The document discusses inventory management concepts, emphasizing the relationship between flow rate, flow time, and inventory using Little's Law. It includes examples from emails and hospitals to illustrate inventory calculation, the Pareto principle, and the significance of inventory turnover in evaluating firm efficiency. Additionally, it outlines the reasons for holding inventory and the impact of demand variability on supply chains.

1. Inventory: Buffer of Suffer
Operations and Supply Chain Management

2. Adaptation
• This is adapted from a
course in Operations
Management on
Coursera from
Wharton.
• Professor Christian
Terwiesch

3. Little’s Law
• I = R * T
• I is Inventory
• R is Flow Rate
• T is Flow Time
• The relationship of flow
and inventory

4. Email Example
• If you have 240 emails
in you in box and you
can answer 60 per day
on average
• How long will it take
you to answer them?
• I = 240
• R = 60
• I/R = T
• 240/60 = 4 days

5. Hospital Example
• In a hospital on average
they birth 10 babies per
day.
• 80% stay two days and
20% stay five days
• How many babies on
average are in the
hospital?

6. Pareto Principle
• The Pareto
principle (also known as
the 80–20 rule, the law
of the vital few, and
the principle of factor
sparsity) states that, for
many events, roughly
80% of the effects come
from 20% of the causes.

7. The Pareto Principal

8. Hospital Example
• R = 10 per day
• T = .8*2 + .2*5 = 2.6 days
• I = R*T = 10 * 2.6
• I = 26
• This is on average so you
would want to build
additional capacity to
handle above average
times
• Perhaps two standard
deviations of capacity

9. Inventory Turns
• Inventory turns =
• COGS/Inventory
• I = R*T
• Inventory Turns = 1/T

10. Computer Example
• Compare Dell and
Compaq
• Calculate Flow Time
• Dell = 391/20,000 = 7
• Compaq = 2003/25,263
= 29 days
• Inventory Turns 1/T
• Dell = 52
• Compaq = 12.6
Dell Compaq
Inventory $391M 2003
Flow Rate 20,000 M 25,263
Flow Time

11. Significance
• As a general rule, the higher the
inventory turnover, the more
efficient and profitable the firm.
It means that the firm is holding a
low level of average inventory in
relation to sales. Holding
inventory means money tied up
in stock. This money is either
borrowed and carries an interest
charge, or is money that could
have earned interest in a bank.
Furthermore, items in inventory
carry storage cost, and carry the
risk of getting spoiled, breaking,
being stolen, or simply going out
of style.

12. Sandwich Flow Rate
• Product: you might
make 0,1 or 2 in ten
minutes
• You might have 0,1 or 2
customers in ten
minutes
• What is the average
flow?
• 1?

13. It is actually reduced to 5/9
Deliver Customers Rate
0 0 0
1 0
2 0
1 0 0
1 1
2 1
2 0 0
1 1
2 2
5/9

14. Buffer or Suffer
• Inventory de-couples
Supply from Demand
• Protects against the
variability of:
– Demand
– Process Time
• Make to Stock
• Make to Order

15. 5 Reasons to carry Inventory
• Pipeline
– I=R*T
• Seasonal
– Variation
• Cycle
– Economies of Scale
• Safety
– Buffer against Demand
• Decouple S&D