Lecture 4 Program Evaluation and Review Technique.pptx
- 1. Program Evaluation and Review Technique (PERT) CSE347 – System Analysis and Design Instructor Prof. Shamim H Ripon, PhD Department of CSE, East West University
- 2. Network Diagram Rules Project network or project diagram can be constructed by using the following rules: • Node 1 represents the start of the project. An arc should lead from node 1 to represent each activity that has no predecessors. • A node (called the finish node) representing the completion of the project should be included in the network. • Number the nodes in a way that the node representing the completion of an activity has larger number that the beginning of the activity • An activity should not be represented by more than one arc in the network. • Two nodes can be connected by at most one arc.
- 4. Example
- 6. Example: PERT The following table shows the job of a network along with their time estimates Task Dependency Estimated Duration (Week) Optimistic (to) Most Likely (tm) Pessimistic (tp) A None 1 7 13 B A 2 14 26 C A 2 5 8 D B 7 10 19 E C 5 5 17 F None 2 5 14 G F 5 8 29 H D, E 3 3 9 I G 8 17 32
- 7. Find solution of the following questions 1. Draw the project Network 2. Find the expected duration and variance of each activity 3. Calculate the earliest and latest occurrence for each event 4. Calculate expected project length 5. Calculate the variance and standard deviations of the project length 6. Find the probability of the project completing in 40 days
- 8. • PERT is a probabilistic method, where the activity times are represented by a probability distribution. • This distribution of activity times is based on three different time estimates made for each activity 1. Optimistic time estimate (to or a) 2. Most likely time estimate (tm or m 3. Pessimistic time estimate (tp or b) The expected time of an activity Variance of an activity
- 9. Example: PERT The following table shows the job of a network along with their time estimates Task Dependency Estimated Duration (Week) Optimistic (to) Most Likely (tm) Pessimistic (tp) A None 1 7 13 (1+4*7+13)/6= 7 B A 2 14 26 14 16 C A 2 5 8 5 1 D B 7 10 19 11 4 E C 5 5 17 7 4 F None 2 5 14 6 4 G F 5 8 29 11 16 H D, E 3 3 9 4 1 I G 8 17 32 18 16
- 11. 1 2 4 3 6 7 5 8 A(7) B(14) C(5) D(11) E(7) F(6) G(11) I(18) 0 7 21 12 32 36 6 17 H(4) Latest Time Earliest Time
- 13. Critical Activity: An activity is said to be critical if the total float (TFij) for any activity (ij) is zero Critical Path condition: i. ESi = LFi ii. ESj = LFj iii. ESj – ESi = LFj – LFi = Tij
- 15. Task Dependency Estimated Duration (Week) Optimistic (to) Most Likely (tm) Pessimistic (tp) A None 1 7 13 (1+4*7+13)/6= 7 B A 2 14 26 14 16 C A 2 5 8 5 1 D B 7 10 19 11 4 E C 5 5 17 7 4 F None 2 5 14 6 4 G F 5 8 29 11 16 H D, E 3 3 9 4 1 I G 8 17 32 18 16 Critical Path: 1 – 2 – 3 – 5 – 8 Expected Project Length: A + B + D + H = 7+14+11+4 = 36 weeks Project Length variance, = 4 + 16 + 4 + 1 = 25 Project Length standard deviation, = 5
- 16. Find the probability of the project completing in 40 days Calculate the standard normal variable Where, - the schedule time to complete the project - Normal expected project length - Expected standard deviation of the project
- 17. The probability that the project will be completed in 40 days in given by = 0.7781 = 77.81%
- 18. Activity Predecessor(s) Duration (Weeks) O M P A None 5 6 7 B None 1 3 5 C None 1 4 7 D A 1 2 3 E B 1 2 9 F C 1 5 9 G C 2 2 8 H E, F 4 4 10 I D 2 5 8 J H, G 2 2 8 Try the following Example