
The
objectives of inventory management are to provide the
required level of customer service and to reduce the sum
of all costs involved. To achieve these objectives, two
basic questions must be answered:

How much should be ordered at one time?

When should an order be placed?

Management must establish decision rules to answer these
questions so inventory management personnel know when
to order and how much. Lacking any better knowledge,
decision rules are often made based on what seems
reasonable. Unfortunately, such rules do not always
produce the best results.

This chapter will examine methods of answering the first
question, and the next chapter will deal with the second
question. First, we must decide what we are ordering and
controlling.
a.
StockKeeping Unit (SKU)
b.
LotSize Decision Rules

The eighth edition
of the APICS
Dictionary defines a
lot, or batch, as a
quantity produced
together and sharing
the same production
costs and
specifications.
Following are some
common decision
rules for
determining what lot
size to order at one
time.
Lotforlot.
The
lotforlot

rule
says to
order
exactly
what is
needed—no
more—no
less.
The
order
quantity
changes
whenever
requirements
change.
This
technique
requires
timephased
information
such as
provided
by a
material
requirements
plan or
a master
production
schedule.
Since
items
are
ordered
only
when
needed,
this
system
creates
no
unused
lotsize
inventory.
Because
of this,
it is
the best
method
for
planning
“A’
items
and is
also
used in
a
justintime
environment.
Fixedorder
quantity

Fixedorder
quantity
rules
specify
the
number
of units
to be
ordered
each
time an
order is
placed
for an
individual
item or
SKU. The
quantity
is
usually
arbitrary,
such as
200
units at
a time.
The
advantage
to this
type of
rule is
that it
is
easily
understood.
The
disadvantage
is that
it does
not
minimize
the
costs
involved.

A
variation
on the
fixedorder
quantity
system
is the
mmmax
system.
In this
system,
an order
is
placed
when the
quantity
available
falls
below
the
order
point
(discussed
in the
next
chapter).
The
quantity
ordered
is the
difference
between
the
actual
quantity
available
at the
time of
order
and the
maximum.
For
example,
if the
order
point is
100
units,
the
maximum
is 300
units,
and the
quantity
actually
available
when the
order is
placed
is 75,
the
order
quantity
is 225
units.
If the
quantity
actually
available
is 80
units,
an order
for 220
units is
placed.
One
commonly
used
method
of
calculating
the
quantity
to order
is the
economicorder
quantity,
which is
discussed
in the
next
section.
Order “n”
periods
supply.
c.
Costs

As shown in the last
chapter, the cost of
ordering and the
cost of carrying
inventory both
depend on the
quantity ordered.
Ideally, the
ordering decision
rules used will
minimize the sum of
these two costs. The
best known system is
the economicorder
quantity.
a.
Assumptions

The assumptions on
which the EOQ is
based are as
follows:

Demand is
relatively
constant and is
known.

The item is
produced or
purchased in
lots or batches
and not
continuously.

Order
preparation
costs and
inventorycarrying
costs are
constant and
known.

Replacement
occurs all at
once.

These assumptions
are usually valid
for finished goods
whose demand is
independent and
fairly uniform.
However, there are
many situations
where the
assumptions are not
valid and the EOQ
concept is of no
use. For instance,
there is no reason
to calculate the EOQ
for madetoorder
items in which the
customer specifies
the order quantity,
the shelf life of
the product is
short, or the length
of the run is
limited by tool life
or raw material
batch size. In
material
requirements
planning, the
lotforlot decision
rule is often used,
but there are also
several rules used
that are variations
of the
economicorder
quantity.
b.
Development of the EOQ
Formula

Under the
assumptions given,
the quantity of an
item in inventory
decreases at a
uniform rate.
Suppose for a
particular item, the
order quantity is
200 units, and the
usage rate is 100
units a week. Figure
10.1 shows how
inventory would
behave.

The vertical lines
represent stock
arriving all at once
as the stock on hand
reaches zero. The
quantity of units in
inventory then
increases
instantaneously by
Q, the quantity
ordered. This is an
accurate
representation of
the arrival of
purchased parts or
manufactured parts
where all parts are
received at once.
From the preceding,
order
quantity
200
Average
lot size
inventory
=
=
=
100
units
2
2
annual
demand
100 X 52
Number
of
orders
per year
=
=
.
order
quantity
200
= 26
times
per year 
c.
Example Problem
Answer
order
quantity
200
Average
cycle
inventory
=
=
=
100
units
2
2
annual
demand
10.075
Number
of
orders
per year
=
=
.
= 15.5
order
quantity
650 

Notice in the example
problem the number of orders per year is rounded
neither up nor down. It is an average figure, and
the actual number of orders per year will vary from
year to year but will average to the calculated
figure. In the example, 16 orders will be placed in
one year and 15 in the second.
d.
Relevant costs

The relevant costs
are as follows:

As the order
quantity increases,
the average
inventory and the
annual cost of
carrying inventory
increase, but the
number of orders per
year and the
ordering cost
decrease. It is a
bit like a seesaw
where one cost can
be reduced only at
the expense of
increasing the
other. The trick is
to find the
particular order
quantity in which
the total cost of
carrying inventory
and the cost of
ordering will be a
minimum.
Let:
A
=
annual usage in
units
S
=
ordering cost in
dollars per
order
i
=
annual carrying
cost rate as a
decimal of a
percentage
c
=
unit cost in
dollars
Q
=
order quantity
in units
Then:
Annual ordering
cost = number of
orders x costs
per order
Annual
carrying
cost =
average
inventory x
cost of
carrying one
unit for one
year
= average
inventory x
unit cost x
carrying
cost
Total annual
costs =
annual
ordering
costs +
annual
carrying
costs
e. Example
Problem

The
annual
demand
is
10,000
units,
the
ordering
cost
$30
per
order,
the
carrying
cost
20%,
and
the
unit
cost
$15.
The
order
quantity
is
600
units.
Calculate:

Annual ordering cost

Annual carrying cost

Total annual cost
Answer
A = 10,000 units
S = $30
i = 0.20
C = $15
Q = 600 units
A 10,000

annual ordering cost = x S = x $30 = $500
Q 600
Q 600

annual carrying cost= x c x i = x $15 x 0.2 = $900
2 2

total annual cost = $1400


Ideally, the total cost will be a minimum. For any situation in which the annual demand (A), the cost of ordering (S), and the cost of carrying inventory (i) are given, the total cost will depend upon the order quantity (Q).
f.
TrialandError Solution
Let:
A
= 1000 units
S
= $20 per order
c
= $5 per unit
i
= 20% = 0.20
Then:
A
1000
Annual ordering
cost =
x S
=
x 20
Q
Q
Q
Q
Annual carrying
cost =
x
c x i =
x
5 x 0.20
2
2
Total annual
cost = annual
ordering cost +
annual carrying
cost 

Figure 10.2 is a
tabulation of the costs
for different order
quantities. The results
from the table in Figure
10.2 are represented on
the graph of Figure
10.3.

Figures 10.2 and 10.3
show the following
important facts:

There is an order
quantity in which
the sum of the
ordering costs and
carrying costs is a
minimum.

This EOQ occurs when
the cost of ordering
equals the cost of
carrying.

The total cost
varies little for a
wide range of lot
sizes about EOQ.

The last point is
important for two
reasons. First, it is
usually difficult to
determine accurately the
cost of carrying
inventory and the cost
of ordering. Since the
total cost is relatively
flat around the EOQ, it
is not critical to have
exact values. Good
approximations are
sufficient. Second,
parts are often ordered
in convenient packages
such as pallet loads,
cases, or dozens, and it
is adequate to pick the
closest package quantity
to the EOQ.
Order Quantity
(Q) 
Ordering Costs
(AS/Q) 
Carrying Costs
(Qci/2) 
Total Costs 
50 
$400

$25

$425

100 
200 
50 
250 
150 
133 
75 
208 
200 
100 
100 
200 
250 
80 
125 
205 
300 
67 
150 
217 
350 
57 
175 
232 
400 
50 
200 
250 
g.
EconomicOrder Quantity
Formula
h.
How to Reduce Lot Size

Looking at the EOQ
formula, there are
four variables. The
EOQ will increase as
the annual demand
(A) and the cost of
ordering (S)
increase, and it
will decrease as the
cost of carrying
inventory (i) and
the unit cost (c)
increase.

The annual demand
(A) is a condition
of the marketplace
and is beyond the
control of
manufacturing. The
cost of carrying
inventory (i) is
determined by the
product itself and
the cost of money to
the company. As
such, it is beyond
the control of
manufacturing.

The unit cost (c) is
either the purchase
cost of the SKU or
the cost of
manufacturing the
item. Ideally, both
costs should be as
low as possible. In
any event, as the
unit cost decreases,
the EOQ increases.

The cost of ordering
(S) is either the
cost of placing a
purchase order or
the cost of placing
a manufacturing
order. The cost of
placing a
manufacturing order
is made up from
production control
costs and setup
costs. Anything that
can be done to
reduce these costs
reduces the EOQ.

Justintime
manufacturing
emphasizes reduction
of setup time. There
are several reasons
why this is
desirable, and the
reduction of order
quantities is one.
Chapter 15 discusses
justintime
manufacturing
further.
a.
Monetary Unit Lot Size
A_{D} =
annual usage in
dollars
S = ordering costs
in dollars
i = carrying cost
rate as a decimal of
a percent
b.
Example Problem
A_{D} =
$5000
S = $20
i = 20% = 0.20

When
material is purchased, suppliers often
give a discount on orders over a certain
size. This can be done because larger
orders reduce the supplier’s costs; to
get larger orders, they are willing to
offer volume discounts. The buyer must
decide whether to accept the discount,
and in doing so, must consider the
relevant costs:

Purchase cost.

Ordering costs.

Carrying costs.
a.
Example Problem

An item has an
annual demand of
25,000 units, a unit
cost of $10, an
order preparation
cost of $10, and a
carrying cost of
20%. It is ordered
on the basis of an
EOQ, but the
supplier has offered
a discount of 2% on
orders of $10,000 or
more. Should the
offer be accepted?
Answer
A_{D} =
25,000 x $10 =
$250,000
S = $10
i = 20%
Discounted order
quantity = $l0,000 X
0.98 = $9,800

No discount 
Discount lot
size 
Unit Price 
$10 
$9.80 
Lot Size 
$5000 
$9800 
Average
LotSize
Inventory
(Qc ± 2) 
$2500 
$4900 
Number of
Orders per
Year 
50 
25 
Purchase
Cost 
$250,000 
$245,000 
InventoryCarrying
Cost (20%) 
500 
980 
Order
Preparation
Cost ($10
each) 
500 
250 
Total Cost 
$251,000 
$246,230 

From the preceding
example problem, it
can be said that
taking the discount
results in the
following:

There is a
saving in
purchase cost.

Ordering costs
are reduced
because fewer
orders are
placed since
larger
quantities are
being ordered.

Inventorycarrying
costs rise
because of the
larger order
quantity.

The buyer must weigh
the first two
against the last and
decide what to do.
What counts is the
total cost.
Depending on the
figures, it may or
may not be best to
take the discount.
5.
Use Of Eoq When
Costs Are Not Known

The EOQ formula
depends upon the
cost of ordering
and the cost of
carrying
inventory. In
practice, these
costs are not
necessarily
known or easy to
determine.
However, the
formula can
still be used to
advantage when
applied to a
family of items.

For a family of
items, the
ordering costs
and the carrying
costs are
generally the
same for each
item. For
instance, if we
were ordering
hardware
items—nuts,
bolts, screws,
nails, and so
on—the carrying
costs would be
virtually the
same (storage,
capital, and
risk costs) and
the cost of
placing an order
with the
supplier would
be the same for
each item. In
cases such as
this, the cost
of placing an
order (S) is the
same for all
items in the
family as is
cost of carrying
inventory (i).
Now

where A (annual
demand) is in
dollars.

Since S is the
same for all the
items and i is
the same for all
items, the ratio
2S ± i must be
the same for all
items in the
family. For
convenience,
let:
a.
Example Problem

Suppose there were a
family of items for
which the decision
rule was to order
each item four times
a year. Since the
cost of ordering (S)
and the cost of
carrying inventory (i)
are not known,
ordering four times
a year is not based
on an EOQ. Can we
come up with a
better decision rule
even if the EOQ
cannot be
calculated?

The sum of all the
lots is $2636. Since
the average
inventory is equal
to half the order
quantity, the
average inventory is
$2636 2 = $1318.

Since this is a
family of items
where the
preparation costs
are the same and the
carrying costs are
the same, the values
for K = (2S j)h/2
should be the same
for all items. The
preceding
calculations show
that they are not.
The correct value
for K is not known,
but a better value
would be the average
of all the values:

The economicorder
quantity attempts to minimize the total cost of
ordering and carrying inventory and is based on the
assumption that demand is uniform. Often demand is
not uniform, particularly in material requirements
planning, and using the EOQ does not produce a
minimum cost.

The periodorder
quantity lotsize rule is based on the same theory
as the economicorder quantity. It uses the EOQ
formula to calculate an economic time between
orders. This is calculated by dividing the
EOQ by the demand rate. This produces a time
interval for which orders are placed. Instead of
ordering the same quantity (EOQ), orders are placed
to satisfy requirements for the calculated time
interval. The number of orders placed in a year is
the same as for an economicorder quantity, but the
amount ordered each time varies. Thus, the ordering
cost is the same but, because the order quantities
are determined by actual demand, the carrying cost
is reduced.
EOQ
Periodorder quantity =
.
average weekly usage 
a.
Example Problem
Answer
b.
Example Problem

Given the following
MRP record and an
EOQ of 250 units,
calculate the
planned order
receipts using the
economicorder
quantity. Next,
calculate the
periodorder
quantities and the
planned order
receipts. In both
cases, calculate the
ending inventory and
the total inventory
carried over the ten
weeks.
Week 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Total 
Net
Requirements 
100 
50 
150 

75 
200 
55 
80 
150 
30 
890 
Planned
Order
Receipt 











Answer
EQQ = 250 units
Week 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Total 
Net
Requirements 
100 
50 
150 

75 
200 
55 
80 
150 
30 
890 
Planned
Order
Receipt 
250 

250 


250 


250 


Ending
Inventory 
150 
100 
200 
200 
125 
175 
120 
40 
140 
110 
1360 
Week 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Total 
Net
Requirements 
100 
50 
150 

75 
200 
55 
80 
150 
30 
890 
Planned
Order
Receipt 
300 



330 


260 



Ending
Inventory 
200 
150 
0 
0 
255 
55 
0 
180 
30 
0 
870 
c.
Practical Considerations
When Using the EOQ
Transportation inventory.
Multiples.

Sometimes, order size is constrained by
package size. For example, a supplier
may ship only in skidload lots. In
these cases, the unit used should be the
minimum package size.

