Operations Research MCQ Quiz!

The correct answer is Critical Path Method. CPM is a project management technique that helps in identifying the most critical tasks and determining the shortest possible duration to complete a project. It involves identifying the critical path, which is the longest sequence of dependent tasks that determines the project's overall duration. By focusing on the critical path, project managers can prioritize resources and activities to ensure timely completion of the project.

The answer is 0.6826 because the given information includes the expected duration of the project and the variance. The expected time for project completion is 50 days, and the variance is 9 days. By using this information, we can calculate the standard deviation, which is the square root of the variance. In this case, the standard deviation is approximately 3 days. The probability of completing the project within three days more or less than the expected time is equivalent to the probability of completing the project within one standard deviation of the expected time. According to the empirical rule, this probability is approximately 68.26%. Therefore, the correct answer is 0.6826.

The given relationship "Interfering float = Total float – Free float" is incorrect because interfering float is a separate concept and is not equal to the difference between total float and free float.

The statement "Of all activities of the project, choose the activity with the least crashing cost" is not true about crashing. When crashing a project, the activity with the least crashing cost may not necessarily be the best choice. Instead, the focus should be on the critical path and choosing between critical activities only. The critical path is the sequence of activities that determines the project's overall duration, so it is important to prioritize these activities for crashing in order to minimize the project's duration.

The correct answer is "redundant predecessors should be dropped." This means that while considering precedence relationships, it is important to eliminate any unnecessary or redundant predecessors. This is because including redundant predecessors can lead to confusion and potential logical faults, such as the formation of a loop in the project schedule. Therefore, it is crucial to focus only on the predecessors that are essential for determining the sequence of activities.

The given information states that the E and L times at node 4 are 8 and 11, respectively, while at node 6, both are equal to 17. This means that the earliest start time (ES) of activity 4-6 is 8. Since the ES of the activity is provided, it implies that it is not a critical activity. Critical activities are those with zero float, meaning any delay in their completion will directly impact the project's overall duration. Therefore, the statement "It is a critical activity" is not true based on the given information.

The answer is 0.1587 because the question is asking for the probability of not completing the project in 50 days. To find this probability, we need to calculate the area under the standard normal distribution curve to the left of the Z-score corresponding to 50 days. The Z-score can be calculated by subtracting the expected duration from the given time and dividing it by the standard deviation. In this case, the Z-score is (50-47)/√9 = 1. Therefore, the area to the left of the Z-score of 1 is 0.1587. This represents the probability of not completing the project in 50 days.

This statement is incorrect because it states that A precedes B, B precedes C, and C precedes A. This is not possible in a network diagram as it creates a loop, which is not allowed in project management. In a network diagram, activities should have a clear sequence and should not have circular dependencies.

The given statement is true as CPM (Critical Path Method) is not event-oriented. CPM is a project management technique that focuses on determining the critical path, which is the longest sequence of activities that determines the project's duration. It does not explicitly consider events or milestones in its methodology. On the other hand, PERT (Program Evaluation and Review Technique) is event-oriented as it emphasizes the identification and sequencing of events or milestones in a project. Both CPM and PERT are project management techniques but differ in their approach and focus.

This statement is incorrect because a project network can only have one critical path. The critical path is the longest path in the network and determines the minimum time required to complete the project. Any delay in activities on the critical path will directly impact the project's completion time.