Pert and cpm

Detail description of PERT and CPM from the point of algorithmist, Computer Science

1. PERT & CPM Submitted By:- Shashank kapoor Mechanical , 154169

2. What is the PERT & CPM ? It is nothing but the technique used in Network analysis of project management, such as planning , management and control of project. So, what is project ?? “ A project is a series of activities directed to accomplishment of a desired objective.” Plan your work first…..then work your plan

3. Project Evaluation & Review Techniques (PERT) In PERT is basically a method to analyze the tasks involved in completing a given project , especially the time needed to complete each task, and to identify the minimum time needed to complete the total project. – Multiple time estimates – Probabilistic activity times USED IN : Project management - for non-repetitive jobs (research and development work), where the time and cost estimates tend to be quite uncertain. This technique uses probabilistic time estimates.

4. Critical Path Method ( CPM) In CPM activities are shown as a network of precedence relationships using activity-on-node network construction. – Single estimate of activity time – Deterministic activity times USED IN : Production management - for the jobs of repetitive in nature where the activity time estimates can be predicted with considerable certainty due to the existence of past experience .

5. KEY ELEMENTS Arrows:- leading from tail to head directionally Indicate Activity Nodes:- Indicate Event, a point in time where one or more activities start and/or finish. Earliest time: It is categorized in two sub elements. 1. Earliest Starting time (ES):- Time at which the activity can start 2. Earliest finishing time(EF):- Equals to the earliest start time for the activity plus the time required to complete the activity Latest time : It is categorized in two sub elements. 1.Latest Starting time (LS):- Time in which the activity can be completed without delaying 2.Latest Finishing time (LF):- equal to the latest finish time minus the time required to complete the activity. S lack time:- The difference between its earliest and latest start time. Critical Path:- The path of activities having zero Slack time.

6. KEY ELEMENTS Optimistic time (a): – It is the shortest time in which the activity can be completed. Most likely time ( m ) – It is the probable time required to perform the activity. Pessimistic time (b) – It is the longest estimated time required to perform an activity . Expected time ( Te ) – approximation time taken to complete an activity. T e Standard deviation (  ) – Higher the SD is the greater amount of uncertainty exists Variance ( Large variance indicates great uncertainty, a small variance indicates a more accurate estimate     

7. ILLUSTRATION ON PERT

8. SOLUTION Activity Optimistic Time (a) Most likely Time(m) Pessimistic Time (b) Expected Time ( Te ) Standard Deviation  1-2 1 1 7 2 1 1-3 1 4 7 4 1 1-4 2 2 8 3 1 2-5 1 1 1 1 3-5 2 5 14 6 2 4-6 2 5 8 5 1 5-6 3 6 15 7 2

9. SOLUTION

10. CRITICAL PATH Paths:- 1-2-5-6 = 2+1+7=10 1-3-5-6 = 4+6+7=17 1-4-6 = 3+5=8 1-3-5-6 is critical path since it take maximum time.

11. CRITICAL PATH NODE LC-ES TOTAL 1 0-0 2 9-2 7 3 4-4 4 12-3 9 5 10-10 6 17-17 On Analyzing the Node which having total =0 is 1-3-5-6 Hence it is critical path

12. PROBABILISTIC DETERMINATION What is the Probability of it taking 20 weeks? Critical Path = 1 -3-5-6 = 17 weeks T = 2 weeks C = 17 weeks   (Variance)   = 1   Look up Z value in normal distribution table P z = .8413 or 8 4 . 13 % Going over 20 weeks would be 100 – 84.13 = 15.87% (Probability of it taking 20 weeks)

13. ILLUSTRATION ON CPM

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25. CRITICAL PATH Paths:- 1-2-5-7-8=2+1+2+1=6 days 1-3-5-7-8=3+2+2+1=8 days 1-3-6-7-8=3+5+3+1=12days 1-4-6-7-8=4+7+3+1=15 days 1-4-6-7-8 is critical path since it take maximum time.

26. CRITICAL PATH NODE LC-ES TOTAL 1 0-0 2 11-2 9 3 6-3 3 4 4-4 5 12-5 7 6 11-11 7 14-14 8 15-15 On Analyzing the Node which having total =0 is 1-4-6-7-8 Hence it is critical path

27. What happen if we have large number of Network problem??

28. Conclusion For large number of network problem Ford F ulkerson Max Flow Algorithm is the point that can give us the optimal critical path since it is use for finding the maximum flow in a flow network for single source and single sink.

29. THANK YOU