Project Management & Decision Theory

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Q1. Consider a project which involves a number of different activities (labelled A, B, C, etc.). The precedence relationships and duration times of these activities are given in following table:
Activity
Predecessors
Duration (weeks)

a) Show the project network (using AON).
b) Determine the minimum time for project completion.
c) Which activities are critical to completing the project in minimum time?
Suppose it is possible to crash some of the activities according to the table provided below.
Activity
Normal Duration (weeks)
Crash Duration (weeks)
Normal Cost ($)
Crash Cost ($)
d) What is the minimum crash completion time and the associated cost? Which activities should be crashed?
e) Determine which activities should be crashed if the project must be completed in 20 weeks and the associated crashing cost. Which activities should be crashed?
2
Q2. Consider a project which involves a number of different activities (labelled A, B, C, etc.).The precedence relationships and estimates of duration times (in months) for these activities are given in the table below.
a) Draw the project AON diagram.
b) Determine the critical path.
c) What is the expected project completion time?
d) What is the standard deviation associated with this expected completion time?
Activity
Predecessors
Optimistic
Time
Most Likely
Time
Pessimistic
Time

Q3. At the beginning of the day, a shop needs to choose if to sell umbrellas or hats. The profits associated with the two alternative strategies will depend on weather. There are two possible states of nature: rain and sunshine. The profits the shop will get in these two alternative scenarios for each strategy are summarized below:
Rain
Sunshine
Umbrella
100
600
Hats
200
300
The shop thinks that the probability of having sunshine is 0.3. What is the strategy the shop should choose under the following alternative decision making criteria (show your working):
a) Maximin;
b) Maximax;
c) Hurwicz, with a coefficient of 0.4;
d) Minimax Regret;
e) Expected value.

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