Simulation, Decision Theory, Learning Curve and Network Analysis — Practice

Question 1

Which decision rule is used when probabilities of future outcomes are known?

Accepted Answer

Expected Monetary Value (EMV) — used under risk.

Question 2

Which decision rule reflects an optimistic attitude, choosing the action with the best possible best-case outcome?

Accepted Answer

Maximax.

Question 3

Should a non-critical-path activity generally be crashed to shorten a project?

Accepted Answer

No — only critical-path activities, since shortening a non-critical activity does not reduce the project's overall duration.

Question 4

A strategy has payoffs of Rs. 60,000 (probability 0.3) and Rs. 20,000 (probability 0.7). Compute its EMV.

Accepted Answer

EMV = (0.3 x 60,000) + (0.7 x 20,000) = 18,000 + 14,000 = Rs. 32,000.

Question 5

An activity has normal time 8 days at Rs. 16,000, and crash time 5 days at Rs. 25,000. Compute the crash cost per day.

Accepted Answer

Crash cost per day = (25,000 - 16,000) / (8 - 5) = 9,000 / 3 = Rs. 3,000 per day.

Question 6

A machine's daily breakdown probability distribution is: 0 breakdowns (60%), 1 breakdown (30%), 2 breakdowns (10%). Assign random number ranges (00-99) to each outcome.

Accepted Answer

0 breakdowns: 00-59 (60%). 1 breakdown: 60-89 (30%). 2 breakdowns: 90-99 (10%).

Question 7

A payoff table (in Rs. '000) shows three strategies under two possible future states: Strategy 1 (State A: 50, State B: 10), Strategy 2 (State A: 30, State B: 30), Strategy 3 (State A: 60, State B: -10). Apply the Maximin rule and explain the choice.

Accepted Answer

Worst-case outcomes: Strategy 1 = 10, Strategy 2 = 30, Strategy 3 = -10. Maximin chooses the best of these worst-case outcomes: max(10, 30, -10) = 30, so Strategy 2 is chosen. This reflects a cautious, pessimistic decision-maker who wants to guarantee the best possible outcome even if the worst state actually occurs, accepting a lower potential upside (Strategy 3's 60 in State A) in exchange for protection against a bad downside (Strategy 3's -10 in State B).

Question 8

A project has two critical-path activities: Activity P (crash cost per day Rs. 1,800, can be crashed by up to 3 days) and Activity Q (crash cost per day Rs. 2,500, can be crashed by up to 2 days). The project needs to be shortened by 4 days. Determine the crashing plan and its total cost.

Accepted Answer

Crash the cheaper activity (P) first, up to its maximum of 3 days, at a cost of 3 x Rs. 1,800 = Rs. 5,400, achieving 3 of the required 4 days' reduction. The remaining 1 day must come from Activity Q (since P's crashing limit is reached), at a cost of 1 x Rs. 2,500 = Rs. 2,500. Total crashing cost = Rs. 5,400 + Rs. 2,500 = Rs. 7,900 for the full 4-day reduction — note that in a full exam answer, the critical path should also be re-verified after each crashing step to confirm it has not shifted to a different path.

Practice — Simulation, Decision Theory, Learning Curve and Network Analysis

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