1. 8-1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Project Management Chapter 8

2. 8-2 What is a project? Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3. 8-3 Project Life Cycle Conception: identify the need Feasibility analysis or study: costs benefits, and risks Planning: who, how long, what to do? Execution: doing the project Termination: ending the project Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

4. 8-4 ■Network representation is useful for project analysis. ■Networks show how project activities are organized and are used to determine time duration of projects. ■Network techniques used are: ▪ CPM (Critical Path Method) ▪ PERT (Project Evaluation and Review Technique) ■Developed independently during late 1950’s. Network Planning Techniques Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

5. 8-5 Project Planning ■All activities (steps) of the project should be identified. ■The sequential relationships of the activities (which activity comes first, which follows, etc.) is identified by precedence relationships. ■Steps of project planning: ■Make time estimates for activities, determine project completion time. ■Compare project schedule objectives, determine resource requirements. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

6. 8-6 Elements of Project Management Project Scheduling ■Project Schedule : Timely completion of project. ■Schedule development steps: 1. Define activities, 2. Sequence activities, 3. Estimate activity times, 4. Construct schedule. ■Gantt chart and CPM/PERT techniques can be useful. ■Computer software packages available, e.g. Microsoft Project. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

7. 8-7 Elements of Project Management Gantt Chart (1 of 2) ■Popular, traditional technique, also known as a bar chart -developed by Henry Gantt (1914). ■Used in CPM/PERT for monitoring work progress. ■A visual display of project schedule showing activity start and finish times and where extra time is available. ■Gantt Chart is suitable for projects with few activities and precedence relationships. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

8. 8-8 Elements of Project Management Gantt Chart (2 of 2) Figure 8.4 A Gantt chart Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

9. 8-9 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall ■A branch reflects an activity of a project. ■A node represents the beginning and end of activities, referred to as events. ■Branches in the network indicate precedence relationships. ■When an activity is completed at a node, it has been realized. The Project Network CPM/PERT Activity-on-Arc (AOA) Network

10. 8-10 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall ■Time duration of activities shown on branches. ■Activities can occur at the same time (concurrently). ■A dummy activity shows a precedence relationship but reflects no passage of time. ■Two or more activities cannot share the same start and end nodes. The Project Network Concurrent Activities Figure 8. 7 A Dummy Activity

11. 8-11 The Project Network AOA Network for House Building Project Figure 8.6 Expanded Network for Building a House Showing Concurrent Activities Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

12. 8-12 The Project Network AON Network for House Building Project Activity-on-Node (AON) Network  A node represents an activity, with its label and time shown on the node  The branches show the precedence relationships  Convention used in Microsoft Project software Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Figure 8.8 Label Duration

13. 8-13 The Project Network Paths Through a Network Table 8.1 Paths Through the House-Building Network Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall PathEvents A12471247 B1256712567 C13471347 D1356713567

14. 8-14 The critical path is the longest path through the network; the minimum time the network can be completed. From Figure 8.8: Path A: 1  2  4  73 + 2 + 3 + 1 = 9 months Path B: 1  2  5  6  73 + 2 + 1 + 1 + 1= 8 months Path C: 1  3  4  73 + 1 + 3 + 1 = 8 months Path D: 1  3  5  6  73 + 1 + 1 + 1 + 1 = 7 months The Project Network The Critical Path Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

15. 8-15 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall The Project Network Detailed Analysis of Critical Path Figure 8.9 Activity start time (1  2  4  7)

16. 8-16 The Project Network Activity-on-Node Configuration Figure 8.10 Activity-on-Node Configuration Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

17. 8-17 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall ■ES is the earliest time an activity can start: ES = Maximum (EF) ■EF is the earliest start time plus the activity time: EF = ES + t The Project Network Activity Scheduling : Earliest Times Figure 8.11 Earliest activity start and finish times

18. 8-18 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall ■LS is the latest time an activity can start without delaying critical path time: LS = LF - t ■LF is the latest finish time. LF = Minimum (LS) The Project Network Activity Scheduling : Latest Times Figure 8.12 Latest activity start and finish times

19. 8-19 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Slack is the amount of time an activity can be delayed without delaying the project: S = LS – ES = LF - EF Slack Time exists for those activities not on the critical path for which the earliest and latest start times are not equal. The Project Network Activity Slack Time (1 of 2) Table 8.2 *Critical path ActivityLSESLFEFSlack, S *100330*0* *233550*0* 343541 *455880*0* 565761 676871 *788990*0*

20. 8-20 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall The Project Network Activity Slack Time (2 of 2) Figure 8.13 Activity slack

21. 8-21 ■Activity time estimates usually cannot be made with certainty. ■PERT used for probabilistic activity times. ■In PERT, three time estimates are used: most likely time (m), the optimistic time (a), and the pessimistic time (b). ■These provide an estimate of the mean and variance of a beta distribution: variance: mean (expected time): Probabilistic Activity Times Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

22. 8-22 Using Beta Probability Distribution to Calculate Expected Time Durations A typical beta distribution is shown below, note that it has definite end points The expected time for finishing each activity is a weighted average

23. 8-23 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Probabilistic Activity Times Example (1 of 3) Figure 8.14 Network for Installation Order Processing System

24. 8-24 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Probabilistic Activity Times Example (2 of 3) Table 8.3 Activity Time Estimates for Figure 8.14

25. 8-25 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Probabilistic Activity Times Example (3 of 3) Figure 8.15 Earliest and Latest Activity Times

26. 8-26 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall ■Expected project time is the sum of the expected times of the critical path activities. ■Project variance is the sum of the critical path activities’ variances ■The expected project time is assumed to be normally distributed. ■Epected project time (t p ) and variance (v p ) are interpreted as the mean (  ) and variance (  2 ) of a normal distribution :  = 25 weeks  2 = 62/9 = 6.9 (weeks) 2 Probabilistic Activity Times Expected Project Time and Variance

27. 8-27 Uncertain Activity Times In the three-time estimate approach, the critical path is determined as if the mean times for the activities were fixed times. The overall project completion time is assumed to have a normal distribution with mean equal to the sum of the means along the critical path and variance equal to the sum of the variances along the critical path.

28. 8-28 ■Using the normal distribution, probabilities are determined by computing the number of standard deviations (Z) a value is away from the mean. ■The Z value is used to find corresponding probability in Table A.1, Appendix A. Probability Analysis of a Project Network (1 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

29. 8-29 Probability Analysis of a Project Network (2 of 2) Figure 8.16 Normal Distribution of Network Duration Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

30. 8-30 What is the probability that the new order processing system will be ready by 30 weeks? µ = 25 weeks  2 = 6.9  = 2.63 weeks Z = (x-  )/  = (30 -25)/2.63 = 1.90 Z value of 1.90 corresponds to probability of.4713 in Table A.1, Appendix A (page 812). Probability of completing project in 30 weeks or less: (.5000 +.4713) =.9713. Probability Analysis of a Project Network Example 1 (1 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

31. 8-31 Probability Analysis of a Project Network Example 1 (2 of 2) Figure 8.17 Probability the Network Will Be Completed in 30 Weeks or Less Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

32. 8-32 ■A customer will trade elsewhere if the new ordering system is not working within 22 weeks. What is the probability that she will be retained? Z = (22 - 25)/2.63 = -1.14 ■Z value of 1.14 (ignore negative) corresponds to probability of.3729 in Table A.1, appendix A. ■Probability that customer will be retained is (0.5 -.3729) =.1271 Probability Analysis of a Project Network Example 2 (1 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

33. 8-33 Probability Analysis of a Project Network Example 2 (2 of 2) Figure 8.18 Probability the Network Will Be Completed in 22 Weeks or Less Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

34. 8-34 Example: Frank’s Fine Floats Frank’s Fine Floats is in the business of building elaborate parade floats. Frank and his crew have a new float to build and want to use PERT/CPM to help them manage the project. The table on the next slide shows the activities that comprise the project. Each activity’s estimated completion time (in days) and immediate predecessors are listed as well. Frank wants to know the total time to complete the project, which activities are critical, and the earliest and latest start and finish dates for each activity.

35. 8-35 Example: Frank’s Fine Floats Immediate Completion Activity Description Predecessors Time (days) A Initial Paperwork --- 3 B Build Body A 3 C Build Frame A 2 D Finish Body B 3 E Finish Frame C 7 F Final Paperwork B,C 3 G Mount Body to Frame D,E 6 H Install Skirt on Frame C 2

36. 8-36 Example: Frank’s Fine Floats Project Network Start Finish B 3 D 3 A 3 C 2 G 6 F 3 H 2 E 7

37. 8-37 Example: Frank’s Fine Floats Latest Start and Finish Times Start Finish B 3 D 3 A 3 C 2 G 6 F 3 H 2 E 7 0 3 3 6 6 9 3 5 12 18 6 9 5 7 5 12 6 9 9 12 0 3 3 5 12 18 15 18 16 18 5 12

38. 8-38 Determining the Critical Path A critical path is a path of activities, from the Start node to the Finish node, with 0 slack times. Critical Path: A – C – E – G The project completion time equals the maximum of the activities’ earliest finish times. Project Completion Time: 18 days Example: Frank’s Fine Floats

39. 8-39 Example: Frank’s Fine Floats Critical Path Start Finish B 3 D 3 A 3 C 2 G 6 F 3 H 2 E 7 0 3 3 6 6 9 3 5 12 18 6 9 5 7 5 12 6 9 9 12 0 3 3 5 12 18 15 18 16 18 5 12

40. 8-40 Example: ABC Associates Consider the following project: Immed. Optimistic Most Likely Pessimistic Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.) A -- 4 6 8 B -- 1 4.5 5 C A 3 3 3 D A 4 5 6 E A 0.5 1 1.5 F B,C 3 4 5 G B,C 1 1.5 5 H E,F 5 6 7 I E,F 2 5 8 J D,H 2.5 2.75 4.5 K G,I 3 5 7

41. 8-41 Example: ABC Associates Project Network 66 44 33 55 55 22 44 11 66 33 55

42. 8-42 Example: ABC Associates Activity Expected Times and Variances t = (a + 4m + b)/6  2 = ((b-a)/6) 2 Activity Expected Time Variance A 6 4/9 B 4 4/9 C 3 0 D 5 1/9 E 1 1/36 F 4 1/9 G 2 4/9 H 6 1/9 I 5 1 J 3 1/9 K 5 4/9

43. 8-43 Example: ABC Associates Critical Path (A-C-F-I-K) 66 44 33 55 55 22 44 11 66 33 55 0 6 9 13 13 18 9 11 9 11 16 18 13 19 14 20 19 22 20 23 18 23 6 7 6 7 12 13 6 9 0 4 5 9 6 11 6 11 15 20

44. 8-44 Probability that the project will be completed within 24 hrs: Variance= 4/9 + 0 + 1/9 + 1 + 4/9 = 2 Standard Deviation= 1.414 z = (24-23)/1.414 =.71 From the Standard Normal Distribution table: P(z <.71) =.5 +.2612 =.7612 Example: ABC Associates

45. 8-45 EarthMover is a manufacturer of road construction equipment including pavers, rollers, and graders. The company is faced with a new project, introducing a new line of loaders. What is the critical Path? Example: EarthMover, Inc.

46. 8-46 Immediate Completion Immediate Completion Activity Description Predecessors Time (wks) Activity Description Predecessors Time (wks) A Study Feasibility --- 6 A Study Feasibility --- 6 B Purchase Building A 4 B Purchase Building A 4 C Hire Project Leader A 3 C Hire Project Leader A 3 D Select Advertising Staff B 6 D Select Advertising Staff B 6 E Purchase Materials B 3 E Purchase Materials B 3 F Hire Manufacturing Staff B,C 10 F Hire Manufacturing Staff B,C 10 G Manufacture Prototype E,F 2 G Manufacture Prototype E,F 2 H Produce First 50 Units G 6 H Produce First 50 Units G 6 I Advertise Product D,G 8 I Advertise Product D,G 8 Example: EarthMover, Inc.

47. 8-47 PERT Network Example: EarthMover, Inc. 66 44 33 1010 33 66 2266 88

48. 8-48 Example: EarthMover, Inc. Critical Activities 66 44 33 1010 33 66 2266 88 0 6 10 20 10 20 20 22 10 16 16 22 22 30 22 28 24 30 6 9 6 9 7 10 7 10 10 13 17 20 6 10 6 10

49. 8-49 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Given this network and the data on the following slide, determine the expected project completion time and variance, and the probability that the project will be completed in 28 days or less. Example Problem Problem Statement and Data (1 of 2)

50. 8-50 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Example Problem Problem Statement and Data (2 of 2)

51. 8-51 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Example Problem Solution (1 of 4) Step 1: Compute the expected activity times and variances.

52. 8-52 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Example Problem Solution (2 of 4) Step 2: Determine the earliest and latest activity times & slacks

53. 8-53 Example Problem Solution (3 of 4) Step 3: Identify the critical path and compute expected completion time and variance.  Critical path (activities with no slack): 1  3  5  7  Expected project completion time: t p = 9+5+6+4 = 24 days  Variance: v p = 4 + 4/9 + 4/9 + 1/9 = 5 (days) 2 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

54. 8-54 Example Problem Solution (4 of 4) Step 4: Determine the Probability That the Project Will be Completed in 28 days or less (µ = 24,  =  5) Z = (x -  )/  = (28 -24)/  5 = 1.79 Corresponding probability from Table A.1, Appendix A, is.4633 and P(x  28) =.4633 +.5 =.9633. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

55. 8-55 XYZ Company is bringing a new product on line to be manufactured in their current facility using existing space. The owners have identified 11 activities and their precedence relationships. Develop an AON for the project.

56. 8-56 Project Network with Deterministic Time Estimates

57. 8-57 LS, LF Network

58. 8-58 © Wiley 2007 Calculating Expected Task Times

59. 8-59 © Wiley 2007 Project Activity Variance ActivityOptimisticMost LikelyPessimisticVariance A2460.44 B37101.36 C2350.25 D4790.69 E1216201.78 F2581.00 G2220.00 H2340.11 I2350.25 J2460.44 K2220.00

60. 8-60 © Wiley 2010 Estimated Path Durations through the Network ABDEGIJK is the expected critical path & the project has an expected duration of 44.83 weeks and expected variance is 4.96.

61. 8-61 QUESTIONS Calculate the probability of finishing the project within 48 weeks Calculate the probability of finishing the project within 40 weeks Calculate the probability of finishing the project within 44.83 weeks Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

62. 8-62 Answers a) P(x<=48)=P(z<=48-44.83/2.23) =P(z<=1.42)=0.5+0.4222 b) P(x<=40)=P(z<=40-44.83/2.23) =P(z<=-2.17)=0.5-0.485 c) p(x<=44.83)=P(z<=0)=0.5 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall