1. Switch off your Mobiles Phones or Change Profile to Silent Mode

2. Tasks 19 – 24

3. 1020507080 3040 60 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3 Activity-On-Arrow (AOA)

4. Critical Path Method: Table ActivityDurationEETLETFloat / Slack A2 B4 C5 D3 E2 F3 G3 H7 I3

5. Forward Pass Computation Earliest Event Time (EET) of First Activity is 0 (EET = 0) Add activity times along each path in the network to get Earliest Finish Time (EFT = EET + Duration). Carry the Earliest Finish Time (EFT) to next activity where it becomes its Earliest Event Time (EET) unless… The next succeeding activity is a merge activity, in which case the largest EET of all preceding activities is selected.

6. Critical Path Method (CPM) 100 202 50 7080 30 40 60 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3EET EET 0 plus duration 2 gives EET 2 for the next activities B, C & D

7. Critical Path Method (CPM) 100 202 507 7080 306 40 605 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3 EET EET 2 plus duration 3 gives EET 5 for the next activity H EET 2 plus duration 5 gives EET 7 for the next activity G EET 2 plus duration 4 gives EET 6 for the next activity E

8. Critical Path Method (CPM) 100 202 507 7012 80 306 408 605 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3 EET From H, EET 5 plus duration 7 gives EET 12 for the next activity I From G, EET 7 plus duration 3 gives EET 10 for the next activity I From F, EET 8 plus duration 3 gives EET 11 for the next activity I 11 10 12

9. Critical Path Method (CPM) 100 202 507 7012 8015 306 408 605 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3 EET latest Choose the latest EET; need to wait until longest activity has finished EET 12 plus duration 3 gives 15 for the end of the project 11 10 12

10. Critical Path Method: Table ActivityDurationEETLETFloat / Slack A20 B42 C52 D32 E26 F38 G37 H75 I312

11. Backward Pass Computation Latest Event Time of Last Activity is equal to Early Event Time (LET = EET) or Latest Event Time of Last Node is equal to Early Event Time for that Node (LET = EET) Subtract activity times along each path in the network (LET = LET - Duration). Carry the LET to the prior activity where it becomes its LET unless The prior activity is a burst activity (left to right), in which case the smallest LET of all preceding activities is selected.

12. Critical Path Method (CPM) 100 202 507 70 12,12 80 15,15 306 408 605 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3 EETLET LET 15 minus duration 3 gives LET 12 for activity I LET = EET for the end of the project

13. Critical Path Method (CPM) 100 202 50 7,9 70 12,12 80 15,15 306 40 8,9 60 5,5 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3 EETLET LET 12 minus duration 3 gives LET 9 for activity F LET 1 minus duration 3 gives LET 9 for activity G LET 12 minus duration 7 gives LET 5 for activity H

14. Critical Path Method (CPM) 100 20 2,2 50 7,9 70 12,12 80 15,15 30 6,7 40 8,9 60 5,5 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3 EETLET LET 7 minus duration 4 gives LET 3 for activity B LET 9 minus duration 5 gives LET 4 for activity C LET 5 minus duration 3 gives LET 2 for activity D 3 4 2

15. Critical Path Method (CPM) 100 20 2,2 50 7,9 70 12,12 80 15,15 30 6,7 40 8,9 60 5,5 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3EETLET earliest Choose the earliest LET so that the longest activity will have enough time to finish 3 4 2

16. Critical Path Method (CPM) 10 0,0 20 2,2 50 7,9 70 12,12 80 15,15 30 6,7 40 8,9 60 5,5 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3 EETLET LET 2 minus duration 2 gives LET 0 for the start of the project 3 4 2

17. Critical Path Method: Table ActivityDurationEETLETFloat / Slack A200 B423 C524 D322 E267 F389 G379 H755 I312

18. Determining Free Slack / Float) Free Slack (or Float) Is the amount of time an activity can be delayed after the start of a longer parallel activity or activities. Is how long an activity can exceed its Early Finish Date without affecting Early Start Dates of any successor(s). Allows flexibility in scheduling scarce resources.

19. Determining Free Slack / Float) Sensitivity The likelihood the Original Critical Path(s) will change once the project is initiated. The Critical Path is the Network Path(s) that has (have) the Least Slack in common. Slack Time Slack Time available for any Task is equal to difference between Earliest Event Time (EET) and Latest Event Time (LET) SLACK TIME = (LET – EET)

20. Critical Path Method: Table ActivityDurationEETLETFloat / Slack A2000 B4231 C5242 D3220 E2671 F3891 G3792 H7550 I312 0

21. Critical Path Is a sequence of Dependent Tasks that have the Largest sum of Estimated Time (ET). It is the Path that has no Slack Time built in. Critical Path on Network Diagram is shown with thick Dark line. To find Critical Path begin with identifying all alternative paths that exist from Event 1 to Final Event.

22. Critical Path Method (CPM) 10 00 0,0 20 22 2,2 50 79 7,9 70 12,12 80 1515 15,15 30 67 6,7 40 89 8,9 60 55 5,5 A2A2 B4B4 D3D3 C5C5 E2E2 F3F3 G3G3 H7H7 I3I3 EETLET Critical path longest The longest path through the network is shortesttime the shortest time the project can take The critical path is the path with any zero float; any delay will mean whole project the whole project will be late 3 4 2

23. PERT Analysis PERT stands for Program Evaluation & Review Technique A way of modelling uncertainty when scheduling If used properly will lead to more stable schedules optimistic time optimistic time (o) if things go well most likely time most likely time (m) usually the original estimate pessimistic time pessimistic time (p) if it can go wrong, it will...

24. PERT Analysis The expected time t e is calculated as: t e omp t e = [o + 4m + p] / 6 Our activity B has estimate of 4. Let us say: omp o = 3, m = 4, p = 11 t e = [3 + 16 + 11] / 6 t e = 30 / 6 t e = 5 Expected time t e is 5, longer than the most likely time

25. Task 19

26. Network Diagrams, CPM, PERT Your computer manager, Lee Constable, has produced following Network Diagram for next programming project that you will be working on together. Lee has specified most likely time for each activity in Table I below, and has asked you to complete table and Network Diagram by doing following: (January 2002 )

27. Network Diagrams, CPM, PERT Using Most Likely Time from Table below, calculate Earliest Event Time (EET), Latest Event Time (LET) and float or slack associated with each activity (15 Marks) Identify Critical Path for Lee's Network Diagram (3 Marks) Enter results of your calculations in table and on Network Diagram Assume times are in days, all activities are appropriate, and Network Diagram is correct.

28. Network Diagrams, CPM, PERT ActivityDurationEETLETFloat / Slack A2 B5 C6 D4 E3 F9 G8 H7 I1 J3

29. Network Diagrams, CPM, PERT

30. Calculate Expected Time using PERT formula ((o + 4m + p) / 6) from Optimistic, Most Likely and Pessimistic Times Lee has identified in Table below. (10 marks) Specify and comment on effect of using Expected Time as opposed to Most Likely Time on the Critical Path for Lee's Network Diagram. (5 marks)

31. Network Diagrams, CPM, PERT Activity Most Likely Time Optimistic Time Pessimistic Time Expected Time A213 B51.55.5 C62.56.5 D435 E324 F9810 G87.514.5 H76.513.5 I10.51.5 J334.5

32. Task 20

33. Network Diagrams, CPM, PERT Your Project Manager, Alex Midway, has produced following Network Diagram for a programming project. Alex has specified duration for each activity in Table I below, and has asked you to complete table and Network Diagram by doing following: (May 2002)

34. Network Diagrams, CPM, PERT Using Duration from Table, calculate Earliest Event Time (EET), Latest Event Time (LET) and float or slack associated with each activity. (15 Marks) Identify Critical Path for Alex's Network Diagram. (3 Marks) Enter results of your calculations in table and on Network Diagram Assume times are in days, all activities are appropriate, and Network Diagram is correct.

35. Network Diagrams, CPM, PERT ActivityDurationEETLETFloat / Slack A2 B3 C5 D4 E6 F9 G8 H6 I3 J1

36. Network Diagrams, CPM, PERT

37. Task 21

38. Network Diagrams, CPM, PERT Your Project Manager, Chas Mildwood, has produced following Network Diagram for a programming project. Note that number of staff required each day for each activity is given in table. Chas has specified duration for each activity in Table I below, and has asked you to complete table and Network Diagram by doing following: (January 2003)

39. Network Diagrams, CPM, PERT Using Duration from Table, calculate Earliest Event Time (EET), Latest Event Time (LET) and float or slack associated with each activity (10 Marks) Identify activities on Critical Path for Chas's Network Diagram. (3 Marks) Enter results of your calculations in table and on Network Diagram Assume times are in days, all activities are appropriate, and Network Diagram is correct.

40. Network Diagrams, CPM, PERT ActivityDurationEETLETFloat / Slack A3 B4 C6 D5 E9 F3 G2 H6 I4 J2

41. Network Diagrams, CPM, PERT

42. Task 22

43. Network Diagrams, CPM, PERT You are Project Manager for a team working on development of a new library system. You have specified duration in days for each activity and constructed Network Diagram for project. Bob Bodgett, one of your project team, has been assigned to calculate Earliest and Latest Event Times, and identify Critical Path. Bob is not sure that Earliest Event Times (EET) and Latest Event Times (LET) he has calculated are correct. Bob’s EETs and LETs are shown in Table II & Network Diagram II below: (May 2003)

44. Network Diagrams, CPM, PERT Using Table I and/or Network Diagram I below, perform your own calculations for Earliest Event Time (EET), Latest Event Time (LET) at start of each activity, and float or slack associated with each activity. (10 Marks) Identify Critical Path based on your calculations. (4 Marks) Enter results of your calculations in table and on Network Diagram

45. Network Diagrams, CPM, PERT ActivityDurationEETLETFloat / Slack A3 B4 C6 D2 E3 F2 G6 H3 I5 J2

46. Network Diagrams, CPM, PERT

47. Using your calculations from Table I and Network Diagram I above, identify and explain any errors in Bob's calculations for Earliest Event Time (EET), Latest Event Time (LET) and float or slack associated with each activity as shown in Table II below. Your answer should demonstrate why any calculations are in error, not simply provide an amended version. (15 Marks)

48. Network Diagrams, CPM, PERT Bob Bodgett has identified Critical Path as B, E, H and J. Is this correct, given Bob’s calculations? Explain your answer. Using Table I and/or Network Diagram I below, perform your own calculations for Earliest Event Time (EET), Latest Event Time (LET) at start of each activity, and float or slack associated with each activity. (4 Marks)

49. Network Diagrams, CPM, PERT ActivityDurationBob’ EETBob’s LETBob’s Float / Slack A30-2 B431 C631 D231 E3770 F288 G633-2 H310 0 I599-2 J213 0

50. Network Diagrams, CPM, PERT

51. Task 23

52. Network Diagrams, CPM, PERT Consider following scenario. (January 2004) “You work for a company that organises conferences for clients, and you are the project manager for a team organising a two-day conference on risk posed by computer viruses. Client is a well-known software developer, and expects delegates to attend from other companies, universities, as well as private individuals. You have been given a shortlist of names of possible speakers for conference.

53. Network Diagrams, CPM, PERT Speakers need to be invited to event, and will then require both travel arrangements and hotel facilities to be organised (at same time) for them. As project manager, you will also need to investigate possible venues for the conference, and then hire most appropriate one. When venue has been hired, and speakers have been organised (including their hotel and travel arrangements), it will be possible to advertise conference, and then take bookings from delegates who wish to attend.

54. Network Diagrams, CPM, PERT When venue has been hired, you will need to evaluate whether it is more cost-effective to buy or rent microphones for speakers, and then acquire microphones for event. After conference has taken place, you will need to arrange payment of expenses for invited speakers.”

55. Network Diagrams, CPM, PERT Identify 10 activities that have been specified from above scenario. Specify these activities in Table I below. Note that you do not need an activity to represent the conference itself. (5 Marks)

56. Network Diagrams, CPM, PERT ActivityDescriptionPredecessor A B C D E F G H I J

57. Network Diagrams, CPM, PERT Construct Network Diagram for activities that you have identified above, using AoA convention. You must indicate which activities have to occur in sequence (dependencies), and which can run in parallel, but you do not need to consider start time or duration of each activity. You may wish to indicate the predecessor of each activity in Table I above, or by a description to accompany your Network Diagram. (13 marks)

58. Network Diagrams, CPM, PERT You are working on another conference for a different client. You have specified duration in days for each activity and constructed Network Diagram for project. Using Table II and/or Network Diagram I below, calculate Earliest Event Time (EET) and Latest Event Time (LET) for start of each activity, and float/slack associated with each activity. (10 marks) Identify Critical Path based on your calculations. (5 Marks)

59. Network Diagrams, CPM, PERT ActivityDurationEETLETFloat / Slack A2 B3 C5 D4 E5 F4 G6 H2 I5 J3

60. Network Diagrams, CPM, PERT

61. Task 24

62. Network Diagrams, CPM, PERT You are working on a project for a client. You have specified duration in days for each activity and constructed network diagram for project. Using Table and/or Network Diagram below, calculate Earliest Event Time (EET) and Latest Event Time (LET) for start of each activity, and float/slack associated with each activity. (10 marks) Identify Critical Path based on your calculations. (2 Marks) (Spring 2010 – 2011)

63. Network Diagrams, CPM, PERT ActivityDurationEETLETFloat / Slack A2 B8 C2 D4 E11 F5 G3 H9 I6 J1

64. Network Diagrams, CPM, PERT

65. You are given opportunity to re-allocate staff working on project, which has effect of making some activities take longer, while others require less time. New duration in days for each activity is specified below, and while structure of Network Diagram is unchanged, you need to do following:

66. Network Diagrams, CPM, PERT Using Table and/or Network Diagram below, calculate Earliest Event Time (EET) and Latest Event Time (LET) for start of each activity, and float/slack associated with each activity. (10 marks) Identify Critical Path based on your new Calculations, and comment on your results. (4 Marks)

67. Network Diagrams, CPM, PERT ActivityDurationEETLETFloat / Slack A2 B4 C3 D9 E8 F9 G5 H6 I7 J2

68. Network Diagrams, CPM, PERT