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 ‹#›
Medtronic’s InSync pacemaker supply chain and
objectives

Supply chain:
 One distribution center (DC) in
Mounds View, MN.
 About 500 sales territories
throughout the country.
Consider Susan Magnotto’s
territory in Madison,
Wisconsin.


Slide ‹#›
Objective:
 Because the gross margins are
high, develop a system to minimize
inventory investment while
maintaining a very high service
target, e.g., a 99.9% in-stock
probability or a 99.9% fill rate.
InSync demand and inventory at the DC
700
Average monthly demand = 349
units
600
Standard deviation of monthly
demand = 122.28
Average weekly demand = 349/4.33
= 80.6
400
300
Standard deviation of weekly
demand = 122.38 / 4.33  58.81
200
100
(The evaluations for weekly demand
assume 4.33 weeks per month and
demand is independent across
weeks.)
Dec
Nov
Oct
Sep
Aug
Jul
Jun
May
Apr
Mar
Feb
0
Jan
Units
500
Month
Monthly implants (columns) and end of
month inventory (line)
Slide ‹#›
InSync demand and inventory in Susan’s territory
16
14
Total annual demand = 75
units
12
Average daily demand =
0.29 units (75/260),
assuming 5 days per week.
8
6
Poisson demand
distribution works better for
slow moving items
4
Dec
Nov
Oct
Sep
Jul
Jun
Apr
May
Feb
Mar
0
Aug
2
Jan
Units
10
Month
Monthly implants (columns) and end of
month inventory (line)
Slide ‹#›
Slide ‹#›
Probability
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
Units
0
1
2
Units
Slide ‹#›
3
Lead time, l
Pipeline
inventory
Exp. demand in
one period
If Normal
demand, s
Loss function
table
Order up-to
level, S, and, if
Normal demand,
z = (S – m) /s
Distribution
function table
Fill rate
Expected
backorder
In-stock
probability
Stockout
probability
Demand over
lead time + 1, m
Slide ‹#›
Expected
inventory
The optimal in-stock probability is usually quite high
Suppose the annual holding cost is 35%, the backorder penalty cost equals
the gross margin and inventory is reviewed daily.
100%
Optimal in-stock probability

98%
96%
94%
92%
90%
88%
0%
20%
40%
60%
Gross margin %
Slide ‹#›
80%
100%
Example with mean demand per week = 100 and standard
deviation of weekly demand = 75.


Inventory over time follows a “saw-tooth” pattern.
Period lengths of 1, 2, 4 and 8 weeks result in average inventory of 597,
677, 832 and 1130 respectively:
1600
1600
1400
1400
1200
1200
1000
1000
800
800
600
600
400
400
200
200
0
0
0
2
4
6
8
10
12
14
16
1600
1600
1400
1400
1200
1200
1000
1000
800
800
600
600
400
400
200
200
0
0
2
4
6
8
10
12
14
16
0
2
4
6
8
10
12
14
16
0
0
2
4
6
8
10
12
14
16
Slide ‹#›
Tradeoff between inventory holding costs and ordering
costs
Costs:
 Ordering costs = $275 per order
 Holding costs = 25% per year
 Unit cost = $50
 Holding cost per unit per year =
25% x $50 = 12.5
22000
20000
18000
Total costs
16000
14000
Cost

12000
Inventory
holding costs
10000
8000

Period length of 4 weeks minimizes
costs:
 This implies the average order
quantity is 4 x 100 = 400 units
6000
4000
Ordering costs
2000
0
0
1
2
3
4
5
6
Period length (in weeks)

EOQ model:
Q
2 K  R
2  275  5200

 478
h
12.5
Slide ‹#›
7
8
9
Better service requires more inventory at an
increasing rate
140

More inventory is
needed as
demand
uncertainty
increases for any
fixed fill rate.

The required
inventory is more
sensitive to the fil
rate level as
demand
uncertainty
increases
120
Expected inventory
100
80
60
40
Inc re a s ing
s ta nda rd de via tion
20
0
90% 91% 92% 93% 94% 95% 96% 97% 98% 99% 100%
Fill rate
The tradeoff between inventory and fill rate with Normally distributed demand
and a mean of 100 over (l+1) periods. The curves differ in the standard
deviation of demand over (l+1) periods: 60,50,40,30,20,10 from top to bottom.
Slide ‹#›
Shorten lead times and you will reduce inventory
600
Expected inventory
500

400
300
200
100
0
0
5
10
Lead time
15
20
The impact of lead time on expected inventory for four fill rate targets,
99.9%, 99.5%, 99.0% and 98%, top curve to bottom curve respectively.
Demand in one period is Normally distributed with mean 100 and
standard deviation 60.
Slide ‹#›
Reducing the lead
time reduces
expected inventory,
especially as the
target fill rate
increases
Do not forget about pipeline inventory

3000
Inventory
2500
2000

1500
1000
500
0
0
5
10
Lead time
15
20
Expected inventory (diamonds) and total inventory (squares), which is
expected inventory plus pipeline inventory, with a 99.9% fill rate requirement
and demand in one period is Normally distributed with mean 100 and
standard deviation 60
Slide ‹#›
Reducing the lead
time reduces
expected inventory
and pipeline
inventory
The impact on
pipeline inventory can
be even more
dramatic that the
impact on expected
inventory
Annual inventory turns for Wal-Mart. (Source: 10-K filings)
8.0
Annual inventory turns
7.5
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03
Year
Slide ‹#›