# DecisionTreePrimer 4

Topics: Decision theory, Decision tree, Influence diagram Pages: 14 (2662 words) Published: November 15, 2014
CHAPTER 4

Solutions for Exercises

4.1 Chapter 1 Exercise Solutions

Exercise 1.1. Arthrodax Company
i) Figure 4.1 shows the decision tree.
ii) As the decision tree shows, the preferred alternative is to accept the order and purchase the injection molder, with an expected pro¯ t of \$154.4 thousand. Exercise 1.2. Arthrodax Company (con't)

i) Figure 4.2 shows the decision tree.
ii) As the decision tree shows, the preferred alternative is to accept the order and purchase the cases, with an expected pro¯ t of \$99.9 thousand. Exercise 1.3. Arthrodax Company (con't)
i) Figure 4.3 shows the decision tree. Note that in addition to the alternatives shown in this decision tree, it would be possible to immediately purchase the injection molder, or to immediately reject the purchase of the injection molder, without waiting to determine how many units will be ordered. These alternatives are shown in Figure 4.2 for the preceding exercise. Of course, these alternatives cannot be more preferred than the alternative of waiting to see how many units are ordered, since it costs nothing to wait, and you gain further information by waiting.

ii) As the decision tree shows, the preferred strategy is to accept the order, and if Ranger orders 100 units then purchase the molder while if Ranger orders 50 units purchase the cases. The expected pro¯ t for this strategy is \$102.1 thousand. Exercise 1.4. Aba Manufacturing

i) This would potentially avoid the second \$250,000 setup cost. ii) Figure 4.4 shows the decision tree for this part.
iii) From the decision tree, we see that the preferred alternative is to manufacture all 200,000 PC boards now.

40

CHAPTER 4 SOLUTIONS FOR EXERCISES

Fixed
Cost

Molder
Variable
Successful?
Cost
Yes

Revenue

\$208

\$500

\$252

\$500

\$252

\$500

(0.6)
Purchase Molder

\$120

Purchase Cases

No

\$100

Reject Ranger Offer

Figure 4.1

\$148
\$0

Units
Purchased

Molder
Variable
Successful?
Cost

Revenue

\$208

\$500

No

\$252

\$500

Yes

\$104

\$300

\$126

\$300

\$252

\$500

\$126

\$300

Yes
(0.6)
100
(0.35)

Purchase
Molder \$120

(0.4)
(0.6)
50

(0.65)

50

\$172

\$128
\$76

EV=\$67.2
(0.4)

100
Purchase
(0.35)
Cases \$100
EV=\$99.9

Net
Profit

EV=\$154.4

EV=\$97.7

(0.65)

No

Reject Ranger
Offer

Figure 4.2

\$128

Arthrodax Company decision tree (dollar amounts in thousands) Fixed
Cost

EV=\$99.9

\$172

EV=\$154.4
(0.4)

EV=\$154.4

Net
Profit

\$54
\$148

\$74
\$0

Arthrodax uncertain units decision tree (dollar amounts in thousands) Exercise 1.5. Kezo Systems
i) The decision tree is shown in Figure 4.5.
ii) The expected value calculations are shown on the decision tree for part a, and these show that Kezo should order all 500,000 PAL chips from KEC. Exercise 1.6. Intermodular Semiconductor Systems

i) The decision tree for this exercise is shown in Figure 4.6. ii) The expected values are shown on the Figure 4.6 tree for each of the four possible alternatives. The preferred alternative is to bid \$5,000.

41

4.1 CHAPTER 1 EXERCISE SOLUTIONS

Units
Ordered

Fixed
Cost

Molder
Variable
Successful?
Cost
Yes

Purchase
Molder
\$120

Accept
Offer

(0.65)
50
EV=\$102.1
EV=\$74.0

\$500

\$252

\$500

\$252

\$500

\$104

\$300

\$126

\$300

\$126

\$300

(0.4)

No

Yes
Purchase
Molder
\$120

(0.6)

\$128
\$148
\$76

EV=\$67.2
(0.4)

No

Purchase
Cases
\$100

Reject Ranger Offer

Figure 4.3

\$172

EV=\$154.4

Purchase
Cases
\$100

EV=\$102.1

\$208

(0.6)

EV=\$154.4
100
(0.35)

Revenue Net
Profit

\$54
\$74
\$0

Arthrodax delay molder decision tree (dollar amounts in thousands)

Immediate Cost
Quantity
Manufactured

Immediate
Revenue

Future
Quantity
Required
100

Cost

Revenue

\$450

\$500

0

\$0

\$0

100

\$0

\$500

\$0

\$0

(0.5)
100

\$450

\$500

Net...

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