Decision analysis

ADM2302 M, N, P and Q Assignment # 4

Winter 2020 Page 1

Assignment # 4

Decision Analysis and Project Scheduling

ADM2302 students are reminded that submitted assignments must be typed (i.e. can NOT be hand

written), neat, readable, and well-organized. Assignment marks will be adjusted for sloppiness, poor

grammar, spelling, for technical errors as well as if you submit a PDF file.

The assignment is to be submitted electronically as a single Word Document file via Brightspace by

Friday April 3rd prior to 23:59. Front page of the Word document has to include title of the assignment,

course code and section, student name and student number. Second page is the individual/group

statement of integrity that must be signed.

E-mail questions related to the assignment should be sent to the Teaching Assistant or posted on the

Brightspace course website “Discussion page” (viewed by all).

Section M: Parisa Keshavarz ([email protected])

Section N: : Niki Khorasanizadeh ([email protected])

Section P: Makbule Kandakoglu ([email protected])

Section Q: Afshin Kamyabniya ([email protected])

Problem 1: Payoffs/Decision Table (13 points)

A small building contractor has recently experienced two successive years in which work opportunities

exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year.

Estimated profits (in $ thousands) under each of the two possible states of nature are as shown in the

table below.

NEXT YEAR’S DEMAND

Alternative Low High

Do nothing

Expand

Subcontract

$50**

20

40

$60

80

70

** Profit in $ thousands.

Which alternative should be selected if the decision criterion is:

a. The optimistic approach? (3 points)

b. The conservative approach? (3 points)

c. Minimize the regret? (7 points)

Problem 2: Payoffs/Decision Table (15 points)

Dorothy Stanyard has three major routes to take to work. She can take Tennessee Street the entire way,

she can take several back streets to work, or she can use the expressway. The traffic patterns are,

however, very complex. Under good conditions, Tennessee Street is the fastest route. When Tennessee

is congested, one of the other routes is preferable. Over the past two months, Dorothy has tried each of

route several times under different traffic conditions. This information is summarized in minutes of

travel time to work in the following table:

ADM2302 M, N, P and Q Assignment # 4

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No Traffic Congestion

(Minutes)

Mild Traffic

Congestion

(Minutes)

Severe Traffic

Congestion

(Minutes)

Tennessee Street

Back roads

Expressway

15

20

30

30

25

30

45

35

30

In the past 60 days, Dorothy encountered severe traffic congestion 10 days and mild traffic congestion

20 days. Assume that the past 60 days are typical of traffic conditions.

a. What route should Dorothy take. Use the EP criterion. (10 points)

b. Dorothy is about to buy a radio for her car that would tell her the exact traffic conditions before

she started to work each morning. How much time in minutes on the average would Dorothy

save by buying the radio? (i.e. Calculate the EVPI) (5 points).

Problem 3: Decision Tree (30 points)

It is January 1 and Justin Case, chief counsel for Chemgoo, is faced with a difficult challenge. It seems

that the firm has two related lawsuits for patent infringement. For each suit, the firm has the option of

going to trial or settling out of court. The trial date for one of the suits, which we will cleverly identify

as suit 1, is scheduled for July 15 and the second (suit 2, of course) is scheduled for January 8, next

year.

Preparation costs for either trial are estimated at $10,000. However, if the firm prepares for both trials,

the preparation costs of the second trial will be only $6,000. These costs can be avoided by settling out

of court.

If the firm wins suit 1, it pays no penalty. If it loses, it pays a $200,000 penalty. Lawyers for the firm

assess the probability of winning suit 1 as 0.5. The firm has the option to settle suit 1 out of court for

$100,000.

Suit 2 can be settled out of court for a cost of $60,000. If you don’t settle suite 2 out of courts then a

trial will result in one of three possible outcomes:

(1) The suit 2 is declared invalid and the firm pays no penalty;

(2) the suit 2 is found valid but with no infringement, and the firm pays a penalty of $50,000; or

(3) the suit 2 is found valid with infringement, and the firm pays a penalty of $90,000.

The likelihood of these outcomes depends in general on the result of suit 1. The judge will certainly

view suit 1 as an important precedent. The lawyers’ assessment of the probability of the three possible

outcomes of suit 2 under three sets of possible conditions (relating to suit 1) are presented in the

following table:

OUTCOMES

NO INFORMATION

CONCERNING SUIT 1a FIRM WINS

SUIT 1

FIRM LOSES

SUIT 1

Invalid

Valid, No infringement

Valid, Infringement

0.3

0.3

0.4

0.7

0.2

0.1

0.1

0.5

0.4 a That is, suit 1 is settled out of court

ADM2302 M, N, P and Q Assignment # 4

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a. Represent the firm’s model with a decision tree. Solve to find the optimal strategy for the firm and the expected loss that the firm will incur if it follows the optimal strategy?

(25 points)

Hint: Since all the figures are costs, you may find it easier to work with the cost figures

and minimize the expected cost.

b. What decisions would be made if the firm treated each suit independently, ignoring any interactions between the two? What is the expected savings from the decision analysis

of this scenario? (5 points)

Problem 4: Project Scheduling (22 points)

Monohan Machinery specializes in developing weed-harvesting equipment that is used to clear small

lakes of weeds. George Monohan, president of Monohan Machinery, is convinced that harvesting

weeds is far better than using chemicals to kill weeds. Chemicals cause pollution, and the weeds seem

to grow faster after chemicals have been used. George is contemplating the construction of a machine

that would harvest weeds on narrow rivers and waterways. The activities that are necessary to build one

of these experimental weed-harvesting machines are listed in the following table.

ACTIVITY IMMEDIATE PREDECESSORS

A

B

C

D

E

F

G

H

__

__

A

A

B

B

C, E

D, F

a. Construct a network for these activities. (4 points)

After consulting with Butch Radner, George Monohan was able to determine the activity times for

constructing the weed-harvesting machine to be used on narrow rivers. The activity times are shown in

the following table:

ACTIVITY TIME (WEEKS)

A

B

C

D

E

F

G

H

6

5

3

2

4

6

10

7

b. Determine the ES, EF, LS, and LF time, and slack for each activity. (12 points) c. Determine the total project completion time and the critical path. (6 points)