1. OPSM 405 Service Management
Koç University
OPSM 405 Service Management
Class 12:
Yield management: discount allocation and pricing
Zeynep Aksin

2. 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

3. Yield Management System
Reservation System
current demand
cancellations
Forecasting
cancellation rate estimates
future
demand
estimates
Overbooking Levels
overbooking levels
Discount Allocation
fare class allocations

4. The displacement cost method A 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!)

5. 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.

6. 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

7. Example: A reservation agent has a group that wants to book
Remaining
Capacity
100 70 A B C
100 85 70
Forecast of Leg
Demand 60 15
KEY
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?
Discount
$60
Full Fare
$100

8. Analysis: Net Revenue = New Revenue - Total Displacement Cost
100 B 70 C
100 20 85 70
Forecast of Demand
to Come 20 60 15
Forecasted revenue
displacement:
15 x $0 + 5 x $60 = $300
Forecasted revenue
displacement:
10 x $ x $100 = $1600
KEY
Discount
$60
Net Revenue = New Revenue - Total Displacement Cost
= 20x$80 - $ $1600 = - $300
==> DO NOT accept the group.
Full Fare
$100

9. Result depends on remaining capacity....
100 B 80 C
100 20 85 80 20
Forecast of Demand
to Come 60 15
Forecasted revenue
displacement:
15 x $0 + 5 x $60 = $300
Forecasted revenue
displacement:
20 x $60 + 0x $100 = $1200
KEY
Discount
$60
Net Revenue = New Revenue - Total Displacement Cost
= 20x$ $ $1200 = $ 100
==> DO accept the group.
Full Fare
$100

10. and the forecast .... A
100 B 80 C
100 95 20 80 20
Forecast of Demand
to Come 60 15
Forecasted revenue
displacement:
20 x $60 + 0x $100 = $1200
Forecasted revenue
displacement:
5 x $ x $60 = $900
KEY
Discount
$60
Net Revenue = New Revenue - Total Displacement Cost
= 20x$ $ $1200 = - $500
==> DO NOT accept the group.
Full Fare
$100

11. Hedging against forecast error
Assumptions:
fare classes
full-fare discount
revenue r r2
demand X X2
Sequence of Events:
discount demand
arrives
accept/reject discount res.
S protection level
A2 = C-S1 discount allocation
full-fare demand
arrives

12. Analysis Approach 1: Deterministic Allocation
If we knew demand for high fare with certainty,
Approximation:

13. Analysis Approach 2: Optimal Allocation Accept if $r1 $0 $r2no
S seats remaining:
accept low fare? $0
yes
$r2
Accept if
Optimal protection level is smallest value of S satisfying
this condition.

14. Example Demand for high fare uniformly distributed between 10 and 50.
C=100 seats
r1=$250
r2=$100
Demand for low fare uniformly
distributed between 50 and 90.

15. Example Reserve 34 seats for full fare demand. Allocate
$250
$100 10 34 50
Reserve 34 seats for full fare demand. Allocate
100-34=66 seats to discount fare demand.

16. EMSR-b Heuristic
“Nested allocations”
#seats remaining
aircraft cabin

17. Set protection levels to satisfy ….
Average fare of classes i and higher
Aggregate demand of
classes i and higher
F(z) standard normal dist.
This is the heuristic used in many commercial systems.

18. Weighted average fares and aggregate mean & variance ..
Example:
Class Fare Mean Variance
1 $
2 $
3 $
Weighted average fares and aggregate mean & variance ..
1 $
2 $
3 $
Set protection level 1:

19. Set protection level 2 (for classes 1 & 2 combined):
There is not protection level for the lowest class (class 3)
#seats remaining
Accept all three
classes
Accept class 1
only
Accept class 1 and 2
only

20. Allocation Procedure
Alternative: demand control chart based on history
Do not accept discount fare demands
Days before arrival
demands
Accept discount fare demands

21. 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

22. 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.

23. Example: Pricing interacts with capacity allocation
Premium customer information
Price
Demand
Scenario 1: unlimited capacity, only premium customers

24. Example cont.
Premium customer information
Price
Demand
Scenario 2: capacity=100, discount unlimited demand at $50
Premium
Discount

25. Example cont.
Premium customer information
Price
Demand
Scenario 3: capacity=100, discount unlimited demand at $ Premium
Discount

26. 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.

27. Solution
Accept full-fare if ;

28. 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
Frequency
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.

29. Solution
No Shows
Frequency
Probability
P(d<x) 6
0.30
0.00 1 5
0.25 2 4
0.20
0.55 3
0.15
0.75
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. Summary: RM is a new twist on some 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

31. 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

32. Illustration of policy to be determined before class24 20 16 12 8 7 6 5 4 3 2 1
Price
Full
1000 
Disc
400 
D. Disc
100 
Seat
120 
Allocation
50  0