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 ‹#›
O’Neill’s Hammer 3/2 wetsuit
Slide ‹#›
Hammer 3/2 timeline and economics
Generate forecast
of demand and
submit an order
to TEC
Spring selling season
Nov Dec Jan
Feb Mar Apr May Jun
Receive order
from TEC at the
end of the
month
Jul Aug
Left over
units are
discounted
Slide ‹#›
Actual demand
Product description
Forecast
JR ZEN FL 3/2
90
140
EPIC 5/3 W/HD
120
83
JR ZEN 3/2
140
143
WMS ZEN-ZIP 4/3
170
163
HEATWAVE 3/2
170
212
JR EPIC 3/2
180
175
WMS ZEN 3/2
180
195
ZEN-ZIP 5/4/3 W/HOOD
270
317
WMS EPIC 5/3 W/HD
320
369
EVO 3/2
380
587
JR EPIC 4/3
380
571
WMS EPIC 2MM FULL
390
311
HEATWAVE 4/3
430
274
ZEN 4/3
430
239
EVO 4/3
440
623
ZEN FL 3/2
450
365
HEAT 4/3
460
450
ZEN-ZIP 2MM FULL
470
116
HEAT 3/2
500
635
WMS EPIC 3/2
610
830
WMS ELITE 3/2
650
364
ZEN-ZIP 3/2
660
788
ZEN 2MM S/S FULL
680
453
EPIC 2MM S/S FULL
740
607
EPIC 4/3
1020
732
WMS EPIC 4/3
1060
1552
JR HAMMER 3/2
1220
721
HAMMER 3/2
1300
1696
HAMMER S/S FULL
1490
1832
EPIC 3/2
2190
3504
ZEN 3/2
3190
1195
ZEN-ZIP 4/3
3810
3289
WMS HAMMER 3/2 FULL
6490
3673
* Error = Forecast - Actual demand
** A/F Ratio = Actual demand divided by
Forecast
Slide
‹#›
Oneill data
Error* A/F Ratio**
-50
1.56
37
0.69
-3
1.02
7
0.96
-42
1.25
5
0.97
-15
1.08
-47
1.17
-49
1.15
-207
1.54
-191
1.50
79
0.80
156
0.64
191
0.56
-183
1.42
85
0.81
10
0.98
354
0.25
-135
1.27
-220
1.36
286
0.56
-128
1.19
227
0.67
133
0.82
288
0.72
-492
1.46
499
0.59
-396
1.30
-342
1.23
-1314
1.60
1995
0.37
521
0.86
2817
0.57
Product description
Forecast Actual demand A/F Ratio* Rank Percentile**
ZEN-ZIP 2MM FULL
470
116
0.25
1
3.0%
ZEN 3/2
3190
1195
0.37
2
6.1%
ZEN 4/3
430
239
0.56
3
9.1%
WMS ELITE 3/2
650
364
0.56
4
12.1%
WMS HAMMER 3/2 FULL
6490
3673
0.57
5
15.2%
JR HAMMER 3/2
1220
721
0.59
6
18.2%
HEATWAVE 4/3
430
274
0.64
7
21.2%
ZEN 2MM S/S FULL
680
453
0.67
8
24.2%
EPIC 5/3 W/HD
120
83
0.69
9
27.3%
EPIC 4/3
1020
732
0.72
10
30.3%
WMS EPIC 2MM FULL
390
311
0.80
11
33.3%
ZEN FL 3/2
450
365
0.81
12
36.4%
EPIC 2MM S/S FULL
740
607
0.82
13
39.4%
ZEN-ZIP 4/3
3810
3289
0.86
14
42.4%
WMS ZEN-ZIP 4/3
170
163
0.96
15
45.5%
JR EPIC 3/2
180
175
0.97
16
48.5%
HEAT 4/3
460
450
0.98
17
51.5%
JR ZEN 3/2
140
143
1.02
18
54.5%
WMS ZEN 3/2
180
195
1.08
19
57.6%
WMS EPIC 5/3 W/HD
320
369
1.15
20
60.6%
ZEN-ZIP 5/4/3 W/HOOD
270
317
1.17
21
63.6%
ZEN-ZIP 3/2
660
788
1.19
22
66.7%
HAMMER S/S FULL
1490
1832
1.23
23
69.7%
HEATWAVE 3/2
170
212
1.25
24
72.7%
HEAT 3/2
500
635
1.27
25
75.8%
HAMMER 3/2
1300
1696
1.30
26
78.8%
WMS EPIC 3/2
610
830
1.36
27
81.8%
EVO 4/3
440
623
1.42
28
84.8%
WMS EPIC 4/3
1060
1552
1.46
29
87.9%
JR EPIC 4/3
380
571
1.50
30
90.9%
EVO 3/2
380
587
1.54
31
93.9%
JR ZEN FL 3/2
90
140
1.56
32
97.0%
EPIC 3/2
2190
3504
1.60
33
100.0%
* A/F Ratio = Actual demand divided by Forecast
** Percentile = Rank divided by total number ofSlide
suits ‹#›
(33)
Oneill data
Forecasts vs actual graph
.
7000
6000
Actual demand
5000
4000
3000
2000
1000
0
0
1000
2000
3000
4000
5000
6000
7000
Forecast
Forecasts and actual demand for surf wet-suits from the previous season
Slide ‹#›
Empirical distribution function for the Hammer 3/2 using
historical A/F ratios
A/F
Ratio
0.25
0.37
0.56
0.56
0.57
0.59
0.64
0.67
0.69
0.72
0.80
Q
800
1184
1792
1792
1824
1888
2048
2144
2208
2304
2560
F (Q )
0.0303
0.0606
0.0909
0.1212
0.1515
0.1818
0.2121
0.2424
0.2727
0.3030
0.3333
A/F
Ratio
0.81
0.82
0.86
0.96
0.97
0.98
1.02
1.08
1.15
1.17
1.19
Q
2592
2624
2752
3072
3104
3136
3264
3456
3680
3744
3808
F (Q )
0.3636
0.3939
0.4242
0.4545
0.4848
0.5152
0.5455
0.5758
0.6061
0.6364
0.6667
A/F
Ratio
1.23
1.25
1.27
1.30
1.36
1.42
1.46
1.50
1.54
1.56
1.60
Q
3936
4000
4064
4160
4352
4544
4672
4800
4928
4992
5120
F (Q )
0.6970
0.7273
0.7576
0.7879
0.8182
0.8485
0.8788
0.9091
0.9394
0.9697
1.0000
Q = A/F ratio times the initial sales forecast, 3200 units
F (Q ) = the probability demand is less than or equal to the quantity Q
Slide ‹#›
A portion of the Standard Normal Distribution Function
Table, F(z).
z
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
0.5000
0.5398
0.5793
0.6179
0.6554
0.6915
0.7257
0.7580
0.01
0.5040
0.5438
0.5832
0.6217
0.6591
0.6950
0.7291
0.7611
0.02
0.5080
0.5478
0.5871
0.6255
0.6628
0.6985
0.7324
0.7642
0.03
0.5120
0.5517
0.5910
0.6293
0.6664
0.7019
0.7357
0.7673
0.04
0.5160
0.5557
0.5948
0.6331
0.6700
0.7054
0.7389
0.7704
0.05
0.5199
0.5596
0.5987
0.6368
0.6736
0.7088
0.7422
0.7734
Slide ‹#›
0.06
0.5239
0.5636
0.6026
0.6406
0.6772
0.7123
0.7454
0.7764
0.07
0.5279
0.5675
0.6064
0.6443
0.6808
0.7157
0.7486
0.7794
0.08
0.5319
0.5714
0.6103
0.6480
0.6844
0.7190
0.7517
0.7823
0.09
0.5359
0.5753
0.6141
0.6517
0.6879
0.7224
0.7549
0.7852
Empirical vs normal demand distribution
1.00
0.90
Probability
.
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0
1000
2000
3000
4000
5000
6000
Quantity
Empirical distribution function (diamonds) and normal distribution function with
mean 3192 and standard deviation 1181 (solid line)
Slide ‹#›
Balancing the risk and benefit of ordering a unit
Expected gain or loss
.
80
70
Expected gain
60
50
40
30
Expected loss
20
10
0
0
800
1600
2400
3200
4000
Q th unit ordered
Slide ‹#›
4800
5600
6400
Hammer 3/2's expected loss sales table if the empirical
distribution is the demand forecast
Q F (Q ) L (Q )
Q F (Q ) L (Q )
Q F (Q ) L (Q )
800 0.0303 2392
2592 0.3636
841
3936 0.6970 191
1184 0.0606 2020
2624 0.3939
821
4000 0.7273 171
1792 0.0909 1448
2752 0.4242
744
4064 0.7576 154
1792 0.1212 1448
3040 0.4545
578
4160 0.7879 131
1824 0.1515 1420
3104 0.4848
543
4352 0.8182
90
1888 0.1818 1366
3136 0.5152
526
4544 0.8485
55
2048 0.2121 1235
3264 0.5455
464
4672 0.8788
36
2144 0.2424 1160
3456 0.5758
377
4800 0.9091
20
2208 0.2727 1111
3680 0.6061
282
4928 0.9394
8
2304 0.3030 1041
3744 0.6364
257
4992 0.9697
5
2560 0.3333
863
3808 0.6667
233
5120 1.0000
1
Q = order quantity
F (Q ) = probability demand is less than or equal to the order quantity
L (Q ) = loss function (the expected amount demand exceeds Q )
Slide ‹#›
Performance measures relationship
Expected
demand, m
Fill rate
Expected
sales
If Normal
demand, s
Loss function
table
Order quantity,
Q, and, if
Normal demand,
z = (Q – m)/s
Distribution
function table
Expected
lost sales
In-stock
probability
Stockout
probability
Price, cost,
salvage value
Slide ‹#›
Exp. left over
inventory
Expected
profit
Service measures of performance
100%
90%
80%
Expected fill
70%
60%
50%
In-stock probability
40%
30%
20%
10%
0%
0
1000
2000
3000
4000
5000
Order quantity
Slide ‹#›
6000
7000
Pareto curve
200
195
190
185
180
175
170
165
160
155
150
75%
80%
85%
90%
95% 100%
In-stock probability
Slide ‹#›