RM Dynamic Pricing

8/7/2019 RM Dynamic Pricing

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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


1 Seat in Class 'Med' Accept 88 61 0 0 0

2 Seats in Class 'Hi' Accept 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

Documents

RM Dynamic Pricing