How can it be that
mathematics, being after all a
product of human thought
independent of experience, is
so admirably adapted to the
objects of reality
Albert Einstein
Importance of Inventory
A typical hospital spends about 20% of its budget on medical,
surgical, and pharmaceutical supplies. For all hospitals it adds
up to $150 billion annually.
The average inventory in US economy about $1.13 trillion on
$9.66 trillion of sales. About $430 billion in manufacturing,
$230 billion in wholesaler, $411 billion in retail.
What happens when a company with a large Work In Process
(WIP) and Finished Goods (FG) inventory finds a market
demand shift to a new product? Two choices:
Fire-sell all WIP and FG inventories and then quickly
introduce the new product  Significant losses
Finish all WIP inventory and sell all output before introducing
the new product  Delay and reduced market response
time
Inventory Classified
Inputs inventory
– Raw materials and Parts
In-process inventory
– Parts and products that are being processed
– Parts and products to decouple operations (line balancing inventory).
– Parts and products to take advantage of Economies of Scale (batch
inventory).
Outputs inventory
– To meet anticipated customer demand (average inventory and safety
stock).
– To smooth production while meeting seasonal demand (seasonal
inventory).
– In transit to a final destination to fill the gap between production and
demand lead times (pipeline inventory).
Inventory
Poor inventory management hampers operations, diminishes
customer satisfaction, and increases operating costs.
A typical firm probably has tied in inventories about
– 30 percent of its Current Assets
– 90 percent of its Working Capital (Current Assets – Current
Liabilities)
Understocking; lost sales, dissatisfied customers.
Overstocking; tied up funds (financial costs), storage and safe
keeping (physical cost), change in customer preferences
(obsolescence cost).
Periodic Inventory [Counting] Systems
At the beginning of each period, the existing inventory level is
identified and the additional required volume to satisfy the
demand during the period is ordered.
The quantity of order is variable but the timing of order is fixed.
Re-Order Point (ROP) is defined in terms of time.
One-Bin System (Periodic)
Order Enough to Refill Bin
Physical count of items made at periodic intervals.
Disadvantage: no information on inventory between two counts.
Advantage: order for several items are made at the same time.
Perpetual Inventory Systems
When inventory reaches ROP an order of EOQ (Economic Order
Quantity) units is placed.
The quantity of order is fixed but the timing of order is variable.
ROP is defined in terms of quantity (inventory on hand).
Two-Bin System (Perpetual)
Order One Bin of Inventory
Full
Empty
Keeps track of removals from inventory continuously, thus
monitoring current levels of each item.
A point-of-sales (POS) system record items at the time of sale.
A classification Approach: ABC Analysis
ABC Analysis in terms of dollars invested, profit potential, sales
or usage volume, and stockout penalties. Perpetual for class A,
Periodic for class C.
Item
Annual
Number Demand
1
2500
2
1000
3
1900
4
1500
5
3900
6
1000
7
200
8
1000
9
8000
10
9000
11
500
12
400
Unit
Cost
330
70
500
100
700
915
210
4000
10
2
200
300
Annual
$ Value
825000
70000
950000
150000
2730000
915000
42000
4000000
80000
18000
100000
120000
Group A: Perpetual
Group C: Periodic
Item
Number
8
5
3
6
1
4
12
11
9
2
7
10
Annual
Demand
1000
3900
1900
1000
2500
1500
400
500
8000
1000
200
9000
Unit
Cost
4000
700
500
915
330
100
300
200
10
70
210
2
Annual % of Total Classification
$ Value
4000000
A
2730000
67%
A
950000
B
915000
B
825000
27%
B
150000
C
120000
C
100000
C
80000
C
70000
C
42000
C
18000
6%
C
The Basic Inventory Model: Economic Order Quantity
Only one product
Demand is known and is constant throughout the year
Each order is received in a single delivery
Lead time does not vary
-Two costs
 Ordering Costs: Costs of ordering and receiving the order
 Holding or Carrying Costs: Cost to carry an item in
inventory for one year
Unit cost of product is not incorporated because we assume it is
fixed. It does not depends on the ordering policy.
The Basic Inventory Model
Annual demand for a product is 9600 units.
D = 9600
Annual carrying cost per unit of product is $16.
H = 16
Ordering cost per order is $75.
S = 75
a) How much should we order each time to minimize our
total cost?
b) How many times should we order?
c) What is the length of an order cycle (288 working
days/year)?
d) What is the total cost?
Do NOT worry if you do not get integer numbers.
Ordering Cost
D = Demand in units / year
Q = Order quantity in units / order
Number of orders / year =
D
Q
S = Order cost / order
Annual order cost =
D
S
Q
Annual Ordering Cost
Order Size Number of Orders Ordering Cost
50
192
14400
100
96
7200
150
64
4800
200
48
3600
250
38.4
2880
300
32
2400
350
27.4
2057
400
24
1800
450
21.3
1600
500
19.2
1440
550
17.5
1309
600
16
1200
650
14.8
1108
700
13.7
1029
750
12.8
960
800
12
900
850
11.3
847
900
10.7
800
Annual Ordering Cost
Ordering Cost
Order Size Number of Orders Ordering Cost
50
192
14400
100
96
7200
150
64
4800
200
48
3600
16000
250
38.4
2880
14000
300
32
2400
12000
350
27.4
2057
10000
400
24
1800
450
21.3
1600
8000
500
19.2
1440
6000
550
17.5
1309
4000
600
16
1200
2000
650
14.8
1108
0
700
13.7
1029
100
200
300
400
750 0
12.8
960 500
Order Size
800
12
900
850
11.3
847
900
10.7
800
D
S
Q
600
700
800
900
1000
The Inventory Cycle
Quantity
on hand
Inventory
Usage
rate
Receive
order
Time
When the quantity on hand is just sufficient to satisfy demand in
lead time, an order for EOQ is placed
At the instant that the inventory on hand falls to zero, the order will
be received (Screencam tutorial on DVD)
Inventory
The Inventory Cycle
Q
Q = Order quantity
At the beginning of the period we get Q units.
At the end of the period we have 0 units.
Q0 Q

2
2
0
Q/2
Average Inventory / Period & Average Inventory / year
This is average inventory / period.
Average inventory / period is also known as
Cycle Inventory
What is average inventory / year ?
Time
Time
Inventory Carrying Cost
Q = Order quantity in units / order
Q
2
Average inventory / year =
H = Inventory carrying cost / unit / year
Annual carrying cost =
Q
H
2
Annual Carrying Cost
Carring Cost
Order Size Average Inventory Carrying Cost
50
25
400
100
50
800
150
75
1200
8000
200
100
1600
7000
250
125
2000
6000
300
150
2400
5000
350
175
2800
400
200
3200
4000
450
225
3600
3000
500
250
4000
2000
550
275
4400
1000
600
300
4800
0
650
325
5200
0
100
200
300
400
500
600
700
350
5600
Order Size
750
375
6000
800
400
6400
850
425
6800
900
450
7200
Q
H
2
700
800
900
1000
Total Cost
Order Size Number of Orders
50
192
100
96
150
64
200
48
250
38.4
300
32
350
27.4
16000
400
24
450
21.3
14000
500
19.2
550
17.5
12000
600
16
650
14.8
10000
700
13.7
750
12.8
8000 12
800
850
11.3
900
6000 10.7
Ordering Cost Average Inventory
14400
25
7200
50
4800
75
3600
100
2880
125
2400
150
2057
175
1800
200
1600
225
1440
250
1309
275
1200
300
1108
325
1029
350
960
375
900
400
847
425
800
450
Carrying Cost Total Ord&Carr. Cost
400
14800
800
8000
1200
6000
1600
5200
2000
4880
2400
4800
2800
4857
3200
5000
3600
5200
4000
5440
4400
5709
4800
6000
5200
6308
5600
6629
Ordering
Cost
6000
6960
Carrying
Cost
6400
7300
6800
7647
Total Ord&Carr.
Cost
7200
8000
4000
2000
0
200
400
600
800
1000
ost
0
EOQ
TC  (Q / 2) H  ( D / Q ) S
EOQ is at the intersection of the two costs.
(Q/2)H = (D/Q)S
Q is the only unknown. If we solve it
EOQ =
2DS
=
H
2(Annual Demand )(Order or Setup Cost )
Annual Holding Cost
Back to the Original Questions
Annual demand for a product is 9600 units.
D = 9600
Annual carrying cost per unit of product is $16.
H = 16
Ordering cost per order is $75.
S = 75
a) How much should we order each time to minimize
our total cost?
b) How many times should we order?
c) What is the length of an order cycle (288 working
days/year)?
d) What is the total cost?
What is the Optimal Order Quantity
2 DS
EOQ 
H
D = 9600, H = 16, S = 75
2(9600)(75)
EOQ 
 300
16
How Many Times Should We Order?
Annual demand for a product is 9600 units.
D = 9600
Economic Order Quantity is 300 units.
EOQ = 300
Each time we order EOQ.
How many times should we order per year?
D/EOQ
9600/300 = 32
What is the Length of an Order Cycle?
Working Days = 288/year
9600 units are required for 288 days.
300 units is enough for how many days?
(300/9600)×(288) = 9 days
What is the Optimal Total Cost
The total cost of any policy is computed as:
TC  (Q / 2) H  ( D / Q ) S
The economic order quantity is 300.
TC  (300 / 2)16  (9600 / 300)75
TC  2400  2400
TC  4800
This is optimal policy that minimizes total cost.
Centura Health Hospital
Centura Health Hospital processes a demand of 31200 units of IV
starter kits each year (D=31200), and places an order of 6000 units
at a time (Q=6000). There is a cost of $130 each time an order is
placed (S = $130). Inventory carrying cost is $0.90 per unit per year
(H = $0.90). Assume 52 weeks per year.
What is the average inventory?
Average inventory = Q/2 = 6000/2 = 3000
What is the total annual carrying cost?
Carrying cost = H(Q/2) = 0.9×3000=2700
How many times do we order?
31200/6000 = 5.2
What is total annual ordering cost?
Total ordering cost = S(D/Q)
Ordering cost = 130(5.2) = $676