Transcript OPSM 451 Service Operations Management

Koç University
OPSM 405 Service Management
Class 12:
Yield management: discount allocation and
pricing
Zeynep Aksin
[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
current demand
cancellations
Forecasting
cancellation rate estimates
future
demand
estimates
Overbooking Levels
overbooking levels
Discount Allocation
fare class allocations
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!)
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:
Remaining
Capacity
100
A
70
B
C
100
85
70
Forecast of Leg
Demand
60
15
0
0
KEY
Discount
$60
A reservation agent has a group that wants to book
20 seats from A to C at a rate of $80 per person.
Full Fare
$100
Should we accept the group?
Analysis:
A
100
B
70
C
100
85
20
70
Forecast of Demand
to Come
20
60
15
0
0
Forecasted revenue
displacement:
Forecasted revenue
displacement:
15 x $0 + 5 x $60 = $300
10 x $60 + 10x $100 = $1600
KEY
Discount
$60
Full Fare
$100
Net Revenue = New Revenue - Total Displacement Cost
= 20x$80 - $300 - $1600 = - $300
==> DO NOT accept the group.
Result depends on remaining capacity....
A
100
B
80
C
100
85
20
80
20
Forecast of Demand
to Come
60
15
0
Forecasted revenue
displacement:
Forecasted revenue
displacement:
15 x $0 + 5 x $60 = $300
20 x $60 + 0x $100 = $1200
KEY
Discount
$60
Full Fare
$100
Net Revenue = New Revenue - Total Displacement Cost
= 20x$80 - $300 - $1200 = $ 100
==> DO accept the group.
and the forecast ....
A
100
B
80
C
100
95
20
80
20
Forecast of Demand
to Come
60
15
0
Forecasted revenue
displacement:
Forecasted revenue
displacement:
5 x $0 + 15 x $60 = $900
20 x $60 + 0x $100 = $1200
KEY
Discount
$60
Full Fare
$100
Net Revenue = New Revenue - Total Displacement Cost
= 20x$80 - $900 - $1200 = - $500
==> DO NOT accept the group.
Hedging against forecast error
Assumptions:
fare classes
full-fare
discount
revenue
r1
r2
demand
X1
X2
Sequence of Events:
discount demand
arrives
accept/reject discount res.
S1
protection level
A2 = C-S1 discount allocation
full-fare demand
arrives
Analysis
Approach 1: Deterministic Allocation
If we knew demand for high fare with certainty, S1  X 1
Approximation:
S1  E ( X 1 )
Analysis
Approach 2: Optimal Allocation
S seats remaining:
accept low fare?
P( X1  S )
$r1
P( X1  S )
$0
no
yes
$r2
Accept if
r2  r1P( X 1  S )
Optimal protection level is smallest value of S satisfying
this condition.
Example
C=100 seats
r1=$250
r2=$100
Demand for high fare uniformly
distributed between 10 and 50.
E ( X 1 )  30
Demand for low fare uniformly
distributed between 50 and 90.
E ( X 2 )  70
Example
r1 P ( X 1  S )
$250
$100
10
34
50
Reserve 34 seats for full fare demand. Allocate
100-34=66 seats to discount fare demand.
EMSR-b Heuristic
n
fi
# fare classes
revenueof fare class i
f1  f 2  ....  f n
i
mean demandof fare class i
 i2
i
variance of demandof fare class i
protectionlevelfor classes i and higher
“Nested allocations”
#seats remaining
aircraft cabin
1
3
2
Set protection levels to satisfy ….
f i 1  f i P( Di   i )
where ...
i
fi 

j 1
i
j

j 1
fj
Average fare of classes i and higher
i
i
i
Di ~ Normalwith mean   j and variance  j
j 1
  i  i  z i ,
where F ( z )  1 
j 1
f i 1
fi
2
Aggregate demand of
classes i and higher
F(z) standard normal dist.
This is the heuristic used in many commercial systems.
Example:
Class
1
2
3
Fare
$100
$80
$40
Mean
30
30
50
Variance
50
80
120
Weighted average fares and aggregate mean & variance ..
i
 i2
$100
30
$90
60
$67.3 110
50
130
250
fi
1
2
3
Set protection level 1:
80
F ( z )  1 
 0.2  z  0.84
100
 1  30  0.84 50  4.06  24 seats
Set protection level 2 (for classes 1 & 2 combined):
40
F ( z )  1 
 0.55  z  1.4
90
  2  60  1.4 130  75.96  76 seats
There is not protection level for the lowest class (class 3)
#seats remaining
Accept all three
classes
Accept class 1 and 2
only
Accept class 1
only
24 seats
76 seats
Allocation Procedure
Alternative: demand control chart based on history
Do not accept discount fare demands
demands
Accept discount fare
demands
0
Days before arrival
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 information
Price
100
110
90
Demand
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 ;
rd  rf P(d f  x f )
49  69P(d f  x f )  P(d f  x f )  0.710
x f  60 

P z 
  0.710  z  0.555  x f  68.325
15 

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 4
Frequency 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) ≤
Co
20

 0.30
Co  C s 20  C s
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
1000
Price
Seat
Allocation
Full
Disc
400
D. Disc
100
Full
120
Disc
50
D. Disc
0
20
16
12
8
7
6
5
4
3
2
1