- Expected completion times and variance attached.
Using PERT charts and the optimistic, most likely and pessimistic times, we can estimate the expected time for each activity. PERT assumes the beta probability distribution for time estimates. A beta distribution can be used to estimate the expected time for each activity using weighted average (Karen K. Kirst-Ashman, 2011).
In the case of variance, three standard deviations are assumed to exist between the optimistic and the pessimistic values.
Thus variance = [(Pessimistic – Optimistic )/6 ]2.
The critical path is the longest path duration of the project. Slack time is the amount of time that a non – critical path activity can be delayed without delaying the activity (Karen K. Kirst-Ashman, 2011). Critical path has the following characteristics; (Biafore, 2010)
- Earliest start - ES.
- Earliest Finish – EF.
- Latest Start – LS.
- Latest Finish – LF.
- PERT CHART ATTACHED
- The expected duration of the entire project is determined from the critical path to be 33.5 weeks.
- Likewise slack for project task H is given by (LS- ES ) = (19-18.5) = 0.5 weeks.
- Project I is scheduled to finish on week 30. The Earliest start and Earliest finish of this task is week 23.5 and it takes 6.5 weeks thus, 23.5 + 6.5 =30.
In order to calculate the probability of completing a given task we must first calculate the variance of the beta probability distribution as follows. (Karen K. Kirst-Ashman, 2011)
Where p is the pessimistic time estimate and of the optimistic time estimate.
Path variance is given as follows;
The probability of completing the project in 34 weeks is given by; (Biafore, 2010)
Sum of variances of the critical path = 1.78 + 0.44 + 1.36 + 2.25 + 0.69 = 6.52 weeks
Standard deviation = sqrt(6.52) = 2.55(approximately)
Probability = 0.5777 or 57.77%
- Maximum reduction in time = Normal – Crash (weeks).
- Crash cost /week = crash cost - normal cost / max. reduction time. Results shown in the table below.
Suppose the project should be reduced from 33.5 weeks to 30 weeks then, the activities to be crashed in order to complete the project in 30 weeks are the most critical and the least expensive on the critical path first based on cost per week (Karen K. Kirst-Ashman, 2011).
For reducing time from 33.5 weeks to 30 weeks, Activity F with lowest crash cost per week
among all critical activities should be crashed by 3.5 weeks. This project completion time reduces to 30 weeks but B-D-H-J becomes critical path. Now choose the activity on this path with lowest crash cost per week. Which is activity D, reduce it by 3 weeks.
2. Number of weeks each of these activities should be crashed to meet the deadline with the lowest possible increase in cost
D 3 weeks
F 3.5 weeks
If we reduce the number of weeks of F activity by 3.5 days then extra cost
= 3.5*1000 = $3500
If we reduce the number of weeks of D activity by 3 days then extra cost
= 3*1778 = $5334
Total increase in cost = 5334+3500 = $8834
Biafore, B. (2010). Microsoft Project 2010: The Missing Manual. O'Reilly Media.
Karen K. Kirst-Ashman, G. H. (2011). Generalist Practice with Organizations and Communities. Cengage Learning.