A
Decision-Making
Tools
QUANTITATIVE
MODULE
DISCUSSION QUESTIONS
1.
The purpose of this question is to make students use a personal experience to distinguish between
good and bad decisions. A “good” decision is one that is based on logic and all available
information.
A “bad” decision is one that is not based on logic and all available information. It is possible for
an unfortunate or undesired outcome to result from a “good” decision (witness a patient expiring after
open-heart surgery). It is also possible to have a favorable or desirable outcome result from a “bad”
decision (you win at Blackjack, even though you drew a card when you already held an “18”).
2.
An alternative is a course of action over which we have control. A state of nature is an event or
occurrence over which we have no control. An example of a choice between alternatives is our
decision as to whether or not to carry an umbrella to work today. The relevant state of nature is
whether or not it will rain.
3.
A decision table for Jenine Duffey might look like the following:
Recession
Inflation
Recession and Inflation
Invest in Process #1
Invest in Process #2
Invest in Process #3
4.
EMV is defined as the expected monetary value. The EMV is the expected or average return that we
would realize if we were to repeat the decision an infinite number of times.
“Expected value under certainty” is the expected or average return that we would realize if we
were to repeat the decision an infinite number of times, each time having “perfect” or complete
information and making the “best” possible decision based on that information. EVPI is defined as
the expected value of perfect information. EVPI is equal to the difference between EMV (the
expected or average return given that we were to make the decision based on current or available
information) and “expected value under certainty” and is the maximum amount we would be willing
to pay for additional (perhaps, perfect) information.
Determination of EVPI is useful any time the manager has the option of expending additional
resources to acquire additional information and making the decision using currently available
information.
5.
Decision trees are most useful when the decision maker faces sequential decisions. They are also
very helpful in visualizing the options available.
6.
Expected value assumes that the decision is made over and over many times. The “expected” or
average outcome then has meaning. For a one-time decision, the criterion can be very misleading.
7.
Decision trees are used in such areas as capacity planning (Chapter 7), new product analysis
(Chapter 5), location analysis (Chapter 8), scheduling (Chapter 15), and maintenance (Chapter 17).
Quantitative Module A: Decision-Making Tools
335
8.
The basic difference between decision making under certainty, risk, or uncertainty is based on the
nature and amount of chance or risk that is involved in making the decision. Decision making under
certainty assumes that we know with complete confidence the outcomes that result from our choice
of each alternative. Decision making under risk implies that we do not know the specific outcome
that will result from our choice of a particular alternative, but that we do know the set of possible
outcomes, and that we are able to objectively measure or estimate the probability of occurrence of
each of the outcomes in the set. Decision making under uncertainty implies that we do not know the
specific outcome that will result from our choice of a particular alternative; we know only the set of
possible outcomes and are unable to objectively measure or estimate the probability of occurrence of
any of the outcomes in the set.
9.
Maximax is the optimistic criterion. It maximizes the maximum outcome.
10.
Maximin is the pessimistic criterion. It maximizes the minimum outcome.
END-OF-MODULE PROBLEMS
A.1
States of Nature
Alternatives
Very
Favorable
Market
Average
Market
Large plant
$275,000
Small plant
Overtime
Unfavorable
Market
Row
Minimum
Row
Maximum
$100,000
–$150,000
–150,000
275,000
75,000
$200,000
$60,000
–$10,000
–10,000
200,000
83,333
$100,000
$40,000
–$1,000
–1,000
100,000
46,333
$0
$0
$0
0
0
0
Do nothing

maximin
A.2
(a)
(b)
(c)
Large plant
Do nothing
Small plant
(a)
Market
Size
of First
Station
Good
Market
Fair
Market
Poor
Market
Small
Medium
Large
50,000
80,000
100,000
20,000
30,000
30,000
–10,000
–20,000
–40,000
–10,000
Very large
300,000
25,000
–160,000
(b)
(c)
(d)
A.3
336

maximax
Row
Row
Minimum Maximum
Row
Average

equally likely
Row
Average
–160,000
50,000
80,000
100,000
300,000
20,000
30,000
30,000
55,000

maximin

maximax

equally likely
–20,000
–40,000
Maximax decision: very large station
Maximin decision: small station
Equally likely decision: very large station
EMV (large stock)  0.322 + 0.512 + 0.22  12.2
EMV (average stock)  0.314  0.510  0.26  10.4
EMV (small stock)  0.39  0.58  0.24  7.5
Maximum EMV is large inventory  $12,200
Instructor’s Solutions Manual t/a Operations Management
A.4
EVPI  $13,800  12,200  $1,600 where: $13,800  0.322 + 0.512 + 0.26
A.5
EMV (assembly line)   0.4$10,000   0.6$40,000  $28,000
EMV (plant)   0.4 $100,000   0.6$600,000  $320,000
EMV (nothing)  0
Select the new plant option.
A.6
EVPI  $364,000  $320,000  $44,000
A.7
(a)
(b)
A.8
EMV (Alt. 1)  0.480  0.3120  0.3140  32  36  42  110  max. EMV
EMV (Alt. 2)  0.490  0.390  0.390  36  27  27  90
EMV (Alt. 3)  0.450  0.370  0.3150  20  21  45  86
EVPI  117  110  7
Expected cost of hiring full-timer  0.2300  + 0.5500  + 0.3 700 
 $60 + 250 + 210  $520
Expected cost of part-timer  0.2 0  + 0.5350  + 0.31,000 
 $0 + 175 + 300  $475
Thus, use part-time lawyers.
A.9
Large has EMV = $75,000 ; small has EMV = $83,333 ; overtime EMV = $46,333 ; and do nothing
 $0
A.10 EMV (major expansion)  150,000*
EMV (minor expansion)  50,000
EMV (do nothing)  0
* Therefore, the company should do the major expansion.
A.11 (a)
Stock 11 cases
Stock 12 cases
Demand
11 Cases
P  0.45
385
Demand
12 Cases
P  0.35
385
Demand
13 Cases
P  0.20
385
EMV
$385.00
385
420
420
$379.05
420
455
$341.25
56
329
Stock
*
(b)
13 cases
385
112
56
273
364
The recommended course of action, based on the expected monetary value criterion, is to stock 11 cases.
It should be intuitively obvious that if no loss due to overstocking is involved, one should
always carry the maximum stock. This observation is confirmed by the following table.
Stock 11 cases
Stock 12 cases
Stock 13 cases
*
Demand
11 Cases
P  0.45
385
385
385
Demand
12 Cases
P  0.35
385
420
420
Demand
13 Cases
P  0.20
385
420
455
EMV
$385.00
$404.25
$411.25
The recommended course of action, based on the expected monetary value criterion, is to stock the maximum of
13 cases.
Quantitative Module A: Decision-Making Tools
337
A.12 Profit from each case sold: $95  $45  $50 . Loss from each case produced but not sold: $45.
Production
(Cases)
6
Demand (Cases)
7
8
P  0.3
P  0.5
300
300
6
P  0.1
300
300
7
9
P  0.1
300
EMV
$300.00
350
350
350
$340.50
350
400
400
$352.50
400
450
$317.00
 45
255
8
9
*
300
90
 45
210
305
300
135
350
90
 45
165
260
355
She should manufacture eight cases per month
A.13 Note: All dollar values in 1,000s
Build
$155
Pilot works (0.5)
$155
Work (0.9)
$171
200
– 10
190
Fail (0.1)
–$16
–150
– 10
–160
–10
Work (0.2)
$38
200
– 10
190
–150
– 10
–160
Do not build
$72.5
Try
pilot
Build
–$90
Pilot fails (0.5)
–$10
Fail (0.8)
–$128
Do not build
Decide
now
–$10
$0
$0
Do not build
–10
Work (0.4)
$80
$200
Fail (0.6)
–$90
–$150
$0
The recommended strategy (EMV = 72.5) is

Try pilot

If pilot is success: build plant
If pilot is failure: do not build plant
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Instructor’s Solutions Manual t/a Operations Management
Note: All costs/revenues have been entered at the end of the branches of the tree. Although this
procedure is not required in this example due to an implicit assumption of linear utility, it is required
when using a more general representation of utility.
A.14 Note: All dollar values are in 1,000s.
Favorable (0.4)
$160
(a)
Build large
–20
400
–$20
Unfavorable (0.6)
–$180
–300
Favorable (0.4)
$32
Build small
26
80
$26
Unfavorable (0.6)
–$6
–10
Favorable (0.4)
$0
Do not build
0
0
$0
Unfavorable (0.6)
–$0
(b)
(c)
Based on the expected monetary value criterion, Penny should elect to build a small plant.
We can find the EVPI from the following:
Expected value under certainty = (0.4) (400,000) + 0.6 (0) = $160,000

Maximum EMV = $26,000

EVPI = $160,000  $26,000 = $134,000

1% Defective
(0.7)
–50
3% Defective
(0.2)
–150
5% Defective
(0.1)
–250
–113
1% Defective
(0.3)
–50
+37 saving
Buy from B
–150
3% Defective
(0.4)
–150
5% Defective
(0.3)
–250
A.15 (a)
Buy from A
–90
–90
(b)
0
Switches should be purchased from supplier A.
Quantitative Module A: Decision-Making Tools
339
A.16 (a)
(b)
Maximum EMV = $11,700
EVPI =13,200  11,700 =1,500
A.17 Note: All dollar values are in 1,000s.
Grow
(a)
150
Build large
Stable
–85
Grow
60
Build small
Stable
–45
Grow
0
Do not build
Stable
(b)
0
Build large wing
Build small wing
Do not build
Population Trend
Growth
Stable
150
–85
60
–45
0
0
Build large wing
Build small wing
Do not build
Population Trend
Growth P  0.5
Stable P  0.5
150
–85
60
–45
0
0
(c)
a
f
a
f
EMV
$32.50
$7.50
$0.00
Based on the expected monetary value criterion with the assumption that the states of nature
are equally likely, she should build the large wing.
(d)
Population Trend
Growth P  0.6
Stable P  0.4
150
–85
60
–45
0
0
a
Build large wing
Build small wing
Do not build
f
a
f
EMV
$56.00
$18.00
$0.00
Based on the expected monetary value criterion, she should build the large wing.
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Instructor’s Solutions Manual t/a Operations Management
Favorable
A.18
Small shop
Unfavorable
Favorable
Survey says favorable
Large shop
Unfavorable
No shop
Favorable
Use survey
Small shop
Unfavorable
Favorable
Survey says unfavorable
Large shop
Unfavorable
No shop
Favorable
Small shop
Unfavorable
Favorable
Decide now
Large shop
Unfavorable
No shop
Quantitative Module A: Decision-Making Tools
341
A.19
Small shop
Survey says
favorable market (0.6)
+$45
Large shop
Favorable (0.9)
$21
Unfavorable (0.1)
Favorable (0.9)
$45
Unfavorable (0.1)
No shop
Use survey
$25
$25
Survey says
unfavorable market (0.4)
–$5
Small shop
Large shop
Decide now
$10
Large shop
No shop
–10 – 5 = –15
60 – 5 = 55
–40 – 5 = –45
0 – 5 = –5
Favorable (0.12)
–$10.2
Unfavorable (0.88)
Favorable (0.12)
–$33
Unfavorable (0.88)
No shop
Small shop
30 – 5 = 25
30 – 5 = 25
–10 – 5 = –15
60 – 5 = 55
–40 – 5 = –45
0 – 5 = –5
Favorable (0.5)
$10
Unfavorable (0.5)
Favorable (0.5)
$10
Unfavorable (0.5)
30
–10
60
–40
0
The optimal strategy is to use the survey. If the survey indicates a favorable market, then build a
large shop. If the survey does not indicate a favorable market, then do nothing.
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Instructor’s Solutions Manual t/a Operations Management
A.20
(0.9)
8,500
(0.1)
Info favorable (0.5)
8500
12000
–23000
(0.9)
500
(0.1)
2000
–13000
–3000
Gather
more information
2750
(0.4)
–9,000
(0.6)
Info unfavorable (0.5)
–3000
12000
–23000
(0.4)
–7,000
(0.6)
2000
–13000
–3000
(0.7)
4,500
(0.3)
Do not gather
more information
4500
15000
–20000
(0.7)
500
(0.3)
5000
–10000
0
Your advice should be to not gather additional information and to build a large video section.
A.21 (a)
5,000
Minor
10,000
Market favorable
(0.5)
Market unfavorable (0.5)
Do nothing
(b)
(0.5)
Market unfavorable (0.5)
Major
10,000
Market favorable
100,000
–90,000
40,000
–20,000
0
EMV (major renovation)  5,000
EMV (minor renovation)  10,000*
* best decision is minor renovation
Quantitative Module A: Decision-Making Tools
343
Good (1/3)
A.22
Small
Fair (1/3)
20,000
Poor (1/3)
Good (1/3)
Medium
Fair (1/3)
30,000
Poor (1/3)
50,000
20,000
–10,000
80,000
30,000
–20,000
55,000
Good (1/3)
Large
Fair (1/3)
30,000
Poor (1/3)
Good (1/3)
Very large
Fair (1/3)
55,000
Poor (1/3)
344
100,000
30,000
–40,000
300,000
25,000
–160,000
Instructor’s Solutions Manual t/a Operations Management
CASE STUDIES
NIGEL SMYTHE’S HEART BY PASS OPERATION
No By pass Surgery
1 year
2 years
5 years
8 years
Prob.
Years
Expected
Rate
0.50
1
0.50
0.20
2
0.40
0.20
5
1.00
0.10
8
0.80
2.70 years
Surgery
0 years
1 year
5 years
10 years
15 years
20 years
25 years


Prob.
Years
Expected
Rate
0.05
0
0.00
0.45
1
0.45
0.20
5
1.00
0.13
10
1.30
0.08
15
1.20
0.05
20
1.00
0.04
25
1.00
5.95 years
Expected survival rate with surgery (5.95 years) exceeds the nonsurgical survival rate of 2.70 years.
Surgery is favorable.
Other factors might include the particular doctor and hospital used and care received.
STARTING RIGHT CORP.
This is a decision-making-under-uncertainty case. There are two events: a favorable market (event 1) and an
unfavorable market (event 2). There are four alternatives, which include do nothing (alternative 1), invest in
corporate bonds (alternative 2), invest in preferred stock (alternative 3), and invest in common stock
(alternative 4). The decision table is presented below. Note that for alternative 2, the return in a good
5
market is $30,000  1  0.13  $55,273 . The return in a good market is $120,000  4  $30,000 for
alternative 3, and $240,000  8  $30,000for alternative 4.
a
f
Quantitative Module A: Decision-Making Tools
345
Alternative 1 (not invest)
Alternative 2 (bonds)
Alternative 3 (preferred)
Alternative 4 (common)
Event 1
0
55,273
120,000
240,000
Event 2
0
–10,000
–15,000
–30,000
Solutions:
Equally Likely
Alternative
Expected Value
1
0.0
2
22,636.5
3
52,500.0
4
105,000.0
best
Maximin
Alternative
Expected Value
1
0
best
2
–10,000
3
–15,000
4
–30,000
Maximax
Alternative
Maximax Payoff
1
0
2
55,273
3
120,000
4
240,000
best
Probability of 0.11 of Success
Alternative
Payoff
1
0.00
2
–2,819.97
3
–150.00
4
–300.00
best
1.
Sue Pansky is a risk avoider and should use the maximin decision approach. She should do nothing
and not make an investment in Starting Right.
2.
Ray Cahn should use a success probability of 0.11. The best decision is to do nothing.
3.
Lila Battle should eliminate alternative 1, doing nothing, and apply the maximin criterion. The result
is to do nothing.
4.
George Yates should use the equally likely decision criterion. The best decision for George is to
invest in common stock.
5.
Pete Metarko is a risk seeker. He should invest in common stock.
6.
Julia Day can eliminate the preferred stock alternative and still offer alternatives to risk seekers
(common stock) and risk avoiders (doing nothing or investing in corporate bonds).
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Instructor’s Solutions Manual t/a Operations Management
INTERNET CASE STUDIES
ARCTIC, INC.
No probabilities have been included in this case study. As an initial analysis, we expect students to input the
data and run Excel OM or POM for Windows.
Student analysis would be to determine something about the expected values. Because the probabilities
are not known, a first try might be to assign equal probabilities—say, 0.1666. The best expected value is
given by “building new,” with a value of nearly 2. However, note that this value is not that much greater
than the value for “expanding” the plant. “Purchasing” has a terrible expected value of (0.35) and can be
eliminated. “Sole sourcing” also has a low expected value and can possibly be eliminated from
consideration. The question that remains is this: How sensitive are the results to the scenario probabilities?
This is where the power of a computer comes in handy. Students can try many different probability
combinations and look at the expected values. We are primarily concerned with expanding, building new,
subcontracting, and expanding and subcontracting.
As “drop” is the worst scenario, try probabilities of 0.125, 0.125, and 0.25 for grow, stable, and drop,
respectively. In this case, “expand” or “expand and subcontract” are better options. To determine the effects
of growth, reverse the probabilities. This brings “building new” to the forefront. It is impossible to give an
exact answer on what option to choose. The analysis shows that building a new plant can be very profitable,
but this strategy can also be very risky. It might be more prudent to focus on the two expansion strategies.
TOLEDO LEATHER COMPANY
1.
Machine 1
(Semiautomated)
Capacity = 5 days wk  50 wks yr
L
M
N
Machine 2
(Automated)
Capacity = 5 days wk  50 wks yr
O
P
Q
L
M
N
1
 640  (640) = 140,000 yr .
8
 800 
O
P
Q
1
(800) = 150,000 units yr .
4
Sales price = $6 / unit
Sales price = $6 / unit
T.C./case = $1.50 (material)
T.C./case = $1.50
af a
T.C./casea
with overtimef= $1.50
+ $2.50 v.c.  $4 no overtime used
+ $2.50  $1.20 = $5.20
f
af
a
+ $1.75 v.c.  $3.25 no overtime used
a
f
T.C./case with overtime = $1.50
+ $1.75  $0.90 = $4.15
Cost of machine = $250,000
Cost of machine = $350,000
Cost to modify = $15,000
Cost to modify = $20,000
Volume
120k
130k
140k (capacity)
150k (overtime)
150k (modify)
160k (overtime)
160k (modify)
Profit
($6  4)(120k) = $240k
($6  4)(130k)  $260k
($6  4)(140k) = $280k
$280k + (80¢ overtime unit)
(10k) = $288k
($6  4)(150k)  $15k = $285k
$280k + (80¢ unit)20k   $296k
($6  4)(160k)  $15k = $305k
Quantitative Module A: Decision-Making Tools
f
Volume
120k
130k
140k
150k (capacity)
Profit
($6  3.25)(120k) = $330k
($6  3.25)(130k) = $357.5k
($6  3.25)(140k) = $385k
($6  3.25)(150k) = $412.5k
160k (overtime)
160k (modify)
$412.5k + (6  4.15)(10k) = $431k
($6  3.25)(160k)  $20 k = $420k
347
2.
Payoff Matrix
Alternative
Machine 1
Machine 2
$120k
240
330
States of Nature—Payoff in $1,000s
$130k
$140k
$150k (OT)
260.0
280
288.0
357.5
385
412.5
(a)
Maximax:
$296k  $250k = $46k
$431k  $350k = $81k maximax (Machine 2)
(b)
Maximin:
$240k  $250k = $10k maximin (Machine 1)
$330k  $350k = $20k
(c)
Equally likely:
Machine 1 = $272.8k  250k = $22.8k
Machine 2 = $383.2k  350k = $33.2k (Machine 2)
Volume = 120,000 (0.15)
V = 130,000 (0.25)
$21,450
(Machine 1)
Semiautomated
$250,000
cost
$271,450
V = 140,000 (0.40)
V = 150,000 (0.15)
Overtime
Modify
V = 160,000 (0.5)
Overtime
$26,300
Modify
Volume = 120,000 (0.15)
V = 130,000 (0.25)
$26,300
(Machine 2)
Automated
$350,000
cost
$376,300
V = 140,000 (0.40)
V = 150,000 (0.15)
V = 160,000 (0.05)
Overtime
Modify
348
$160k (OT)
296
431
$240k
$260k
$280k
$288k
$285k
$296k
$305k
$330k
$357.5k
$385k
$412.5k
$431k
$420k
Instructor’s Solutions Manual t/a Operations Management