UNIT 3

Inventory Control
 INVENTORY

• Inventory simply means ‘a stock of goods’.

• Inventory is any stored resource that is used to
satisfy a current or a future need.
• Raw materials, work-in-process, and finished
goods are examples of inventory.
 TYPES OF INVENTORY

1. Movement Inventory:
It refers to stock of goods that take substantial
amount of time to be transported from one
place to another. They are also known as
transit inventories.
2. Buffer Inventory: Goods held in stock to
meet the uncertainties related to demand and
supply of goods are called buffer inventories.
These are goods that require a substantial
lead time (time taken between placing an
order and having the good ready for use) and
hence are held in excess of the time expected
demand to meet emergency situations and
fluctuations in demand or supply.
3. Anticipation Inventories: it refers to stock
of good that are held in bulk due to an
anticipated shortage or expected demand rise
in the future.
For e.g. Rain coats and umbrellas kept in
stock just before a rainy season, or stock of
air conditioners before summers.
4. Decoupling Inventories: Stock of good held
between different stages in a production
process to decouple or disengage on stage
from the other are known as decoupling
inventories.
The main purpose of holding such good is to
ensure smooth running of the production
process, therefore, even if one machine
required for a particular stage breaks down,
work on other stages in production won’t be
hampered.
5. Cycle Inventories: are maintained for goods
that are sold in bulk or big quantities
therefore, rather than making frequent
purchases in small amounts which increases
the cost of obtaining the products, goods are
bought in very large lots to reduce to cost of
obtaining goods.
 Inventory Cost
A major objective in controlling inventory is to
minimize total inventory costs. Some of the
most significant inventory costs follow:
1. Cost of the items (purchase cost or material
cost)
2. Cost of ordering
3. Cost of carrying, or holding, inventory
4. Cost of stockouts
1. Purchase Costs: cost of purchasing raw materials
from various sources.
2. Ordering Cost/procurement cost: cost associated
with replenishment of raw material i.e. Processing
of order, transportation, quality inspection etc.
3. Carrying Cost/Holding cost: cost related to
storage of goods like rent of warehouse, electricity,
heating and lighting, staff salaries etc.
4. Stock out Cost: Cost associated with lack of goods
or not serving the customers due to shortage of
goods
 Holding /Carrying Cost

• The cost associated with carrying or holding the goods in stock.

• C1 or Ch per unit of goods for a unit of time.
• Cost of Money or capital : money borrowed from the banks cost
interest of about 12% but usually the problem is viewed in different
way i .e how much the organization would have earned, had the
capital been invested in an alternative project such as developing a
new product, etc
• Cost of storage space: the rent of storage space or depreciation and
interest even if the own space is used. beside space expenses, this will
also include heating, lighting and other atmospheric control expenses.
• Depreciation and deterioration cost: such cost arise due to the items
in stock being out of fashion or the items undergoing chemical
changes during storage(e.g. Rusting in steel)Fragile items such as
crockery are liable to damage, breakage, etc
• Taxes and insurance costs: most organization have
insurance cover against possible loss from theft, fire
etc.
• Handling costs: these include all cost associated with
movement of stock such as: cost of labour, over head
cranes and other machinery required for this purpose.
• Record keeping and administrative cost: this
signifies the need of keeping funds for maintaining the
records and necessary administration.
• Obsolescence Costs :it depends upon the nature of the
item in stock. Electronic and computer components are
likely to be fast outdated. Changes in design also lead
to obsolescence.
• Purchase price or production costs: purchase price per
unit item is affected by the quantity purchased due to
quantity discounts or price-breaks. production cost per
unit item depends upon the length of production runs. for
long smooth production run this cost is lower due to
more efficiency of men and machines. So the order
quantity must be suitably modified to take the advantages
of these price discounts.
• Salvage Costs Or Selling Price: when the demand for
an item is affected by the quantity in stock the decision
model of the problem depends upon the profit
maximization criterion and includes the revenue for the
sales of items.
 Shortage costs or Stock outs (Cs)

• The penalty costs that are associated with

either a delay in meeting demands or the
inability to meet it at all.
• These costs arise due to shortage of goods,
sales may be lost, good will may be lost either
by a delay in meeting the demand or being
quite unable to meet the demand at all.
 Procurement / Set up/Order Costs

• These include the fixed cost associated with

obtaining goods through placing of an order or
purchasing or manufacturing or setting up a
machinery before starting production.
• So they include costs of purchase, requisition ,
follow-up, receiving the goods, quality control etc.
• They are assumed to be independent of the
quantity ordered or produced but directly
proportional to the number of orders placed.
 Purchase cost
• It is the price that is paid for purchasing /producing an item.
• It may be constant per unit or may vary with the quantity
purchased /produced.
• the purchase cost does not depend on the particular order
policy found to be optimal, because regardless of how many
orders are placed each year, we still incur the same annual
purchase cost of C* D, where C is the purchase cost per unit
and D is the annual demand in units.
• If the cost/unit is constant, it does not affect the inventory
control decision.
• However , the purchase cost is definitely considered when it
varies as in quantity discount situations.
 Inventory control

• It refers to the process employed to maximize

a company’s inventory. It is a systematic
control and regulation of purchases, storage
and usage of materials to maintain a smooth
flow in production and to avoid excessive
investment in inventory.
 Importance of Inventory Control

• Inventory control serves several important

functions and adds a great deal of flexibility to the
operation of the firm. Consider the following five
uses of inventory:
1. The decoupling function
2. Storing resources
3. Irregular supply and demand
4. Quantity discounts
5. Avoiding stockouts and shortages
 Inventory Decisions

• Even though there are literally millions of

different types of products produced in our society,
there are only two fundamental decisions that you
have to make when controlling inventory:
1. How much to order
2. When to order
• The purpose of all inventory models and
techniques is to determine rationally how much to
order and when to order.
Economic Order Quantity: Determining
How Much to Order
• Economic order quantity is the size of the
order representing standard quality of material
and it is the one for which the aggregates of
the costs of procuring the inventory and the
costs of holding the inventory is minimum.
 Some of the most important assumptions follow:

• It is relatively easy to use, but it does make a number of assumptions.

1. Demand is known and constant.
2. The lead time—that is, the time between the placement of the order
and the receipt of the order—is known and constant.
3. The receipt of inventory is instantaneous. In other words, the
inventory from an order arrives in one batch, at one point in time.
4. The purchase cost per unit is constant throughout the year. Quantity
discounts are not possible.
5. The only variable costs are the cost of placing an order, ordering cost,
and the cost of holding or storing inventory over time, holding or
carrying cost. The holding cost per unit per year and the ordering cost
per order are constant throughout the year.
6. Orders are placed so that stockouts or shortages are avoided
completely.
• The objective of the simple EOQ model is to
minimize total inventory cost. The relevant costs are
the ordering and holding costs.
• The annual ordering cost is simply the number of
orders per year times the cost of placing each order.
• The average inventory level is one-half the maximum
level.
• Average inventory level = Q/2
• Using the following variables, we can develop
mathematical expressions for the annual ordering and
carrying costs:
Q = number of pieces of order
EOQ = Q* = optimal number of pieces to order
D = annual demand in units for the inventory item
Co = ordering cost of each order
Ch = holding or carrying cost per unit per year
• Annual ordering cost = (Number of orders placed per
year) * (Ordering cost per order)
= (Annual demand/Number of units in
each order) * (Ordering cost per order)
= ( D/Q)Co
• Annual holding
or carrying cost = (Average inventory) * (Carrying cost per
unit per year)
= ( Order quantity/2) *
(Carrying cost per unit per year)
= (Q/2)Ch
We derive the EOQ equation by setting ordering cost equal to
carrying cost.
• Let I be the annual inventory holding charge as a
percent of unit price or cost. Then the cost of storing
one unit of inventory for the year, is given by where
C is the unit price or cost of an inventory item. can be
expressed, in this case, as
Key Equations
Q1.Patterson Electronics supplies microcomputer circuitry to a
company that incorporates microprocessors into refrigerators
and other home appliances. One of the components has an
annual demand of 250 units, and this is constant throughout
the year. Carrying cost is estimated to be $1 per unit per year,
and the ordering cost is $20 per order.
a. To minimize cost, how many units should be ordered each
time an order is placed?
b. How many orders per year are needed with the optimal
policy?
c. What is the average inventory if costs are minimized?
d. Suppose the ordering cost is not $20, and Patterson has been
ordering 150 units each time an order is placed. For this order
policy to be optimal, what would the ordering cost have to be?
 Reorder Point: Determining When to Order

• The reorder point (ROP) determines when to

order inventory. It is found by multiplying the
daily demand times the lead time in days. ROP
= (Demand per day)* (Lead time for a new
order in days)
=d*L
Q3. The F. W. Harris Company sells an industrial
cleaner to a large number of manufacturing
plants in the Houston area. An analysis of the
demand and costs has resulted in a policy of
ordering 300 units of this product every time an
order is placed. The demand is constant, at 25
units per day. In an agreement with the supplier,
F. W. Harris is willing to accept a lead time of 20
days since the supplier has provided an excellent
price. What is the reorder point? How many
units are actually in inventory when an order
should be placed?
• Solution
The reorder point is ROP = d x L = 25(20) = 500 units
This means that an order should be placed when the
inventory position is 500. Since the ROP is greater than
the order quantity, an order must have been placed already
but not yet delivered. So the inventory position must be
Inventory position = (Inventory on hand) + (Inventory on
order)
500 = 200 + 300
There would be 200 units on hand and an order of 300
units in transit.
EOQ Without the Instantaneous Receipt Assumption

• New model is applicable when inventory continuously

flows or builds up over a period of time after an order has
been placed or when units are produced and sold
simultaneously.
• Under these circumstances, the daily demand rate must be
taken into account.
• As this model is especially suited to the production
environment, it is commonly called the production run
model.
• In the production process, instead of having an ordering
cost, there will be a setup cost
 Annual Carrying Cost for Production Run
Model
• Solving the production run model involves setting
setup costs equal to holding costs and solving for Q.
• Q = number of pieces per order, or production run
• t = length of production run in days
• d = daily demand rate
• p = daily production rate
• Ch = holding or carrying cost per unit per year
• Cs = setup cost
• Annual holding cost = Q/2(1 –d/p)Ch
• Annual Setup Cost or Annual Ordering Cost
• When a product is produced over time, setup cost
replaces ordering cost. Both of these are independent
of the size of the order and the size of the production
run. This cost is simply the number of orders (or
production runs) times the ordering cost (setup cost).
Thus, Annual setup cost =(D/Q)Cs
• And Annual ordering cost =(D/Q)Co
 Determining the Optimal Production Quantity
• When the assumptions of the production run model
are met, costs are minimized when the setup cost
equals the holding cost. We can find the optimal
quantity by setting these costs equal and solving for
Q. Thus, Annual holding cost = Annual setup cost
• Q/2(1 –d/p)Ch =(D/Q)Cs

It should be noted that if the situation does not involve

production but rather involves the receipt of inventory over a
period of time, this same model is appropriate, but replaces in the
formula.
Q4. Dorsey Distributors has an annual demand
for a metal detector of 1,400. The cost of a
typical detector to Dorsey is $400. Carrying
cost is estimated to be 20% of the unit cost,
and the ordering cost is $25 per order. If
Dorsey orders in quantities of 300 or more, it
can get a 5% discount on the cost of the
detectors. Should Dorsey take the quantity
discount? Assume the demand is constant.
Key Equations
• Reorder Point
• Production Run Model

• The quantity discount Model

Q5. Brown Manufacturing produces commercial
refrigeration units in batches. The firm’s estimated
demand for the year is 10,000 units. It costs about
$100 to set up the manufacturing process, and the
carrying cost is about 50 cents per unit per year. When
the production process has been set up, 80 refrigeration
units can be manufactured daily. The demand during
the production period has traditionally been 60 units
each day. Brown operates its refrigeration unit
production area 167 days per year. How many
refrigeration units should Brown Manufacturing
produce in each batch? How long should the
production part of the cycle shown ?
Q6
 Q7. Lila Battle has determined that the annual demand for
number 6 screws is 100,000 screws. Lila, who works in her
brother’s hardware store, is in charge of purchasing. She
estimates that it costs $10 every time an order is placed. This
cost includes her wages, the cost of the forms used in placing
the order, and so on. Furthermore, she estimates that the cost
of carrying one screw in inventory for a year is one-half of 1
cent. Assume that the demand is constant throughout the year.
(a) How many number 6 screws should Lila order at a time if
she wishes to minimize total inventory cost?
(b) How many orders per year would be placed? What would
the annual ordering cost be?
(c) What would the average inventory be? What would the
annual holding cost be?
Given :
a)D= 100000 screws,
C0 = $10,
Ch =1/2x1%= 0.005$ for a year

= 20,000 screws
b)n (number of orders per year ) = D/q = 5
So the annual ordering cost be (D/q)x C0 = $50
c) The average inventory = q/2 = 10,000
So the annual holding cost = (q/2)x Ch = $50
Total Cost = $100
Q8.It takes approximately 8 working days for an
order of number 6 screws to arrive once the
order has been placed. (Refer to Problem 7.)
The demand for number 6 screws is fairly
constant, and on the average, Lila has
observed that her brother’s hardware store
sells 500 of these screws each day. Because
the demand is fairly constant, Lila believes
that she can avoid stock outs completely if she
only orders the number 6 screws at the correct
time. What is the ROP?
• Given L = 8 days(lead time for a new order in days)
d = 500( demand per day)
So, ROP = d x L
Reorder point = 4,000 units.
Q9 Lila’s brother believes that she places too
many orders for screws per year. He believes
that an order should be placed only twice per
year. If Lila follows her brother’s policy, how
much more would this cost every year over the
ordering policy that she developed in Problem
7? If only two orders were placed each year,
what effect would this have on the ROP?
• As per previous problem we have

But we want n = 2
So, as we know n = D/q
2 = 100000/q
q = 50,000 units
So annual ordering cost = D/q x Co = $20 and the annual holding cost =
q/2 x Ch = $123
Therefore total cost = $145
In previous problem , total cost was $100 , so $145-$100 = $45 which is
more than previous problem when n = 5
ROP = 4000 , no change on ROP if only 2 orders were placed each.
Q10.In Problem 7 you helped Lila Battle
determine the optimal order quantity for
number 6 screws. She had estimated that the
ordering cost was $10 per order. At this time,
though, she believes that this estimate was too
low. Although she does not know the exact
ordering cost, she believes that it could be as
high as $40 per order. How would the optimal
order quantity change if the ordering cost were
$20, $30, and $40?
Q11.Barbara Bright is the purchasing agent for West Valve
Company. West Valve sells industrial valves and fluid control
devices. One of the most popular valves is the Western, which
has an annual demand of 4,000 units. The cost of each valve is
$90, and the inventory carrying cost is estimated to be 10% of the
cost of each valve. Barbara has made a study of the costs
involved in placing an order for any of the valves that West Valve
stocks, and she has concluded that the average ordering cost is
$25 per order. Furthermore, it takes about two weeks for an order
to arrive from the supplier, and during this time the demand per
week for West valves is approximately 80.
(a) What is the EOQ?
(b) What is the ROP?
(c) What is the average inventory? What is the annual holding cost?
(d) How many orders per year would be placed? What is the annual
ordering cost?
Q12. Ken Ramsing has been in the lumber business for
most of his life. Ken’s biggest competitor is Pacific
Woods. Through many years of experience, Ken
knows that the ordering cost for an order of plywood
is $25 and that the carrying cost is 25% of the unit
cost. Both Ken and Pacific Woods receive plywood
in loads that cost $100 per load. Furthermore, Ken
and Pacific Woods use the same supplier of plywood,
and Ken was able to find out that Pacific Woods
orders in quantities of 4,000 loads at a time. Ken also
knows that 4,000 loads is the EOQ for Pacific
Woods. What is the annual demand in loads of
plywood for Pacific Woods?
Q13. Shoe Shine is a local retail shoe store
located on the north side of Centerville. Annual
demand for a popular sandal is 500 pairs, and
John Dirk, the owner of Shoe Shine, has been in
the habit of ordering 100 pairs at a time. John
estimates that the ordering cost is $10 per order.
The cost of the sandal is $5 per pair. For John’s
ordering policy to be correct, what would the
carrying cost as a percentage of the unit cost
have to be? If the carrying cost were 10% of the
cost, what would the optimal order quantity be?
Q14. Ross White’s machine shop uses 2,500 brackets during the
course of a year, and this usage is relatively constant throughout the
year. These brackets are purchased from a supplier 100 miles away
for $15 each, and the lead time is 2 days. The holding cost per
bracket per year is $1.50 (or 10% of the unit cost) and the ordering
cost per order is $18.75.There are 250 working days per year.
(a) What is the EOQ?
(b) Given the EOQ, what is the average inventory? What is the annual
inventory holding cost?
(c) In minimizing cost, how many orders would be made each year?
What would be the annual ordering cost?
(d) Given the EOQ, what is the total annual inventory cost (including
purchase cost)?
(e) What is the time between orders?
(f) What is the ROP?