OPSM 405 Service Management Class 12: Yield management: discount allocation and pricing Koç University Zeynep Aksin zaksin@ku.edu.tr.
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OPSM 405 Service Management
Class 12:
Yield management: discount allocation and pricing
Koç University
Zeynep Aksinzaksin@ku.edu.tr
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
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