20–1
Chapter Twenty
McGraw-Hill/Irwin
Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.
20–2
• LO20–2: Analyze how different
inventory control systems work
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
• LO20–1: Explain how inventory is used
and understand what it costs
• LO20–3: Analyze inventory using the
Pareto principle
20–3
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
• Inventory can be visualized as stacks of money
sitting on forklifts, on shelves, and in trucks and
planes while in transit.
• For many businesses, inventory is the largest
asset on the balance sheet at any given time.
• Inventory can be difficult to convert back into
cash.
• It is a good idea to try to get your inventory
down as far as possible.
– The average cost of inventory in the United States
is 30 to 35 percent of its value.
20–4
20–5
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• Used when we are making a one-time purchase of an
item
Fixed-order quantity model
• Used when we want to maintain an item “in-stock,” and
when we restock, a certain number of units must be
ordered
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
Single-period model
Fixed–time period model
• Item is ordered at certain intervals of time
20–6
– Includes raw materials, finished products,
component parts, supplies, and work-in-process
– Manufacturing inventory: refers to items that
contribute to or become part of a firm’s product
• Inventory system: the set of policies and
controls that monitor levels of inventory
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
• Inventory: the stock of any item or resource
used in an organization
– Determines what levels should be maintained,
when stock should be replenished, and how large
orders should be
20–7
To meet variation in
product demand
To provide a
safeguard for
variation in raw
material delivery
time
To allow flexibility
in production
scheduling
To take advantage
of economic
purchase order size
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
To maintain
independence of
operations
20–8
• Costs for storage, handling,
insurance, and so on
Setup (or production
change) costs
• Costs for arranging specific
equipment setups, and so on
Costs
Ordering costs
Shortage costs
• Costs of placing an order
• Costs of running out
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Holding (or carrying) costs
20–9
• For example, a workstation may produce
many parts that are unrelated but meet
some external demand requirement
Dependent demand – the need
for any one item is a direct result
of the need for some other item
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
Independent demand – the
demands for various items are
unrelated to each other
• Usually a higher-level item of which it is
part
20–10
20–11
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• One-time purchasing decision
(e.g., vendor selling T-shirts at a
football game)
• Seeks to balance the costs of
inventory overstock and under
stock
Multi-period inventory models
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Single-period inventory
model
• Fixed-order quantity models
• Event triggered (e.g., running out of
stock)
• Fixed-time period models
• Time triggered (e.g., monthly sales call
by sales representative)
20–12
Too few papers and some
customers will not be able
to purchase a paper, and
profits associated with
these potential sales are
lost.
Too many papers and the
price paid for papers that
were not sold during the
day will be wasted,
lowering profit.
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
Consider the problem of
deciding how many newspapers
to put in a hotel lobby
20–13
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• Consider how much risk we are willing to take of running out
of inventory.
• Assume a mean of 90 papers and a standard deviation of 10
papers.
• Assume we want an 80 percent chance of not running out.
• Assume that the probability distribution associated of sales is
normal, stocking 90 papers yields a 50 percent chance of
stocking out.
20–14
– Using Excel, “=NORMSINV(0.8)” =
0.84162
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
• From Appendix E, we see that we
need approximately 0.85 standard
deviation of extra papers to be 80
percent sure of not stocking out.
20–15
Co = cost per unit of demand over stocking level
Cu = cost per unit of demand under stocking level
P = probability that a given unit will be sold
• We should increase the size of the
inventory so long as the probability of
selling the last unit added is equal to or
𝐶𝑢
greater than the ratio
𝐶𝑜+𝐶𝑢
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Where:
𝑃 ≤
𝐶𝑢
𝐶𝑜+𝐶𝑢
20–16
=
800
200+80
= 0.2857
• Mean demand is 5
– Standard deviation of demand is 3
– Room rate is $80 (this is the cost if overbookings
are less than cancelations - Cu)
– Penalty for overbooking is $200 (this is the cost if
overbookings are more than cancelations - Co)
For the Excel template visit
www.mhhe.com/sie-chase14e
Excel:
Overbooking
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
𝑃 ≤
𝐶𝑢
𝐶𝑜+𝐶𝑢
20–17
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
• From Appendix E, we see that our
desired level falls about 0.55 standard
deviations below the mean (z = -0.55)
– Using Excel, “=NORMSINV(0.2857)”
= 0.56599
20–18
If we overbook by 1 and
we have three no-shows,
we have lost sales of $80.
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
If we overbook by 1 and
we have zero no-shows,
we incur the penalty of
$200 – one person must
be compensated for
having no room.
Total cost of a policy of
overbooking by 9 rooms
is the weighted average
of the events (number of
no-shows) and the
outcome of those events.
20–19
Ordering of clothing and other fashion items
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Overbooking of airline flights
One-time order for events – e.g., t-shirts for a
concert
20–20
- Also called the economic
order quantity, EOQ, and Q-
model
- Event triggered
Fixed–time period models
- Also called the periodic system,
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
Fixed-order quantity models
periodic review system, fixed-
order interval system, and P-mode
- Time triggered
20–21
– Inventory remaining must
be continually monitored
– Has a smaller average
inventory
– Favors more expensive
items
– Is more appropriate for
important items
– Requires more time to
maintain – but is usually
more automated
– Is more expensive to
implement
• Fixed-Time Period
– Counting takes place
only at the end of the
review period
– Has a larger average
inventory
– Favors less expensive
items
– Is sufficient for lessimportant items
– Requires less time to
maintain
– Is less expensive to
implement
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• Fixed-Order Quantity
20–22
20–23
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20–24
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Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
• Demand for the product is constant and uniform
throughout the period.
• Lead time (time from ordering to receipt) is
constant.
• Price per unit of product is constant.
• Inventory holding cost is based on average
inventory.
• Ordering or setup costs are constant.
• All demands for the product will be satisfied.
20–25
Inventory is consumed at a
constant rate, with a new
order placed when the
reorder point (R) is reached
once again.
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Always order Q units when
inventory reaches reorder
point (R).
Inventory arrives after
lead time (L). Inventory is
raised to maximum level
(Q).
20–26
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The optimal order
quantity (Qopt) occurs
where total costs are at
their minimum
20–27
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• Annual demand (D) =
1,000 units
– Average daily demand
𝑑 = 1000
= 2.74
365
units
– Ordering cost (S) = $5
per order
– Holding cost (H) = $1.25
per unit per year
– Lead time (L) = 5 days
– Cost per unit (C) =
$12.50
For the Excel template visit
www.mhhe.com/sie-chase14e
Excel: Economic
Order Quantity
20–28
• Safety stock can be determined based on many different criteria.
A common approach is to simply keep a certain number
of weeks of supply.
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Safety stock – refers to the amount of inventory carried
in addition to expected demand.
A better approach is to use probability.
•Assume demand is normally distributed.
•Assume we know mean and standard deviation.
•To determine probability, we plot a normal distribution for expected demand and
note where the amount we have lies on the curve.
20–29
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Demand is variable, but
follows a known
distribution/
After the reorder is placed, demand
during the lead time may be higher
than expected, consuming some (or
all) of the safety stock/
20–30
(𝑑) = 60
For 95%
probability,
z = 1.64.
• Annual demand (D) =
60(365) = 21,900
• Standard deviation of
demand during lead time
(σD) = 7
• Ordering cost (S) = $10 per
order
• Holding cost (H) = $0.50 per
unit per year
• Lead time (L) = 6 days
For the Excel template visit
www.mhhe.com/sie-chase14e
Policy – place a new
order for 936 units
whenever stock falls
to 388 units on hand.
This results in a 95%
probability of not
stocking out during
the lead time.
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
• Average daily demand
Excel: Reorder
Point
20–31
q = quantity to be ordered
T = number of days between reviews
L = lead time in days
𝑑 = forecast average daily demand
Z = number of standard deviations required for
specific service level
• σT+L= standard deviation of demand during the review
and lead time
• I = current inventory level (including items on order)
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
•
•
•
•
•
𝑞 = 𝑑 𝑇 + 𝐿 + 𝑧𝜎𝑇+𝐿
20–32
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Time periods
are equal, but
ending
inventory
varies.
Reorder quantity varies,
depending upon ending
inventory level. Beginning
inventory is always the
same.
20–33
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
• Daily demand (𝑑) of 10
units
• Daily standard deviation
(𝜎𝐷 ) of 3 units
• Review period (T) of 30
days
• Lead time (L) of 14 days
• 98 percent of demand
should be met from items
in stock
• 150 units in inventory (I)
For the Excel template visit
www.mhhe.com/sie-chase14e
Excel: Fixed
Time Period
Model
20–34
• Inventory turns –
number of times
inventory is cycled
through over time –
a measure of how
efficiently inventory
is used
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• Average inventory –
expected amount of
inventory over time
20–35
• To find the lowest-cost, calculate the order
quantity for each price and see if the quantity
is feasible.
– Sort prices from lowest to highest and calculate the
order quantity for each price until a feasible order
quantity is found.
– If the first feasible order quantity is the lowest price,
this is best; otherwise, calculate the total cost for the
first feasible quantity and calculate total cost at each
price lower than the first feasible order quantity.
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
• Price varies with the order size.
20–36
20–37
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– 1–499 → $5.00
– 500–999 → $4.50
– 1000 or more → $3.90
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
• Annual demand (D ) =
10,000
• Ordering cost (S ) =
$20 per order
• Interest/carrying cost
(i ) = 20%
• Cost per unit (C )
20–38
20–39
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20–40
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
Copyright © 2014 by McGraw Hill Education (India) Private Limited. All rights reserved.
Inventory accuracy –
refers to how well the
inventory records agree
with physical count
Cycle counting – a
physical inventory-taking
technique in which
inventory is counted on a
frequent basis rather
than once or twice a year
20–41