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 ‹#›
Low critical ratios  high mismatch costs

The mismatch cost is high when (f(z) / F(z)) is high …

… (f(z) / F(z)) is high when the critical ratio is low:
Slide ‹#›
High demand uncertainty  high mismatch costs
The mismatch cost is high when the coefficient of variation, s/m, is high.
The coefficient of variation is the right measure of demand uncertainty:
 The probability demand is within 20% of the forecast demand depends
on the coefficient of variation (COV) and not the standard deviation:


Normal demand, m = 60
1.0
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
Probability
Probability
Normal demand, m = 20, s = 10, COV =0.5
31%
0.5
0.4
0.3
0.2
0.2
20%
31%
0.4
0.3
0.1
95%
0.5
s = 30
COV = 30 / 60 = 0.5
s = 10
COV = 10 / 60 = 0.17
20%
0.1
0.0
0.0
0
4
8
12
16
20
24
28
32
36
10
40
20
30
40
50
60
Demand
Demand
Slide ‹#›
70
80
90
100
110
Find your product’s mismatch cost (as % of
maximum profit) …
Critical ratio
Coefficient
of variation
0.10
0.25
0.40
0.55
0.70
0.85
1.00
0.4
10%
24%
39%
53%
68%
82%
97%
0.5
8%
20%
32%
44%
56%
68%
80%
0.6
6%
16%
26%
35%
45%
55%
64%
Slide ‹#›
0.7
5%
12%
20%
27%
35%
42%
50%
0.8
3%
9%
14%
19%
24%
30%
35%
0.9
2%
5%
8%
11%
14%
17%
19%
Unlimited, but expensive reactive capacity




TEC charges a premium of 20% per unit ($132 vs. $110) in the second
order.
There are no restrictions imposed on the 2nd order quantity.
O’Neill forecast of total season sales is nearly perfect after observing initial
season sales.
How many units should O’Neill order in October?
Slide ‹#›
Limited reactive capacity


Units in the 2nd order are no more expensive than in the 1st order
But there is limited capacity for a 2nd order
Slide ‹#›
Sample of wetsuits
Sport
Model
DIVE
DIVE COMP 3/2 FULL
DIVE
WMS 7000X 7MM FULL
SURF
EPIC 5/3 W/HD
SURF
HEAT 3/2
SURF
HEATWAVE 4/3
SURF
ZEN-ZIP 4/3
TRIATHLON
TRIATHLON 4/3 FULL
WAKE-BOARD REACTOR 3/2
WINDSURF
CYCLONE 4/3
WINDSURF
WMS EVOLUTION 4/3
m = expected demand
m
s
sm
1100 660
600 360
800 296
1200 444
700 259
3100 1147
2600 1690
1500 750
950 665
850 595
0.60
0.60
0.37
0.37
0.37
0.37
0.65
0.50
0.70
0.70
Price Margin Discount
120
275
225
110
140
165
210
150
325
275
38%
38%
38%
38%
38%
38%
45%
45%
45%
45%
65%
65%
50%
50%
50%
50%
65%
65%
65%
65%
s = standard deviation of demand
Price = wholesale price
Margin = gross margin as a % of price
Discount = anticipated end of season discount as % of price to sell left over inventory

1st order must be at least 10,200 suits so that there is enough capacity for
the 2nd order.

What should we produce in the 1st order?
Slide ‹#›
Profit and mismatch with only 1 ordering
opportunity

Use the Newsvendor model to evaluate the optimal order quantity, expected
profit, maximum profit and mismatch cost
Sport
DIVE
DIVE
SURF
SURF
SURF
SURF
TRIATHLON
WAKE BOARD
WINDSURF
WINDSURF
Total

Model
DIVE COMP 3/2 FULL
WMS 7000X 7MM FULL
EPIC 5/3 W/HD
HEAT 3/2
HEATWAVE 4/3
ZEN-ZIP 4/3
TRIATHLON 4/3 FULL
REACTOR 3/2
CYCLONE 4/3
WMS EVOLUTION 4/3
Order
quantity
1241
677
1009
1514
883
3910
3449
1877
1284
1149
16993
Expected
Maximum Mismatch
profit
profit
cost
$30,086
$50,160 $20,074
$37,608
$62,700 $25,092
$58,048
$68,400 $10,352
$42,568
$50,160
$7,592
$31,604
$37,240
$5,636
$164,953
$194,370 $29,417
$164,582
$245,700 $81,118
$75,536
$101,250 $25,714
$89,538
$138,938 $49,399
$67,788
$105,188 $37,399
$762,311 $1,054,105 $291,794
A suits produced in the 1st order earns the Newsvendor profit but a suit
produced in the 2nd order earns the maximum profit.
Slide ‹#›
Produce “safer” products early, produce “risky”
products with reactive capacity


Sort items by their mismatch cost to order quantity ratio.
Fill the 1st order up to the minimum quantity (10,200) with the items that
have the lowest mismatch – quantity ratio
Order
quantity
Model
HEAT 3/2
1514
HEATWAVE 4/3
883
ZEN-ZIP 4/3
3910
EPIC 5/3 W/HD
1009
REACTOR 3/2
1877
DIVE COMP 3/2 FULL
1241
TRIATHLON 4/3 FULL
3449
WMS EVOLUTION 4/3
1149
WMS 7000X 7MM FULL
677
CYCLONE 4/3
1284
Total
16993

Newsvendor
expected Mismatch
profit
cost
$42,568
$7,592
$31,604
$5,636
$164,953 $29,417
$58,048 $10,352
$75,536 $25,714
$30,086 $20,074
$164,582 $81,118
$67,788 $37,399
$37,608 $25,092
$89,538 $49,399
$762,311 $291,794
The mismatch cost is reduced by 66%!
Slide ‹#›
Mismatch costorder quantity First order
ratio
quantity
Profit
5.0
1514 $42,568
6.4
883 $31,604
7.5
3910 $164,953
10.3
1009 $58,048
13.7
1877 $75,536
16.2
1241 $30,086
23.5
0 $245,700
32.6
0 $105,188
37.1
0 $62,700
38.5
0 $138,938
10434 $955,320
$1,100,000
$1,050,000
$1,000,000
Profit
$950,000
$900,000
$850,000
$800,000
$750,000
$700,000
0
2500
5000
7500
10000 12500 15000 17500
Total quantity in the initial order
Slide ‹#›
0
20
0.45
0
0.40
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Slide ‹#›
CYCLONE 4/3
CYCLONE 4/3
WMS 7000X
WMS EVO
TRIA 4/3
DIVE COMP 3/2
REACTOR 3/2
EPIC 5/3
ZEN-ZIP 4/3
0.70
WMS 7000X
120
HEAT 4/3
0.75
WMS EVO
140
HEAT 3/2
60
Critical ratio
0.80
TRIA 4/3
CYCLONE 4/3
WMS 7000X
WMS EVO
TRIA 4/3
DIVE COMP 3/2
REACTOR 3/2
80
DIVE COMP 3/2
0.50
EPIC 5/3
100
REACTOR 3/2
EPIC 5/3
ZEN-ZIP 4/3
HEAT 4/3
HEAT 3/2
Coefficient of variation
40
ZEN-ZIP 4/3
HEAT 4/3
HEAT 3/2
Gross margin ($)
160
0.65
0.60
0.55