Tom Schriber, a director of personnel of Management Resources, Inc., is in the process of designing a program that its customers can use in the job-finding process. Some of the activities include preparing resumés, writing letters, making appointments to see prospective employers, researching companies and industries, and so on. Some of the information on the activities is shown in the following table:
(1) Construct a network for this problem.
(2) Determine the expected time and variance for each activity.
(3) Determine ES, EF, LS, LF, and slack for each activity.
(4) Determine the critical path and project completion time.
(5) Determine the probability that the project will be finished in 70 days or less.
(6) Determine the probability that the project will be finished in 80 days or less.
(7) Determine the probability that the project will be finished in 90 days or less.
no ideas of your own? There's a small chance someone here will do this considerable body of work for you, especially since you provide no data.
To solve this problem, you will need to perform a critical path analysis, which involves constructing a network, determining the expected time and variance for each activity, calculating the ES, EF, LS, LF, and slack for each activity, identifying the critical path, and finally, determining the project completion time and the probabilities of finishing within specific time frames.
Here's how you can approach each step:
1. Construct a network: First, create a flowchart or diagram representing the activities and their dependencies. Each activity should be represented as a node, and the arrows should indicate the sequence and dependencies between activities.
2. Determine the expected time and variance for each activity: For each activity, estimate the time it will take to complete. You should also calculate the variance, which measures the uncertainty or variability associated with the completion time. The expected time and variance can be determined based on historical data, expert judgment, or a combination of both.
3. Determine ES, EF, LS, LF, and slack for each activity: ES (Earliest Start), EF (Earliest Finish), LS (Latest Start), LF (Latest Finish), and slack are essential parameters for analyzing project scheduling. Start by calculating the earliest start and earliest finish times for each activity, working forward through the network. Then, calculate the latest start and latest finish times, working backward through the network. Finally, calculate the slack for each activity (slack = LF - EF or LS - ES).
4. Determine the critical path and project completion time: The critical path is the longest path in the network, consisting of activities with zero slack. The project completion time is the total duration of the critical path. By summing up the durations of activities on the critical path, you can determine the project completion time.
5. Determine the probability that the project will be finished in 70 days or less: To calculate this probability, you need to use the expected time and variance for each activity. By summing up the expected times for all activities on the critical path, you can find the expected project completion time. Then, using the variances of these activities, calculate the standard deviation of the critical path. Finally, use statistical tables or software to find the probability of completing the project in 70 days or less based on the expected completion time and standard deviation.
6. Determine the probability that the project will be finished in 80 days or less: Follow the same procedure as in step 5, but use the desired completion time of 80 days to calculate the probability.
7. Determine the probability that the project will be finished in 90 days or less: Repeat the process outlined in step 5, using the desired completion time of 90 days for the calculation.
Keep in mind that the calculations for steps 5, 6, and 7 require knowledge of probability theory and statistical tools, such as the normal distribution and Z-scores.
By following these steps, you will be able to construct the network, calculate the expected times and variances, determine the ES, EF, LS, LF, and slack, find the critical path and project completion time, and calculate the probabilities of finishing the project within specific time frames.