1 Supplement Solutions to Selected Problems
Operational Decision-Making Tools: Decision Analysis
S1-1. a. Minimin:
South Korea 15.2
China 17.6
Taiwan 14.9
Poland 13.8
Mexico 12.5 minimum
Select Mexico
b. Minimax:
South Korea 21.7
China 19.0 minimum
Taiwan 19.2
Poland 22.5
Mexico 25.0
Select China
c. Hurwicz ( = 0.40 ) :
South Korea: 15.2 ( 0.40 ) + 21.7 ( 0.60 ) = 19.10
China: 17.6 ( 0.40 ) + 19.0 ( 0.60 ) = 18.44
Taiwan: 14.9 ( 0.40 ) + 19.2 ( 0.60 ) = 17.48 minimum
Poland: 13.8 ( 0.40 ) + 22.5 ( 0.60 ) = 19.02
Mexico: 12.5 ( 0.40 ) + 25.0 ( 0.60 ) = 20.0
Select Taiwan
d. Equal likelihood:
South Korea:
21.7 ( 0.33) + 19.1( 0.33) + 15.2 ( 0.33) = 18.48
China: 19.0 ( 0.33) + 18.5 ( 0.33) + 17.6 ( 0.33) = 18.18
Taiwan: 19.2 ( 0.33) + 17.1( 0.33) + 14.9 ( 0.33) = 16.90 minimum
Poland: 22.5 ( 0.33) + 16.8 ( 0.33) + 13.8 ( 0.33) = 17.52
Mexico: 25.0 ( 0.33) + 21.2 ( 0.33) + 12.5 ( 0.33) = 19.37
Select Taiwan
S1-2.
EV ( South Korea ) = 21.7 ( .30 ) + 19.1(.40 ) + 15.2 (.30 ) = 18.71
EV ( China ) = 19.0 (.30 ) + 18.5 (.40 ) + 17.6 (.30 ) = 18.38
EV ( Taiwan ) = 19.2 ( .30 ) + 17.1(.40 ) + 14.9 (.30 ) = 17.07 minimum
EV ( Poland ) = 22.5 (.30 ) + 16.8 (.40 ) + 13.8 (.30 ) = 17.61
EV ( Mexico ) = 25.0 (.30 ) + 21.2 (.40 ) + 12.5 (.30 ) = 19.73
Select Taiwan
Expected value of perfect information = 19 (.30 ) + 16.8 (.40 ) + 12.5 (.30 ) = 16.17
EVPI = 16.17 17.07 = $ 0.9 million
The EVPI is the maximum amount the cost of the facility could be reduced (.9 million) if perfect information
can be obtained.
S1-3. a. Maximax criteria:
Office building 4.5 maximum
Parking lot 2.4
Warehouse 1.7
Shopping mall 3.6
Condominiums 3.2
Select office building
b. Maximin criteria:
Office building 0.5
Parking lot 1.5 maximum
Warehouse 1.0
Shopping mall 0.7
Condominiums 0.6
Select parking lot
c. Equal likelihood:
Office building: 0.5 ( 0.33) + 1.7 ( 0.33) + 4.5 ( 0.33) = 2.21 maximum
Parking lot: 1.5 ( 0.33) + 1.9 ( 0.33) + 2.4 ( 0.33) = 1.91
Warehouse: 1.7 ( 0.33) + 1.4 ( 0.33) + 1.0 ( 0.33) = 1.35
Shopping mall: 0.7 ( 0.33) + 2.4 ( 0.33) + 3.6 ( 0.33) = 2.21 maximum
Condominiums: 3.2 ( 0.33) + 1.5 ( 0.33) + 0.6 ( 0.33) = 1.75
Select office building or shopping mall
d. Hurwicz criteria ( = 0.3) :
Office building: 4.5 ( 0.3) + 0.5 ( 0.7 ) = 1.70
Parking lot: 2.4 ( 0.3) + 1.5 ( 0.7 ) = 1.77 maximum
Warehouse: 1.7 ( 0.3) + 1.0 ( 0.7 ) = 1.21
Shopping mall: 3.6 ( 0.3) + 0.7 ( 0.7 ) = 1.57
Condominiums: 3.2 ( 0.3) + 0.6 ( 0.7 ) = 1.38
Select parking lot
S1-4. a) EV ( Office building ) = .5 ( .50 ) + 1.7 (.40 ) + 4.5 (.10 ) = 1.38
EV ( Parking lot ) = 1.5 (.50 ) + 1.9 (.40 ) + 2.4 (.10 ) = 1.75
EV ( Warehouse ) = 1.7 (.50 ) + 1.4 (.40 ) + 1.0 (.10 ) = 1.51
EV ( Shopping mall ) = 0.7 (.50 ) + 2.4 (.40 ) + 3.6 (.10 ) = 1.67
EV ( Condominiums ) = 3.2 (.50 ) + 1.5 (.40 ) + .06 (.10 ) = 2.26 maximum
Select Condominium project
b) EVPI = Expected value of perfect informationexpected value without perfect information
= 3.012.26 = $0.75 million
S1-5. a.
b.
c.
d.
Maximax: Risk fund, maximax payoff = $167, 000
Maximin: Savings bond maximin payoff = $30, 000
Equal likelihood: Bond fund, maximum payoff = $35, 000
Best decision, given probabilities: Bond fund, maximum payoff = $35, 000
S1-7. a.
Product
Widget
Expected Value
160, 000 ( 0.2 ) + 90,000 ( 0.5) 50, 000 ( 0.3) = $62, 000
Hummer
70, 000 ( 0.2 ) + 40, 000 ( 0.5 ) + 20, 000 ( 0.3) = $40, 000
Nimnot
45, 000 ( 0.2 ) + 35,000 ( 0.5 ) + 30, 000 ( 0.3) = $35,500
The best option is to introduce the widget.
b. EV given perfect information:
160, 000 ( 0.2 ) + 90, 000 ( 0.5) + 30, 000 ( 0.3) = $86,000.
EV without perfect information: Widget at $62,000.
Value of perfect information: $86, 000 $62, 000 = $24, 000
The company would consider this a maximum; since perfect information is rare, it would probably pay
less than $24,000.
c. Maximax: Introduce widget, maximax payoff = $160, 000
Maximin: Introduce nimnot, maximin payoff = $30, 000.
Minimax regret: widget, Introduce Minimax regret = $80, 000
Equal likelihood: Introduce widget, maximum payoff = $66, 000
S1-9.
Publication Decision
Paperback
Similar revision
Major content revision
Major physical revision
Expected Value
$216,290
386,340
468,780
405,970
Best decision = major content revision
Overall best decision appears to be a major content revision
EVPI = (.23)(68,000) + (.46)(515,000) + (.31)(972,000) 468,780
= $85,080
This is the maximum amount Wiley would pay an expert for additional information about the future
competitive market.
S1-15
Service Facility
Child care center
Swimming pool
Lockers and showers
Food court
Spa
Expected Value
$30,560
7,610
44,150
15,440
20,580
Best decision = Lockers and showers
S1-16. a.
Payoff table:
Stock (lb)
20
21
22
23
24
20
0.10
20.00
18.50
17.00
15.50
14.00
21
0.20
20.00
21.00
19.50
18.00
16.50
Demand
22
0.30
20.00
21.00
22.00
20.50
19.00
23
0.30
20.00
21.00
22.00
23.00
21.50
24
0.10
20.00
21.00
22.00
23.00
24.00
EV ( 20 ) = $20
EV ( 21) = 18.50 ( 0.1) + 21( 0.2 ) + 21( 0.3) + 21( 0.3) + 21( 0.1) = $20.75
EV ( 22 ) = 17 ( 0.1) + 19.50 ( 0.2 ) + 22 ( 0.3) + 22 ( 0.3) + 22 ( 0.1) = $21.00
EV ( 23) = 15.50 ( 0.1) + 18 ( 0.2 ) + 20.50 ( 0.3) + 23 ( 0.3) + 23 ( 0.1)
= $20.50
EV ( 24 ) = 14 ( 0.1) + 16.50 ( 0.2 ) + 19 ( 0.3) + 21.50 ( 0.3) + 24 ( 0.1)
= $19.25
Order 22 lb of apples for a profit of $21.00.
b. Maximax: Stock 24 lb for a maximax profit of $24.00.
Maximin: Stock 20 lb for a maximin profit of $20.00.
S1-17. a. Payoff table:
Demand
Stock (lb)
(boxes)
25
26
27
28
29
30
25
0.10
50
49
48
47
46
45
26
0.15
50
52
51
50
49
48
27
0.30
50
52
54
53
52
51
28
0.20
50
52
54
56
55
54
29
0.15
50
52
54
56
58
57
EV ( 25 ) = 50 ( 0.1) + 50 ( 0.15 ) + 50 ( 0.3) + 50 ( 0.2 ) + 50 ( 0.15) + 50 ( 0.1) = $50.00
EV ( 26 ) = 49 ( 0.1) + 52 ( 0.15 ) + 52 ( 0.3) + 52 ( 0.2 ) + 52 ( 0.15) + 52 ( 0.1) = $51.70
EV ( 27 ) = 48 ( 0.1) + 51( 0.15 ) + 54 ( 0.3) + 54 ( 0.2 ) + 54 ( 0.15) + 54 ( 0.1) = $52.95
EV ( 28 ) = 47 ( 0.1) + 50 ( 0.15) + 53 ( 0.3) + 56 ( 0.2 ) + 56 ( 0.15 ) + 56 ( 0.1)
= $53.30
30
0.10
50
52
54
56
58
60
EV ( 29 ) = 46 ( 0.1) + 49 ( 0.15 ) + 52 ( 0.3) + 55 ( 0.2 ) + 58 ( 0.15) + 58 ( 0.1)
= $53.05
EV ( 30 ) = 45 ( 0.1) + 48 ( 0.15) + 51( 0.3) + 54 ( 0.2 ) + 57 ( 0.15) + 60 ( 0.1)
= $52.35
Best decision: Stock 28 boxes, for a profit of $53.30.
b. Expected value under uncertainty:
EV = 500 ( 0.10 ) + 52 ( 0.15) + 54 ( 0.30 ) + 56 ( 0.20 ) + 58 ( 0.15) + 60 ( 0.10 ) = $54.90
EVPI = $54.90 $53.30 = $1.60
S1-18. a) Stock 25, maximum of minimum payoffs = $50
b) Stock 30, maximum of maximum payoffs = $60
c) 25 : 50 (.4 ) + 50 (.6 ) = 50;
26 : 52 (.4 ) + 49 (.6 ) = 50.2;
27 : 54 (.4 ) + 48 (.6 ) = 50.4;
28 : 56 (.4 ) + 47 (.6 ) = 50.6; 29 : 58 (.4 ) + 46 (.6 ) = 50.8; 30 : 60 (.4 ) + 45 (.6 ) = 51; stock 30 boxes.
d) Stock 28 or 29 boxes; minimum regret = $4.
S1-20.
1-28.
EV ( snow shoveler ) = $30 (.12 ) + 60 (.19 ) + 90 (.24 ) + 120 (.22 ) + 150 (.13) + 180 (.08 ) + 210 (.02 ) = $101.10
The cost of the snow blower ($575) is much more than the annual cost of the snow shoveler, thus on the
basis of one year the snow shoveler should not be purchased. However, the snow blower could be used for an
extended period of time such that after approximately 6 years the cost of the snow blower would be
recouped. Thus, the decision hinges on weather or not the decision maker thinks 6 years is too long to wait to
recoup the cost of the snow blower.
S1-29.
Since cost of installation ($900,000) is greater than expected value of not installing ($552,000), do not install
an emergency power generator
S1-30.
Select strategy 3; Change oil regularly; EV = $98.80
S1-31.
Select Strategy 4; Change oil and sample; EV = $716.40
S1-32. a.
b.
.98 9.2 x + 1.5 (1 x ) + (.02 )(1.5 ) = 3.810
.98 [ 7.7 x + 1.5] + .030 = 3.810
7.546 x + 1.47 + .030 = 3.810
7.546 x = 2.31
x = .306 probability of winning in overtime
S1-33.
S1-35.
S1-36.