### CPM-PERT.ppt

1. 1 Project Scheduling CPM/PERT
2. 2  Network techniques  Developed in 1950’s  CPM by DuPont for chemical plants (1957)  PERT by Booz, Allen & Hamilton with the U.S. Navy, for Polaris missile (1958)  Consider precedence relationships and interdependencies  Each uses a different estimate of activity times PERT and CPM
3. why networks/CPM/PERT?  Gantt charts don’t explicitly show task relationships  don’t show impact of delays or shifting resources well  network models clearly show interdependencies
4. 4 Is the project on schedule, ahead of schedule, or behind schedule? Is the project over or under cost budget? Are there enough resources available to finish the project on time? If the project must be finished in less than the scheduled amount of time, what is the way to accomplish this at least cost? Questions Which May Be Addressed by PERT & CPM
5. 5 The Six Steps Common to PERT & CPM  Define the project and prepare the work breakdown structure,  Develop relationships among the activities. (Decide which activities must precede and which must follow others.)  Draw the network connecting all of the activities  Assign time and/or cost estimates to each activity  Compute the longest time path through the network. This is called the critical path  Use the network to help plan, schedule, monitor, and control the project
6. 6 Terminology  Activity: A specific or set of tasks required by the project  Event: Outcome of one or more activities  Network: Combination of all activities and events  Path: Series of connected activities or between any two events  Critical path: Longest - Any delay would delay the project  Slack/float: Allowable slippage for a path
7. 7 Activity Relationships Predecessor – an activity that is required to start or finish before the next activity(s) can proceed Successor – an activity that must start or finish after the previous activity can finish Types of relationships are defined from the predecessor to the successor
8. 8 1 A B A & B can occur concurrently 2 3 Activity Relationships
9. 9 1 4 2 3 A B C A must be done before C & D can begin D Activity Relationships
10. 10 1 4 2 3 A B E C B & C must be done before E can begin D Activity Relationships
11. AOA Project Network for a House 3 2 0 1 3 1 1 1 1 2 4 6 7 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house
12. 12  Activities are defined often by beginning & ending events  Every activity must have unique pair of beginning & ending events  Otherwise, computer programs get confused  Dummy activities maintain precedence  Consume no time or resources Dummy Activities
13. 13 Job on Arc Network  Not allowed: no two jobs can have the same starting and ending node!  Need to introduce a dummy job. A B D C A B D C
14. 14 1 4 3 1-2 2-3 Incorrect 1 4 2 3 5 2 2-3 3-4 1-2 2-3 2-4 4-5 3-4: Dummy activity Correct Dummy Activity Example
15. 15 Critical Path The longest continuous path of activities through a project, which determines the project end date
16. 16 A General Hospital’s Activities and Predecessors Activity Description Immediate Predecessors A - B - C A D A, B E C F C G D, E H F, G
17. 17 AON Network for General Hospital Start A B C D F F G H
18. Program Evaluation and Review Technique (PERT) PERT is based on the assumption that an activity’s duration follows a probability distribution instead of being a single value. The probabilistic information about the activities is translated into probabilistic information about the project.
19. PERT  reflects PROBABILISTIC nature of durations  assumes BETA distribution  same as CPM except THREE duration estimates optimistic most likely pessimistic
20. PERT Calculation a = optimistic duration estimate m = most likely duration estimate b = pessimistic duration estimate expected duration: variance: Te a + 4m + b 6 V = b - a 6        2
21. 21  3 time estimates  Optimistic times (a)  Most-likely time (m)  Pessimistic time (b)  Follow beta distribution  Expected time: t = (a + 4m + b)/6  Variance of times: v = (b - a)2/6 PERT Activity Times
22. 22 Variability of Completion Time for Noncritical Paths Variability of times for activities on non-critical paths must be considered when finding the probability of finishing in a specified time. Variation in non-critical activity may cause change in critical path.
23. 23 Advantages of PERT/CPM  Especially useful when scheduling and controlling large projects.  Straightforward concept and not mathematically complex.  Graphical networks aid perception of relationships among project activities.  Critical path & slack time analyses help pinpoint activities that need to be closely watched.  Project documentation and graphics point out who is responsible for various activities.  Applicable to a wide variety of projects.  Useful in monitoring schedules and costs.
24. 24 Questions Answered by CPM & PERT Completion date? On Schedule? Within Budget? Critical Activities? How can the project be finished early at the least cost?
25. 25  Assumes clearly defined, independent, & stable activities  Specified precedence relationships  Activity times (PERT) follow beta distribution  Subjective time estimates  Over-emphasis on critical path Limitations of PERT/CPM
26. Example 2. CPM with Three Activity Time Estimates Ta s k Im m e d ia t e P re d e c e s o rs O p t im is t ic M o s t L ik e ly P e s s im is t ic A N o n e 3 6 1 5 B N o n e 2 4 1 4 C A 6 1 2 3 0 D A 2 5 8 E C 5 1 1 1 7 F D 3 6 1 5 G B 3 9 2 7 H E , F 1 4 7 I G , H 4 1 9 2 8
27. Example 2. Expected Time Calculations T a s k Im m e d i a t e P re d e c e s o rs E x p e c t e d T i m e A N o n e 7 B N o n e 5 . 3 3 3 C A 1 4 D A 5 E C 1 1 F D 7 G B 1 1 H E , F 4 I G , H 1 8
28. Example 2. Probability Exercise What is the probability of finishing this project in less than 53 days? p(t < D) TE = 54 Z = D - TE cp 2   t D=53
29. Activity variance, = ( Pessim. - Optim. 6 ) 2 2  Ta s k O p tim is tic M o s t L ik e ly P e s s im is tic V a ria n c e A 3 6 1 5 4 B 2 4 1 4 C 6 1 2 3 0 1 6 D 2 5 8 E 5 1 1 1 7 4 F 3 6 1 5 G 3 9 2 7 H 1 4 7 1 I 4 1 9 2 8 1 6 (Sum the variance along the critical path.) 2  = 41
30. p(Z < -0.156) = 0.5 - 0.0636 = 0.436, or 43.6 % Z = D - T = 53- 54 41 = -.156 E cp 2   TE = 54 p(t < D) t D=53
31. 32 A Comparison of AON and AOA Network Conventions