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Chapter 8

Chapter 8. Scheduling. Month. 0 2 4 6 8 10. | | | | |. Activity Design house and obtain financing Lay foundation Order and receive materials Build house Select paint Select carpet Finish work. 1 3 5 7 9. Month. A Gantt Chart. Standard Abbreviations. CPM – Critical Path Method

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Chapter 8

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  1. Chapter 8 Scheduling

  2. Month 0 2 4 6 8 10 | | | | | Activity Design house and obtain financing Lay foundation Order and receive materials Build house Select paint Select carpet Finish work 1 3 5 7 9 Month A Gantt Chart

  3. Standard Abbreviations • CPM – Critical Path Method • PERT - Program Evaluation and Review Technique

  4. Background • Schedule is the conversion of a project action plan into an operating timetable • Basis for monitoring a project • One of the major project management tools • Work changes daily, so a detailed plan is essential • Not all project activities need to be scheduled at the same level of detail

  5. Background Continued • Most of the scheduling is at the WBS level, not the work package level • Only the most critical work packages may be shown on the schedule • Most of the scheduling is based on network drawings

  6. Network Scheduling Advantage • Consistent framework • Shows interdependences • Shows when resources are needed • Ensures proper communication • Determines expected completion date • Identifies critical activities

  7. Network Scheduling Advantage Continued • Shows which of the activities can be delayed • Determines start dates • Shows which task must be coordinated • Shows which task can be run parallel • Relieves some conflict • Allows probabilistic estimates

  8. Network Scheduling Techniques: PERT (ADM) and CPM (PDM) • PERT was developed for the Polaris missile/submarine project in 1958 • CPM developed by DuPont during the same time • Initially, CPM and PERT were two different approaches • CPM used deterministic time estimates and allowed project crunching • PERT used probabilistic time estimates • Microsoft Project (and others) have blended CPM and PERT into one approach

  9. Terminology • Activity - A specific task or set of tasks that are required by the project, use up resources, and take time to complete • Event - The result of completing one or more activities • Network - The combination of all activities and events that define a project • Drawn left-to-right • Connections represent predecessors

  10. Terminology Continued • Path - A series of connected activities • Critical - An activity, event, or path which, if delayed, will delay the completion of the project • Critical Path - The path through the project where, if any activity is delayed, the project is delayed • There is always a critical path • There can be more than one critical path

  11. Terminology Continued • Sequential Activities - One activity must be completed before the next one can begin • Parallel Activities - The activities can take place at the same time • Immediate Predecessor - That activity that must be completed just before a particular activity can begin

  12. Terminology Continued • Activity on Arrow - Arrows represent activities while nodes stand for events • Activity on Node - Nodes stand for events and arrows show precedence

  13. AON and AOA Format Figure 8-2 Figure 8-3

  14. Constructing the Network • Begin with START activity • Add activities without precedences as nodes • There will always be one • May be more • Add activities that have those activities as precedences • Continue

  15. Solving the Network Table 8-1

  16. The AON Network from the previous table Figure 8-13

  17. 3 Lay foundation Dummy Build house Finish work 2 0 3 1 1 2 4 6 7 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet 5 Project Network for a House

  18. Critical Path • A path is a sequence of connected activities running from start to end node in network • The critical path is the path with the longest duration in the network • Project cannot be completed in less than the time of the critical path

  19. Lay foundation Dummy Build house Finish work 2 0 3 1 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet 3 1 2 4 6 7 5 The Critical Path A: 1-2-3-4-6-73 + 2 + 0 + 3 + 1 = 9 months B: 1-2-3-4-5-6-73 + 2 + 0 + 1 + 1 + 1 = 8 months C: 1-2-4-6-73 + 1 + 3 + 1 = 8 months D: 1-2-4-5-6-73 + 1 + 1 + 1 + 1 = 7 months

  20. Lay foundation Dummy Build house Finish work 2 0 3 1 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet 3 1 2 4 6 7 5 The Critical Path A: 1-2-3-4-6-7 3 + 2 + 0 + 3 + 1 = 9 months B: 1-2-3-4-5-6-7 3 + 2 + 0 + 1 + 1 + 1 = 8 months C: 1-2-4-6-7 3 + 1 + 3 + 1 = 8 months D: 1-2-4-5-6-7 3 + 1 + 1 + 1 + 1 = 7 months The Critical Path

  21. Lay foundation Dummy Build house Finish work 2 0 3 1 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet 3 3 Finish at 9 months Start at 5 months 2 0 1 3 1 1 2 4 6 7 1 2 4 6 7 3 1 1 Start at 8 months Start at 3 months 5 5 The Critical Path Activity Start Times

  22. Lay foundation Dummy Build house Finish work 2 0 3 1 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet 3 1 2 4 6 7 5 Early Times • ES - earliest time activity can start • Forward pass starts at beginning of CPM/PERT network to determine ES times • EF = ES + activity time • ESij=maximum (EFi) • EFij=ESij- tij • ES12=0 • EF12 =ES12- t12=0 + 3 = 3months

  23. Lay foundation Dummy Build house Finish work 2 0 3 1 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet 3 1 2 4 6 7 5 Computing Early Times • ES23 = max EF2 = 3 months • ES46 = max EF4 = max 5,4 = 5 months • EF46 = ES46 - t46 = 5 + 3 = 8 months • EF67 = 9 months, the project duration

  24. Lay foundation Dummy Build house Finish work 2 0 3 1 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet Early Start and Finish Times 3 3 (ES = 3, EF = 5) (ES = 5, EF = 5) 2 0 (ES = 5, EF = 8) 1 2 4 6 7 1 3 1 1 2 4 6 7 3 (ES = 0, EF = 3) (ES = 3, EF = 4) (ES = 8, EF = 9) 1 1 (ES = 5, EF = 6) (ES = 6, EF = 7) 5 5 Computing Early Times

  25. Late Times • LS - latest time activity can start & not delay project • Backward pass starts at end of CPM/PERT network to determine LS times • LF = LS + activity time • LSij=LFij-tij • LFij= minimum (LSj)

  26. Lay foundation Dummy Build house Finish work 2 0 3 1 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet 3 1 2 4 6 7 5 Computing Late Times • LF67 = 9 months • LS67 = LF67 - t67 = 9 - 1 = 8 months • LF56 = minimum (LS6) = 8 months • LS56 = LF56 - t56 = 8 - 1 = 7 months • LF24 = minimum (LS4) = min(5, 6) = 5 months • LS24 = LF24 - t24 = 5 - 1 = 4 months

  27. Lay foundation Dummy Build house Finish work 2 0 3 1 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet Early and Late Start and Finish Times 3 3 ( ) ( ) ES = 3, EF = 5 LS = 3, LF = 5 ES = 5, EF = 5 LS = 5, LF = 5 ( ) ES = 5, EF = 8 LS = 5, LF = 8 2 0 1 2 4 6 7 1 3 1 1 2 4 6 7 3 ( ) ( ) ( ) ES = 0, EF = 3 LS = 0, LF = 3 ES = 3, EF = 4 LS = 4, LF = 5 ES = 8, EF = 9 LS = 8, LF = 9 1 1 5 ( ) ( ) 5 ES = 5, EF = 6 LS = 6, LF = 7 ES = 6, EF = 7 LS =7, LF = 8 Computing Late Times • LF67 = 9 months • LS67 = LF67 - t67 = 9 - 1 = 8 months • LF56 = minimum (LS6) = 8 months • LS56 = LF56 - t56 = 8 - 1 = 7 months • LF24 = minimum (LS4) = min(5, 6) = 5 months • LS24 = LF24 - t24 = 5 - 1 = 4 months

  28. Activity Slack • Activities on critical path have ES = LS & EF = LF • Activities not on critical path have slack • Sij = LSij - ESij • Sij = LFij - EFij • S24 = LS24 - ES24 = 4 - 3 = 1 month

  29. Lay foundation Dummy Build house Finish work 2 0 3 1 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet 3 Activity LS ES LF EF Slacks *1-2 0 0 3 3 0 *2-3 3 3 5 5 0 2-4 4 3 5 4 1 *3-4 5 5 5 5 0 4-5 6 5 7 6 1 *4-6 5 5 8 8 0 5-6 7 6 8 7 1 *6-7 8 8 9 9 0 * Critical path 1 2 4 6 7 5 Activity Slack Data

  30. Lay foundation Dummy Build house Finish work 2 0 3 1 3 1 Design house and obtain financing Order and receive materials 1 1 Select paint Select carpet 3 3 Activity Slack Activity LS ES LF EF Slacks *1-2 0 0 3 3 0 *2-3 3 3 5 5 0 2-4 4 3 5 4 1 *3-4 5 5 5 5 0 4-5 6 5 7 6 1 *4-6 5 5 8 8 0 5-6 7 6 8 7 1 *6-7 8 8 9 9 0 * Critical path S = 0 S = 0 1 2 4 6 7 1 2 4 6 7 2 0 S = 0 1 3 1 S = 0 S = 1 S = 0 3 5 5 1 1 S = 1 S = 1 Activity Slack Data

  31. Probabilistic Time Estimates • Reflect uncertainty of activity times • Beta distribution is used in PERT

  32. a + 4m + b 6 Mean (expected time): t = 2 b - a 6 Variance: 2 = where a = optimistic estimate m = most likely time estimate b= pessimistic time estimate Probabilistic Time Estimates • Reflect uncertainty of activity times • Beta distribution is used in PERT

  33. P(time) P(time) a m t b a t m b Time Time P(time) a m = t b Time Example Beta Distributions Figure 6.11

  34. E 2 6 Equipment testing and modification Equipment installation Final debugging A D Dummy L System development F I M 1 3 5 7 9 B Manual Testing System Training System changeover Position recruiting Job training System Testing C G J K Dummy H 4 8 Orientation Southern Textile Company

  35. 2 6 1 3 5 7 9 4 8 TIME ESTIMATES (WKS) ACTIVITYa m b 1 - 2 A 6 8 10 1 - 3 B 3 6 9 1 - 4 C 1 3 5 2 - 5 D 0 0 0 2 - 6 E 2 4 12 3 - 5 F 2 3 4 4 - 5 G 3 4 5 4 - 8 H 2 2 2 5 - 7 I 3 7 11 5 - 8 J 2 4 6 8 - 7 K 0 0 0 6 - 9 L 1 4 7 7 - 9 M 1 10 13 Activity Estimates

  36. 2 6 1 3 5 7 9 4 8 TIME ESTIMATES (WKS) MEAN TIME VARIANCE ACTIVITYa m b t2 1 - 2 6 8 10 8 0.44 1 - 3 3 6 9 6 1.00 1 - 4 1 3 5 3 0.44 2 - 5 0 0 0 0 0.00 2 - 6 2 4 12 5 2.78 3 - 5 2 3 4 3 0.11 4 - 5 3 4 5 4 0.11 4 - 8 2 2 2 2 0.00 5 - 7 3 7 11 7 1.78 5 - 8 2 4 6 4 0.44 8 - 7 0 0 0 0 0.00 6 - 9 1 4 7 4 1.00 7 - 9 1 10 13 9 4.00 Activity Estimates

  37. 2 6 1 3 5 7 9 4 8 6 + 4(8) + 10 6 a + 4m + b 6 2 b - a 6 4 9 10 - 6 6 t = = = 8 weeks  2 = = = week 2 Early and Late Times For Activity 1-2 a= 6, m = 8, b = 10

  38. 2 6 1 3 5 7 9 4 8 ACTIVITYtES EF LS LF S 1 - 2 8 0.44 0 8 1 9 1 1 - 3 6 1.00 0 6 0 6 0 1 - 4 3 0.44 0 3 2 5 2 2 - 5 0 0.00 8 8 9 9 1 2 - 6 5 2.78 8 13 16 21 8 3 - 5 3 0.11 6 9 6 9 0 4 - 5 4 0.11 3 7 5 9 2 4 - 8 2 0.00 3 5 14 16 11 5 - 7 7 1.78 9 16 9 16 0 5 - 8 4 0.44 9 13 12 16 3 8 - 7 0 0.00 13 13 16 16 3 6 - 9 4 1.00 13 17 21 25 8 7 - 9 9 4.00 16 25 16 25 0 Early and Late Times

  39. ES = 8, EF = 13 LS = 16, LF = 21 2 6 5 ES = 0, EF = 8 LS = 1, LF = 9 ES = 8, EF = 8 LS = 9, LF = 9 ES = 13, EF = 17 LS = 21, LF = 25 8 0 4 ES = 0, EF = 6 LS = 0, LF = 6 ES = 6, EF = 9 LS = 6, LF = 9 ES = 9, EF = 16 LS = 9, LF = 16 9 1 3 5 7 9 6 3 7 ES = 16, EF = 25 LS = 16, LF = 25 ES = 3, EF = 7 LS = 5, LF = 9 4 0 3 ES = 0, EF = 3 LS = 2, LF = 5 ES = 9, EF = 13 LS = 12, LF = 16 ES = 13, EF = 13 LS = 16, LF = 16 2 4 8 ES = 3, EF = 5 LS = 14, LF = 16 Southern Textile Company

  40. ES = 8, EF = 13 LS = 16, LF = 21 2 6 5 Total project variance ES = 0, EF = 8 LS = 1, LF = 9 ES = 8, EF = 8 LS = 9, LF = 9 ES = 13, EF = 17 LS = 21, LF = 25 8 0 4 2 = 2 + 2 + 2 + 2 = 1.00 + 0.11 + 1.78 + 4.00 = 6.89 weeks^2 13 35 57 79 ES = 0, EF = 6 LS = 0, LF = 6 ES = 6, EF = 9 LS = 6, LF = 9 ES = 9, EF = 16 LS = 9, LF = 16 9 1 3 5 7 9 6 3 7 ES = 16, EF = 25 LS = 21, LF = 25 ES = 3, EF = 7 LS = 5, LF = 9 4 0 3 ES = 0, EF = 3 LS = 2, LF = 5 ES = 9, EF = 13 LS = 12, LF = 16 ES = 13, EF = 13 LS = 16, LF = 16 2 4 8 ES = 3, EF = 5 LS = 14, LF = 16 Southern Textile Company

  41. x -   Z = Probabilistic Network Analysis Determine probability that project is completed within specified time where  = tp = project mean time  = project standard deviation x = proposed project time Z = number of standard deviations xis from mean

  42. Probability Z  = tp x Time Normal Distribution Of Project Time

  43. What is the probability that the project is completed within 30 weeks? Southern Textile Example

  44. What is the probability that the project is completed within 30 weeks? P(x 25 weeks)  = 25 x = 30 Time (weeks) Southern Textile Example

  45. What is the probability that the project is completed within 30 weeks? Z = = = 1.91 P(x 25 weeks)  2 = 6.89 weeks  = 6.89  = 2.62 weeks x -   30 - 25 2.62  = 25 x = 30 Time (weeks) Southern Textile Example

  46. What is the probability that the project is completed within 30 weeks? Z = = = 1.91 P(x 25 weeks)  2 = 6.89 weeks  = 6.89  = 2.62 weeks x -   30 - 25 2.62  = 25 x = 30 Time (weeks) From Excel, a Z score of 1.91 corresponds to a probability = normsdist(1.91) = 0.9719 Southern Textile Example

  47. What is the probability that the project is completed within 22 weeks? P(x 22 weeks) 0.3729 x = 22  = 25 Time (weeks) Southern Textile Example

  48. What is the probability that the project is completed within 22 weeks? Z = = = -1.14  2 = 6.89 weeks  = 6.89  = 2.62 weeks P(x 22 weeks) x -   0.3729 22 - 25 2.62 x = 22  = 25 Time (weeks) Southern Textile Example

  49. What is the probability that the project is completed within 22 weeks? Z = = = -1.14  2 = 6.89 weeks  = 6.89  = 2.62 weeks P(x 22 weeks) x -   0.3729 22 - 25 2.62 x = 22  = 25 Time (weeks) From Excel, a Z score of -1.14 corresponds to a probability = normsdist(-1.14) = 0.1271 Southern Textile Example

  50. Calculating Activity Times

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