Transcript Session 01 - Introduction

Matching Supply with Demand:
An Introduction to Operations Management
Gérard Cachon
ChristianTerwiesch
All slides in this file are copyrighted by Gerard Cachon and Christian
Terwiesch. Any instructor that adopts Matching Supply with
Demand: An Introduction to Operations Management as a required
text for their course is free to use and modify these slides as desired.
All others must obtain explicit written permission from the authors to
use these slides.
Slide ‹#›
Revenue management and margin arithmetic

Small changes in revenue can have a big impact on profit, especially for
high gross margin and low net profit % industries:
Percentage change in profit for different gross margins, revenue increases and net profits as a
percentage of revenue.
Net profit % = 2%
Net profit % = 6%
Revenue increase
Gross
margin
100%
90%
75%
50%
25%
15%
1%
2%
5%
8%
50% 100% 250% 400%
45% 90% 225% 360%
38% 75% 188% 300%
25% 50% 125% 200%
13% 25% 63% 100%
8% 15% 38% 60%
Revenue increase
Gross
margin
100%
90%
75%
50%
25%
15%
Slide ‹#›
1%
17%
15%
13%
8%
4%
3%
2%
33%
30%
25%
17%
8%
5%
5%
8%
83% 133%
75% 120%
63% 100%
42% 67%
21% 33%
13% 20%
Hyatt example

Critical ratio:

Poisson distribution with mean 27.3:
Cu
r  r 225  159 66
 h l 

 0.2933
Co  Cu
rh
225
225
Q
10
11
12
13
14
15
16
17
18
19

F (Q )
0.0001
0.0004
0.0009
0.0019
0.0039
0.0077
0.0140
0.0242
0.0396
0.0618
Q
20
21
22
23
24
25
26
27
28
29
F (Q )
0.0920
0.1314
0.1802
0.2381
0.3040
0.3760
0.4516
0.5280
0.6025
0.6726
Q
30
31
32
33
34
35
36
37
38
39
F (Q )
0.7365
0.7927
0.8406
0.8803
0.9121
0.9370
0.9558
0.9697
0.9797
0.9867
Answer: 24 rooms should be protected for high fare travelers. Similarly, a
booking limit of 118-24 = 94 rooms should be applied to low fare
reservations.
Slide ‹#›
Q
10
11
12
13
14
15
16
17
18
19
F (Q )
0.0001
0.0004
0.0009
0.0019
0.0039
0.0077
0.0140
0.0242
0.0396
0.0618
L (Q )
17.30
16.30
15.30
14.30
13.30
12.31
11.31
10.33
9.35
8.39
Q
20
21
22
23
24
25
26
27
28
29
F (Q ) L (Q )
0.0920 7.45
0.1314 6.55
0.1802 5.68
0.2381 4.86
0.3040 4.10
0.3760 3.40
0.4516 2.78
0.5280 2.23
0.6025 1.76
0.6726 1.36
Slide ‹#›
Q
30
31
32
33
34
35
36
37
38
39
F (Q ) L (Q )
0.7365 1.03
0.7927 0.77
0.8406 0.56
0.8803 0.40
0.9121 0.28
0.9370 0.19
0.9558 0.13
0.9697 0.09
0.9797 0.06
0.9867 0.04
A solution to the multi-leg customer: buckets
Heathrow
Fare class
Y
M
Q
O’Hare
JFK



With segment control there are only three
booking limits for the O’Hare-JFK leg, one
for each fare class.
But an O’Hare-Heathrow customer may be
more valuable, so you could have six
booking limits, one for each fare-itinerary
combination.
But that leads to many booking limits, so
group similar fare-itineraries into buckets:
Bucket Itinerary
0
1
2
3
Slide ‹#›
O'Hare to
JFK
$724
$475
$275
O'Hare to Heathrow
O'Hare to Heathrow
O'Hare to JFK
O'Hare to Heathrow
O'Hare to JFK
O'Hare to JFK
O'Hare to
Heathrow
$1,610
$829
$525
Fare class
Y
M
Y
Q
M
Q
Another solution to multi-legs: bid prices
Heathrow
Fare class
Y
M
Q
O’Hare
JFK
O'Hare to
JFK
$724
$475
$275
O'Hare to JFK
$290
O'Hare to
Heathrow
$1,610
$829
$525
JFK to Heathrow
$170

Assign a bid price to each segment:

A fare is accepted if it exceeds the sum of the bid prices on the segments
it uses:
 For example, an O’Hare-JFK fare is accepted if it exceeds $290
 A O’Hare-Heathrow fare is accepted if it exceeds $290+$170 = $460

The trick is to choose good bid-prices.
Slide ‹#›
Bid price
Optimal overbooking level

Poisson distribution with mean 8.5
Q
0
1
2
3
4
5
6
7
8
9



F (Q )
0.0002
0.0019
0.0093
0.0301
0.0744
0.1496
0.2562
0.3856
0.5231
0.6530
Q
10
11
12
13
14
15
16
17
18
19
F (Q )
0.7634
0.8487
0.9091
0.9486
0.9726
0.9862
0.9934
0.9970
0.9987
0.9995
Optimal number of overbooked rooms is Y=7.
Hyatt should allow up to 118+7 reservations.
There is about F(6)=25.62% chance that Hyatt will find itself turning down
travelers with reservations.
Slide ‹#›