### Question details

A firm is faced with the attractive situation in which it can obtain immediate
\$ 15.00

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COMM 225: POM

TOPIC

4

:

INVENTORY

MANAGEMENT

(

Practice

Questions

)

Q1 (Ref: Q. 1

3

-

3, p58

2

-

58

3

)

:

A firm is faced with the

attractive situation in which it can obtain immediate

delivery of an item it stocks for retail sale. The firm has

therefore not bothered to order the item

in any systematic

way.

However, recently profits have

been

squeezed due to

increasing competitive

pressures,

and the

firm has reta

ined

a management consultant to

study its

inventory

management. The consultant has determined that

the

various costs associated with making an order for the

item

stocked are approximately \$70 per

order. She has also

determined that the costs of carrying the item in inventory

amount

to approximately \$27 per unit per year (primarily

direct storage costs and forgone profit on investment in

inventory). Demand for the item is reasonably constant

over

ti

me, and the forecast is for 16,500 units per year.

When an

order is placed for the item, the entire order is

immediately

delivered to the firm by the supplier. The firm

operates 6

days a week plus a few

Sundays

or approximately

320 days

per year. Determine

the following:

(a)

Optimal order

quantity per order

, (b

)

Total

annual inventory costs

, (c)

Optimal number of orders to place per year

, (d)

Number of

operating days between orders, based on the

optimal

ordering

.

Ans

wers

:

(a) Optimal order quantity per

order = 292.5, (b)

Total annual inventory costs

= \$7897.47

, (c) Optimal number

of orders to place per year

= 56.41

, (d) Number of operating

days between orders, based on the optimal ordering

= 5.67

days

Q2

(Ref: Q. 1

3

-

11, p583

)

:

The Shotz

Brewery produces an

ale, which it stores in barrels

in its warehouse and supplies

to its distribut

ors on demand.

The demand for ale is 1800

barrels per day. The brewery can produce 3000 barrels per

day. It costs \$7500

to set up a production run for ale. O

nce it

is brewed, the ale

is stored in a refrigerated warehouse at

an annual cost of

\$60 per barrel. Determine th

e

economic

order quantity and

the minimum total annual inventory cost.

E

conomic order quantity

=

20,263.88

and the

minimum total annu

al inventory cost

= \$486,333.22

Q3

(Ref: Q. 1

3

-

15, p584

)

:

The Deer Valley Farm produces a

natural organic fertilizer,

which it sells mostly to gardeners

and homeowners.

The annual demand for fertilizer is

220,000 pounds. The

farm is able to produce

305,000

pounds annually. The

cost to transport the fertilizer from

the plant to the farm

is \$620 per load. The annual carrying

cost is \$0.12 per

pound.

(a)

Compute the optimal order size,

the maximum inventory

level, and the total minimum cost.

(b)

If the

farm can increase production capacity to 360,000

pounds per year, will it reduce total inventory cost?

(a) optimal order size

= 90,317.52

, the maximum

inventory level

= 25,179.46, and the total minimum cost

=\$ 3020.45

(b) If the farm can increase production capacity to 360,000

pounds per year,

optimal order size

= 76,457.27

,

and the total

minimum cost =\$ 30568.01.

It increase the inventory cost.

Q4

(Ref: Q. 1

3

-

25

, p53

9

of textbook)

:

The offi

ce

manager for

the Metro

Life Insurance Company

stationery from an office products firm in

boxes of 500

sheets. The company uses 6500 boxes per

year. Annual

carrying costs are \$3 per box, a

nd

ordering

costs are \$28.

The

discount price schedule is

provided by the

office supply

in the table below. Determine the optimal order quantity

and the total annual inventory cost.

Order Quantity (boxes)

Price per Box

200

-

999

1000

-

2999

3000

-

5999

6000+

\$16

14

13

12

Optimal order quantity = 6,000 and the total

annual inventory cost = \$87,030.33

Q5

(Ref: Q. 1

3

-

29, p585

)

:

The amoun

t of

denim used daily

by the Southwest Apparel

Company in its manufacturing

process to make jeans is

normally distributed with an

average

of 4000 yards of

denim and a standard deviation of

required to receive an order of

denim from the textil

e

mill

is a constant 7 days. Determine

the safety stoc

k

and reorder

point if the company wants to

limit th

e

probability of

a st

ock

out and work stoppage to 5%.

S

afety stock = 2603.42 yards

and R

eorder point =

30,603.42 yards.

Q6

(Ref: Q. 1

3

-

30, p585

)

:

In Problem 13

-

29, what level of

service would a safety stock of 2000 yards provide?

Service Level = 90%.

Q7

(Ref: Q. 1

3

-

37, p586

)

:

Food Place Market stocks frozen

pizzas in a refrigerate

d

display case. The average daily

demand for the pizzas is

normally

distributed, with a mean

of 8 pizzas and a standard deviation of 2.5 pizzas. A vendor

for a packaged food dis

tributor checks the market's

inventory of frozen

foods

every 10 days; during a particular

visit there were no pizzas in stock. The lead time to receive

an order is three days. Determine the order size for this

order period that will result in a 98% service

level. During

the vendor's following visit there were 5 frozen pizzas in

stock. What is the order size for the next order period?

O

rder size for the next order period

= 122 pizzas.

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2

Q7

(Ref: Q. 1

3

-

39, p586

)

:

Th

e Aztec

Company stocks a

variety

of parts and materials it uses in its manufacturing

processes. Recently, as demand for its finished goods has

increased, management has had difficulty managing parts

inventory; they frequently run out of some crucial parts and

seem to have an endless supp

ly of others. In an effort to

control inventory more effectively, they would like to

classify their inventory of parts according to the ABC

approach. Following is a list of selected parts and the annual

usage and unit for each:

Item

Number

Annual

demand

Unit

cost

Item

Number

Annual

demand

Unit

cost

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

36

510

50

300

18

500

710

80

344

67

510

682

95

10

820

\$350

30

23

45

1900

8

4

26

28

440

2

35

50

3

1

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

60

120

270

45

19

910

12

30

24

870

244

750

45

46

165

\$610

20

15

50

3200

3

4750

2710

1800

105

30

15

110

160

25

Classify the

inventory items according to the ABC approach

using dollar value of annual demand.

%

%

Unit

Annual

Annual

Annual

Item

Usage

Cost

Usage

Value

Usage

Class

25

870

105

\$91,350

15.97%

10.43%

A

23

30

2,710

81,300

14.21

0.36

A

20

19

3,200

60,800

10.63

0.23

A

22

12

4,750

57,000

9.97

0.14

A

24

24

1,800

43,200

7.55

0.29

A

16

60

610

36,600

6.40

0.72

A

5

18

1,900

34,200

5.98

0.22

A

10

67

440

29,480

5.15

0.80

B

12

682

35

23,870

4.17

8.18

B

2

510

30

15,300

2.68

6.11

B

4

300

45

13,500

2.36

3.60

B

1

36

350

12,600

2.20

0.43

B

27

750

15

11,250

1.97

8.99

B

9

344

28

9,632

1.68

4.12

B

29

46

160

7,360

1.29

0.55

B

26

244

30

7,320

1.28

2.92

B

28

45

110

4,950

0.87

0.54

B

13

95

50

4,750

0.83

1.14

C

30

165

25

4,125

0.72

1.98

C

18

270

15

4,050

0.71

3.24

C

6

500

8

4,000

0.70

5.99

C

7

710

4

2,840

0.50

8.51

C

21

910

3

2,730

0.48

10.91

C

17

120

20

2,400

0.42

1.44

C

19

45

50

2,250

0.39

0.54

C

8

80

26

2,080

0.36

0.96

C

3

50

23

1,150

0.20

0.60

C

11

510

2

1,020

0.18

6.11

C

15

820

1

820

0.14

9.83

C

14

10

3

30

0.01

0.12

C

8,342

571,957

100.00%

100.00%

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