# Matching supply with demand: an introduction to operations management

Dan’s Independent Book Store is trying to decide on how many copies of a book to

purchase at the start of the upcoming selling season. The book retails at $28.00. The

publisher sells the book to Dan at $20.00. Dan will dispose of all of the unsold copies of

the book at 50% off the retail price, at the end of the season. Dan estimates that demand

for this book during the season is Normal with a mean of 1000 and a standard deviation

of 250.

Suppose Dan orders 1415 copies of the book. What would be his expected mismatch

cost? Choose the closest answer. Show all work.

a) $2180

b) $2560

c) $5450

d) $5820

e) $7000

Handi Inc., a maker of cellphones, procures a standard display from LCD Inc. via an

options contract. At the start of quarter 1 (Q1) Handi pays LCD $4.5 per option. At that

time Handi’s forecast of demand in Q2 is Normally distributed with mean 24000 and

standard deviation 8000. At the start of Q2 Handi learns exact demand for Q2 and then

exercises options at the fee of $3.5 per option (for every exercised option LCD delivers

one display to Handi). Assume Handi starts Q2 with no display inventory and displays

owned at the end of Q2 are worthless. Should Handi’s demand in Q2 be larger than the

number of options held, Handi purchases additional displays on the spot market for $9

per unit.

For example, suppose Handi purchases 30000 options at the start of Q1 but at the start of

Q2 Handi realizes that demand will be 35000 units. Then Handi exercises all of its

options and purchases 5000 additional units on the spot market. If, on the other hand,

Handi realizes demand is only 27000 units, then Handi merely exercises 27000 options.

How many options should Handi purchase from LCD? Choose the closest answer. Show

all work.

a) 18000

b) 20000

c) 22000

d) 24000

e) 26000

f) 28000

g) 30000

h) 32000

SEC, a Semiconductor (fabrication) Equipment Company, has a central spare parts

warehouse to support its chip fabrication plant customers located around the world. As

new generations of fab equipment are introduced, the installed base of older models

declines and ultimately disappears. As a consequence, SEC must at some point retire

support for the older model. Once a model has been scheduled for retirement, SEC makes

a “final buy” for service parts that are required to maintain support of the equipment until

the retirement date. If inventory of a part runs out before retirement, then an emergency

order is placed with the part vendor. Inventory remaining in the warehouse at the

retirement date is scrapped for salvage materials.

Consider one model that has 50 machines installed throughout the world and SEC has

just announced the model will be retired in one year. Focus on part A in this machine.

Part A’s current cost to purchase is $10,000. The expected cost for an emergency order

of part A after the final buy is $25,000. Part A’s estimated salvage value is $2,000 and

its total annual demand (across the 50 machines) is estimated to be Poisson with mean

3.5. Suppose there are currently 2 of these parts in inventory.

If SEC does not order any of these parts in the final buy, what fraction of demand until

retirement will be filled without the use of an emergency order? Choose the closest

answer.

a) 15%

b) 25%

c) 35%

d) 45%

e) 55%

f) 65%

g) 75%

h) 85%

i) 95%

How many part As should SEC order in the final buy to minimize its expected cost?

(Recall, there are currently two parts in inventory.) Choose the closest answer.

a) 0

b) 1

c) 2

d) 3

e) 4

f) 5

g) 6

h) 7

SEC recognizes that reliable service is critically important to its customers. Hence, SEC’s

goal is to fill 99.93% of orders for part A immediately from on-hand inventory between

now and the retirement date. How many parts As should SEC order in the final buy?

(Recall, there are currently two parts in inventory.) Choose the closest answer.

a) 3

b) 4

c) 5

d) 6

e) 7

f) 8

g) 9

h) 10

A construction company has signed a contract to build an office tower. The contract

stipulates that the project will be completed in 1500 days from today and also includes a

penalty on the construction company of $30,000 per day the project is late. In addition,

the construction company estimates that its internal cost is $60,000 for each day the

project is late. However, completing the project early is costly to the firm as well: each

day the project is early costs the firm $45,000. (This includes opportunity cost of capital

and idle capacity.) The firm estimates the project will take 1200 days to complete. The

following are data on the ratios of the firm’s actual completion times to forecasted

completion times on previous projects with comparable complexity. (For example, one

project’s actual completion time was only 69% of forecasted time whereas another

project’s actual completion time was 210% of the forecast. Note, these 20 observations

have been already sorted in ascending order.)

0.690.891.111.44

0.710.911.171.50

0.750.951.211.75

0.771.051.261.91

0.811.081.312.10

Given these data, how many days should the firm wait to begin construction? Choose the

closest answer.

a) 0 days, they should start immediately

b) 50 days

c) 100 days

d) 170 days

e) 200 days

f) 400 days

g) 1000 days

h) 1200 days

i) 1500 days

Nordic Inc. has designed four ski boot styles it plans to sell in the 2006 winter season:

Terrain, Blizzard, IceFix and Freezdom. Nordic can produce some ski boot styles well in

advance of the selling season with the remaining styles produced after the 2006 Ski Elite

Athletes Trade (SEAT) show that occurs before the selling season. At the time it makes

its initial production decision, Nordic’s forecast for each boot’s demand is normally

distributed with means and standard deviations listed in the table below. The table also

lists results from the Newsvendor model when expected profit is maximized.

Boot

Price Mean Std dev Co Cu Q Expected

Newsvendor

Profit

Terrain 200 100 30 16 48 120 4190

Blizzard 150 150 50 20 60 184 7730

IceFix 120 200 70 9.6 28.8 248 4906

Freezdom 100 300 50 8 24 334 6692

After the trade show, and before it makes its final production decision, Nordic will know

exact demand for each boot.

What is Nordic’s expected profit if Nordic chooses to produce all four boot styles before

the SEAT show? Choose the closest answer.

a) 4190

b) 4906

c) 6692

d) 7730

e) 8996

f) 9096

g) 11598

h) 11920

i) 12636

j) 15000

k) 23000

What is Nordic’s expected profit if Nordic chooses to produce every boot style after the

SEAT show (and assuming that all of its production arrives by the start of the selling

season)? Choose the closest answer.

a) 4800

b) 6000

c) 7200

d) 13200

e) 15000

f) 17200

g) 18000

h) 20000

i) 22000

j) 24000

j) 24000

Expected profit if all boots produced after the show = Maximum profit = sum (C u

= 48 100 + 60150+28.8 200 + 24 300

= 4800 + 9000+5760 + 7200

= 26,760

Because the SEAT show concludes shortly before the selling season, Nordic has limited

capacity for production after the SEAT show. As a result, it needs to produce at least 300

pairs of boots before the SEAT show. Recall, each boot style is produced either before or

after SEAT show (i.e., no style is produced both before and after the show). How many

pairs of boots should Nordic produce before the SEAT Trade show? Choose the closest

answer.

a) 248

b) 300

c) 304

d) 334

e) 368

f) 432

g) 454

h) 518

i) 582

j) 702

8 of 18

d) 334

Boots Exp

Prof

it

Max

Prof

it

Mismatch

Cost

Ratio

(MC/

Q)

1 st Run

Production

2 nd Run

Production

Terrain 4190 4800 610 5.08 — 100

Blizzard 7730 9000 1270 6.91 — 150

IceFix 4906 5760 854 3.44 — 200

Freezdom 6692 7200 508 1.52 334 —

Total production run before the show is 334 units of Freezdom

***

Montgomery County PA (MC) predicts that its total road salt needs during the next

winter will be normally distributed with a mean of 3400 tons and a standard deviation of

1800 tons. MC currently has no road salt in inventory. MC and the supplier American

Salt Inc. (ASI) have signed the following contract. MC will receive salt on an as needed

basis during the winter season (in other words, MC will buy in sufficiently small

quantities and ASI will deliver with a sufficiently small lead time that MC’s total

purchase for the season will be essentially equal to its total road salt needs). MC will pay

$62 per ton for the first 3600 tons purchased and $75 per additional ton above 3600.

For example, if MC purchases 2500 tons then their total payment to ASI is 2500 × $62 =

$155,000, and if MC purchases 4000 tons, then its total payment to ASI is 3600 × $62 +

400 × $75 = $253,200. How much can MC expect to pay ASI? Choose the closest

answer.

a) $181,000

b) $211,000

c) $219,000

d) $225,000

e) $233,000

f) $255,000

g) The expected payment cannot be determined with these data

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