OPSM 405 Service Management Class 12: Yield management: discount allocation and pricing Koç University Zeynep Aksin [email protected].

OPSM 405 Service Management

Class 12:

Yield management: discount allocation and pricing

Koç University

Zeynep [email protected]

Announcements

Next group case assignment due next Monday

(groups of 2-3)– Instructions on last slide– Data on student CD of the textbook and handouts section of

course webpage– There is no one right answer, though there are better answers..– … groups will compete in class

Yield Management System

Reservation System

Forecasting

Overbooking Levels

Discount Allocation

current demandcancellations

cancellation rate estimates

overbooking levels

futuredemandestimates

fare class allocations

The displacement cost methodA general framework for allocation

Attempt to evaluate the opportunity cost (displacement cost/bid prices) of using resources required to meet current demand

Accept current request if ...

Revenue > Displacement Cost

Advantages – intuitive– conceptually simple– sophisticated applications

• O-D control (airlines)• multi-night stays (hotels)• group evaluations

– near-optimal (provided “correct” displacement costs are used!)

Generic procedure

STEP 1: Forecast demand-to-come for each ...

- product (e.g. fare-class/booking class)

- resource (e.g. flight leg, day-of-week)

STEP 2: Using forecast, determine best allocation of remaining capacity to products.

STEP 3: Using the results of STEP 2, calculate the displacement cost of the capacity required by a new request to the revenue it brings in to evaluate accept/deny decisions.

A rough-cut approach: Simple deterministic displacement

Assumptions– Forecast is perfect– Future demand for each resource (flight-leg, hotel room-day)

is independent

Procedure - Determine revenue (net contribution) of each demand class - Rank demand from highest revenue to lowest - Greedy allocation/displacement

- allocation: highest revenue classes first - displacement: lowest revenue classes first

Example:

A B C

Forecast of LegDemand

Discount $60

Full Fare $100

KEY

0

15

85

100

100 70

A reservation agent has a group that wants to book 20 seats from A to C at a rate of $80 per person.

Should we accept the group?

0

60

70

Remaining Capacity

0

60

70

Analysis: A B C

Forecast of Demandto Come

Discount $60

Full Fare $100

KEY

0

15

85

100

100 70

20

20

Forecasted revenuedisplacement:

15 x $0 + 5 x $60 = $300

Forecasted revenuedisplacement:

10 x $60 + 10x $100 = $1600

Net Revenue = New Revenue - Total Displacement Cost = 20x$80 - $300 - $1600 = - $300

==> DO NOT accept the group.

Result depends on remaining capacity....A B C

Forecast of Demandto Come

Discount $60

Full Fare $100

KEY

0

15

85

100

100 80

20

Forecasted revenuedisplacement:

15 x $0 + 5 x $60 = $300

Forecasted revenuedisplacement:

20 x $60 + 0x $100 = $1200

Net Revenue = New Revenue - Total Displacement Cost = 20x$80 - $300 - $1200 = $ 100

==> DO accept the group.

60

80

20

and the forecast ....A B C

Forecast of Demandto Come

Discount $60

Full Fare $100

KEY

0

15

95

100

100 80

20

Forecasted revenuedisplacement:

5 x $0 + 15 x $60 = $900

Forecasted revenuedisplacement:

20 x $60 + 0x $100 = $1200

Net Revenue = New Revenue - Total Displacement Cost = 20x$80 - $900 - $1200 = - $500

==> DO NOT accept the group.

60

80

20

Hedging against forecast error

Assumptions:

fare classes

full-fare discount

revenue r1 r2

demand X1 X2

Sequence of Events:

discount demandarrives

accept/reject discount res.

S1 protection level

A2 = C-S1 discount allocation

full-fare demandarrives

Approach 1: Deterministic Allocation

If we knew demand for high fare with certainty, S X1 1Approximation:

S E X1 1 ( )

Analysis

Analysis

Approach 2: Optimal Allocation

S seats remaining:accept low fare?

no

yes$r2

$r1

P X S( )1

P X S( )1

$0

Accept if )( 112 SXPrr

Optimal protection level is smallest value of S satisfying this condition.

Example

r1=$250r2=$100

Demand for high fare uniformlydistributed between 10 and 50.

C=100 seats

Demand for low fare uniformlydistributed between 50 and 90.

E X( )1 30

70)( 2 XE

Example

$250

r P X S1 1( )

10 50

$100

34

Reserve 34 seats for full fare demand. Allocate100-34=66 seats to discount fare demand.

EMSR-b Heuristic

higher and classesfor level protection

class fare of demand of iance var

class fare of demandmean

....

class fare of revenue

classes fare#

2

21

i

i

i

fff

if

n

i

i

i

n

i

2

1

3

aircraft cabin

“Nested allocations”

#seats remaining

i

jj

i

jji

i

ji

i

jjj

i

iiii

D

f

f

DPff

1

2

1

1

1

1

varianceand mean with Normal~

... where

)(

Set protection levels to satisfy ….

Average fare of classes i and higher

Aggregate demand of classes i and higher

This is the heuristic used in many commercial systems.

i

iiii f

fzFz 11)( where, F(z) standard normal dist.

Example: Class Fare Mean Variance1 $100 30 502 $80 30 803 $40 50 120

Set protection level 1:

seats 2406.45084.030

84.02.0100

801)(

1

zzF

1 $100 30 502 $90 60 1303 $67.3 110 250

if i 2i

Weighted average fares and aggregate mean & variance ..

Set protection level 2 (for classes 1 & 2 combined):

seats 7696.751304.160

4.155.090

401)(

2

zzF

seats 76

seats 24

There is not protection level for the lowest class (class 3)

Accept all threeclasses

Accept class 1 and 2only

Accept class 1only

#seats remaining

Allocation Procedure

Alternative: demand control chart based on history

0Days before arrival

demands

Accept discount fare demands

Do not accept discount fare demands

Some complications in pricing

Multiple products are more complex– Diversion/demand shifting

• Other products• Competitor’s products• Same product on different day• Ex: Peak load pricing

– Cross-elasticity: demand for one product is affected by price of other available products

– Joint capacity constraints often mean incremental sales of one product require reduction in sales of other products

• “shadow price” of joint capacity constraint is important to understand

Competition often forces price matching (e.g. discount airline fares)

As a result of all these factors, pricing is often done at an aggregate level considering long-term supply/demand balances and competitor’s actions. Capacity allocation is then used to manage short-run fluctuations.

Example: Pricing interacts with capacity allocation

Premium customer information

Price 100 110 90

Demand 100 80 120

Scenario 1: unlimited capacity, only premium customers

10000 8800 10800

Example cont.

Premium customer informationPrice 100 110 90Demand 100 80 120

Scenario 2: capacity=100, discount unlimited demand at $50

Premium 10000 8800 9000 Discount 0 1000 0

Example cont.

Premium customer information

Price 100 110 90

Demand 100 80 120

Scenario 3: capacity=100, discount unlimited demand at $75 Premium 10000 8800 9000

Discount 0 1500 0

Discount allocation example

During the recent economic slump, Blackjack Airline discovered that airplanes on its Los Angeles-to-Las Vegas route have been flying with more empty seats than usual. To stimulate demand, it has decided to offer a special, nonrefundable, 14-day advance-purchase “gamblers fare” for only $49 one-way based on a round-trip ticket. The regular full-fare coach ticket costs $69 one-way. The Boeing 737 used by Blackjack, has a capacity 95 in coach, and management wants to limit the number of seats that are sold at the discount fare in order to sell full-fare tickets to passengers who have not made advance travel plans. Considering recent experience, the demand for full-fare tickets appears to have a normal distribution, with a mean of 60 and a standard deviation of 15. Calculate the number of full-fare seats to reserve.

Solution

Accept full-fare if ;

710.0)xd(P)xd(P6949

)xd(Prr

ffff

fffd

325.68x555.0z710.015

60xzP f

f

Overbooking example

A commuter airline overbooks all its flights by one passenger (i.e., the ticket agent will take seven reservations for an airplane that only has six seats). The no-show experience for the past 20 days is shown below:

No-shows 0 1 2 3 4Frequency 6 5 4 3 2

Using the critical fractile P(d<x) ≤ Co/(Co+Cs), find the maximum implied overbooking opportunity loss Cs if the revenue Co from a passenger is $20.

Solution

No Shows Frequency Probability P(d<x)

0 6 0.30 0.00

1 5 0.25 0.30

2 4 0.20 0.55

3 3 0.15 0.75

4 2 0.10 0.90

If overbook by 1, then P(d<x) must be at least .30 and less than .55.

P(d<x) ≤ 30.0C20

20

s

so

o

CC

C

Summary: RM is a new twist on some old demand management ideas

Old demand management ideas ...– segmentation– peak-load pricing

With some new twists ...– tactical application of these concepts

Small differences matter!– systematic/disciplined approach– data intensive/ IS intensive

For Monday Prepare MotherLand Air at the end of chapter (9 in old edition) Analyze the information provided and develop a dynamic policy on

– Price (select from list provided in the case)– Overbooking level– Seat allocation (nested reservation limits)

Inform me of your group’s policy at least 2 hours before class (for each of the “weeks away from takeoff” on Table 9.8) If you want to start out with a static policy, I just need one set of price, overbooking, discount allocation numbers.

Bring printout of data to class for use during the game Write up a report describing your analysis and justifying your choice

for the above tactics. Clearly state all of your assumptions and explain all of your work. Also articulate how you plan to react to demand announcements in class; i.e. what is your plan.

In class we will play a game: I will announce demand realizations, you as a group can update/change your strategy

Illustration of policy to be determined before class

24 20 16 12 8 7 6 5 4 3 2 1

Price Full

1000                       

Disc 400                       

D. Disc 100                       

Seat Full 120                       

Allocation Disc 50                       

D. Disc 0