Annual demand for the notebook binders at duncans

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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.

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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

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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

a.

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D = 8, 000 S = $45 H = $2

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b. If the holding cost per unit was $6 instead of $5, what would be the optimal order quantity?

• 12.9 Southeastern Bell stocks a certain switch connector at its central warehouse for supplying field service offices. The yearly demand for these connectors is 15,000 units. Southeastern estimates its annual holding cost for this item to be $25 per unit. The cost to place and process an order from the supplier is $75. The company operates 300 days per year, and the lead time to receive an order from the supplier is 2 working days.

a. Find the economic order quantity. b. Find the annual holding costs. c. Find the annual ordering costs. d. What is the reorder point?

• 12.10 Lead time for one of your fastest-moving products is 21 days. Demand during this period averages 100 units per day.

a. What would be an appropriate reorder point? b. How does your answer change if demand during lead time

doubles? c. How does your answer change if demand during lead time drops

in half?

• 12.11 Annual demand for the notebook binders at Duncan’s Stationery Shop is 10,000 units. Dana Duncan operates her business 300 days per year and finds that deliveries from her supplier generally take 5 working days.

a. Calculate the reorder point for the notebook binders that she stocks.

b. Why is this number important to Duncan?

• • 12.12 Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas’s fastest-moving inventory item has a demand of 6,000 units per year. The cost of each unit is $100, and the

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inventory carrying cost is $10 per unit per year. The average ordering cost is $30 per order. It takes about 5 days for an order to arrive, and the demand for 1 week is 120 units. (This is a corporate operation, and there are 250 working days per year.)

a. What is the EOQ? b. What is the average inventory if the EOQ is used? c. What is the optimal number of orders per year? d. What is the optimal number of days in between any two orders? e. What is the annual cost of ordering and holding inventory? f. What is the total annual inventory cost, including the cost of the

6,000 units?

• • 12.13 Joe Henry’s machine shop uses 2,500 brackets during the course of a year. These brackets are purchased from a supplier 90 miles away. The following information is known about the brackets:

a. Given the above information, what would be the economic order quantity (EOQ)?

b. Given the EOQ, what would be the average inventory? What would be the annual inventory holding cost?

c. Given the EOQ, how many orders would be made each year? What would be the annual order cost?

d. Given the EOQ, what is the total annual cost of managing the inventory?

e. What is the time between orders? f. What is the reorder point (ROP)?

• • 12.14 Abey Kuruvilla, of Parkside Plumbing, uses 1,200 of a certain spare part that costs $25 for each order, with an annual holding cost of $24.

a. Calculate the total cost for order sizes of 25, 40, 50, 60, and 100. b. Identify the economic order quantity and consider the

implications for making an error in calculating economic order quantity.

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• • • 12.15 M. Cotteleer Electronics supplies microcomputer circuitry to a company that incorporates microprocessors into refrigerators and other home appliances. One of the components has an annual demand of 250 units, and this is constant throughout the year. Carrying cost is estimated to be $1 per unit per year, and the ordering cost is $20 per order.

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

b. How many orders per year are needed with the optimal policy? c. What is the average inventory if costs are minimized? d. Suppose that the ordering cost is not $20, and Cotteleer has

been ordering 150 units each time an order is placed. For this order policy (of ) to be optimal, determine what the ordering cost would have to be.

• • 12.16 Race One Motors is an Indonesian car manufacturer. At its largest manufacturing facility, in Jakarta, the company produces subcomponents at a rate of 300 per day, and it uses these subcomponents at a rate of 12,500 per year (of 250 working days). Holding costs are $2 per item per year, and ordering costs are $30 per order.

a. What is the economic production quantity? b. How many production runs per year will be made? c. What will be the maximum inventory level? d. What percentage of time will the facility be producing

components? e. What is the annual cost of ordering and holding inventory?

Radovilsky Manufacturing Company, in Hayward, California, makes flashing lights for toys. The company operates its production facility 300

Q = 150

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• • 12.17

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days per year. It has orders for about 12,000 flashing lights per year and has the capability of producing 100 per day. Setting up the light production costs $50. The cost of each light is $1. The holding cost is $0.10 per light per year.

a. What is the optimal size of the production run? b. What is the average holding cost per year? c. What is the average setup cost per year? d. What is the total cost per year, including the cost of the lights?

• • 12.18 Arthur Meiners is the production manager of Wheel-Rite, a small producer of metal parts. Wheel-Rite supplies Cal-Tex, a larger assembly company, with 10,000 wheel bearings each year. This order has been stable for some time. Setup cost for Wheel-Rite is $40, and holding cost is $.60 per wheel bearing per year. Wheel-Rite can produce 500 wheel bearings per day. Cal-Tex is a just-in-time manufacturer and requires that 50 bearings be shipped to it each business day.

a. What is the optimum production quantity? b. What is the maximum number of wheel bearings that will be in

inventory at Wheel-Rite? c. How many production runs of wheel bearings will Wheel-Rite

have in a year? d. What is the total cost for Wheel-Rite?

• • 12.19 Cesar Rego Computers, a Mississippi chain of computer hardware and software retail outlets, supplies both educational and commercial customers with memory and storage devices. It currently faces the following ordering decision relating to purchases of very high- density disks:

setup+holding

D

S

H

Purchase price Discount price

= = = = =

36, 000 disks $25 $0.45 $. 85 $0.82

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• • 12.20 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

a. What is the optimal order quantity and the minimum annual cost for Bell Computers to order, purchase, and hold these integrated chips?

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?

• • 12.21 Wang Distributors has an annual demand for an airport metal detector of 1,400 units. The cost of a typical detector to Wang is $400. Carrying cost is estimated to be 20% of the unit cost, and the ordering cost is $25 per order. If Ping Wang, the owner, orders in quantities of 300 or more, he can get a 5% discount on the cost of the detectors. Should Wang take the quantity discount? • • 12.22 The catering manager of La Vista Hotel, Lisa Ferguson, is disturbed by the amount of silverware she is losing every week. Last Friday night, when her crew tried to set up for a banquet for 500 people, they did not have enough knives. She decides she needs to order some more silverware, but wants to take advantage of any quantity discounts her vendor will offer. For a small order (2,000 or fewer pieces), her vendor quotes a price of $1.80ypiece. If she orders 2,001–5,000 pieces, the price drops to $1.60ypiece. 5,001 –10,000 pieces brings the price to $1.40ypiece, and 10,001 and above reduces the price to $1.25. Lisa’s order costs are $200 per order, her annual holding costs are 5%, and the annual demand is 45,000 pieces. For the best option:

Quantity needed to qualify for the discount = 6, 000 disks

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a. What is the optimal order quantity? b. What is the annual holding cost? c. What is the annual ordering (setup) cost? d. What are the annual costs of the silverware itself with an optimal

order quantity? e. What is the total annual cost, including ordering, holding, and

purchasing the silverware?

• • 12.23 Rocky Mountain Tire Center sells 20,000 go-cart tires per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is $20 per tire if fewer than 500 tires are ordered, $18 per tire if 500 or more—but fewer than 1,000—tires are ordered, and $17 per tire if 1,000 or more tires are ordered.

a. How many tires should Rocky Mountain order each time it places an order?

b. What is the total cost of this policy?

• • 12.24 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 cost is $50, and annual holding cost per unit is $5.

a. What is the economic order quantity? b. Which supplier should be used? Why? c. What is the optimal order quantity and total annual cost of

ordering, purchasing, and holding the component?

• • • 12.25 Chris Sandvig Irrigation, Inc., has summarized the price list from four potential suppliers of an underground control valve. See the accompanying table. Annual usage is 2,400 valves; order cost is $10 per order; and annual inventory holding costs are $3.33 per unit.

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