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Discussion Questions 1. Describe four types of inventory.  Raw material ▶Purchased but not processed  Work-in-process (WIP) ▶Undergone some change but not completed ▶A function of cycle time for a product  Maintenance/repair/operating (MRO) ▶Necessary to keep machinery and processes productive  Finished goods ▶Completed product awaiting shipment 3. What is the purpose of the ABC classification system ? ABC classification system is used to establish policies that focus on the few critical parts and not the many trivial ones 4. Identify and explain the types of costs that are involved in an inventory system . ▶Holding costs - the costs of holding or “carrying” inventory over time ▶Ordering costs - the costs of placing an order and receiving goods ▶Setup costs - cost to prepare a machine or process for manufacturing an order -May be highly correlated with setup time 5. Explain the major assumption of the basis EOQ model . 1.Demand is known, constant, and independent 2.Lead time is known and constant 3.Receipt of inventory is instantaneous and complete 4.Quantity discounts are not possible 5.Only variable costs are setup (or ordering) and holding 6.Stockouts can be completely avoided

7. Explain why it is not necessary to include product cost (price or price times quantity) in the EOQ model , but the quantity discount model requires this information.

Price times quality is not variable in the EOQ model , but is in the discount model . When quality discounts are variable ,the unit purchase price of the item depends on the order quantity . 13. Describe the difference between a fixed quantity (Q) and a fixed-period (P) inventory system . In a fixed-quantity inventory system , when the quantity on hand reaches the reorder point , an order is placed for the specified quantity . In a fixed-quantity inventory system , an order is placed at the end of period . The quantity ordered is that needed to bring on-hand inventory up to a specified level . 15. What is “safety stock”? What does safety stock provide safety against ? Safety stock is inventory beyond average demand during lead time , held to control the level of the shortages when demand and/or lead time are not constant ; inventory carried to assure that the desired service level is reached .

PROBLEMS 12.1 Jean-Marie Bourjolly’s restaurant has the following inventory items that it orders on a weekly basis :

INVENTORY ITEM Ribeye Steak Lobster tail Pasta Salt Napkins Tomato sauce French Fries Pepper Garlic Powder Trash can liners Table cloths Fish Fillets Prime rib toast Oil Lettuce (case) Chicken Order pads Eggs (case) Bacon Sugar

$VALUE/CASE 135 245 23 3 12 23 43 3 11 12 32 143 166 28 35 75 12 22 56 4

a) Which is the most expensive item , using annual dollar volume?

#ORDERED/WEEK 3 3 12 2 2 11 32 3 3 3 5 10 6 2 24 14 2 7 5 2

Exercise 12.1 Solution Demand

Fish Fillets

143

10

1430

17.54

17.54

A

French Fries

43

32

1376

16.88

34.43

A

Chicken

75

14

1050

12.88

47.31

A

Prime rib toast

166

6

996

12.22

59.53

A

Lettuce (case)

35

24

840

10.31

69.83

B

Lobster tail

245

3

735

9.02

78.85

B

Ribeye Steak

135

3

405

4.97

83.82

B

Bacon

56

5

280

3.44

87.25

B

Pasta

23

12

276

3.39

90.64

B

Tomato sauce

23

11

253

3.1

93.74

B

Table cloths

32

5

160

1.96

95.71

C

Eggs (case)

22

7

154

1.89

97.6

C

Oil

28

2

56

.69

98.28

C

Trash can liners

12

3

36

.44

98.72

C

Garlic Powder

11

3

33

.4

99.13

C

Napkins

12

2

24

.29

99.42

C

Order pads

12

2

24

.29

99.72

C

Pepper

3

3

9

.11

99.83

C

Sugar

4

2

8

.1

99.93

C

Salt

3

2

6

.07

100

C

TOTAL

1083

Price Dollar Volume

Percent of $- Cumultv $-vol Vol %

Item name

8151

Fish Fillets b) Which are C items?  Table cloths  Eggs (case)  Oil  Trash can liners  Garlic Powder  Napkins  Order pads  Pepper  Sugar  Salt c) What is the annual dollar volume for all 20 items? $ 8151

Category

12.2 Lindsay Electronics , a small manufacturer of electronic research equipment , has approximately 7,000 items in its inventory and has hired Joan Blasco-Paul to manage its inventory . Joan has determined that 10% of the items in inventory are A items , 35% are B items , and 55% are C items . She would like to set up a system in which all A items are counted monthly (every 20 working days) , all B items are counted quarterly (every 60 working days) and all items C are counted semiannually (every 120 working days) . How many items need to be counted each day ?

ITEM CLASS

PERCENT OF ITEMS (%)

QUANTITY

CYCLE COUNTING POLICY

A

10% × 7000

700

Each Month (20 days)

NUMBER OF ITEMS COUNTED PER DAY 700 =35/day 20

B

35% × 7000

2450

Each Quarter (60 days)

2450 =41/day 60

C

55% × 7000

3850

Each 6 months (120 days)

3850 =32/day 120

12.4 Boreki Enterprises has the following 10 items in inventory . Theodore Boreki asks you , a recent OM graduate , to divide these items into ABC classifications. ITEM A2 B8 C7 D1 E9 F3 G2 H2 I5 J8

ANNUAL DEMAND 3000 4000 1500 6000 1000 500 300 600 1750 2500

COST/UNIT 50 12 45 10 20 500 1500 20 10 5

a) Develop an ABC classification system for the 10 items . 12.4 Solution Demand

Price

Dollar Volume

Percent of $Vol

Cumultv $-vol %

Category

G2

300

1500

450000

41.38

41.38

A

F3

500

500

250000

22.99

64.37

A

A2

3000

50

150000

13.79

78.16

B

C7

1500

45

67500

6.21

84.37

B

D1

6000

10

60000

5.52

89.89

B

B8

4000

12

48000

4.41

94.3

C

E9

1000

20

20000

1.84

96.14

C

I5

1750

10

17500

1.61

97.75

C

J8

2500

5

12500

1.15

98.9

C

H2

600

20

12000

1.1

100

C

Item name

TOTAL

21150

1087500

Created by POM-QM for Windows b) How can Boreki use this information ? c) Boreki reviews the classification and then places item A2 into the A category. Why might he do so? Because he want to classified the A2 is the high annual dollar volume item .

12.5 Williams Beville’s computer training school , in Richmond , stocks workbooks with the following characterictics : Demand D = 19500 units/year Ordering cost S = $25/order Holding cost H = $4/unit/year 12.5 Solution Parameter

Value

Parameter

Value

19500

Optimal order quantity (Q*)

493.71

25

Maximum Inventory Level (Imax)

493.71

Holding cost(H)

4

Average inventory

246.86

Unit cost

0

Orders per period(year)

39.5

Annual Setup cost

987.42

Annual Holding cost

987.42

Unit costs (PD)

0

Total Cost

1974.84

Demand rate(D) Setup/Ordering cost(S)

Created by POM-QM for Windows a) Calculate the EOQ for the workbooks. 2 DS Q= H Q=

√ √

2(19500)(25) 4 Q=493.71 units

b) What are the annual holding costs for the workbooks? Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Q ¿ H 2 ¿

493.71 ($ 4 ) 2

¿ $ 987.42

c) What are the annual ordering costs? Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order) D ¿ (S ) Q ¿

19500 ( $ 25 ) 493.71

¿ $ 987.42

12.23 M. P. VanOyen Manufacturing has gone out on bid for a regulator component . Expected demand is 700 units per month . The item can be purchased from either Allen Manufacturing or Baker Manufacturing . Their price lists are shown in the table . Ordering costs is $50, and annual holding cost per unit is $5 . ALLEN MFG QUANTITY 1-499 500-999 1,000+

BAKER MFG QUANTITY 1-399 400-799 800+

UNIT PRICE $16.00 15.50 15.00

UNIT PRICE $16.10 15.60 15.10

a) What is the economic order quantity ? Economic Order Quantity is the order quantity that minimizes the total holding costs and ordering costs . 12.23 Solution Parameter

Value

Parameter

Value

700

Optimal order quantity (Q*)

118.32

50

Maximum Inventory Level (Imax)

118.32

Holding cost(H)

5

Average inventory

59.16

Unit cost

0

Orders per period(year)

5.92

Annual Setup cost

295.8

Annual Holding cost

295.8

Unit costs (PD)

0

Total Cost

591.61

Demand rate(D) Setup/Ordering cost(S)

Created by POM-QM for Windows b) Which supplier should be used ? Why ? Allen Manufacturing because c) What is the optimal order quantity and total annual cost of ordering , purchasing , and holding the component ? Total Cost = Order Cost + Holding Cost + Purchase Cost DS QH + + PD = Q 2

Quantity 410

Allen MFG Total Cost 8400 410 + +8400(16) 410 2

Quantity 410

= $ 136 449.36 500

1000

8400 50 0 + + 8400(15.5) 50 0 2 = $ 132 290 8400 100 0 + +8400 (15) 100 0 2 = $ 128 290 (BEST)

Baker MFG Total Cost 8400 410 + +8400(50) 410 2 = $ 133 089.39

500

8400 50 0 + + 8400(1 5.5) 50 0 2 = $ 129 36.5

12.24 Bell Computers purchases integrated chips at $350 per chip . The holding cost is $35 per unit per year , the ordering cost is $120 per order , and sales are steady , at 400 per month . The company’s supplier , Rich Blue Chip Manufacturing , Inc ., decides to offer price concessions in order to attract larger orders . The price structure is shown below . Rich Blue Chip’s Price Structure QUANTITY PURCHASED 1-99 UNITS 100-199 UNITS 200 OR MORE UNITS

PRICE / UNIT $350 $325 $300

a) What is the optimal order quantity and the minimum annual cost for the Bell Computers to order , purchased , and hold these integrated chips ? D=400 , S=120 , P=350 , H=35 , P=35 , (35/20)×120% = 29% 2 DS Optimal order quantity = Q= 1P

√

=

√

=

√ 9458

2(400)( 120) (0.29)(35)

= 97 units Total Cost = ( D/Q )(S) + (Q/2)(H) +PD 400 97 ( 120 ) + ( 35 ) +(350)(400) = 97 2 = 494.85 + 1697.50 + 140 000 = 142 192.35 b) Bell Computers wishes to use a 10% holding cost rather than the fixed $35 holding cost in (a) . What is the optimal order quantity , and what is the optimal annual cost ? 2 DS 2 DS Optimal Order Quantity = Q = = 1P 1P

√

√

12.32 Emarphy Appliance is a company that produces all kinds of major appliances . Bud Banis , the president of Emarpy , is concerned about the production policy of the company’s best-selling refrigerator . The annual demand has been about 8000 units each year , and this demand has been constant throughout the year . The production capacity is 200 units per day . Each time production starts, it costs the company $120 to move materials into place , reset the assembley line , and clean the equipment . The holding cost of a refrigerator is $50 per year . The current production plan calls for 400 refrigerators to be produced in each production run . Assume there are 250 working days per year . D= 8000 units per year Production capacity = 200 units per day Ordering cost / setup cost S= $ 120 Holding cost H= $ 50 per year a) What is the daily demand of this product ? Daily Demand , d =

8000 units 250 working days

= 32 units per day

b) If the company were to continue to produce 400 units each time production starts , how many days would production continue ? Q 400 P = 200 = 2 days c) Under the current policy , how many production runs per year would be required ?What would annual setup cost be? Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order)

¿

D (S ) Q

¿

8000 ( 120 ) 400

¿ $ 240

d) If the current policy continues , how many refrigerators would be in inventory when production stops ? What would the average inventory level be? d 1− p ) ¿Q¿ ¿ 400(1−

32 ) 200

= 336 maximum 336 = =168 Average inventory = 2 2 e) If the company produces 400 refrigerator at a time , what would the total annual setup cost and holding cost be ? ¿ 168 (50 )+ 20 ( 120 ) ¿ $ 10 800

f) If Bud Banis wants to minimize the total annual inventory cost , how many refrigerator should be produced in each production run ? How much would this save the company in inventory costs compared to the current policy of producing 400 in each production run ? 2 DS d Q= H (1− ) p

√

=

√

2(8000)(120) 32 50(1− ) 200 = 213.81