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# Chapter 12 Part A –

Inventory Management
Suman Niranjan
Inventory
Inventory: a stock or store of
goods Independent
Demand

A Dependent
Demand

B C
(4) (2)

D E D F(2)
(2) (1) (3)

2
Independent demand is uncertain.
Dependent demand is certain.
Inventory Models
 Independent demand – finished goods, items
that are ready to be sold
E.g. a computer
 Dependent demand – components of finished
products
E.g. parts that make up the computer

3
Key Inventory Terms
 Lead time: time interval between ordering
and receiving the order
 Holding (carrying) costs: cost to carry an
item in inventory for a length of time, usually
a year
 Ordering costs: costs of ordering and
receiving inventory
 Shortage costs: costs when demand exceeds
supply

4
Types of Inventories

##  Raw materials & purchased parts

 Partially completed goods called
work in progress
 Finished-goods inventories
 (manufacturing firms)
or merchandise
(retail stores)
 Replacement Parts
 Pipeline Inventory
5
Functions of Inventory
 To meet anticipated demand
 To smooth production requirements
 To decouple operations
 To protect against stock-outs
 To take advantage of order cycles
 To help hedge against price increases
 To permit operations
 To take advantage of quantity discounts

6
Little’s Law
 Little’s Law:
The average amount of inventory in a system is
equal to the product of the average demand rate
and the average time a unit spends in the
system
 Example
If a unit is in system for an average of 10 days
and the demand for each day is 5 units, the
average inventory:
 5 units/day * 10 days = 50 units

7
Objective of Inventory Control
 To achieve satisfactory levels of customer service
while keeping inventory costs within reasonable
bounds
 Level of customer service
 Costs of ordering and carrying inventory
 Two fundamental decisions of inventory control
 When to order; how much to order
 Days of inventory on-hand
 Higher – excess inventory; Lower – risk of running out

## Inventory turnover is the ratio

of 8
average cost of goods sold to
Effective Inventory
Management
 A system to keep track of inventory on-hand
and order
 A reliable forecast of demand and forecast
error
variability
 Reasonable estimates of
Holding costs
Ordering costs
Shortage costs
 A classification system of inventory items
9
Inventory Counting Systems
 Periodic System
Physical count of items made at periodic
intervals
 Perpetual Inventory System
System that keeps track
of removals from inventory
continuously, thus
monitoring
current levels of
each item

10
Inventory Counting Systems
(Cont’d)
 Two-Bin System - Two containers of
inventory; reorder when the first is empty
 Universal Bar Code - Bar code
printed on a label that has
to which it is attached
 RFID tags

214800 232087768
11
ABC Classification System

## Classifying inventory according to some measure

of importance and allocating control efforts
accordingly.
A- very important

B- mod. important

C- least important H
A
igh

Annual B
\$ value
of
Lo C
w 12
Low H
Percentage ofigh
Items
Inventory Counting
 Increase Customer service
 Improve Operations

 Cycle Counting
Purpose is to reduce the discrepancy amounts
indicated by the records and actual inventory
A physical count of items in inventory
 Cycle counting management
How much accuracy is needed?
When should cycle counting be performed?
Who should do it?

13
Economic Order Quantity
Models
 Basic Economic order quantity (EOQ) model
The order size that minimizes total annual cost
 Economic production model
 Quantity discount model

14
Assumptions of EOQ Model
 Only one product is involved
 Annual demand requirements known

##  There are no quantity discounts

15
The Inventory Cycle

## Profile of Inventory Level

Q Usage Over Time
Quantit rate
y
on hand

Reorder
point

T
Receiv Plac Receiv Plac Receiv ime
e e e e e
order orde order orde order 16
time
Total Cost

Annual Annual
Total cost carryi + orderi
ng ng
Q DS
TC H +
2 Q
=
TC: Total Cost
Q: Order Quantity in Units
H: Holding Cost Per Unit
D: Demand, Usually in Units Per Year
S: Ordering Cost
17
Cost Minimization Goal
The Total-Cost Curve is U-
Shaped
Annual
Cost

Ordering
Costs
Order
QO(optimal order
quantity) Quantity 18
(Q)
Deriving the EOQ
Using calculus, we take the derivative of the
total cost function and set the derivative
(slope) equal to zero and solve for Q.

19
Minimum Total Cost
The total cost curve reaches its minimum
where the carrying and ordering costs are
equal.
Q DS
H =
2 Q

20
Example 2
 A local distributor for a national tire company
expects to sell approximately 9,600 steel-
design next year. Annual carrying cost is \$16
per tire, and ordering cost is \$75. The
distributor operates 288 days a year.
a) What is the EOQ?
b) How many times per year does the store
reorder?
c) What is the length of an order cycle?
d) What is the total annual cost if the EOQ
quantity is ordered?
21
Economic Production Quantity
(EPQ)
 Production done in batches or lots
Capacity to produce a part exceeds the part’s
usage or demand rate
 Assumptions of EPQ are similar to EOQ
during production

22
Economic Production Quantity
Assumptions
 Only one item is involved
 Annual demand is known

##  Lead time does not vary

 No quantity discounts

23
EOQ with Incremental Inventory
Replenishment

24
Economic Run Size

25
Example 4
 A toy manufacturer uses 48,000 rubber
wheels per year for its popular dump truck
series. The firm makes its own wheels, which
it can produce at a rate of 800 per day. The
toy trucks are assembled uniformly over the
entire year. Carrying cost is \$1 per wheel a
year. Setup cost for a production run of
wheels is \$45. The firm operates 240 days
per year. Determine the
Optimal run size.
Minimum total annual cost for carrying and
setup.
26
Cycle time for the optimal run size.
Run time.
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