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MINI CASE
Andria Mullins, financial manager of Webster Electronics, has been asked by the firm's
CEO, Fred Weygandt, to evaluate the company's inventory control techniques and to lead a
discussion of the subject with the senior executives. Andria plans to use as an example one
of Webster's "big ticket" items, a customized computer microchip which the firm uses in its
laptop computer. Each chip costs Webster $200, and in addition it must pay its supplier a
$1,000 setup fee on each order. Further, the minimum order size is 250 units; Webster's
annual usage forecast is 5,000 units; and the annual carrying cost of this item is estimated
to be 20 percent of the average inventory value.
Andria plans to begin her session with the senior executives by reviewing some basic
inventory concepts, after which she will apply the EOQ model to Webster's microchip
inventory. As her assistant, you have been asked to help her by answering the following
questions:
a. Why is inventory management vital to the financial health of most firms?
Answer: Inventory management is critical to the financial success of most firms. If insufficient
b. What assumptions underlie the EOQ model?
Answer: the standard form of the EOQ model requires the following assumptions:
All values are known with certainty and constant over time.
Mini Case: 28 - 1
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
These assumed conditions are not met in the real world, and, as a result, safety
stocks are carried, and these stocks raise average inventory holdings above the
amounts that result from the "pure" EOQ model.
c. Write out the formula for the total costs of carrying and ordering inventory, and
then use the formula to derive the EOQ model.
Answer: Under the assumptions listed above, total inventory costs (TIC) can be expressed as
follows:
TIC = total carrying costs + total ordering costs = CP(Q/2) + F(S/Q) (1)
Here,
C = annual carrying cost as a percentage of inventory value.
Note that S/Q is the number of orders placed each year, and, if no safety stocks
The economic (optimal) order quantity (EOQ) is that order quantity which
0
Q
)S)(F(
2
)P)(C(
dQ
)TIC(d
2
.
Mini Case: 28 - 2
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
Now, solving for Q, we obtain:
.
)P)(C(
)S)(F(2
EOQQ
)P)(C(
)S)(F(2
Q
Q
)S)(F(
2
)P)(C(
2
2
d. What is the EOQ for custom microchips? What are total inventory costs if the
EOQ is ordered?
Answer: EOQ =
)P)(C(
)S)(F(2
=
)200($2.0
)000,5)(000,1($2
=
000,250
= 500 units.
When 500 units are ordered each time an order is placed, total inventory costs equal
$20,000:
TIC = CP(Q/2) + F(S/Q)
= 0.2($200)(500/2) + $1,000(5,000/500)
= $40(250) + $1,000(10) = $10,000 + $10,000 = $20,000.
Note that the average inventory of custom microchips is 250 units, and that 10 orders
are placed per year. Also, at the EOQ level, total carrying costs equal total ordering
costs.
e. What is Webster's added cost if it orders 400 units at a time rather than the
EOQ quantity? What if it orders 600 per order?
Answer: 400 units:
Mini Case: 28 - 3
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
Note the following points:
At any order quantity other than EOQ = 500 units, total inventory costs are higher
The added cost of not ordering the EOQ amount is not large if the quantity
If the quantity ordered is less than the EOQ, then total carrying costs decrease, but
If the quantity ordered is greater than the EOQ, then total carrying costs increase,
f. Suppose it takes 2 weeks for Webster's supplier to set up production, make and
test the chips, and deliver them to Webster's plant. Assuming certainty in
delivery times and usage, at what inventory level should Webster reorder?
(assume a 52-week year, and assume that Webster orders the EOQ amount.)
Answer: With an annual usage of 5,000 units, Webster's weekly usage rate is 5,000/52 96
Mini Case: 28 - 4
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
g. Of course, there is uncertainty in Webster's usage rate as well as in delivery
times, so the company must carry a safety stock to avoid running out of chips
and having to halt production. If a 200-unit safety stock is carried, what effect
would this have on total inventory costs? What is the new reorder point? What
protection does the safety stock provide if usage increases, or if delivery is
delayed?
Answer: There are two ways to view the impact of safety stocks on total inventory costs.
Webster's total cost of carrying the operating inventory is $20,000 (see part d). Now
Another approach is to recognize that, with a 200-unit safety stock, Webster's
TIC = CP(average inventory) + F(S/Q)
Webster must still reorder when the operating inventory reaches 192 units. However,
with a safety stock of 200 units in addition to the operating inventory, the reorder
Mini Case: 28 - 5
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
h. Now suppose Webster's supplier offers a discount of 1 percent on orders of 1,000
or more. Should Webster take the discount? Why or why not?
Answer: First, note that since the discount will only affect the orders for the operating
inventory, the discount decision need not take account of the safety stock. Webster's
TIC = CP(Q/2) + F(S/Q)
Note that we have reduced the unit price by the amount of the discount. Since total
i. For many firms, inventory usage is not uniform throughout the year, but, rather,
follows some seasonal pattern. Can the EOQ model be used in this situation? If
so, how?
Answer: The EOQ model can still be used if there are seasonal variations in usage, but it must
be applied to shorter periods during which usage is approximately constant. For
j. How would these factors affect an EOQ analysis?
1. The use of just-in-time procedures.
Answer: Just-in-time procedures are designed specifically to reduce inventories. If a just in
Mini Case: 28 - 6
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
j. 2. The use of air freight for deliveries.
j. 3. The use of a computerized inventory control system, wherein as units were
removed from stock, an electronic system automatically reduced the inventory
account and, when the order point was hit, automatically sent an electronic
message to the supplier placing an order. The electronic system ensures that
inventory records are accurate, and that orders are placed promptly.
Answer: Computerized control systems would, generally, enable the company to keep better
j. 4. The manufacturing plant is redesigned and automated. Computerized process
equipment and state-of-the-art robotics are installed, making the plant highly
flexible in the sense that the company can switch from the production of one
item to another at a minimum cost and quite quickly. This makes short
production runs more feasible than under the old plant setup.
Answer: The trend in manufacturing is toward flexibly designed plants, which permit small
Mini Case: 28 - 7
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
k. Webster runs a $100,000 cash deficit per month, requiring periodic transfers
from its marketable securities portfolio. Broker fees are $32 per transfer and
Webster earns 7% on its investment portfolio. Can Andrea use the EOQ model
to determine how frequently Webster should liquidate part of its portfolio?
Answer: The EOQ model can be applied directly to this problem.
)P)(C(
)S)(F(2
needed each year, and the carrying cost per dollar per year is 7%, which is the
opportunity cost for investing that dollar.
EOQ = C* =
123,33$
07.0
)000,200,1)(32(2
)P)(C(
)S)(F(2
.
So Webster should liquidate its portfolio in chunks of about $33,000. This translates
Mini Case: 28 - 8
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
