INVENTORY
Based on slides for Chase Acquilano and Jacobs, Operations Management,
McGraw-Hill
Inventory System
 What is inventory?
 the stock of any item or resource used in an organization and
can include: raw materials, finished products, component parts,
supplies, and work-in-process
 What is an inventory system?
 the set of policies and controls that monitor levels of inventory
and determines what levels should be maintained, when stock
should be replenished, and how large orders should be
 What are some purposes of inventory?
Independent vs. Dependent
Demand
Independent Demand (Demand for the final endproduct or demand not related to other items)
Finished
product
E(1
)
Component parts
Dependent
Demand
(Derived demand
items for
component
parts,
subassemblies,
raw materials,
etc)
Independent Demand Inventory
Issues:
How much to order?
When to order?
Some Models:
Single period (Newsvendor)
Order quantity and order level
Fixed order period
Inventory Costs
 Holding (or carrying) costs
Costs for storage, handling, insurance, etc
 Setup (or production change) costs
Costs for arranging specific equipment
setups, etc
 Ordering costs
Costs of someone placing an order, etc
 Shortage costs
Costs of canceling an order, etc
Multi-Period Models: Fixed-Order Quantity
Model Model Assumptions
 Demand for the product is
constant and uniform
throughout the period
 Inventory holding cost is
based on average
inventory
 Lead time (time from
ordering to receipt) is
constant
 Ordering or setup costs
are constant
 Price per unit of product
is constant
 All demands for the
product will be satisfied
(No back orders are
allowed)
Basic Fixed-Order Quantity Model and
Reorder Point Behavior
4. The cycle then repeats.
1. You receive an order quantity Q.
Number
of units
on hand
Q
Q
Q
R
2. Your start using
them up over time.
L
R = Reorder point
Q = Economic order quantity
L = Lead time
Time
L
3. When you reach down to
a level of inventory of R,
you place your next Q
sized order.
Basic Formulas
TC=Total annual cost
 Total Cost
 Total Ordering and
Carrying Cost
 Economic Order
Quantity
 Reorder Point
D = Yearly Demand (d is daily demand)
C =Cost per unit
Q =Order quantity
S =Cost of placing an order or setup
cost
R =Reorder point
L =Lead time
i=Annual holding and storage cost per
unit of inventory expressed at a
percentage
EOQ Example (1) Problem Data
Determine EOQ and ROP for:
• Annual Demand = 1,000 units
• Days per year considered in average daily demand = 365
• Cost to place an order = $10
• Holding cost per unit per year = $2.50
• Lead time = 7 days
• Cost per unit = $15
Q OPT =
2DS
=
H
2(1,000 )(10)
= 89.443 units or 90 units
2.50
1,000 units / year
d =
= 2.74 units / day
365 days / year
_
R eorder point, R = d L = 2.74units / day (7days) = 19.18 or 20 u n its
EOQ Example (2) Problem Data
Determine EOQ and ROP for –
•Annual Demand = 10,000 units
•Days per year considered in average daily demand = 365
•Cost to place an order = $10
•Holding cost per unit per year = 10% of cost per unit
•Lead time = 10 days
•Cost per unit = $15
Q OPT =
2D S
=
H
2 (1 0 ,0 0 0 )(1 0 )
= 3 6 5 .1 4 8 u n its, o r 3 6 6 u n its
1 .5 0
10,000 units / year
d=
= 27.397 units / day
365 days / year
_
R = d L = 27.397 units / day (10 days) = 273.97 or 274 u n its
Summary of Some Key Points
Re: EOQ Model
How much to order: Economic Order
Quantity Q*
When to order: Reorder Point
Total Cost (Item plus Holding plus Ordering)
EOQ Class Problem
Dickens Electronics stocks and sells a particular
brand of PC. It costs the firm $450 each
time it places and order with the
manufacturer. The cost of carrying one PC
in inventory for a year is $170. The store
manager estimates that total annual demand
for computers will be 1200 units with a
constant demand rate throughout the year.
Orders are received two days after
placement from a local warehouse maintained
by the manufacturer. The store policy is to
never have stockouts. The store is open for
business every day of the year. Determine
the following:
 Optimal order quantity per order.
 Minimum total annual inventory costs (i.e.
carrying plus ordering – ignore item costs).
 The optimum number of orders per year (D/Q*)
 The reorder point.
Problem 1
Demand
Ordering Cost
Carrying Cost
Lead Time
Q*
Ordering + Carrying= $
Orders/year =
Reorder Point
1200
450
170
2
79.7
13,549.91
15.1
6.6
Rounding up …
$
80
13,550.00
7
Problem 2
A store specializing in selling wrapping
paper is analyzing their inventory
system. Currently the demand for
paper is 100 rolls per week, where
the company operates 50 weeks
per year.. Assume that demand is
constant throughout the year. The
company estimates it costs $20 to
place an order and each roll of
wrapping paper costs $5.00 and
the company estimates the yearly
cost of holding one roll of paper to
be 50% of its cost.
a) If the company currently orders
200 rolls every other week (i.e., 25
times per year), what are its
current holding and ordering costs
(per year)?
D
S
c
i
H
per year
5000
$20.00
$5.00
0.5
$2.50
part a
Ordering
Holding
Total
$500.00
$250.00
$750.00
Problem 2
b)
The company is considering
c)
implementing an EOQ model. If
they do this, what would be the
new order size (round-up to the
next highest integer)? What is
the new cost? How much money in
ordering and holding costs would
be saved each relative to their
current procedure as specified in
part a)?
The vendor says that if they order
only twice per year (i.e., order 2500
rolls per order), they can save 10
cents on each roll of paper – i.e.,
each roll would now cost only $4.90.
Should they take this deal (i.e.,
compare with part b’s answer)
[Hint: For c]. calculate the item,
holding, and ordering costs in your
analysis.]
part c
part b
EOQ
282.8
Ordering
$353.55
Holding
$353.55
Total
$707.11
$$ Saved:
$42.89
283
Ordering
Holding
Total
$40.00
$3,062.50
$3,102.50
Item Cost
Holding
Ordering Net Total
Part b) option $
25,000.00
$353.55 $353.55
$25,707.11
Part c) option
$24,500.00
$3,062.50
Do not accept the deal
$40.00
$27,602.50
ABC Classification System
 Items kept in inventory are not of equal
importance in terms of:

dollars invested

profit potential

sales or usage volume

stock-out penalties
60
% of
$ Value 30
0
% of
Use
30
A
B
C
60
So, identify inventory items based on percentage of total
dollar value, where “A” items are roughly top 15 %, “B”
items as next 35 %, and the lower 65% are the “C” items