Project Scheduling, Probability and Decision Models

Chapter 1: Models and Methods

Models: Mathematical, Analog, Iconic

• Mathematical model - It represents a real-world problem and is based on mathematical formulas and expressions.
• Analog model - It is physical in form but it does not physically resemble the object being modeled.
• Iconic model - A look-alike representation of real objects. It's a scalar representation.

CPM and PERT

PERT — Program Evaluation and Review Technique: nodes represent activities and arcs reflect the precedence relationships.

Critical path (CP) for the network is a path consisting of activities with zero slack.

Activity Table and Slack Rules

1. In a list of activity table, only the immediate predecessor of each activity needs to be listed for that activity — True.
2. In the most basic activity table, which of the following times should be included — expected completion time.
3. To calculate the slack in CPM/PERT you can take either Latest Start − Earliest Start or Latest Finish − Earliest Finish — True.

The critical path is determined by the tasks with slack = 0 — True.

4. When using uncertainty in task times, the expected time for the project is given by the sum of the expected values of all the tasks in the project — False.
5. When using uncertainty in task times, the variance for completion time for the project is given by the sum of the variance for all the tasks in the project — False.

Formulas and Notes

• Slack = LF − EF or LS − ES
• Mean (expected time) = (a + 4m + b) / 6, where a = optimistic estimate, m = most likely estimate, b = pessimistic estimate.
• Variance = ((b − a) / 6)^2. Standard deviation (SD) = sqrt(variance).
• 90th percentile = the area under the curve equal to 0.90 (90%).

Decision Strategy

EVWOPI = just the expected value (EV) for the best decision in the basic decision tree — no further calculations are needed.

EVWPI = the expected value of payoffs if we could determine which state would occur.

Decision Criteria and Properties

• The decision criteria is prescriptive; that is, it tells us how we must make decisions properly — False.
• A conservative decision maker would use which criteria for his or her decision, based on a payoff table — MAXIMIN.
• Which of the following is NOT a property of a binomial experiment? — The probability of failure, denoted by 1 − p, can change from trial to trial.

Random Variables and Probability Rules

• A random variable assigns a number to the outcome of a categorical variable to make it quantitative. Random variables are never used for quantitative variables — False.
• In a random variable table, each probability must be between 0 and 1, inclusive of 0 and 1 — True.
• P(A and B) = P(A)P(B) is always true, whether or not A and B are independent events — False.