# MHC 503 Economics Case Study Worksheet

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246
CHAPTER 6. INVENTORY CONTROL MODELS
price would drop from \$15 per bracket to \$14.50 per
bracket if Ross would purchase the brackets in lots
of 1,000. Lead times, however, would increase to 3
days for this larger quantity.
(a) What is the total annual inventory cost plus pur-
chase cost if Ross buys the brackets in lots of
1,000 at \$14.50 each?
(b) If Ross does buy in lots of 1,000 brackets, what
is the new ROP?
(c) Given the options of purchasing the brackets at
\$15 each, producing them in-house at \$14.80,
and taking advantage of the discount, what is
your recommendation to Ross White?
the holding cost per unit was \$6 instead of \$5, what
would the optimal order quantity be?
6-26 In Problem 6-20, 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 order-
ing 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?
6-27 Ross White’s machine shop uses 2,500 brackets dur-
ing the course of a year, and this usage is relatively
constant throughout the year. These brackets are pur-
chased 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
placed each year? What would be the annual
ordering cost?
(d) Given the EOQ, what is the total annual inven-
tory cost (including purchase cost)?
(e) What is the time between orders?
(f) What is the ROP?
1: 6-28 Ross White (see Problem 6-27) wants to reconsider
his decision of buying the brackets and is consider-
ing making the brackets in-house. He has determined
that setup cost would be \$25 in machinist time and
lost production time and that 50 brackets could be
produced in a day once the machine has been set up.
Ross estimates that the cost (including labor time
and materials) of producing one bracket would be
\$14.80. The holding cost would be 10% of this cost.
(a) What is the daily demand rate?
(b) What is the optimal production quantity?
(c) How long will it take to produce the optimal
quantity? How much inventory is sold during
this time?
(d) If Ross uses the optimal production quantity,
what would be the maximum inventory level?
What would be the average inventory level?
What is the annual holding cost?
(e) How many production runs would there be each
year? What would be the annual setup cost?
(f) Given the optimal production run size, what is
the total annual inventory cost?
(g) If the lead time is one-half day, what is the ROP?
:6-30 After analyzing the costs of various options for ob-
taining brackets, Ross White (see Problems 6-27
through 6-29) recognizes that although he knows
that the lead time is 2 days and the demand per day
averages 10 units, the demand during the lead time
often varies. Ross has kept very careful records and
has determined that lead time demand is normally
distributed with a standard deviation of 1.5 units.
(a) What Z value would be appropriate for a 98%
service level?
(b) What safety stock should Ross maintain if he
wants a 98% service level?
(c) What is the adjusted ROP for the brackets?
(d) What is the annual holding cost for the safety
stock if the annual holding cost per unit is \$1.50?
1:6-31 Annual demand for the Dobbs model airplane kit is
80,000 units. Albert Dobbs, president of Dobbs’ Ter-
rific Toys, controls one of the largest toy companies
in Nevada. He estimates that the ordering cost is \$40
per order. The carrying cost is \$7 per unit per year. It
is 25 days from the time that Albert places an order
for the model airplane kits until they are received at
his warehouse. During this time, the daily demand is
estimated to be 450 units.
(a) Compute the EOQ, ROP, and optimal number of
orders per year.
(b) Albert now believes that the carrying cost may
be as high as \$14 per unit per year. Furthermore,
he estimates that the lead time may be 35 days
instead of 25 days. Redo part (a), using these re-
vised estimates.
: 6-32 Morgan Arthur has spent the past few weeks deter-
mining inventory costs for Armstrong, a toy manu-
facturer located near Cincinnati, Ohio. She knows
that annual demand will be 30,000 units per year and
that the carrying cost will be \$1.50 per unit per year.
The ordering cost, on the other hand, can vary from
\$45 per order to \$50 per order. During the past 450
working days, Morgan has observed the following
frequency distribution for the ordering cost:
6-29 Upon hearing that Ross White (see Problems 6-27
and 6-28) is considering producing the brackets in-
house, the vendor has notified Ross that the purchase
DISCUSSION QUESTIONS AND PROBLEMS
245
6-9 Let the annual demand for an arbitrary commodity
be 1,000 units per year and the associated EOQ be
400 units per order. Under this circumstance, the
number of orders per year would be (D/Q) = 2.5
orders per year. How can this be so?
6-10 What is the purpose of sensitivity analysis?
6-11 What assumptions are made in the production run
model?
6-12 Explain the basic differences between the simple
EOQ model and the production run model.
6-13 Discuss why it is sometimes prudent not to order the
minimum level required to obtain a quantity discount.
6-14 When using safety stock, how is the standard devia-
tion of demand during the lead time calculated if
daily demand is normally distributed but lead time
is constant? How is it calculated daily demand is
constant but lead time is normally distributed? How
is it calculated if both daily demand and lead time
are normally distributed?
6-15 Briefly explain the marginal analysis approach to
the single-period inventory problem.
6-16 Briefly describe what is meant by ABC analysis.
What is the purpose of this inventory technique?
6-17 What is the overall purpose of MRP?
6-18 What is the difference between the gross and the net
material requirements plans?
6-19 What is the objective of JIT?
has been placed. (Refer to Problem 6-20.) The de-
mand for number 6 screws is fairly constant, and on
average, Lila has observed that her brother’s hard-
ware store sells 500 of these screws each day. Be-
cause the demand is fairly constant, Lila believes
that she can avoid stockouts completely if she orders
the number 6 screws only at the correct time. What
is the ROP?
: 6-22 Lila’s brother believes that she places too many or-
ders 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 de-
veloped in Problem 6-20? If only two orders were
placed each year, what effect would this have on the
ROP?
:6-23 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 \$25 per order. Fur-
thermore, it takes about two weeks for an order to
arrive from the supplier, and during this time, the de-
mand per week for West valves is approximately 80.
(a) What is the EOQ?
(b) What is the ROP?
(c) Is the ROP greater than the EOQ? If so, how is
this situation handled?
(d) What is the average inventory? What is the an-
nual holding cost?
(e) How many orders per year would be placed?
What is the annual ordering cost?
Problems
 6-20 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 ev-
ery time an order is placed. This cost includes her
wages, the cost of the forms used in placing the or-
der, 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 con-
stant 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?
.6-24 East Valve Distributors distributes industrial valves
and control devices. The Eastern control device has
an annual demand of 9,375 units and sells for \$100
per unit. The cost of ordering is \$160 per order and
the average carrying cost per unit per year is \$0.75.
Determine the economic order quantity.
.6-25 Everett Mann’s Dream Store sells waterbeds and
supplies. The best-selling bed in the store has an an-
nual demand of 400 units. The ordering cost is \$40,
while the holding cost is \$5 per unit per year. There
are 250 working days per year, and the lead-time
is 6 days. To minimize total cost, how many units
should be ordered each time an order is placed? If
 6-21 It takes approximately eight working days for an
order of number 6 screws to arrive once the order
Note: 2 means the problem may be solved with QM for Windows; means the problem may be solved with
Excel QM; and means the problem may be solved with QM for Windows and/or Excel QM.
DISCUSSION QUESTIONS AND PROBLEMS
247
ORDERING COST
FREQUENCY
85
\$45
\$46
\$47
95
90
series of average inventory costs. Lisa thought that
these costs would be appropriate for the new prod-
uct. The results are summarized in the following ta-
ble. These data were compiled for 10,000 inventory
items that were carried or held during the year and
were ordered 100 times during the past year. Help
Lisa determine the EOQ.
80
\$48
\$49
55
\$50
45
COST FACTOR
COST (\$)
2,000
1,500
2,500
500
50
600
800
750
Taxes
Processing and inspection
New product development
Bill paying
Ordering supplies
Inventory insurance
Spoilage
Inventory inquiries
Warehouse supplies
Research and development
Warehouse salaries
Inventory theft
Purchase order supplies
Inventory obsolescence
800
450
280
2.750
3,000
2,800
800
500
300
Morgan’s boss would like Morgan to determine an
EOQ value for each possible ordering cost and to
determine an EOQ value for the expected ordering
cost.
:6-33 Douglas Boats is a supplier of boating equipment for
the states of Oregon and Washington. It sells 5,000
White Marine WM-4 diesel engines every year.
These engines are shipped to Douglas in a ship-
ping container of 100 cubic feet, and Douglas Boats
keeps the warehouse full of these WM-4 motors.
The warehouse can hold 5,000 cubic feet of boating
supplies. Douglas estimates that the ordering cost is
\$10 per order, and the carrying cost is estimated to
be \$10 per motor per year. Douglas Boats is consid-
ering the possibility of expanding the warehouse for
the WM-4 motors. How much should Douglas Boats
expand, and how much would it be worth for the
company to make the expansion? Assume demand is
constant throughout the year.
6-34 Northern Distributors is a wholesale organization
that supplies retail stores with lawn care and house-
hold products. One building is used to store Neverfail
lawn mowers. The building is 25 feet wide by 40 feet
deep by 8 feet high. Anna Oldham, manager of the
warehouse, estimates that about 60% of the ware-
house can be used to store the Neverfail lawn mow-
ers. The remaining 40% is used for walkways and a
small office. Each Neverfail lawn mower comes in a
box that is 5 feet by 4 feet by 2 feet high. The annual
demand for these lawn mowers is 12,000, and the
ordering cost for Northern Distributors is \$30 per or-
der. It is estimated that it costs Northern \$2 per lawn
mower per year for storage. Northern Distributors is
thinking about increasing the size of the warehouse.
The company can do this only by making the ware-
house deeper. At the present time, the warehouse
is 40 feet deep. How many feet of depth should be
added onto the warehouse to minimize the annual
inventory costs? How much should the company be
willing to pay for this addition? Remember that only
60% of the total area can be used to store Neverfail
lawn mowers. Assume all EOQ conditions are met.
6-35 Lisa Surowsky was asked to help in determining the
best ordering policy for a new product. Currently,
the demand for the new product has been projected
to be about 1,000 units annually. To get a handle
on the carrying and ordering costs, Lisa prepared a
 6-36 Jan Gentry is the owner of a small company that
produces electric scissors used to cut fabric. The
annual demand is 8,000 scissors, and Jan produces
the scissors in batches. On average, Jan can produce
150 scissors per day, and during the production pro-
cess, demand for scissors has been about 40 scissors
per day. The cost to set up the production process is
\$100, and it costs Jan 30 cents to carry one pair of
scissors for one year. How many scissors should Jan
produce in each batch?
6-37 Jim Overstreet, inventory control manager for Itex,
receives wheel bearings from Wheel-Rite, a small
producer of metal parts. Unfortunately, Wheel-Rite
can produce only 500 wheel bearings per day. Itex
receives 10,000 wheel bearings from Wheel-Rite
each year. Since Itex operates 200 working days
each year, its average daily demand for wheel bear-
ings is 50. The ordering cost for Itex is \$40 per
order, and the carrying cost is 60 cents per wheel
bearing per year. How many wheel bearings should
Itex order from Wheel-Rite at one time? Wheel-Rite
has agreed to ship the maximum number of wheel
bearings that it produces each day to Itex when an
order has been received.
248
CHAPTER 6. INVENTORY CONTROL MODELS
needs about 16,000 of this type of PCB each year.
Demand is relatively constant throughout the year,
and the ordering cost is about \$25 per order; the
holding cost is 20% of the price of each PCB. Two
companies are competing to become the dominant
supplier of the PCBs, and both have now offered
discounts, as shown in the following table. Which
of the two suppliers should be selected if Thaarugo
wishes to minimize total annual inventory cost?
What would be the annual inventory cost?
SUPPLIERA
SUPPLIER B
PRICE
QUANTITY
1-199
200-499
PRICE
39.50
38.40
QUANTITY
1-299
300-999
1,000 or more
35.80
34.70
35.40
34.60
2:6-38 North Manufacturing has a demand for 1,000 pumps
each year. The cost of a pump is \$50. It costs North
Manufacturing \$40 to place an order, and the carry-
ing cost is 25% of the unit cost. If pumps are ordered
in quantities of 200, North Manufacturing can get a
3% discount on the cost of the pumps. Should North
Manufacturing order 200 pumps at a time and take
the 3% discount?
:6-39 Linda Lechner is in charge of maintaining hospital
supplies at General Hospital. During the past year,
the mean lead time demand for bandage BX-5 was
60. Furthermore, the standard deviation for BX-5
was 7. Linda would like to maintain a 90% service
level. What safety stock level do you recommend for
BX-5?
:6-40 Linda Lechner has just been severely chastised for
her inventory policy. (See Problem 6-39.) Sue Sur-
rowski, her boss, believes that the service level
should be either 95% or 98%. Compute the safety
stock levels for a 95% and a 98% service level.
Linda knows that the carrying cost of BX-5 is 50
cents per unit per year. Compute the carrying cost
that is associated with a 90%, a 95%, and a 98% ser-
vice level
:6-41 Ralph Janaro simply does not have time to ana-
lyze all of the items in his company’s inventory. As
a young manager, he has more important things to
do. The following is a table of six items in inventory
along with the unit cost and the demand in units.
(a) Find the total amount spent on each item during
the year. What is the total investment for all of
these?
(b) Find the percentage of the total investment in in-
ventory that is spent on each item.
500 or more
IDENTIFICATION
CODE
UNIT COST
(\$)
DEMAND
IN UNITS
:6-43 Dillard Travey receives 5,000 tripods annually from
Quality Suppliers to meet his annual demand. Dil-
lard runs a large photographic outlet, and the tripods
are used primarily with 35-mm cameras. The order-
ing cost is \$15 per order, and the carrying cost is
50 cents per unit per year. Quality is starting a new
option for its customers. When an order is placed,
Quality will ship one-third of the order every week
for three weeks instead of shipping the entire order
at one time. Weekly demand over the lead time is
100 tripods.
(a) What is the order quantity if Dillard has the en-
tire order shipped at one time?
(b) What is the order quantity if Dillard has the or-
der shipped over three weeks using the new op-
tion from Quality Suppliers, Inc.? To simplify
your calculations, assume that the average inven-
tory is equal to one-half of the maximum inven-
tory level for Quality’s new option.
(c) Calculate the total cost for each option. What do
you recommend?
:6-44 Quality Suppliers, Inc., has decided to extend its
shipping option. (Refer to Problem 6-43 for de-
tails.) Now, Quality Suppliers is offering to ship the
amount ordered in five equal shipments, one each
week. It will take five weeks for this entire order to
be received. What are the order quantity and total
cost for this new shipping option?
36-45 The Hardware Warehouse is evaluating the safety
stock policy for all its items, as identified by the
SKU code. For SKU M4389, the company always
orders 80 units each time an order placed. The
daily demand is constant, at 5 units per day; the lead
time is normally distributed, with a mean of three
days and a standard deviation of two days. Holding
cost is \$3 per unit per year. A 95% service level is to
be maintained.
XX1
5.84
1,200
1,110
B66
3CPO
33CP
5.40
1.12
896
74.54
R2D2
RMS
2.00
2.08
1,104
1,110
961
(c) Based on the percentages in part (b), which
item(s) would be classified in categories A, B,
and C using ABC analysis?
(d) Which item(s) should Ralph most carefully con-
trol using quantitative techniques?
6-42 Thaarugo, Inc., produces a GPS device that is be-
coming popular in parts of Scandinavia. When
Thaarugo produces one of these, a printed circuit
board (PCB) is used, and it is populated with several
electronic components. Thaarugo determines that it
252
CHAPTER 6. INVENTORY CONTROL MODELS
Internet Homework Problems
See our Internet home page, at www.pearsonglobaleditions.com/render, for additional home-
work problems, Problems 6-68 to 6-75.
Case Study
Martin-Pullin Bicycle Corporation
Martin-Pullin Bicycle Corp. (MPBC), located in Dallas, is a
wholesale distributor of bicycles and bicycle parts. Formed in
1981 by cousins Ray Martin and Jim Pullin, the firm’s primary
retail outlets are located within a 400-mile radius of the dis-
tribution center. These retail outlets receive their orders from
Martin-Pullin within two days after notifying the distribution
center, provided that the stock is available. However, if an or-
der is not fulfilled by the company, no backorder is placed; the
retailers arrange to get their shipment from other distributors,
and MPBC loses that amount of business.
Demands for AirWing Model
The company distributes a wide variety of bicycles. The
most popular model, and the major source of revenue for the
company, is the Air Wing. MPBC receives all the models from
a single manufacturer overseas, and shipment takes as long as
four weeks from the time an order is placed. With the cost of
communication, paperwork, and customs clearance included,
MPBC estimates that each time an order is placed, it incurs a
cost of \$65. The purchase price paid by MPBC, per bicycle,
is roughly 60% of the suggested retail price for all the styles
available, and the inventory carrying cost is 1% per month (12%
per year) of the purchase price paid by MPBC. The retail price
(paid by the customers) for the Air Wing is \$170 per bicycle.
MPBC is interested in making an inventory plan for 2016.
The firm wants to maintain a 95% service level with its cus-
tomers to minimize the losses on the lost orders. The data
collected for the past two years are summarized in the accom-
panying table. A forecast for AirWing model sales in 2016 has
been developed and will be used to make an inventory plan for
MPBC.
MONTH
2014
2015
FORECAST FOR 2016
6
8
7
14
15
12
24
31
27
53
46
59
75
86
97
54
60
January
February
March
April
May
June
July
August
September
October
November
December
Total
47
30
34
39
18
21
24
Discussion Questions
1. Develop an inventory plan to help MPBC.
2. Discuss ROPs and total costs.
3. How can you address demand that is not at the level of the
planning horizon?
Source: Professor Kala Chand Seal, Loyola Marymount University.
13
15
16
13
15
12
22
38
25
28
42
47
343
391
439

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