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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

Product advertising

Spoilage

Sending purchasing orders

Inventory inquiries

Warehouse supplies

Research and development

Purchasing salaries

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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