Inventory Modeling for
Independent Demand
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Explain what inventory is
Describe how inventory is classified
Explain ABC analysis
Explain cycle counting
Compare inventory models
Use inventory models to find how much &
when to order
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
Stock of materials
Stored capacity
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Stock of materials
Stored capacity
Examples
© 1995 Corel Corp.
© 1995
Corel
Corp.
© 1984-1994 T/Maker Co.
© 1984-1994 T/Maker Co.
The Functions of
Inventory

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To ”decouple” or separate various
parts of the production process
To provide a stock of goods that will
provide a “selection” for customers
To take advantage of quantity
discounts
To hedge against inflation and
upward price changes
Types of Inventory

Raw material

Work-in-progress


Maintenance/repair/operating
supply
Finished goods

Higher costs
◦ Item cost (if purchased)
◦ Ordering (or setup) cost
 Costs of forms, clerks’ wages etc.
◦ Holding (or carrying) cost


 Building lease, insurance, taxes etc.
Difficult to control
Hides production problems
Category
% of
Inventory Value
Housing (building) cost
Material handling costs
Labor cost
Inventory investment costs
Pilferage, scrap, & obsolescence
Total holding cost
6%
3%
3%
11%
3%
26%
Inventory
© 19841994
T/Maker
Co.
Process
Stage
Number
& Value
Demand
Type
Other
Raw Mat'l
WIP
Fin. Goods
A Items
B Items
C Items
Independent
Dependent
Mainten.
Repair
Operating

Divides on-hand inventory into 3 classes
◦ A class, B class, C class

Basis is usually annual $ volume
◦ $ volume = Annual demand x Unit cost

Policies based on ABC analysis
◦ Develop class A suppliers more
◦ Give tighter physical control of A items
◦ Forecast A items more carefully
% Annual $ Usage
Class % $ Vol % Items
100
80
60
40
20
0
0
20
40
60
80
% of Inventory Items
100
% Annual $ Usage
Class % $ Vol % Items
A
80
15
B
15
30
C
5
55
100
80
60
A
40
B
20
C
0
0
20
40
60
80
% of Inventory Items
100
You’re a buyer for Auto Palace. Classify the
following items as A, B, or C.
Stock #
Annual Volume (Units)
Unit Cost
206
105
019
144
207
26,000
200
2,000
20,000
7,000
$ 36
600
55
4
10
Note: Example is for illustration only; too few items.
Stock #
Vol.
206
105
019
144
207
26,000
200
2,000
20,000
7,000
Total
Cost
$ Vol.
$ 36 $936,000
600 120,000
55 110,000
4
80,000
10
70,000
%
71.1
9.1
8.4
6.1
5.3
1,316,000 100.0
ABC
A
A
B
B
C
You’re an inventory control supervisor for
USX. Classify the following items as A, B, or
C.
Stock # Annual Volume (Units) Unit Cost
Z-206
W-105
Z-019
P-144
K-207
13,000
75
1,700
12,000
3,000
$
22
200
25
1
2
Stock #
Z-206
W-105
Z-019
P-144
K-207
Total
Vol.
Cost
$ Vol.
13,000 $ 22 $286,000
75 200
15,000
1,700
25
42,500
12,000
1
12,000
3,000
2
6,000
%
79.1
4.1
11.8
3.3
1.7
$361,500 100.0
ABC
A
B
B
C
C
Cycle Counting


Physically counting a sample of
total inventory on a regular
basis
Used often with ABC
classification

A items counted most often (e.g.,
daily)
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Eliminates shutdown and
interruption of production necessary
for annual physical inventories
Eliminates annual inventory
adjustments
Provides trained personnel to audit
the accuracy of inventory
Allows the cause of errors to be
identified and remedial action to be
taken
Maintains accurate inventory records


How much to order?
When to order?
Purchase Order
Description Qty.
Microwave
1000

Fixed order quantity models
◦ Economic order quantity
◦ Production order quantity
◦ Quantity discount
Help answer the inventory
planning questions!
© 1984-1994
T/Maker Co.
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Known & constant demand
Known & constant lead time
Instantaneous receipt of material
No quantity discounts
Only order (setup) cost & holding cost
No stockouts
Minimize Total Cost (TC)
TC = Holding + Order/Setup Cost
TC = H + S
Annual Cost
Order Quantity
Annual Cost
Holding Cost
Order Quantity
Annual Cost
Holding Cost
Order (Setup) Cost
Order Quantity
Annual Cost
Total Cost Curve
Holding Cost
Order (Setup) Cost
Order Quantity
Annual Cost
Total Cost Curve
Holding Cost
Order (Setup) Cost
Optimal
Order Quantity (Q*)
Order Quantity

More units must be stored if more ordered
Purchase Order
Descriptio Qty.
n
Microwave
1
Order
quantity
Purchase Order
Descriptio Qty.
n
Microwave
1000
Order
quantity

Cost is spread over more units
Example: You need 1000 microwave ovens
1 Order (Postage $ 0.32)
1000 Orders (Postage $320)
Purchase Order
Descriptio Qty.
n
Microwave
1000
PurchaseOrder
Order
Purchase
Purchase
Order
Descriptio
Qty.
Purchase
Order
Descriptio
Qty.
Descriptio
Qty.1
n
Microwave
Descriptio
Qty.
n
Microwave
1
n
Microwave
1
n
Microwave
1
Order
quantity
Inventory Level
Optimal Order
Quantity
(Q*)
Time
Inventory Level
Optimal Order
Quantity
(Q*)
Decrease due to
constant demand
Time
Inventory Level
Optimal Order
Quantity
(Q*)
Instantaneous
receipt of optimal
order quantity
Time
Inventory Level
Optimal Order
Quantity
(Q*)
Time
Inventory Level
Optimal Order
Quantity
(Q*)
Reorder
Point
(ROP)
Lead Time
Time
Inventory Level
Optimal Order
Quantity
(Q*)
Average
Inventory (Q*/2)
Reorder
Point
(ROP)
Lead Time
Time

When the inventory of microwaves gets down
to 15 units (reorder point), order 35 units
(EOQ).
1
5
left
Purchase Order
Description Qty.
Microwave 35
2 D S
Optimal Order Quantity  Q * 
H
D
Expected Number Orders  N 
Q*
Expected Time Between Orders  T 
d
D
Working Days / Year
ROP  d  L
Working Days / Year
N
D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
L = Lead time in days
You’re a buyer for Wal-Mart.
Wal-Mart needs 1000 coffee
makers per year. The cost of
each coffee maker is $78.
Ordering cost is $100 per
order. Carrying cost is 40% of
per unit cost. Lead time is 5
days. Wal-Mart is open 365
days/yr. What is the optimal
order quantity & ROP?
2 D S
Optimal Order Quantity  Q * 
H
D
Expected Number Orders  N 
Q*
Expected Time Between Orders  T 
d
D
Working Days / Year
ROP  d  L
Working Days / Year
N
D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
L = Lead time in days
Q* 
2XDXS
H

2X1000X10
 80 units
0.40 (78)
D
1000

 2.74 units/day
d
Working Days /Year
365
ROP  d  L  2.74 X5  137
. units
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
Answers how much to order & when to
order
Allows partial receipt of material
◦ Other EOQ assumptions apply

Suited for production environment
◦ Material produced, used immediately
◦ Provides production lot size

Lower holding cost than EOQ model
Inventory Level
Supply
Begins
Time
Inventory Level
Supply Supply
Begins Ends
Time
Inventory Level
Inventory level with NO
demand during supply of
optimum order quantity
Supply Supply
Begins Ends
Time
Inventory Level
Inventory level with NO
demand during supply of
optimum order quantity
Q*
Supply Supply
Begins Ends
Q* is optimum
order qty
Time
Inventory Level
Q*
Inventory level with CONSTANT
demand during supply of
optimum order quantity
Supply Supply
Begins Ends
Q* is optimum
order qty
Time
Inventory Level
Q*
Quantity used before
becoming inventory
Supply Supply
Begins Ends
Time
Inventory Level
Decrease due to
no supply &
constant demand
Supply Supply
Begins Ends
Time
Inventory Level
Production portion
of cycle
Demand portion of cycle
with no supply
Supply Supply
Begins Ends
Time
Inventory Level
Next Cycle
Time
Inventory Level
Next Cycle
Supply
Begins
Time
Inventory Level
Supply Supply
Begins Ends
Time
Inventory Level
Supply Supply
Begins Ends
Time
Inventory Level
Max. Inventory
Q*·(1- d/p)
Time
Inventory Level
Inventory level with no demand
Production
Portion of Cycle
Q*
Supply
Begins
Supply
Ends
Max. Inventory
Q·(1- d/p)
Demand portion of cycle
with no supply
Time
Optimal Order Quantity = Qp*
=
2xDxS
H x (1- d/p)
Max. Inventory Level  Q
D
Setup Cost 
Q
x
x1
d
p
S
Holding Cost =
Q
1 - (d/p)
H
D = Demand per year
S = Setup cost
H = Holding cost
d = Demand per day
p = Production per
day
You’re a production planner
for Stanley Tools. Stanley
Tools makes 30,000 screw
drivers per year. Demand is
100 screw drivers per day &
production is 300 per day.
Production setup cost is $150
per order. Carrying cost is
$1.50 per screw driver. What
is the optimal lot size?
Optimal Order Quantity = Qp*
=
2xDxS
H x (1- d/p)
Max. Inventory Level  Q
D
Setup Cost 
Q
x
x1
d
p
S
Holding Cost =
Q
1 - (d/p)
H
D = Demand per year
S = Setup cost
H = Holding cost
d = Demand per day
p = Production per
day
Qp * 
2 D  S
H
1-
d
p

2  30000  150
 3000
100
1.5  1 300
Max. Inventory Level  3000
D = Demand Per Year
S = Setup Cost
H = Holding Cost
d = Demand Per Day
p = Production Per Day
1
100
 2000
300


Answers how much to order &
when to order
Allows quantity discounts
◦ Reduced price when item is purchased in larger
quantities
◦ Other EOQ assumptions apply

Trade-off is between lower price & increased
holding cost
Total Cost
Order
Quantity
Total Cost
Price 1
Discount Quantity
1
Order
Quantity
Total Cost
Price 1
Price 2
Discount Quantity
Discount Quantity
1
2
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
Discount Quantity
Discount Quantity
1
2
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
Discount Quantity
Discount Quantity
1
2
TC for
Discount 1
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
Discount Quantity
Discount Quantity
Q*
1
2
TC for
Discount 1
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
TC for
Discount 1
Outside
discount
range
Discount Quantity
Discount Quantity
Q*
1
2
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
TC for
Discount 1
TC for
Discount 2
Discount Quantity
Discount Quantity
1
2
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
TC for
Discount 1
TC for
Discount 2
Q*Disc1Qty
Discount Quantity
2
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
TC for
Discount 1
TC for
Discount 2
Outside
discount
range
Outside discount
range
Q*Disc1Qty
Discount Quantity
2
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
TC for
Discount 1
TC for
Discount 2
X
Q*
adjusted
Disc Qty Discount Quantity
2
1
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
TC for
Discount 1
TC for
Discount 2
TC for
Discount 3
Discount
Quantity 1
Discount Quantity
2
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
TC for
Discount 1
TC for
Discount 2
TC for
Discount 3
Discount
Quantity 1
Q*
Discount Quantity
2
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
TC for
Discount 1
TC for
Discount 2
TC for
Discount 3
Outside discount
range
Disc QtyQ*
1
Discount Quantity
2
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
TC for
Discount 1
TC for
Discount 2
TC for
Discount 3
X
Discount
Quantity 1
Q* adjusted
Disc Qty
2
Order
Quantity
Total Cost
Price 1
Price 2
Price 3
TC for
Discount 1
TC for
Discount 2
TC for
Discount 3
Quantity
Ordered
Lowest cost not in
discount range
Discount Quantity
Discount Quantity
1
2
Order
Quantity


Compute EOQ for each quantity discount
price
Is computed EOQ in discount range?
◦ If not, use the lowest cost quantity in discount
range


Compute total cost for EOQ or lowest cost
quantity in discount range
Select quantity with lowest total cost