rm dynamic pricing
TRANSCRIPT
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DYNAMIC PRICING
Sreelata Jonnalagedda
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Announcements
Swapping Feb 4th with Feb 10th
Schedule your presentations for Feb 10th and Guest
Lecture on Feb 4th.
All the presentations will be on Feb 10th and 11th .
If we need extra time well use last class day!
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From Last Class
Key Learnings
Product Variety Based Price Discrimination
Coupons and Equilibrium
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The Pay-off Matrix
Total
Market 100
Firm B, unit cost = 10, No-Coupon
Firm A, unit
cost =10,
Coupon =
10 for 50consumers
20 21 25 29 30
20 (0,500) (500,0) (500,0) (500,0) (500,0)
21 (50,500) (50,550) (600,0) (600,0) (600,0)
25 (250,500) (250,550) (250,750) (1000,0) (1000,0)
29 (450,500) (450,550) (450,750) (450,950) (1400,0)30 (500,500) (500,550) (500,750) (500,950) (500,1000)
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This Class
Dynamic Pricing
Pricing Capacity
Revenue Management
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Dynamic Pricing
What is Dynamic Pricing?
What are the conditions conducive to DP?
Dynamic Supply &Demand, large market size, real time
matching
High consumer heterogeneity
Perishable capacity
one-off transactions (auctions)Quick recovery (negotiations)
Cost delinked with price
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Supply Constraints
Services
Barberthe number of seats in his saloon
Fords Capacity 475,000 vehicles/month
End of life cycle - products for retailers
Unique Items
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Hard vs. Soft Constraint
Kd(p)
tosubject
c)d(p)(pmax
Soft Constraint: Management would like to keeps
its contribution margins at 10%Hard Constraint: The number of rooms in the hotel
is 100
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A Numerical Example
A widget maker has a price response function:
Unit Production Cost = 5/unit
What is the optimal price?
)80010000()( ppd
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Graphical Representation
-60000
-50000
-40000
-30000
-20000
-10000
0
10000
20000
0 2 4 6 8 10 12 14MC
Total ProfitMR
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Contribution vs Revenue
Under what conditions may companies want to
maximize contribution vs revenue?
When MC is negligible?
For Airlines for example/hotels/ you have orderedyour apparel for the season.
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Num Example: Extension
Suppose that the widget maker faces a capacity
constraint of 2000
How should we determine the new price?
p*
0
2000
4000
6000
8000
10000
12000
0.0 5.0 10.0 15.0
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Pricing With Supply Constraints
The Options
DO Nothing
Figure a prefered allocation
Raise price to meet supply
Combination of Segmentation + Price Optimization
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Supply Constraints and Profits
What do supply constraints do to overall profit?
Reduce/increase?
For example, if Maruti experiences a plant strike
shutting 20% of capacity, they will likely see lowerprofits
If renovation causes some hotel rooms to be out of
service then hotel will suffer losses? The extent of losses will depend on how binding the
supply constraint is?
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Opportunity Cost: Total vs Marginal
Widget Example:
Opportunity Cost of having a supply constraint of
2000 units
How much would the seller pay to eliminate that supplyconstraint entirely?
How much would the seller pay to increase capacity by
a unit?
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One Approach
LP
Answer is obvious
80 for economy vs 20 for business
What is the problem with this approach?
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Formally
C = 100
There are 2 possible faresE (100), B(300)
b}{e,iDyo
Cyy
tosubject
ypypmax
ii
be
bbee
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Another approach
Should AA limit the number of business class tickets?
What should be the limit on the economy tickets
sold?
Marginal analysis at the limit
Suppose AA gets a request for Economy ticket
AA has the opportunity to make $100
Accepting this offer denies AA the ability to sell this seat tobusiness class which could get them $300
AA has to weigh these options.
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One Way to do this (MR = MC)
100 = 300 P(Demand for Business Class > C-y)
Ccapacity of the plane
yeconomy booking limit
0.333 = 1-F(C-y)
F(C-y)=0.667
100-y = F-1(0.667) =22.15
Then y = 100 -22 = 78
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Another way to do this
Suppose we want to allocate a capacity of x to thehigh fare class on the plane
Overage cost (CO) = how much money was not made because ofsetting x too high by one unit
CO = 100 Underage cost (CU) = how much money was not made because of
setting x too low by one unit Cu = (300100) = 200
Critical Fractile = 200/300 = 0.667
x = F-1(0.667) =22.15
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Motel Overbooking
Suppose a Motel in NY has 20 rooms available.
Average price/night of a hotel room is $50
If a consumer with a reservation shows up but you
dont have availability, it costs you $200 to put him
up in the neighboring hotel.
How many reservations will you accept?
Make an assumption on the No-Show Distribution SupposeNormal (5,2)
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The marginal request
50 P(Number of No Shows> B - C) = 200
P(Number of No Shows< B - C)
Ccapacity of the hotel
BTotal reservations you decide to accept
50 (1-F(B-C)) - 200 F(B-C) = 0
50 = 250 F(B-C)
B - 20 = F-1(0.2) =3.3 Then B = 23.3
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Newsvendor approach
Suppose we want to make x excess bookings over thecapacity (20)
Overage cost (CO) = how much does it cost by setting x too high by oneunit
CO = 200 Underage cost (CU) = how much money was not made because of
setting x too low by one unit Cu = 50
Critical Fractile = 50/250 = 0.2 x = F-1(0.2) =3.3
Accept 23 bookings
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Revenue Management
American Airlines vs People Express
Deregulation of American Airline Industry in 1978
People ExpressFares @ 70% of the major airlines
Encroached AAs key routes (1984)
Choices to AAeither match or go under
1985AA introduced Super Saver Fares, with a
restriction on number of Discount seats By mid 1985People Express bought over for
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What is RM?
Maximize expected profits from constrained
resources
Perishable Capacity
Fare/Demand Classes Adjust availability to Demand Class
Purchase prior to use
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The Levels of Revenue Management
Strategic
What are the different market segments? What should be
the price
TimingQuarterly/Annually Tactical
At what capacity should booking for a segment be
capped?
TimingDaily/Weekly
Booking ControlReal time
Which bookings should be accepted/rejected.
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Segmentation
Consumer based
Business or Leisure
Price sensitive or not
How about the product variety? Remember almost all the seats are identical
So how do they create differentiated products (is it just
based on fares?) RestrictionsNo cancellation/advance booking only
Group incentives
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Booking Control
Real time
Example:-
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Allotment vs. Nesting
Suppose you have two fare classes: Economy and
Business (Economy fare < Business Fare)
Allotment: On a 100 seat plane, you could allocate 25
seats to Business Class and 75 seats to Economy.OR
Nesting: Booking limit in the Economy class is 75
Which means that upto 75 tickets can be issued for Economy
class (naturally booking limit for Business is 100)
Suppose first you get a request for 30 business class tickets,
how will you adjust the booking limit on the Economy class?
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Interpreting Nested Booking Limits
blow =4
bmed =12
bhi =73
bstar =100
b0 = 0
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Processing Booking Requests
Booking Limit
Sequence of Requests Action Class 'Star' Class 'Hi' Class 'Med' Class 'Low' Class '0'
2 Seats in Class '0' Reject 100 73 12 4 0
5 Seats in Class 'Hi' Accept 100 73 12 4 0
1 Seat in Class 'Hi' Accept 95 68 7 0 01 Seat in Class 'Low' Accept 94 67 6 0 0
3 Seats in Class 'Med' Accept 91 64 3 0 0
4 Seats in Class 'Med' Reject 91 64 3 0 0
2 Seats in Class 'Med' Accept 89 62 1 0 0
4 Seats in Class 'Med' Reject 89 62 1 0 0
1 Seat in Class 'Med' Accept 88 61 0 0 0
2 Seats in Class 'Hi' Accept 86 59 0 0 0
2 Seats in Class 'Med' Reject 86 59 0 0 0
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One Simple Rule
Cannot close a higher class before a lower fare
class closes.
H d i h b ki
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How do you come up with booking
limits?
Typically solve an IP
of gigantic proportions
On a daily basis
With forecast updating ( to get new estimates ofdemand)
The capacity allocation solution of LP is used to comeup with booking limits
Another way which is less used is Simulation Ability to simulate risk
Emulate opportunity cost approach
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Real Time Decisions
Opportunity Costs
For example:
If you get a request for a ticket with fare 100 on a
flight BOM - HYD (with current capacity 50) By accepting the request your expected profit is 100 +
E(49)
By not accepting the request your expected profit is
E(50)
Accept only if 100 + E(49) E(50)
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Adding Complications
The marginal value of a request is not that easy to
compute. Mostly people resort to heuristics.
Inaccuracies in demand will further complicate matters
What if you have a network of resources. That isyour flight from Austin to San Diego has a
connection in LA.
The no-show probability is typically a function ofthe current bookings.
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Current Approaches
In a network of resources
Airline network (flight of multiple legs)
Multiple night hotel booking
Use shadow prices of resource constraints LP as proxyfor opportunity cost
Marginal value of each resource do not add up to
give the displacement cost or opportunity cost
Heuristics are used
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Other Applications
RM has huge investment costs and very huge pay
offs too
RM in television advertising is picking up
Upfront and Scatter Markets Inventory of Slot vs Request Mismatch
Sporting events
http://www.portfolio.com/views/blogs/odd-numbers/2008/08/27/price-discrimination-and-
baseball-tickets