Inventory Problems

MGMT 326Self-study Problems for Inventory ManagementABC Analysis1. The following inventory data is given:ItemAnnual

DemandUnit

Price ($)Annual Usage ($)Annual Usage

Percentage

21500$5

22350$100

23400$30

24600$5

25400$60

2650$200

2750$40

281,000$2

29200$10

3050$20

(a) Compute the annual usage for each item.(b) Compute the total annual usage.

(c) Compute the annual usage percentage for each item.

2. Use your results from problem 1. In the table below, arrange the items in order of descending annual usage percentage (largest to smallest). Then compute the cumulative annual usage percentages. Finally, classify the items as A items, B items, or C items.

ItemAnnual Usage

PercentageCumulative

Annual Usage

PercentageCategory

Economic order quantity and reorder point3. Do Solved Problem 1, pages 457-458, without using Excel. Note that H = 0.2($15) = $3.

4. Problem 9, page 461. (Answer in textbook, page 641).5. Problem 11, page 461. In part (g), compute the amount of money saved by using the order quantity in this problem instead of the order quantity in problem 9. (Answer in textbook, page 641).6. A lumber yard is open 6 days per week (300 days per year) and sells 3,600 sheets of plywood per year. Order lead time is one week. Inventory holding cost is $2. The cost of placing an order is $30.

(a) Find the economic order quantity.

(b) Find the annual cost of placing orders and holding inventory for the economic order

quantity.

(c) If the economic order quantity is used, how many orders will be placed per year?

(d) If the economic order quantity is used, what will the average inventory be?

(e) Find the reorder point, if no safety stock is kept.

(f) The standard deviation of demand during the lead time is 3. Find the reorder point for a

95% service level.

7. In problem 4, the lumber yard now orders plywood from the supplier's Web site. This change has reduced order cost to $10 and lead time to 2 days.

(a) Find the economic order quantity.

(d) Find the annual cost of placing orders and holding inventory for the economic order

quantity.

(c) Find the reorder point, if no safety stock is kept.

8. A hospital uses an average of 10 cases of surgical gloves per week. The order cost is $40. Inventory holding cost is $2.60 per case per year.(a) Find the economic order quantity.

(b) Find the annual cost of placing orders and holding inventory for the economic order

quantity.

9. A large law firm uses 8 cases of bond paper per day. The firm operates 5 days per week (250 days per year). The cost of placing an order is $20. Inventory holding cost is $2.50. Order lead time is 3 business days. The standard deviation of demand during the lead time is 4.(a) Find the economic order quantity.

(b) Find the annual cost of placing orders and holding inventory for the economic order

quantity.

(c) Find the reorder point.

(d) Find the reorder point for a 97% service level.

10. Crafty Crafts has many customers who practice the art of origami, or folding stiff paper into various decorative shapes. The store is open 5 days per week (250 days per year) and sells 2,000 packages of origami paper per year. Inventory holding cost is $2. Origami paper must be ordered from Japan. The order lead time is 2 weeks. Cost per order is $50. The standard deviation of demand during the lead time is 10 packages of paper.(a) Find the economic order quantity.

(b) Find the annual cost of placing orders and holding inventory for the economic order

quantity.

(c) Find the reorder point, if no safety stock is kept.

(d) Find the reorder point for a 90% service level.

Economic Production Quantity11. Solved Problem 2, page 458.12. Frank's Machine shop operates 250 days per year. Frank sells 5,000 units per year of his most popular item, a specialty gear. The setup cost for this gear is $100, and the cost of holding inventory is $5. When the gear is being produced, the shop can make 80 gears per day.

(a) Find the economic production quantity.

(b) Find the annual cost of setups and holding inventory for the economic production quantity.13. Wonderful Wood Stuff operates 300 days per year and makes a variety of small wood products. The demand for one popular item, a set of napkin rings, is 12,000 per year. Setup cost for this item is $50. Inventory holding cost is $0.50. The daily production rate is 200.

(a) Find the economic production quantity.

(b) Find the annual cost of setups and holding inventory for the economic production quantity.14. Fantastic Frames makes picture frames. Demand for its most popular item, a 9" x 12" frame, is 32 per day. The factory operates 250 days per year. Setup cost for this frame is $40, and the inventory holding cost is $2. The daily production rate is 320.

(a) Find the economic production quantity.

(b) Find the annual cost of setups and holding inventory for the economic production quantity.15. Wacky Wood operates 250 days per year and sells an average of 40 wooden paper towel holders per day. When paper towel holders are being made, 160 can be made per day. Setup cost is $60. Inventory holding cost is $4. Find the economic production quantity.

Solutions Not Given in TextbookProblem 1:

ItemAnnual

DemandUnit

Price ($)Annual

Usage ($)Annual Usage

Percentage

215005$2,5002.82%

22300100$30,00033.90%

2340025$10,00011.30%

246005$3,0003.39%

2540060$24,00027.12%

2650200$10,00011.30%

275040$2,0002.26%

2810002$2,0002.26%

2920020$4,0004.52%

305020$1,0001.13%

The total annual usage is $93,500.

Problem 2:

ItemAnnual Usage

PercentageCumulative

Annual Usage

PercentageCategory

2237.43%37.43%A

2525.67%63.10%A

2312.83%75.94%B

2610.70%86.63%B

243.21%89.84%C

212.67%92.51%C

272.14%94.65%C

282.14%96.79%C

292.14%98.93%C

301.07%100.00%C

Note: In problems 6 15, answers may vary slightly due to rounding off.

Problem 6: (a) 328.63 sheets of plywood, (b) $656.26, (c) 11 (round up), (d) 164.32 or 164,

(e) 72 sheets of plywood - Note: L = 1 week = 6 working days. (f) 77 Note: round the reorder point up.Problem 7: (a) 189.74 sheets of plywood; (b) $379.48, (c) 24 sheets of plywood.

Problem 8: (a) 126.49 cases of gloves - Note: D = 52(10) = 520 cases, (b) $328.88

Problem 9: (a) 178.89 cases of paper - Note: D = 8(250) = 2,000 cases, (b) $447.22, (c) 24 case(d) 32 cases

Problem 10: (a) 316.23 packages of paper, (b) $632.46, (c) 80 packages of paper. Note: d = 2,000/250 = 8 and L = 2 weeks = 2(5) = 10 working days. (d) 93 packages of paperProblem 12: (a) 516.40 gears - Note: d = 5,000/250 = 200, (b) $1,936.50Problem 13: (a) 1,732 napkin rings - Note: d = 12,000/300 = 40, (b) $692.82Problem 14: (a) 596.48 picture frames - Note: D = 32(250) = 8,000, (b) $1,073.32Problem 15: 632.45 paper towel holders.

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