1. Project Scheduling A. A. Elimam FinishStart

2. Project Scheduling Need to plan and control large/time consuming projects

3. Projects Characteristics n Projects are unique n Time Estimation Difficulty n Control Decomposition into smaller tasksDecomposition into smaller tasks Responsibility of a task given to a specific individualResponsibility of a task given to a specific individual

4. Project Management: Stages 1.Define:Describe goal or Final outcome of Project 2.Plan:Identify tasks / resources / time 3.Execute / Control: Time-cost Trade-off

5. Activity The smallest unit of work effort consuming both time and resources that the project manager can schedule and control.

6. Precedence Relationship A sequencing constraint between interrelated activities by which one activity cannot start until a preceeding activity has been completed.

7. Schedule A plan that sets priorities, determines start and finish times, and allocates resources to accomplish the activities.

8. Examples Q Constructing a building or amusement park Q Constructing a road, dam, or oil pipeline Q Renovating a blighted urban area Q Developing a prototype for a new airplane Q Installing a large computer system Q Introducing a new product Q Organizing a state fair Q Redesigning an office layout

9. Measuring Success of a project ConformanceTimeBudget

10. Basic Questions 1.Project completion time? 2.Critical activities? 3.Activities that can be delayed? How Long? 4.Starting / ending time of each activity? 5.Range of $’s spent on project? 6.Time-cost trade-off

11. Project Management Basic Steps i.Describe project ii.Draw a network diagram iii.Provide time estimates iv.Analyze network v.Develop project plan vi.Update project plan

12. i. Describe project n Activities / precedence n end points

13. ii. Draw a network diagram AOA:  Arcs:  Activities Nodes:  Event AOA:  Arcs:  Activities Nodes:  Event AON:  Nodes:  ActivitiesArcs:  Sequence AON:  Nodes:  ActivitiesArcs:  Sequence

14. AOA and AON relationships 1 2 A B C 3 4 (a) AOA approach: Event 4 cannot take place until activities A, B and C have been completed. (b) AON approach: Activity C cannot take place until activities A and B completed. A B C Event Activity Implies time and resource consumption Software

15. Activity Relationships Activity Relationship AOAAON

16. Activity Relationships Activity Relationship S precedes T, which precedes U. AOAAON 12 S 3 T 4 U STU

17. Activity Relationships Activity Relationship S and T must be completed before U can be started. AOAAON S T U 1 2 3 T S 4 U

18. Activity Relationships Activity Relationship T and U cannot begin until S has been completed. AOAAON T U S 3 4 1 T U 2 S

19. Activity Relationships Activity Relationship U and V cannot begin until both S and T have been completed. AOAAON 1 2 4 5 U V S T 3 S T U V

20. Activity Relationships Activity Relationship U cannot begin until both S and T have been completed; V cannot begin until T has been completed. AOAAON S T U V 13 Dummy 5 246 SU TV

21. Activity Relationships Activity Relationship T and U cannot begin until S has been completed; V cannot begin until both T and U have been completed. AOAAON 124 3 ST 5 V UDummy STV U

22. iii. Provide Time Estimates n Deterministic CPM Critical Path Method or Probabilistic  PERT Probabilistic  PERT Program Evaluation and Review Technique then CPM

23. iv. Analyze Network n Identify critical path (CP) and activities on it n Estimate probability of completing project on time n Explore time-cost trade-off

24. v. Develop project plan n Schedule each activity (particularly on CP) Monitor actual  planned. Monitor actual  planned.

25. vi. Update project plan n Adjust schedule on the basis of actuals

26. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff. BSelect site and do site survey. CSelect equipment. DPrepare final construction plans and layout. EBring utilities to the site. FInterview applicants and fill positions in nursing, support staff, maintenance, and security. GPurchase and take delivery of equipment. HConstruct the hospital. IDevelop and information system. JInstall the equipment. KTrain nurses and support staff.

27. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J

28. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network A Start

29. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network A B Start

30. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network A C B Start

31. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network A C DB Start

32. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network A C D E B Start

33. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network AF C D E B Start

34. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network AF CG D E B Start

35. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network AF CG D E HB Start

36. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network

37. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network

38. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network

39. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J AON Network

40. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s) ASelect administrative and medical staff.— BSelect site and do site survey.— CSelect equipment.A DPrepare final construction plans and layout.B EBring utilities to the site.B FInterview applicants and fill positions in nursing, support staff, maintenance, and security.A GPurchase and take delivery of equipment.C HConstruct the hospital.D IDevelop and information system.A JInstall the equipment.E,G,H KTrain nurses and support staff.F,I,J Completion Time FinishStart A 12 C 10 G 35 H 40 D 10 E 24 J 4 K 6 F 10 I 15 B 9

41. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 I 15 F 10 Earliest Start and Earliest Finish Times

42. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 I 15 F 10 Earliest Start and Earliest Finish Times Earliest start time

43. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 Earliest Start and Earliest Finish Times Earliest start time Earliest finish time

44. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 0 9 Earliest Start and Earliest Finish Times

45. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 9 33 0 9 9 19 Earliest Start and Earliest Finish Times

46. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 9 33 0 9 9 19 12 22 Earliest Start and Earliest Finish Times

47. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 19 59 9 33 0 9 9 19 12 22 Earliest Start and Earliest Finish Times

48. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 22 57 19 59 9 33 0 9 9 19 12 22 Earliest Start and Earliest Finish Times

49. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 22 57 59 6319 59 9 33 0 9 9 19 12 22 Earliest Start and Earliest Finish Times

50. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 Earliest Start and Earliest Finish Times

51. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 Latest Start and Latest Finish Times

52. St. Adolf’s Hospital Latest Start and Latest Finish Times FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 63 69 Latest finish time

53. St. Adolf’s Hospital Latest Start and Latest Finish Times FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 63 69 Latest start time Latest finish time

54. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 53 63 63 69 59 63 Latest Start and Latest Finish Times

55. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 53 63 63 69 24 59 19 59 35 59 59 63 Latest Start and Latest Finish Times

56. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 53 63 63 69 14 24 24 59 9 19 19 59 35 59 59 63 Latest Start and Latest Finish Times

57. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 2 14 53 63 63 69 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Latest Start and Latest Finish Times

58. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 2 14 53 63 63 69 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Activity Slack Analysis

59. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 2 14 53 63 63 69 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Activity Slack Analysis LS - ES = S

60. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 2 14 53 63 63 69 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Activity Slack Analysis LS - ES = S 63 - 63 = 0

61. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 2 14 53 63 63 69 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Activity Slack Analysis LF - EF = S 69 - 69 = 0

62. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 2 14 53 63 63 69 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Activity Slack Analysis 0

63. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 2 14 53 63 63 69 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Activity Slack Analysis 0000 0

64. St. Adolf’s Hospital FinishStart A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 63 69 22 57 59 6319 59 9 33 0 9 9 19 12 22 48 63 2 14 53 63 63 69 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Activity Slack Analysis 0000 2 2 26 41 36 0 2

65. St. Adolf’s Hospital FinishStart A 12 C 10 G 35 E 24 0 12 I 15 F 10 12 27 12 22 22 57 9 33 12 22 48 63 2 14 53 63 14 24 24 59 35 59 0000 2 2 26 41 36 0 2 B9B9 0 9 D 10 9 19 H 40 19 59 J4J4 59 63 K6K6 63 69 Critical Path

66. Probabilistic Time Estimates

67. Time Probability

68. Probabilistic Time Estimates Mean mab Time Probability

69. Probabilistic Time Estimates Mean Time Probability abm 3s

70. St. Adolf’s Hospital Probabilistic Time Estimates

71. St. Adolf’s Hospital Activity B Most OptimisticLikelyPessimistic (a)(m)(b) 7815 Probabilistic Time Estimates

72. St. Adolf’s Hospital Activity B Most OptimisticLikelyPessimistic (a)(m)(b) 7815 Probabilistic Time Estimates t e = = 9 weeks 7 + 4(8) + 15 6

73. St. Adolf’s Hospital Activity B Most OptimisticLikelyPessimistic (a)(m)(b) 7815 Probabilistic Time Estimates t e = = 9 weeks 7 + 4(8) + 15 6  2 = = 1.78 ( ) 15 - 7 6 2

74. St. Adolf’s Hospital OptimisticLikelyPessimisticExpectedVariance Activity(a)(m)(b)Time (t e )(  2 ) Time Estimates (wk)Activity Statistics

75. St. Adolf’s Hospital OptimisticLikelyPessimisticExpectedVariance Activity(a)(m)(b)Time (t e )(  2 ) Time Estimates (wk)Activity Statistics A111213120.11 B781591.78 C51015102.78 D8916101.78 E142530247.11 F6918104.00 G253641357.11 H354045402.78 I101328159.00 J121545.44 K56760.11

76. St. Adolf’s Hospital Probabilities Critical Path = B - D - H - J - K T = 72 days T E = 69 days

77. St. Adolf’s Hospital  2 =  (variances of activities) z = T - T E  2 Probabilities Critical Path = B - D - H - J - K T = 72 days T E = 69 days

78. St. Adolf’s Hospital  2 =  (variances of activities) z = T - T E  2  2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89 Probabilities Critical Path = B - D - H - J - K T = 72 days T E = 69 days

79. St. Adolf’s Hospital  2 =  (variances of activities) z = T - T E  2  2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89 z = 72 - 69 11.89 Probabilities Critical Path = B - D - H - J - K T = 72 days T E = 69 days

80. St. Adolf’s Hospital  2 =  (variances of activities) z = T - T E  2  2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89 z = = 0.87 72 - 69 11.89 Probabilities Critical Path = B - D - H - J - K T = 72 days T E = 69 days

81. St. Adolf’s Hospital  2 =  (variances of activities) z = T - T E  2  2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89 z = = 0.87 72 - 69 11.89 Probabilities Critical Path = B - D - H - J - K T = 72 days T E = 69 days From Appendix 2 P z =.8078 .81

82. St. Adolf’s Hospital Project duration (weeks) 6972 Probability of meeting the schedule is 0.8078 Length of critical path Normal distribution: Mean = 69 weeks;  = 3.45 weeks Probability of exceeding 72 weeks is 0.1922

83. St. Adolf’s Hospital  2 =  (variances of activities) z = T - T E  2  2 = 0.11 + 2.78 + 7.11 + 5.44 + 0.11 = 15.55 z = = 1.27 72 - 67 15.55 Probabilities Path = A - C - G - J - K T = 72 days T E = 67 days From Appendix 2 P z =.8980 .90

84. St. Adolf’s Hospital AF I CGFinish D E HBJ K Start Project duration (weeks) 6769 Probability path B- D-H-J-K is less than 67 weeks Normal distribution for path B-D-H-J-K: Mean = 69 weeks;  = 3.45 weeks Probability path A-C-G-J-K is more than 69 weeks Normal distribution for path A-C-G-J-K: Mean = 67 weeks;  = 3.94 weeks

85. St. Adolf’s Hospital 8000 — 7000 — 6000 — 5000 — 4000 — 3000 — 0 — Direct cost (dollars) |||||| 567891011

86. St. Adolf’s Hospital 8000 — 7000 — 6000 — 5000 — 4000 — 3000 — 0 — Direct cost (dollars) Crash cost (CC) Normal cost (NC) |||||| 567891011 Time (weeks) (Crash time)(Normal time)

87. St. Adolf’s Hospital 8000 — 7000 — 6000 — 5000 — 4000 — 3000 — 0 — Direct cost (dollars) Crash cost (CC) Linear cost assumption Normal cost (NC) |||||| 567891011 Time (weeks) (Crash time)(Normal time)

88. St. Adolf’s Hospital 8000 — 7000 — 6000 — 5000 — 4000 — 3000 — 0 — Direct cost (dollars) 5200 Crash cost (CC) Linear cost assumption Normal cost (NC) Estimated costs for a 2-week reduction, from 10 weeks to 8 weeks |||||| 567891011 Time (weeks) (Crash time)(Normal time)

89. St. Adolf’s Hospital Minimum Cost Schedule A-I-K:33 weeksB-D-H-J-K:69 weeks A-F-K:28 weeksB-E-J-K:43 weeks A-C-G-J-K:67 weeks Total cost = $2,624,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65

90. St. Adolf’s Hospital Minimum Cost Schedule A-I-K:33 weeksB-D-H-J-K:69 weeks A-F-K:28 weeksB-E-J-K:43 weeks A-C-G-J-K:67 weeks Total cost = $2,624,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65

91. St. Adolf’s Hospital Minimum Cost Schedule A-I-K:33 weeksB-D-H-J-K:69 weeks A-F-K:28 weeksB-E-J-K:43 weeks A-C-G-J-K:67 weeks Total cost = $2,624,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Critical Path B-D-H-J-K: 69 weeks Crash Activity J by 3 weeks @ $1,000/week

92. St. Adolf’s Hospital Minimum Cost Schedule A-I-K:33 weeksB-D-H-J-K:69 weeks A-F-K:28 weeksB-E-J-K:43 weeks A-C-G-J-K:67 weeks Total cost = $2,624,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Critical Path B-D-H-J-K: 69 weeks Crash Activity J by 3 weeks @ $1,000/week 3($28,000) - 3($1,000) = $81,000

93. St. Adolf’s Hospital Minimum Cost Schedule A-I-K:33 weeksB-D-H-J-K:69 weeks A-F-K:28 weeksB-E-J-K:43 weeks A-C-G-J-K:67 weeks Total cost = $2,624,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Critical Path B-D-H-J-K: 66 weeks Crash Activity J by 3 weeks @ $1,000/week 3($28,000) - 3($1,000) = $81,000 $2,624,000 - $81,000 = $2,543,000

94. St. Adolf’s Hospital Minimum Cost Schedule A-I-K:33 weeksB-D-H-J-K:69 weeks A-F-K:28 weeksB-E-J-K:43 weeks A-C-G-J-K:67 weeks Total cost = $2,624,000 $2,543,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Critical Path B-D-H-J-K: 66 weeks Crash Activity J by 3 weeks @ $1,000/week 3($28,000) - 3($1,000) = $81,000 $2,624,000 - $81,000 = $2,543,000

95. St. Adolf’s Hospital FinishStart A 12 C 10 G 35 E 24 0 12 I 15 F 10 12 27 12 22 22 57 9 33 12 22 48 63 2 14 53 63 14 24 24 59 35 59 0000 2 2 26 41 36 0 2 B9B9 0 9 D 10 9 19 H 40 19 59 J4J4 59 63 K6K6 63 69

96. Precedence for Playground activities CodeActivity DescriptionTimeImmediate Name (days)Predecessors APlanningFind location, determine resource requirements20None BPurchasingRequisition lumber and sand60Planning (A) CExcavationDig and grade100Planning (A) DSawingSaw lumber into appropriate sizes30Purchasing (B) EPlacementPosition lumber in correct locations20Sawing, excavation (D,C) FAssemblyNail lumber together`10Placement (E) GInfillPut sand in and under equipment20Assembly (F) HOutfillPut dirt around equipment10Assembly( F) IDecorationLandscape, paint30Infill, outfill (G,H)

97. Playground Project APlanning BPurchasing DSawing EPlacement CExcavation FAssembly HOutfill IDecoration GInfill

98. A Planning B Purchasing D Sawing E Placement C Excavation F Assembly H Outfill I Decoration G Infill ES=20EF=80ES=80EF=110 ES=120EF=140 ES=20EF=120 ES=140EF=150 ES=170EF=200 ES=150EF=160 ES=150EF=170 ES=0EF=20 Two pass approach Forward Pass

99. Playground Project A Planning B Purchasing D Sawing E Placement C Excavation F Assembly H Outfill I Decoration G Infill ES=20EF=80LF=90LS=30ES=80EF=110LF=120LS=90 ES=120EF=140LF=140LS=120 ES=20EF=120LF=120LS=20 ES=140EF=150LF=150LS=140 ES=170EF=200LF=200LS=170 ES=150EF=160LF=170LS=160 ES=150EF=170LF=170LS=150 ES=0EF=20LF=20LS=0 Two pass approach Backward Pass

100. Playground Project A Planning B Purchasing D Sawing E Placement C Excavation F Assembly H Outfill I Decoration G Infill ES=20EF=80LF=90LS=30 S B =10 ES=80EF=110LF=120LS=90 S D =10 ES=120EF=140LF=140LS=120 S E =0 ES=20EF=120LF=120LS=20 S C =0 ES=140EF=150LF=150LS=140 S F =0 ES=170EF=200LF=200LS=170 S I =0 ES=150EF=160LF=170LS=160 S H =10 ES=150EF=170LF=170LS=150 S G =0 ES=0EF=20LF=20LS=0 S A =0 Two pass approach

101. Playground Project A Planning B Purchasing D Sawing E Placement C Excavation F Assembly H Outfill I Decoration G Infill ES=20EF=80LF=90LS=30 S B =10 ES=80EF=110LF=120LS=90 S D =10 ES=120EF=140LF=140LS=120 S E =0 ES=20EF=120LF=120LS=20 S C =0 ES=140EF=150LF=150LS=140 S F =0 ES=170EF=200LF=200LS=170 S I =0 ES=150EF=160LF=170LS=160 S H =10 ES=150EF=170LF=170LS=150 S G =0 ES=0EF=20LF=20LS=0 S A =0 Critical Path

102. Cost-time relationships analysis 567891011 Activity time duration (weeks) Total direct activity cost ($) 8,0007,0006,0005,0004,0003,000 Crash time, cost Linear cost assumption Estimated costs for a 2-week reduction Normal time, cost Hypothetical actual cost curve NT NC CT CC Cost to crash per week = CC - NC NT - CT

103. Limitations of PERT / CPM n project activities must be clearly defined, independent, and stable in their relationships n precedence relationships must be specified and networked together n time activities in PERT are assumed to follow the beta probability distribution this may be difficult to verify n time estimates tend to be subjective, and are subject to fudging by managers n there is inherent danger in too much emphasis being placed on the critical path

104. Resource Limitations 2B52B5 4C24C2 5A15A1 6D36D3 Activity time in days Workers required per day Finish Start 3E33E3

105. 123456789101112 Day Activity A B C D E Resource Requirements Resource Limitations Gantt Charts