Matching supply with demand: an introduction to operations management

Matching supply with demand: an introduction to operations management

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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 + 60150+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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