PERT CPM- Operations Research Quiz

The correct answer is Critical Path Method (CPM). CPM is a project management technique used to identify the longest sequence of dependent activities in a project, known as the critical path. It helps in determining the minimum time required to complete a project and identifies the activities that cannot be delayed without delaying the entire project. CPM is widely used in project planning and scheduling to optimize resources and ensure timely completion of projects.

The answer is 0.6826 because the expected duration of the project is 47 days with a variance of 9 days. The expected time for project completion is 50 days. By using the Z-score formula, we can calculate the probability of completing the project within three days of the expected time. The Z-score for three days is (3 - 50) / √9 = -47 / 3 = -15.67. Looking up this Z-score in the Z-table, we find that the corresponding probability is 0.6826. Therefore, there is a 68.26% chance of completing the project within three days, more or less than the expected time.

The given answer states that CPM is event-oriented. This means that CPM focuses on identifying and sequencing specific events or activities that need to occur in a project. CPM does not consider the probabilistic nature of activities and does not involve calculating the expected time or probability of completion for each activity. Instead, it focuses on determining the critical path, which is the sequence of activities that takes the longest time to complete and determines the overall project duration. Therefore, the statement that CPM is event-oriented is correct.

The rule of network construction states that only one arrow should define each activity. This means that each activity should have a clear and unambiguous starting and ending point. The statement "Final nodes and identical initial can identify two activities" contradicts this rule, as it suggests that multiple activities can be identified by the same starting or ending point. Therefore, this statement is not a rule of network construction.

The given answer is incorrect because it states that an activity cannot be represented by more than one arrow. In reality, an activity can be represented by multiple arrows, but an arrow can only represent one activity.

The given answer states that "It is a critical activity" is not a true statement about activity 4-6. This means that activity 4-6 is not a critical activity. A critical activity is one that has zero float, meaning any delay in its completion will cause a delay in the overall project. Since the activity 4-6 has a total float of three days, it means that it can be delayed by up to three days without affecting the project's overall timeline. Therefore, it is not a critical activity.

The correct answer is "All of these." This means that all the options mentioned in the question are not required in Precedence relationships. The question is asking which option is not necessary when considering the predecessors of an activity. The correct answer implies that it is not necessary to focus on all the predecessors of an activity, but rather only the immediate ones. Additionally, any redundant predecessors should be dropped, meaning they are not required to be considered in the Precedence relationships.

The given relationship "Interfering float = Total float – Free float" is incorrect. Interfering float refers to the amount of float that affects the project's critical path, while total float represents the total amount of time a task can be delayed without delaying the project. Free float, on the other hand, refers to the amount of time a task can be delayed without delaying the start of any successor tasks. Therefore, the correct relationship should be "Interfering float = Total float + Free float".

The answer of 0.1587 represents the probability of not completing the project in 50 days. This probability is calculated using the Z-score and the standard normal distribution table. The Z-score is calculated by taking the difference between the expected duration of the project (47 days) and the given duration (50 days), and dividing it by the square root of the variance (9 days). The Z-score of 0.33 corresponds to an area of 0.1293 in the standard normal distribution table. Since the probability of not completing the project in 50 days is the area to the left of the Z-score, the answer is 0.1587.

The statement "Always choose the activity with the least crashing cost" is not true about crashing. While it may seem intuitive to choose the activity with the least crashing cost, it is not always the most effective strategy. The decision of which activity to crash should be based on a variety of factors, such as the impact on the critical path, the time saved, and the cost involved. It is important to carefully analyze these factors and make a strategic decision rather than simply choosing the activity with the lowest crashing cost.