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Projects: Critical Paths

Projects: Critical Paths. Dr. Ron Lembke Operations Management. PERT & CPM. Network techniques Developed in 1950’s CPM by DuPont for chemical plants PERT by U.S. Navy for Polaris missile Consider precedence relationships & interdependencies Each uses a different estimate of activity times.

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Projects: Critical Paths

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  1. Projects:Critical Paths Dr. Ron Lembke Operations Management

  2. PERT & CPM • Network techniques • Developed in 1950’s • CPM by DuPont for chemical plants • PERT by U.S. Navy for Polaris missile • Consider precedence relationships & interdependencies • Each uses a different estimate of activity times

  3. Questions Answered by PERT & CPM • Completion date? • On schedule? Within budget? • Probability of completing by ...? • Critical activities? • Enough resources available? • How can the project be finished early at the least cost?

  4. PERT & CPM Steps • Identify activities • Determine sequence • Create network • Determine activity times • Find critical path • Earliest & latest start times • Earliest & latest finish times • Slack

  5. 1 2 3 Activity on Node (AoN) Project: Obtain a college degree (B.S.) Receive diploma Attend class, study etc. Enroll 1 month 4? Years 1 day

  6. 1 2 3 4 Activity on Arc (AoA) Project: Obtain a college degree (B.S.) Attend class, study, etc. Receive diploma Enroll 1 month 4,5 ? Years 1 day

  7. 1 2 3 4 AoA Nodes have meaning Project: Obtain a college degree (B.S.) GraduatingSenior Applicant Student Alum

  8. Liberal Arts Sidebar • Alum = ? Alumnus Alumna Alumni Alumnae Alumni

  9. Network Example You’re a project manager for Bechtel. Construct the network. Activity Predecessors A --B A C AD B E BF C G DH E, F

  10. A E C B D G H Z Network Example - AON F

  11. 7 2 9 5 1 3 6 8 Network Example - AOA G D B E A H C F 4

  12. 2 2 3 1 5 3 1 4 4 AOA Diagrams A precedes B and C, B and C precede D B A D C B A C D Add a phantom arc for clarity.

  13. Critical Path Analysis • Provides activity information • Earliest (ES) & latest (LS) start • Earliest (EF) & latest (LF) finish • Slack (S): Allowable delay • Identifies critical path • Longest path in network • Shortest time project can be completed • Any delay on activities delays project • Activities have 0 slack

  14. Critical Path Analysis Example

  15. Network Solution B D E A G 2 6 3 1 1 C F 3 4

  16. Earliest Start & Finish Steps • Begin at starting event & work forward • ES = 0 for starting activities • ES is earliest start • EF = ES + Activity time • EF is earliest finish • ES = Maximum EF of all predecessors for non-starting activities

  17. B D E A G 2 6 3 1 1 C F 3 4 Activity A Earliest Start Solution For starting activities, ES = 0.

  18. B D E A G 2 6 3 1 1 C F 3 4 Earliest Start Solution

  19. Latest Start & Finish Steps • Begin at ending event & work backward • LF = Maximum EF for ending activities • LF is latest finish; EF is earliest finish • LS = LF - Activity time • LS is latest start • LF = Minimum LS of all successors for non-ending activities

  20. B D E A G 2 6 3 1 1 C F 3 4 Earliest Start Solution

  21. B D E A G 2 6 3 1 1 C F 3 4 Latest Finish Solution

  22. Compute Slack

  23. B D E A G 2 6 3 1 1 C F 3 4 Critical Path

  24. New notation • Compute ES, EF for each activity, Left to Right • Compute, LF, LS, Right to Left ES EF C 7 LS LF

  25. Exhibit 6 F 8 C 7 A 21 G 2 B 5 D 2 E 5

  26. Exhibit 6 21 28 28 36 F 8 C 7 0 21 36 38 A 21 G 2 28 33 21 26 26 28 B 5 D 2 E 5 F cannot start until C and D are done. G cannot start until both E and F are done.

  27. Exhibit 6 21 28 28 36 F 8 C 7 21 28 28 36 0 21 36 38 A 21 G 2 0 21 36 38 28 33 21 26 26 28 B 5 D 2 E 5 21 26 26 28 31 36 E just has to be done in time for G to start at 36, so it has slack. D has to be done in time for F to go at 28, so it has no slack.

  28. Gantt Chart - ES A C B D E F G 0 5 10 15 20 25 30 35 40

  29. Solved Problem 2 B4 E6 G7 C3 A 1 I4 F2 D7 H9

  30. Solved Problem 2 1 5 511 B4 E6 1118 1 5 511 G7 1118 1 4 0 1 1822 C3 A 1 I4 6 9 0 1 810 1822 F2 1 8 911 817 D7 H9 2 9 918

  31. Summary • Activity on Node representation • Calculated • ES, EF for all activities • LS, LF for all activities (working backwards) • Slack for each activity • Identified critical path(s)

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