# Business

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Solved Problems Virtual Office Hours help is available at www.myomlab.com

Solved Problem 12.1

David Alexander has compiled the following table of six items in inventory at Angelo Products, along with the unit cost and the annual demand in units:

Use ABC analysis to determine which item(s) should be carefully controlled using a quantitative inventory technique and which item(s) should not be closely controlled.

Solution

The item that needs strict control is 33CP, so it is an A item. Items that do not need to be strictly controlled are 3CPO, R2D2, and RMS; these are C items. The B items will be XX1 and B66.

70% of

Total cost = $100, 516.56

total cost = $70, 347.92

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Solved Problem 12.2

The Warren W. Fisher Computer Corporation purchases 8,000 transistors each year as components in minicomputers. The unit cost of each transistor is $10, and the cost of carrying one transistor in inventory for a year is $3. Ordering cost is $30 per order.

What are (a) the optimal order quantity, (b) the expected number of orders placed each year, and (c) the expected time between orders? Assume that Fisher operates on a 200-day working year.

Solution

a.

b.

c.

With 20 orders placed each year, an order for 400 transistors is placed every 10 working days.

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= = = 400 unitsQ∗ 2DS H

− −−√ 2(8,000) (30)3 − −−−−−−−√

N = = = 20 ordersD Q∗

8,000 400

Time between orders = T = = = 10 working dNumber of working days N

200 20

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Solved Problem 12.3

Annual demand for notebook binders at Meyer’s Stationery Shop is 10,000 units. Brad Meyer operates his business 300 days per year and finds that deliveries from his supplier generally take 5 working days. Calculate the reorder point for the notebook binders.

Solution

Thus, Brad should reorder when his stock reaches 167 units.

Solved Problem 12.4

Leonard Presby, Inc., has an annual demand rate of 1,000 units but can produce at an average production rate of 2,000 units. Setup cost is $10; carrying cost is $1. What is the optimal number of units to be produced each time?

Solution

L

d

ROP

=

=

=

5 days

= 33.3 units per day10,000300 d × L = (33.3 units per day)(5 days) = 166.7 units

= =Q∗p 2DS H(1− )Annual demand rate

Annual production rate

− −−−−−−−−−−−−−√ 2(1,000) (10)1[1−(1,000/2,000)] − −−−−−−−−−−√

= = = 200 units20,000 1/2

− −−−√ 40, 000− −−−−−√

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Solved Problem 12.5

Whole Nature Foods sells a gluten-free product for which the annual demand is 5,000 boxes. At the moment, it is paying $6.40 for each box; carrying cost is 25% of the unit cost; ordering costs are $25. A new supplier has offered to sell the same item for $6.00 if Whole Nature Foods buys at least 3,000 boxes per order. Should the firm stick with the old supplier, or take advantage of the new quantity discount?

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Solution

Under the present price of $6.40 per box:

Economic order quantity, using Equation (12-10) :

where

Note: Order and carrying costs are rounded.

Under the quantity discount price of $6.00 per box:

We compute which is below the required order level of 3,000 boxes. So Q* is adjusted to 3,000.

Q∗

Q∗

=

=

=

2DS IP

− −−√ 2(5,000) (25) (0.25) (6.40)

− −−−−−−−√ 395.3, or 395 boxes

D

S

P

I

H

= = = = =

period demand ordering cost price per box holding cost as percent holding cost = IP

Total cost = Order cost + Holding cost + Purchase cost

= + H + PDDS Q

Q

2

= + + (6.40) (5, 000)(5,000) (25)395 (395) (0.25) (6.40)

2

= 316 + 316 + 32, 000 = $ 32, 632

= 408.25,Q∗

= + H + PDDS Q

Q

2

= + + (6.00) (5, 000)(5,000) (25)3,000 (3,000) (0.25) (6.00)

2

= 42 + 2, 250 + 30, 000 = $32, 292

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Therefore, the new supplier with which Whole Nature Foods would incur a total cost of $32,292 is preferable, but not by a large amount. If buying 3,000 boxes at a time raises problems of storage or freshness, the company may very well wish to stay with the current supplier.

Solved Problem 12.6

Children’s art sets are ordered once each year by Ashok Kumar, Inc., and the reorder point, without safety stock (dL), is 100 art sets. Inventory carrying cost is $10 per set per year, and the cost of a stockout is $50 per set per year. Given the following demand probabilities during the lead time, how much safety stock should be carried?

Solution

The safety stock that minimizes total incremental cost is 50 sets. The reorder point then becomes or 150 sets.

PRINTED BY: stacymarlow@yahoo.com. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.

100 sets + 50 sets,

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Solved Problem 12.7

What safety stock should Ron Satterfield Corporation maintain if mean sales are 80 during the reorder period, the standard deviation is 7, and Ron can tolerate stockouts 10% of the time?

Solution

From Appendix I , Z at an area of and Equation (12-14) :

. 9 (or 1 − . 10) = 1.28,

Safety stock = =

ZσdLT

1.28(7) = 8.96 units, or 9 units

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Solved Problem 12.8

The daily demand for 52ʺ flat-screen TVs at Sarah’s Discount Emporium is normally distributed, with an average of 5 and a standard deviation of 2 units. The lead time for receiving a shipment of new TVs is 10 days and is fairly constant. Determine the reorder point and safety stock for a 95% service level.

Solution

The ROP for this variable demand and constant lead time model uses Equation (12-15) :

where

So, with

The safety stock is 10.4, which can be rounded up to 11 TVs.

Solved Problem 12.9

The demand at Arnold Palmer Hospital for a specialized surgery pack is 60 per week, virtually every week. The lead time from McKesson, its main supplier, is normally distributed, with a mean of 6 weeks for this product and a standard deviation of 2 weeks. A 90% weekly service level is desired. Find the ROP.

ROP = (Average daily demand × Lead time in days) + ZσdLT

=σdLT σd Lead time − −−−−−−−√

Z = 1.65,

ROP =

=

(5 × 10) + 1.65(2) 10−−√

50 + 10.4 = 60.4 ≅60 TVs, or rounded up to 61 TVs

PRINTED BY: stacymarlow@yahoo.com. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.

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Problems

Note: means the problem may be solved with POM for Windows and/or Excel OM.

• • 12.1 L. Houts Plastics is a large manufacturer of injection-molded plastics in North Carolina. An investigation of the company’s manufacturing facility in Charlotte yields the information presented in the table below. How would the plant classify these items according to an ABC classification system?

L. Houts Plastics’ Charlotte Inventory Levels

• • 12.2 Boreki Enterprises has the following 10 items in inventory. Theodore Boreki asks you, a recent OM graduate, to divide these items into ABC classifications.

a. Develop an ABC classification system for the 10 items. 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?

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

a. Which is the most expensive item, using annual dollar volume? b. Which are C items? c. What is the annual dollar volume for all 20 items?

• 12.4 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 C items are counted semiannually (every 120 working days). How many items need to be counted each day?

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• 12.5 William Beville’s computer training school, in Richmond, stocks workbooks with the following characteristics:

Calculate the EOQ for the workbooks. b. What are the annual holding costs for the workbooks? c. What are the annual ordering costs?

• 12.6 If per month, per order, and per unit per month,

a. What is the economic order quantity? b. How does your answer change if the holding cost doubles? c. What if the holding cost drops in half?

• • 12.7 Henry Crouch’s law office has traditionally ordered ink refills 60 units at a time. The firm estimates that carrying cost is 40% of the $10 unit cost and that annual demand is about 240 units per year. The assumptions of the basic EOQ model are thought to apply.

a. For what value of ordering cost would its action be optimal? b. If the true ordering cost turns out to be much greater than your

answer to (a), what is the impact on the firm’s ordering policy?

• 12.8 Matthew Liotine’s Dream Store sells beds and assorted supplies. His best-selling bed has an annual demand of 400 units. Ordering cost is $40; holding cost is $5 per unit per year.

a. To minimize the total cost, how many units should be ordered each time an order is placed?

Demand D = 19, 500 units/year

Ordering cost S = $25/order

Holding cost H = $4/unit/year