Koç University
OPSM 405 Service Management
Class 16:
Yield management: overbooking
Zeynep Aksin
zaksin@ku.edu.tr
1
Yield Management System
Reservation System
current demand
cancellations
Forecasting
cancellation rate estimates
future
demand
estimates
Overbooking Levels
overbooking levels
Discount Allocation
fare class allocations
2
Dealing with cancellations
Overbooking control
total cost
Basic Problem:
E[Rev] $
0
opportunity cost of unsold seats
overbooking costs
capacity
overbooking
limit (BL)
#seats sold
3
Overbooking
Two basic costs:
1)Stock outs
customers have a reservation and there
are no rooms left
2)Overage
customers denied advance reservation
and rooms are unoccupied
4
Example: Hotel California
Stock outs: 0.8 x $150 = $120
Overage: $50
5
Table 9.1: Hotel California No-Show Experience
No-Shows
0
1
2
3
4
5
6
7
8
9
10
% of Experiences
5
10
20
15
15
10
5
5
5
5
5
Cumulative % of
Experiences
5
15
35
50
65
75
80
85
90
95
6
100
Overbooking Approach 1: Using Averages
In Table 9.1 the average number of noshows is calculated by 0x0.05 + 1x0.10 + 2x0.20 +
3x0.15 +…+ 10x0.05 = 4.05.
Take up to four overbookings.
7
Overbooking Approach 2: Spreadsheet Analysis
8
Overbooking Approach 3: Marginal Cost Approach
Book more guests until:
E(cost of dissatisfied customer) = E(cost of
empty room)
• Cost of dissatisfied customer *
Probability that there are fewer no-shows
than overbooked rooms =
• Cost of empty room *
Probability that there are more no-shows
than overbooked rooms
9
Hotel California
 Co/(Cs + Co) = P(Overbook  No Shows)
Hotel Data
• Cs = $120, Co = $50.00
• Co/(Cs + Co) = 29.%
–
Overbook 2 rooms
Table 9.1: Hotel California No-Show Experience
No-Shows
% of Experiences
Cumulative % of
Experiences
0
5
5
29%
1
10
15
2
20
35
10
14
Dynamic Overbooking
Overbooking
Time to Event
Event Occurs
Reservations Start
15
Overbooking over time
%Capacity
booking limit
reservations with overbooking
100%
reservations without overbooking
90
days to departure
o
16
Bulvar Palas
 The contribution of each room is 40YTL per
night.
 If a guest holding a reservation is turned
away owing to overbooking, then other costs
are incurred:
– Arrangements with a nearby hotel
– Penalties associated with lost good will
 Management estimates this cost as 100YTL
per guest “walked”
17
Example: Bulvar Palas
Bulvar Palas No-Show Experience: (Daily)
No-shows
Probability P[no show] Cum. Prob. P[no show<x]
0
0.07
0.00
1
0.19
0.07
2
0.22
0.26
3
0.16
0.48
4
0.12
0.64
5
0.10
0.76
6
0.07
0.86
7
0.04
0.93
8
0.02
0.97
9
0.01
0.99
18
Marginal analysis
How much can I overbook?
Overbook too few 40YTL, P(no show>x)
Overbook too many 100YTL, P(no show<x)
Keep overbooking as long as
40*P(no show>x)
> 100*P(no show<x)
or
P(no show<x) < 40/(40+100)=0.286
Overbook 2 rooms based on no-show distribution
19
Example
 The Ozhas bus company is currently assessing
its Istanbul-Adana run. The number of
customers that do not show up after making a
reservation are uniformly distributed from 1 to
10. Tickets costs are 45YTL, and if a particular
bus run is full, a passenger with a reservation is
given passage on a rival company’s bus at a
cost of 75YTL. Using the averages method,
what should Ozhas’s overbooking policy be?
20
Averages method
 Using the averages method, the average
number of no shows is calculated by:
0(0.0)+1(0.1)+2(0.1)+3(0.1)+4(0.1)+5(0.1)
+6(0.1)+7(0.1)+8(0.1)+9(0.1)+10(0.1)
= 5.5
21
Spreadsheet approach
C0 =
$45
Cs =
$75
Number of Reservations Overbooked
No shows
Total cost
Probability
0
1
2
3
4
5
6
7
0
0
$0
($75)
($150)
($225)
($300)
($375)
($450)
($525)
1
0.1
($45)
$0
($75)
($150)
($225)
($300)
($375)
($450)
2
0.1
($90)
($45)
$0
($75)
($150)
($225)
($300)
($375)
3
0.1
($135)
($90)
($45)
$0
($75)
($150)
($225)
($300)
4
0.1
($180)
($135)
($90)
($45)
$0
($75)
($150)
($225)
5
0.1
($225)
($180)
($135)
($90)
($45)
$0
($75)
($150)
6
0.1
($270)
($225)
($180)
($135)
($90)
($45)
$0
($75)
7
0.1
($315)
($270)
($225)
($180)
($135)
($90)
($45)
$0
8
0.1
($360)
($315)
($270)
($225)
($180)
($135)
($90)
($45)
9
0.1
($405)
($360)
($315)
($270)
($225)
($180)
($135)
($90)
10
0.1
($450)
($405)
($360)
($315)
($270)
($225)
($180)
($135)
($248)
($203)
($170)
($149)
($140)
($143)
($158)
($185)
22
Likya World
 Number of customers who book a night
and fail to show up is Normally distributed
with mean 20 and standard deviation 10
 Bumping a customer costs 300 YTL
 If room is not sold, hotel loses revenue of
105 YTL
23
Likya World
 105/(300+105)=0.2592
 Look up in a standard normal table to
obtain z=-0.645
 So number of seats to overbook=
20-0.645*10=13.5
 Alternatively use NORMINV(0.2592,20,10)
24
Obtaining the Probability
Standardized Normal Probability
Table (Portion)
Z
.00
.01
.02
sZ =1
0.0 .50000 .50399 .50798
:
:
:
:
2.0 .97725 .97784 .97831
.97725
2.1 .98214 .98257 .98300
mz = 0 2.0
Z
Probabilities in body
25