Project Development

1. Project Development Scheduling and Probability of Completion

2. Learning Objectives • To define project Terminology • To illustrate AOA and AON diagrams • To calculate Project Duration, Critical Path, and slack • To compute and interpret probability of completing a project for a specific time

3. Project Networks • A flow chart that graphically depicts the sequence, interdependencies, and start and finish times of the project job plan of activities that is the critical path through the network. • Provides the basis for scheduling labor and equipment. • Enhances communication among project participants. • Provides an estimate of the project’s duration. • Provides a basis for budgeting cash flow. • Identifies activities that are critical. • Highlights activities that are “critical” and can not be delayed. • Help managers get and stay on plan.

4. Terminology A • Activity (task): an element of the project that requires time. • Merge Activity: an activity that has two or more preceding activities on which it depends. • Parallel (Concurrent) Activities: Activities that can occur independently and, if desired, not at the same time. B D C

5. Terminology continued • Path: a sequence of connected, dependent activities. • Critical path: the longest path through the activity network that allows for the completion of all project-related activities; C A B D

6. Terminology continued • Slack (or Float) • The amount of time an activity can be delayed after the start of a longer parallel activity or activities. • Total slack • The amount of time an activity can be delayed without delaying the entire project.

7. Terminology continued • Event: a point in time when an activity is started or completed. It does not consume time. • Burst Activity: an activity that has more than one activity immediately following it (more than one dependency arrow flowing from it). • Two Approaches • Activity-on-Node (AON) • Uses a node to depict an activity. • Activity-on-Arrow (AOA) • Uses an arrow to depict an activity. B C A D

8. CPM • Critical Path Method was developed by Dupont. It is a deterministic model where time estimates are accurate and do not vary. A project is made up of a sequence of activities or tasks that form a network representing a project • The path taking the longest time through this network of activities is called the "critical path". The critical path provides a wide range of scheduling information useful in managing a project. Critical Path Method (CPM) helps to identify the critical path(s) in the project networks. A network diagram is a graphic representation of the project and consists of directed arrows and nodes. To create a workable network diagram a project must have: • well-defined jobs or tasks whose completion marks the end of the project; • independent jobs or tasks; • and tasks that follow a given sequence.

9. Basic Rules to Follow in Developing Project Networks • Networks typically flow from left to right. • An activity cannot begin until all preceding connected activities are complete. • Arrows indicate precedence and flow and can cross over each other. • Each activity must have a unique identify number that is greater than any of its predecessor activities. (AOA) • Looping is not allowed. • Conditional statements are not allowed.

10. Illogical Loop FIGURE 6.10

11. AOA AON Activity Relationship Activity Relationships

12. AOA AON S T U S T U 1 2 3 4 S precedes T, which precedes U. Activity Relationships

13. AOA AON S 1 S U 3 4 U T 2 T S and T must be completed before U can be started. Activity Relationships

14. AOA AON 3 T T S 1 2 S U 4 U T and U cannot begin until S has been completed. Activity Relationships

15. AOA AON S 1 4 S U U 3 T V 2 5 T V U and V cannot begin until both S and T have been completed. Activity Relationships

16. AOA AON S U 1 3 5 S U Dummy T V 2 4 6 T V U cannot begin until both S and T have been completed; V cannot begin until T has been completed. Activity Relationships

17. AOA AON S T V 1 2 4 5 S T V Dummy U 3 U T and U cannot begin until S has been completed; V cannot begin until both T and U have been completed. Activity Relationships

18. Immediate Activity Description Predecessor(s) Responsibility A Select administrative and medical staff. B Select site and do site survey. C Select equipment. D Prepare final construction plans and layout. E Bring utilities to the site. F Interview applicants and fill positions in nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. H Construct the hospital. I Develop an information system. J Install the equipment. K Train nurses and support staff. St. Adolf’s Hospital

19. Immediate Activity Description Predecessor(s) Responsibility A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson St. Adolf’s Hospital

20. Immediate Activity Description Predecessor(s) Responsibility AON Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson St. Adolf’s Hospital Example 8.1

21. Immediate Activity Description Predecessor(s) Responsibility AON Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A Start St. Adolf’s Hospital Example 8.1

22. Immediate Activity Description Predecessor(s) Responsibility AON Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A Start B St. Adolf’s Hospital Example 8.1

23. Immediate Activity Description Predecessor(s) Responsibility AON Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A C Start B St. Adolf’s Hospital Example 8.1

24. Immediate Activity Description Predecessor(s) Responsibility AON Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A C Start D B St. Adolf’s Hospital Example 8.1

25. Immediate Activity Description Predecessor(s) Responsibility AON Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A C Start D B E St. Adolf’s Hospital Example 8.1

26. Immediate Activity Description Predecessor(s) Responsibility AON Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A F C Start D B E St. Adolf’s Hospital Example 8.1

27. Immediate Activity Description Predecessor(s) Responsibility AON Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A F C G Start D B E St. Adolf’s Hospital Example 8.1

28. Immediate Activity Description Predecessor(s) Responsibility AON Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A F C G Start D B H E St. Adolf’s Hospital Example 8.1

29. Immediate Activity Description Predecessor(s) Responsibility AON Network I A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A F C G Start D B H E St. Adolf’s Hospital Example 8.1

30. Immediate Activity Description Predecessor(s) Responsibility AON Network I A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A F C G Start D B H J E St. Adolf’s Hospital Example 8.1

31. Immediate Activity Description Predecessor(s) Responsibility AON Network I A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A F K C G Start D B H J E St. Adolf’s Hospital Example 8.1

32. Immediate Activity Description Predecessor(s) Responsibility AON Network I A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A F K C G Start Finish D B H J E St. Adolf’s Hospital Example 8.1

33. Immediate Activity Description Predecessor(s) Responsibility AOA Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson St. Adolf’s Hospital Example 8.1

34. Immediate Activity Description Predecessor(s) Responsibility AOA Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson 2 A Start 1 St. Adolf’s Hospital Example 8.1

35. Immediate Activity Description Predecessor(s) Responsibility AOA Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson 2 A Start 1 B 4 St. Adolf’s Hospital Example 8.1

36. Immediate Activity Description Predecessor(s) Responsibility AOA Network A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson 2 C A 3 Start 1 5 B D 4 St. Adolf’s Hospital Example 8.1

37. Immediate Activity Description Predecessor(s) Responsibility AOA Network F A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson 8 2 I C A 3 7 G Start 1 H 5 6 B E D 4 St. Adolf’s Hospital Example 8.1

38. Immediate Activity Description Predecessor(s) Responsibility AOA Network F A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson 8 2 I C A 3 7 J G Start 1 H 5 6 B E D 4 St. Adolf’s Hospital Example 8.1

39. Immediate Activity Description Predecessor(s) Responsibility AOA Network F A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson 8 2 I Dummy C A 3 7 J G Start 1 H 5 6 B E D 4 St. Adolf’s Hospital Example 8.1

40. Immediate Activity Description Predecessor(s) Responsibility AOA Network F A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson 8 2 I Dummy C K A 3 7 J G Start 1 Finish 9 H 5 6 B E D 4 Figure 8.5 St. Adolf’s Hospital Example 8.1

41. Network Computation Process • Forward Pass—Earliest Times • How soon can the activity start? (early start—ES) • How soon can the activity finish? (early finish—EF) • How soon can the project finish? (expected time—ET) • Backward Pass—Latest Times • How late can the activity start? (late start—LS) • How late can the activity finish? (late finish—LF) • Which activities represent the critical path? • How long can activity be delayed? (slack or float—SL)

42. Forward Pass Computation • Add activity times along each path in the network (ES + Duration = EF). • Carry the early finish (EF) to the next activity where it becomes its early start (ES) unless… • The next succeeding activity is a merge activity, in which case the largest EF of all preceding activities is selected.

43. I 15 F 10 A 12 K 6 C 10 G 35 Start Finish H 40 J 4 B 9 D 10 E 24 St. Adolf’s Hospital Forward Pass: Earliest Start & Earliest Finish

44. Backward Pass Computation • Subtract activity times along each path in the network (LF - Duration = LS). • Carry the late start (LS) to the next activity where it becomes its late finish (LF) unless • The next succeeding activity is a burst activity, in which case the smallest LF of all preceding activities is selected.

45. I 15 12 27 F 10 A 12 K 6 0 12 63 69 12 22 C 10 G 35 12 22 22 57 H 40 J 4 B 9 D 10 9 19 19 59 59 63 0 9 E 24 9 33 St. Adolf’s Hospital Backward Pass: Latest Start and Latest Finish Times Start Finish

46. Determining Free Slack (or 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. • 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.

47. Special • Laddering • Activities are broken into segments so the following activity can begin sooner and not delay the work. • Lags • The minimum amount of time a dependent activity must be delayed to begin or end. • Hammock

48. Probability of completion

49. The equation below is used to compute the “Z” value found in statistical tables (Z = number of standard deviations from the mean), which, in turn, tells the probability of completing the project in the time specified. Probability of Completing the Project

50. Immediate Activity Description Predecessor(s) Responsibility AON Network I A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans and layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson A F K C G Start Finish D B H J E St. Adolf’s Hospital Example 8.1