department store and that of a

Inventory: Definition hospital.

Inventory management is a core

operations management activity.
Effective inventory management is Functions of inventory
important for the successful operation Inventories serve a number of
of most businesses and their supply functions.
chains. Poor inventory management
hampers operations, diminishes  To meet anticipated
customer satisfaction, and increases customer demand.
operating costs.
A customer can be a person who
An inventory is a stock or store of walks in off the street to buy a new
goods used in an organization. stereo system, a mechanic who
requests a tool at a tool crib, or a
Firms typically stock hundreds or manufacturing operation. These
even thousands of items in inventory, inventories are referred to
ranging from small things such as as anticipation stocks because they
pencils, paper clips, screws, nuts, and are held to satisfy expected (i.e.,
bolts to large items such as machines, average ) demand.
trucks, construction equipment, and
airplanes.  To smooth production
requirements.
Inventory could also mean stored
capacity. This statement suggests
Firms that experience seasonal
that the inventory held by a business
patterns in demand often build up
serves as a reserve or a stored
inventories during preseason periods
potential for future activities or
to meet overly high requirements
operations.
during seasonal periods. These
Thus, inventory is not just a collection inventories are aptly named seasonal
of goods but represents a strategic inventories.
asset for the business. It signifies that
the inventory serves as a reservoir  To decouple operations.
of capacity that the business can tap
into to meet customer demand, Decoupling operations generally refer
respond to market fluctuations, or to the practice of minimizing
maintain smooth production dependencies between different
processes. In essence, the stored components or processes within a
inventory is a form of readiness, system. This is often done to enhance
allowing the business to be prepared flexibility, scalability, and
and responsive to changing maintainability. When operations are
circumstances. tightly coupled, changes in one part of
a system can have a significant impact
Naturally, many of the items a firm on other parts, making it harder to
carries in inventory relate to the kind modify or extend the system.
of business it engages in. Thus, a Decoupling aims to reduce these
manufacturing firm will carry interdependencies.
inventory that is different from a
In manufacturing firms, decoupling or setup (if inventories are produced
means the use of inventories as a or manufactured) costs. Carrying
buffer between successive operations costs refer to the costs of inventory
to maintain continuity of production while they are held in storage,
that may be disrupted by events such and ordering costs refer to the costs
as equipment breakdown or of placing and receiving the order.
accidents.
Stored inventories (purchased or
The inventory buffer permits other produced) would lead to an increase
operations to continue temporarily in holding costs. Thus, inventory
while the problem is resolved. storage enables a firm to buy and
produce in economic lot sizes even
There are other ways that inventory if purchases or production does not
buffers are used to decouple match with demand requirements in
operations, but we will limit our the short run. This results in periodic
example to what we have discussed so orders or order cycles.
far.
To effectively implement this, firms
 To protect against stockouts. will use inventory models that will
help them determine the economic
The risk of stockouts or shortages can lot size - (which could also mean the
happen due to delayed deliveries and fixed order size, or the economic
unexpected increases in demand. order quantity or economic
Delays can occur because of weather production quantity) that will
conditions, supplier stockouts, minimize both ordering/setup costs
deliveries of wrong materials, quality and holding or carrying costs.
problems, and so on.
 To hedge against price
The risk of shortages can be reduced increases.
by holding safety stocks, which are
stocks in excess of expected demand Occasionally a firm will suspect that a
to compensate for variabilities in substantial price increase is about to
demand and lead time (time interval occur and purchase larger-than-
between ordering and receiving the normal amounts to beat the increase.
order). The ability to store extra goods also
allows a firm to take advantage of
 To take advantage of order price discounts for larger orders.
cycles.
This leads us to the next function of
To minimize purchasing and inventory inventory which is to:
costs, a firm often buys in quantities
that exceed immediate requirements  To take advantage of
or produce in large rather than small quantity discounts.
quantities. This necessitates storing
some or all of the purchased amount  To permit operations.
or the excess output.
Production operations take a certain
Inventory costs include holding or amount of time (i.e., they are not
carrying costs and ordering (if instantaneous) means that there will
inventories are purchased) generally be some work-in-process
inventory. In addition, intermediate 1. The level of customer
stocking of goods—including raw service, that is, to have the
materials, semifinished items, and right goods, in sufficient
finished goods at production sites, as quantities, in the right place, at
well as goods stored in warehouses— the right time.
leads to pipeline inventories 2. The costs of ordering and
throughout a production distribution carrying inventories.
system.
The overall objective of inventory
Pipeline inventories refer to the management is to achieve
stocks or quantities of goods, satisfactory levels of customer service
materials, or work-in-progress items while keeping inventory costs within
that are in transit between different reasonable bounds.
stages of a production or distribution
process. These inventories are part of Toward this end, the decision maker
a supply chain and are in the process tries to achieve a balance in stocking
of being moved from one point to inventories. He or she must make two
another, such as from the fundamental decisions:
manufacturer to the distributor, from
the distributor to the retailer, or from 1. the timing of orders (When to
a production facility to a warehouse. order?)
2. the size of orders (How much
Thus, any form of inventory (raw to order?)
materials, work-in-process, finished
goods, and those stored in The answer to these two questions
warehouses) is considered a pipeline will be answered using the different
inventory, because, without these inventory models which will be
inventories, operations will not discussed later in this lesson.
proceed as planned.

Objectives of Performance Measure

Inventory Control of Effective Inventory
Inadequate control of inventories can
result in both under- and overstocking Management
of items. Understocking results in Managers have a number of
missed deliveries, lost sales, performance measures they can use
dissatisfied customers, and production to judge the effectiveness of inventory
bottlenecks; overstocking unnecessa management.
rily ties up funds that might be more
productive elsewhere. It is better to 1. Customer satisfaction, which
avoid overstocking because the cost of can be measured by the
excessive overstocking can be number and quantity of
staggering when inventory holding backorders and/or customer
costs are high. complaints.
2. Inventory turnover, which is
Inventory management has two main the ratio of the annual cost of
concerns. goods sold to average inventory
 investment. The turnover ratio be demanded prior to the next
indicates how many times a delivery period and bases the order
year the inventory is sold. quantity on that information.
Generally, the higher the ratio,
the better, because that implies  PERPETUAL INVENTORY
more efficient use of SYSTEM
inventories.
3. Days of inventory on hand, A perpetual inventory system (also
which represents the number known as a continual system) keeps
that indicates the expected track of removals from inventory on a
number of days of sales that continuous basis, so the system can
can be supplied from existing provide information on the current
inventory. This performance level of inventory for each item. When
metric measures the average the amount on hand reaches a
number of days a company predetermined minimum, a fixed
takes to sell its entire inventory quantity, Q, is ordered.
during a specific period. It
provides insights into how Moreover, a physical count of
efficiently a company manages inventories must still be performed
its inventory and how quickly it periodically to verify records because
can turn inventory into sales. of possible errors, pilferage, spoilage,
and other factors that can reduce the
effective amount of inventory.

TWO-BIN SYSTEM
Perpetual systems range from very
simple to very sophisticated. A two-
bin system uses two containers for
inventory. Items are withdrawn from
the first bin until its contents are
exhausted. It is then time to reorder.

Inventory Counting Sometimes an order card is placed at

the bottom of the first bin. The second
Systems bin contains enough stock to satisfy
expected demand until the order is
filled, plus an extra cushion of stock
 PERIODIC SYSTEM that will reduce the chance of a
stockout if the order is late or if usage
Under a periodic system, a physical is greater than expected.
count of items in inventory is made at
periodic intervals (e.g., weekly, Supermarkets, discount stores, and
monthly) in order to decide how much department stores have always been
to order for each item. major users of periodic counting
systems. Today, most have switched
Many small retailers use this to computerized checkout systems
approach: A manager periodically using a laser scanning device that
checks the shelves and stockroom to reads a universal product
determine the quantity on hand. Then code (UPC), or bar code, printed on
the manager estimates how much will an item tag or on the packaging that
has information about the item to amount per order, regardless
which it is attached. Point-of-sale of order size.
(POS) systems electronically record
actual sales.  When a firm produces its own
inventory instead of ordering it
from a supplier, machine setup
Inventory Costs costs (S) (which refers to the
costs of preparing equipment
Four basic costs are associated with for the job by adjusting the
inventories: machine and changing cutting
tools, etc) are analogous to
 Purchase cost is the amount ordering costs; that is, they are
paid to a vendor or supplier to expressed as a fixed amount
buy the inventory. It is typically per production
the largest of all inventory run, regardless of the size of
costs. the run.

 Holding or carrying costs  Shortage costs result when

(H) relate to costs for demand exceeds the supply of
physically having items in inventory on hand. These costs
storage. Costs include interest, can include the opportunity
insurance, depreciation, cost of not making a sale, loss
obsolescence (the state of the of customer goodwill, late
product being obsolete), charges, backorder costs, and
deterioration, spoilage, similar costs. Furthermore, if
pilferage (theft), breakage, the shortage occurs in an item
tracking, picking, and carried for internal use (e.g., to
warehousing costs (heat, light, supply an assembly line), the
rent, security). They also cost of lost production or
include opportunity costs downtime is considered a
associated with having funds shortage cost.
that could be used elsewhere
tied up in inventory. Holding
costs are stated in either of two
ways: as a percentage of unit
A-B-C

price or amount per unit.

Ordering costs (S) are the

Approach
costs of ordering and receiving An important aspect of inventory
inventory. They are the costs management is that items held in
that vary with the actual inventory are not of equal importance
placement of an order. Besides in terms of money invested, profit
shipping costs, they include potential, sales or usage volume, or
determining how much is stockout penalties.
needed, preparing invoices,
inspecting goods upon arrival The A-B-C approach classifies
for quality and quantity, and inventory items according to some
moving the goods to temporary measure of importance, usually
storage. Ordering costs are annual monetary value (i.e., monetary
generally expressed as a fixed value per unit multiplied by annual
usage rate), and then allocates control
efforts accordingly.

Typically, three classes of items are

used:

1. A (very important) - generally

accounts for about 10 to 20
percent of the number of items
in inventory but about 60 to 70
percent of the annual monetary Arranging the annual dollar values in
value descending order can facilitate
2. B (moderately important) assigning items categories:
3. C (least important) - might
account for about 50 to 60
percent of the number of items
but only about 10 to 15 percent
of the monetary value of an
inventory.

However, the actual number of

categories may vary from organization
to organization, depending on the
extent to which a firm wants to
differentiate control efforts.

HOW the A-B-C approach is

implemented?

 Sort products from largest to Note that category A has the fewest
smallest annual value. number of items but the highest
 Divide into A, B, and C classes. percentage of annual dollar value,
 Focus on A products. while category C has the most items
 Develop class A suppliers more. but only a small percentage of the
 Give tighter physical control of annual dollar value.
A items.
 Forecast A items more


carefully.
Consider B products only after
How Much to Order: EOQ
A products. The question of how much to order
can be determined by using an
EXAMPLE: economic order quantity (EOQ)
A manager has obtained a list of unit model. EOQ models identify the
costs and estimated annual demands optimal order quantity by minimizing
for 10 inventory items and now wants the sum of certain annual costs that
to categorize the items on an A-B-C vary with order size and order
basis. Multiplying each item’s annual frequency. Three order size models
demand by its unit cost yields its are as follows:
annual dollar value:
 1. The basic economic order  Annual demand requirements
quantity model. are known
2. The economic production  Demand is spread evenly
quantity model. throughout the year so that the
3. The quantity discount model. demand rate is reasonably
constant
 Lead time does not vary
 Each order is received in a
single delivery
 There are no quantity discounts

 Basic EOQ:
Basic EOQ: Introduction Inventory
The basic EOQ model is the simplest
of the three models. Ordering
It is used to identify a fixed order size
that will minimize the sum of the Cycles
annual costs of holding inventory and  Inventory ordering and usage
ordering inventory. occur in cycles. The figure
illustrates several inventory
The unit purchase price of items in cycles.
inventory is not generally included in  A cycle begins with the receipt
the total cost because the unit cost is of an order of Q units (in this
unaffected by the order size unless case it's 350 units), which are
quantity discounts are a factor. If withdrawn at a constant rate
holding costs are specified as a over time (in this illustration,
percentage of unit cost, then unit cost the usage rate is 50 units per
is indirectly included in the total cost day). Thus, the inventory will be
as a part of holding costs. fully consumed on the 7th day.
 When the quantity on hand is
just sufficient to satisfy demand
Basic EOQ: Assumptions during the lead time (in this
case the lead time is 2 days), an
The inventory models described in order for Q units is submitted
this chapter relate primarily to what to the supplier (since the usage
are referred to as independent- rate is 50 units per day and
demand items, that is, items that are lead time is 2 days, 100 units
ready to be sold or used. will be ordered on the 5th day).
 Because it is assumed that both
On the other hand, dependent- the usage rate and the lead
demand items, are components of time do not vary, the order will
finished products, rather than the be received at the precise
finished products themselves. instant that the inventory on
hand falls to zero. Thus, orders
Assumptions of the basic EOQ model
are timed to avoid both excess
stock and stockouts.
 Only one product is involved
  Annual carrying cost is computed by
multiplying the average amount of
inventory on hand by the cost to carry
one unit for one year. The average
inventory is simply half of the order
quantity: The amount on hand
decreases steadily from Q units to 0,
for an average of ( Q + 0)/2, or Q /2.
Using the symbol H to represent the
average annual carrying cost per unit,
the total annual carrying cost is:

Basic EOQ: Carrying [Math Processing Error]

and Ordering Costs Basic EOQ: Ordering Costs

The optimal order quantity reflects a
balance between carrying costs and Annual ordering cost will decrease as
ordering costs: As order size varies, order size increases because for a
one type of cost will increase while given annual demand, the larger the
the other decreases. For example, if order size, the fewer the number of
the order size is relatively small, the orders needed.
average inventory will be low,
resulting in low carrying costs. Annual ordering cost is a function of
However, a small order size will the number of orders per year and the
necessitate frequent orders, which ordering cost per order:
will drive up annual ordering costs.
Conversely, ordering large quantities Annual Ordering Costs = D S
at infrequent intervals can hold down Q
annual ordering costs, but that would where
result in higher average inventory D - Demand, usually in units per year
levels and therefore increased S - Ordering cost per order
carrying costs. The figure illustrates
these two extremes. Because the number of orders per
year, D/Q, decreases as Q increases,
annual ordering cost is inversely
related to order size, as illustrated
below.

Basic EOQ: Carrying Cost Ordering costs are inversely and

nonlinearly related to order size.
 Thus, given the annual demand,
Basic EOQ: Total Costs the ordering cost per order, and
the annual carrying cost per unit,
The total annual cost (TC) associated
with carrying and ordering inventory
one can compute the optimal
when Q units are ordered each time (economic) order quantity or the
is: economic order quantity.

TC = Annual Carrying Costs + Annu We also discussed that the optimal

al Ordering Costs = Q/2 H + Q/Q S order quantity is found when the
(Note that D and H must be in the annual carrying cost equals the
same units, e.g., months, years) annual ordering cost, thus:
The figure below reveals that the
total-cost curve is U-shaped (i.e., Q2H = DQS
convex, with one minimum) and that it which translates to:
reaches its minimum at the quantity
where carrying and ordering costs are QH2=DSQ
equal. To solve for Q*, we simply cross-
multiply terms and isolate Q on the
left of the equal sign:

Q2 H= 2DS
then:
Q2=2DSH
therefore, solving for Q:

Q = √ 2DSH
We can also compute for the
length of the order cycle, ot the
time between order using this
formula:
BASIC EOQ Length of order cycle = QDx nu
Key concepts of the basic EOQ mber of work days in a year
model was already discussed last
meeting, and this is a continuation Economic Production
of our discussion.

Last time, we ended our discussion Quantity: Assumptions

with the formula to computing the The batch mode is widely used in
total cost of inventory which is the production. Even in assembly
sum of the annual carrying operations, portions of the work are
cost and the annual ordering done in batches. The reason for this is
that in certain instances, the capacity
cost, as follows:
to produce a part exceeds the part’s
usage or demand rate. As long as
TC = Q2H + DQS production continues, inventory will
continue to grow. In such instances, it
makes sense to periodically produce
such items in batches, or lots, instead
of producing continually.

The assumptions of the EPQ model

are similar to those of the EOQ model,
except that instead of orders received
in a single delivery, units are received
incrementally during production.

The assumptions are:

1. Only one item is involved.

2. Annual demand is known.
3. The usage rate is constant.
4. Usage occurs continually, but
production occurs periodically.
5. The production rate is constant.
6. Lead time does not vary.
7. There are no quantity
discounts.

How inventory is affected

by periodic production?
The figure illustrates how inventory is
affected by periodically producing a
batch of a particular item.

During the production phase of the

cycle, inventory builds up at a rate
equal to the difference between
production and usage rates. For
example, if the daily production rate
is 20 units and the daily usage rate is
5 units, inventory will build up at the
rate of 20 - 5 = 15 units per day.

As long as production occurs, the

inventory level will continue to build;
when production ceases, the
inventory level will begin to decrease.
Hence, the inventory level will be
maximum at the point where
production ceases. When the amount
of inventory on hand is exhausted,
production is resumed, and the cycle
repeats itself.