Question

a small project consisting of eight activities has the following characteristics: time - estimates (in weeks) activity preceding activity most optimistic time (a) most likely time (m) most pessimistic time (b) a none 2 4 12 b none 10 12 26 c a 8 9 10 d a 10 15 20 e a 7 7.5 11 f b, c 9 9 9 g d 3 3.5 7 h e, f, g 5 5 5 a) draw the pert network for the project. b) prepare the activity schedule for the project. c) determine the critical path. d) if a 30-week deadline is imposed, what is the probability that the project will be finished within the time limit

Answer 1

To answer the student's questions involving a PERT network, the steps include constructing a network diagram, preparing an activity schedule, determining the critical path, and calculating the probability of meeting a 30-week deadline using the Z-score in relation to the project's standard deviation.

The student's project involves eight activities with given optimistic (a), most likely (m), and pessimistic (b) time estimates for completion. To address the student's questions:

1. Construct a PERT (Program Evaluation and Review Technique) network diagram for the project, showing all activities, dependencies, and time estimates.
2. Prepare an activity schedule by calculating the expected time for each activity using the formula: Expected Time (TE) = (a + 4m + b) / 6.
3. Determine the critical path by identifying the longest path through the network, which is the path that dictates the minimum project duration.
4. Calculate the probability that the project will finish within a 30-week deadline using PERT's statistical tools, specifically the Z-score formula, and standard project variance.

As for the probability calculation, if the project deadline is imposed at 30 weeks, one would need the standard deviation of the project completion time to calculate a Z-score, and subsequently use the standard normal distribution table to find the corresponding probability.

Answer 2

To draw the PERT network, identify dependencies and create the network. Prepare the activity schedule by calculating earliest and latest times. Determine the critical path. The project cannot be finished within the 30-week deadline.

Step-by-step explanation:

To draw the PERT network for the project, we need to identify the activities and their dependencies. From the given information, we can create the following network:

To prepare the activity schedule, we need to determine the earliest start time (ES), earliest finish time (EF), latest start time (LS), and latest finish time (LF) for each activity. Using the PERT network, we can calculate these times:

The critical path is the longest path from the start node to the end node in the network. In this case, the critical path is A - B - F - H, with a duration of 35 weeks. Any delay in activities on the critical path will delay the overall project.

To find the probability that the project will be finished within the 30-week deadline, we can use the concept of critical path. Since the critical path duration (35 weeks) is greater than the deadline (30 weeks), it is not possible to finish the project within the time limit.