• Customer service
• Sales
• Reservations
• Scheduling
• RM can be used to increase profits and serve
  customers better
• Bring in those who otherwise would not use the
  service
• Provide higher LOS to those who pay a lot by
  given them more frequent service, higher
  probability of service, etc.
• Increase utilization by smoothing demand patterns
• The essence of RM is the judicious management of
  capacity and pricing simultaneously
• The trick reserve capacity to the highest paying
  customers

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Any Questions?
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