MEANING
Inventory-A physical resource that a firm holds
in stock with the intent of selling it or
transforming it into a more valuable state.
 Inventory System- A set of policies and
controls that monitors levels of inventory and
determines what levels should be maintained,
when stock should be replenished, and how
large orders should be. It involves inventory
planning and decision making with regard to the
quantity and time of purchase, fixation of stock
levels, maintenance of stores record and
continuous stock taking.

THE INVENTORY DECISION

1.
2.
3.
In an Inventory control situation, there
are three basic questions to be
answered. They are:How much to order?
When should the order be placed?
How much safety stock should be kept?
TYPES OF INVENTORIES
Types of
Inventories
Direct
Inventories
Raw
Material
Work in
Progress
Transit
Inventories
Indirect
Inventories
Finished
Goods
Buffer
Inventories
Lot Size
Inventories
Decoupling
Inventories
Seasonal
Inventories
Fluctuation
Inventories
Factors Affecting Inventory
Control Policy
A.
1.
2.
3.
4.
5.
Characteristics of the
manufacturing system:
Degree of Specialization
and differentiation of the
products
at
various
stages.
Process capability and
flexibility.
Production capacity and
storage facility.
Quality requirements.
Nature of production
system.
B.
1.
2.
3.
4.
5.
6.
Amount
of
protection
against storages:
Changes in size and
frequency of orders.
Unpredictability of sales.
Physical and economic
structure of distribution
pattern.
Costs
associated
with
failure to meet demand.
Accuracy, frequency and
detail of demand forecasts.
Protection
against
breakdown
or
other
interruptions in production.
Objectives of Inventory Control
A hedge against inflation.
2. Protection against fluctuation in demand.
3. Protection against fluctuation in supply.
4. To avoid stock outs and shortages.
5. Quantity discounts.
6. Optimum use of men, machines & materials.
7. Maintaining different level of stock.
8. Control of stock volume.
9. The decoupling function.
1.
Scope of Inventory Control
Formulation of policy.
2. Organization structure.
3. Determination of economic order quantity.
4. Determination of safety stock.
5. Determination of lead time.
6. Minimum material handling & storage cost.
7. Effectiveness towards running of store.
1.
TOOLS & TECHNIQUES OF
INVENTORY MANAGEMENT
1. DETERMINATION OF STOCK LEVELS
2.DETERMINATION OF SAFETY STOCKS
3. INVENTORY CONTROL SYSTEMS
4. ECONOMIC ORDER QUANTITY
5. PRODUCTION QUANTITY MODEL
6. QUANTITY DISCOUNTS
7. ABC ANALYSIS
8. JIT CONTROL SYSTEM
9. VED ANALYSIS
10. FNSD ANALYSIS
11. PREPETUAL INVENTORY SYSTEM
12. PRICE BREAKS APPROACH
13. OTHER MODELS OF INVENTORY CONTROL
1. Determination Of Stock Levels
Reorder Point
Level of inventory at which a new order is placed.
R = dL
where
d = demand rate per period
L = lead time
Re-ordering level
It is the level of stock quantity between
minimum and maximum level and
material order was sent for getting fresh
stock.
Formula
:
maximum usage of stock X maximum
delivery
period
Minimum level

It is the minimum balance, which must be
maintained in hand at all times, so that
there is no stoppage of production due to
non availability of inventory.
Remember
You must need re-order level for
getting it.
Formula
:
Re-order level - ( Normal usage X
average period )
Maximum level

It shows maximum quantity which
should be in the stock, if we buy more, it
means we are wasting money.
Formula
:
re-order level X re-order quantity - (
minimum usage X minimum period )
Average Stock Level

This is the average of minimum and
maximum level and it can be calculated
by adding minimum level and maximum
level and divided by 2.
formula
minimum level + maximum level / 2
:
Danger level

It is the level at which normal issues of
the raw material inventory are stopped
and emergency issues are only made.
formula :
average consumption X lead time for
emergency
purchases
2. Determination of Safety Stocks
Safety stock
buffer added to on hand inventory during lead
time
Stockout
an inventory shortage
Service level
probability that the inventory available during lead
time will meet demand
Variable Demand with
a Reorder Point
Inventory level
Q
Reorder
point, R
0
LT
LT
Time
Inventory level
Reorder Point with
a Safety Stock
Q
Reorder
point, R
Safety Stock
0
LT
LT
Time
Reorder Point With
Variable Demand
R = dL + zd L
where
d = average daily demand
L = lead time
d = the standard deviation of daily demand
z = number of standard deviations
corresponding to the service level
probability
zd L = safety stock
Reorder Point for
a Service Level
Probability of
meeting demand during
lead time = service level
Probability of
a stockout
Safety stock
zd L
dL
Demand
R
Reorder Point for
Variable Demand
The carpet store wants a reorder point with a 95%
service level and a 5% stockout probability
d = 30 yards per day
L = 10 days
d = 5 yards per day
For a 95% service level, z = 1.65
R = dL + z d L
Safety stock = z d L
= 30(10) + (1.65)(5)( 10)
= (1.65)(5)( 10)
= 326.1 yards
= 26.1 yards
3. Inventory Control Systems
Continuous system (fixedorder-quantity or Q
Systems)
constant amount ordered when
inventory declines to
predetermined level
Periodic system (fixed-timeperiod or P Systems)
order placed for variable amount
after fixed passage of time
Fixed Order Quantity System or Q
Systems – In reorder level system, a
replenishment order fixed size (Q) is
placed when the stock level falls to the
fixed reorder level (R). Thus a fixed
quantity is ordered at various interval of
time.
 Periodic Review System or P System –
In periodic review system, the inventory
levels are reviewed at fixed points of time,
when the quantity to be ordered is decided.
By this method variable quantities are
ordered at fixed time intervals

4. ECONOMIC ORDER QUANTITY (EOQ)

Economic order quantity is the size of the lot to be
purchased which is economically viable. This the quantity of
materials which can be purchased at minimum costs.

ASSUMPTIONS

Demand rate D is constant, recurring, and known
Amount in inventory is known at all times
Ordering (setup) cost S per order is fixed
Lead time L is constant and known.
Unit cost C is constant (no quantity discounts)
Annual carrying cost is i time the average RUPEE value of
the inventory
No stock outs allowed.
Material is ordered or produced in a lot or batch and the lot
is received all at once







EOQ Inventory Order Cycle
Order qty, Q
Inventory
Level
Demand
rate
ave = Q/2
Reorder point, R
0
As Q increases, average
inventory level increases,
but number of orders placed
decreases
Lead
time
Order
Order
Placed Received
Lead
Time
time
Order
Order
Placed
Received
EOQ Cost Model
Co - cost of placing order
Cc - annual per-unit carrying cost
D - annual demand
Q - order quantity
Annual ordering cost =
Co D
Q
Annual carrying cost =
CcQ
2
Total cost =
CoD
+
Q
CcQ
2
EOQ Cost Model
Proving equality of
costs at optimal point
Deriving Qopt
CoD
CcQ
TC =
+
Q
2
CoD
Cc
TC
=
+
Q2
2
Q
C0D
Cc
0=
+
Q2
2
Qopt =
2CoD
Cc
Co D
CcQ
=
Q
2
Q2
2CoD
=
Cc
Qopt =
2CoD
Cc
EOQ Cost Model (cont.)
Annual
cost ($)
Total Cost
Slope = 0
CcQ
Carrying Cost =
2
Minimum
total cost
CoD
Ordering Cost = Q
Optimal order
Qopt
Order Quantity, Q
EOQ Example
Cc = $0.75 per yard
Qopt =
2CoD
Cc
Qopt =
2(150)(10,000)
(0.75)
Co = $150
Qopt = 2,000 yards
Orders per year = D/Qopt
= 10,000/2,000
= 5 orders/year
D = 10,000 yards
CoD
CcQ
TCmin =
+
Q
2
TCmin
(150)(10,000) (0.75)(2,000)
=
+
2,000
2
TCmin = $750 + $750 = $1,500
Order cycle time = 311 days/(D/Qopt)
= 311/5
= 62.2 store days
5. Production Quantity Model
An inventory system in which an order is
received gradually, as inventory is
simultaneously being depleted
 AKA non-instantaneous receipt model

 assumption that Q is received all at once is
relaxed
p - daily rate at which an order is received
over time, a.k.a. production rate
 d - daily rate at which inventory is
demanded

Production Quantity Model
(cont.)
Inventory
level
Q(1-d/p)
Maximum
inventory
level
Q
(1-d/p)
2
Average
inventory
level
0
Order
receipt period
Begin
End
order order
receipt receipt
Time
Production Quantity Model
(cont.)
p = production rate
d = demand rate
Maximum inventory level = Q - Q d
p
=Q1- d
p
Q
d
Average inventory level =
12
p
CoD CcQ
d
TC = Q + 2 1 - p
2CoD
Qopt =
d
Cc 1 p
Production Quantity Model: Example
Cc = $0.75 per yard
Co = $150
d = 10,000/311 = 32.2 yards per day
2CoD
Qopt =
Cc 1 - d
p
D = 10,000 yards
p = 150 yards per day
2(150)(10,000)
=
CoD CcQ
d
TC = Q + 2 1 - p
32.2
0.75 1 150
= 2,256.8 yards
= $1,329
2,256.8
Q
Production run =
=
= 15.05 days per order
150
p
Production Quantity Model: Example
(cont.)
Number of production runs =
10,000
D
=
= 4.43 runs/year
2,256.8
Q
Maximum inventory level = Q 1 -
d
p
= 2,256.8 1 -
= 1,772 yards
32.2
150
6. QUANTITY DISCOUNTS
Price per unit decreases as order
quantity increases
CoD
CcQ
TC =
+
+ PD
Q
2
where
P = per unit price of the item
D = annual demand
Quantity Discount Model (cont.)
ORDER SIZE
0 - 99
100 – 199
200+
PRICE
$10
8 (d1)
6 (d2)
TC = ($10 )
TC (d1 = $8 )
Inventory cost ($)
TC (d2 = $6 )
Carrying cost
Ordering cost
Q(d1 ) = 100 Qopt
Q(d2 ) = 200
Quantity Discount: Example
QUANTITY
1 - 49
50 - 89
90+
Qopt =
PRICE
$1,400
1,100
900
2CoD
=
Cc
Co = $2,500
Cc = $190 per computer
D = 200
2(2500)(200)
= 72.5 PCs
190
For Q = 72.5
CcQopt
Co D
TC =
+
2 + PD = $233,784
Qopt
For Q = 90
CcQ
CoD
TC =
+ 2 + PD = $194,105
Q
7. ABC ANALYSIS

The materials are divided in to a number of categories
for adopting a selective approach for material control.

Classification of items as a, b, or c

Purpose: set priorities for management attention.
‘A’ items: 20% of the items contributes, 80% value
‘B’ items: 30 % of Items contributes , 15% Value
‘C’ items: 50 % of Items contributes , 5% value
Three classes is arbitrary; could be any number.
Percents are approximate.





Percentage of dollar value
100 —
+Class C
+Class B
90 —
Class A
80 —
70 —
60 —
50 —
40 —
30 —
20 —
10 —
0—
10
20
30
40
50
60
70
Percentage of items
80
90 100
ABC Classification

Class A
 5 – 15 % of units
 70 – 80 % of value

Class B
 30 % of units
 15 % of value

Class C
 50 – 60 % of units
 5 – 10 % of value
8. JIT CONTROL SYSTEM

Just in Time purchasing is the purchase
of material in such a way that delivery of
purchased items is assured before their
use or demand.
9. VED Analysis

VED – Vital, Essential, Desirable –
analysis is used primarily for control of
spare parts. The spare, parts can be
divided into three categories – vital,
essential or desirable – keeping in view
the critically to production.
10. FNSD Analysis
FNSD analysis divides the items into
four categories in the descending order
of their usage rate as follows:
 ‘F’ means Fast moving items
 ‘N’ means normal moving items
 ‘S’ means slow moving items
 ‘D’ means dead stock.

11. Perpetual Inventory System
Perpetual Inventory is a system of records
maintained by the controlling department, which
reflects the physical movement of stocks and their
current balance. It aims at devising the system of
records by which the receipts and issues of stores
may be recorded immediately at the time of each
transaction and the balance may be brought out
so as to show the up-to-date position.
The records used for perpetual inventory are:
(i) Bin Cards;
(ii) Store Ledger Accounts or Stores Record cards;
(iii) The forms and documents used for receipt,
issue and transfer of materials.