1. Planning and Managing Projects
Chapter 8
This presentation covers Chapter 8 – Planning and Managing Projects. The graphic is based on the example used through the Chapter.
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2. St. Adolf’s Hospital
The next series of slides presents Example 4.1. The series builds in steps to the conclusion of the Example showing the development of key equations along the way.
This slide advances automatically.
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3. St. Adolf’s Hospital 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.
The first step is to create the list of activities and the required predecessors.
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4. St. Adolf’s Hospital 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 Johnson
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5. St. Adolf’s Hospital AON Network 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
Then a network can be drawn. In fact, this step is not strictly necessary for management purposes and large projects are very difficult to represent in this fashion. But it is helpful to visualize this small project in this way. This series builds Figure 4.2.
This slide advances automatically.
This entire sequence can be automated by selecting automatic advance for each slide and setting the desired delay.
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6. St. Adolf’s Hospital AON Network A Immediate
Start A
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
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7. St. Adolf’s Hospital AON Network A B Immediate
Start A B
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
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8. St. Adolf’s Hospital AON Network A C B Immediate
Start A B C
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
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9. St. Adolf’s Hospital AON Network A B C D Immediate
Start A B C D
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
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10. St. Adolf’s Hospital AON Network A B C D E Immediate
Start A B C D E
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
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11. St. Adolf’s Hospital AON Network A B C D E F Immediate
Start A B C D E F
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
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12. St. Adolf’s Hospital AON Network A B C D E F G Immediate
Start A B C D E F G
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
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13. St. Adolf’s Hospital AON Network A B C D E F G H Immediate
Start A B C D E F G H
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
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14. St. Adolf’s Hospital AON Network A B C D E F G H I Immediate
Start A B C D E F G H I
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
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15. St. Adolf’s Hospital AON Network A B C D E F G H I J Immediate
Start A B C D E F G H I J
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
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16. St. Adolf’s Hospital AON Network I A F K C G B D H J E 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
AON Network I A F K
Start C G B D H J E
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17. St. Adolf’s Hospital AON Network I A F K C G B D H J E 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
AON Network I A F K
Start C G
Finish B D H J E
Figure 8.4
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18. St. Adolf’s Hospital Completion Time 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
Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40
Start
Finish
We start with the completed project as shown in Figure 4.4. J 4
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19. St. Adolf’s Hospital Completion Time 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
Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40
Start
Finish
We can then trace all the possible paths through the project.
This sequence is not shown in the text but can be a useful learning tool for students. J 4
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20. St. Adolf’s Hospital Completion Time 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
Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40
Start
Finish J 4
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21. St. Adolf’s Hospital Completion Time 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
Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40
Start
Finish J 4
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22. St. Adolf’s Hospital Completion Time 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
Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40
Start
Finish J 4
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23. St. Adolf’s Hospital Completion Time 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
Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40
Start
Finish J 4
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24. St. Adolf’s Hospital Path Expected Time (wks) A-F-K 28 A-I-K 33
A-C-G-J 61
B-D-H-J 63
B-E-J 37
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
Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40
Start
Finish
The path with the longest time, B-D-H-J-K, is the critical path. J 4
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25. St. Adolf’s Hospital Path Expected Time (wks) A-F-K 28 A-I-K 33
A-C-G-J 61
B-D-H-J 63
B-E-J 37
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
Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40
Start
Finish
This slide advances automatically. J 4
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26. St. Adolf’s Hospital Completion Time 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
Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40
Start
Finish
This slide advances automatically. J 4
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27. St. Adolf’s Hospital
The next series of slides presents Example 4.2. The series builds in steps to the conclusion of the Example showing the development of key equations along the way.
This slide advances automatically.
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28. St. Adolf’s Hospital Earliest Start and Earliest Finish Times Start15 A 12 F 10 K 6 C 10 G 35
Start
Finish
We can calculate the earliest possible starting times and earliest possible finishing times for each activity. B 9 D 10 H 40 J 4
Earliest Start
and
Earliest Finish Times E 24
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29. St. Adolf’s Hospital Earliest Start and Earliest Finish Times15
Earliest start time A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Earliest Start
and
Earliest Finish Times E 24
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30. St. Adolf’s Hospital Earliest Start and Earliest Finish Times15
Earliest finish time
Earliest start time A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Earliest Start
and
Earliest Finish Times E 24
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31. St. Adolf’s Hospital Earliest Start and Earliest Finish Times Start15 A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Earliest Start
and
Earliest Finish Times E 24
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32. St. Adolf’s Hospital Earliest Start and Earliest Finish Times Start15 A 12 F 10 K 6 C 10 G 35
Start
Finish
The calculations must proceed through the network after earlier activities are calculated. For example, activity D can not start until activity B is complete. B 9 D 10 H 40 J 4
Earliest Start
and
Earliest Finish Times E 24
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33. St. Adolf’s Hospital Earliest Start and Earliest Finish Times Start15 A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Earliest Start
and
Earliest Finish Times E 24
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34. St. Adolf’s Hospital Earliest Start and Earliest Finish Times Start15 A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Earliest Start
and
Earliest Finish Times E 24
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35. St. Adolf’s Hospital Earliest Start and Earliest Finish Times Start15 A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Earliest Start
and
Earliest Finish Times E 24
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36. St. Adolf’s Hospital Earliest Start and Earliest Finish Times Start15 A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Earliest Start
and
Earliest Finish Times E 24
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37. St. Adolf’s Hospital Earliest Start and Earliest Finish Times Start15 A 12 F 10 K 6 C 10 G 35
Start
Finish
In this way ES and EF times can be completed for the entire network. B 9 D 10 H 40 J 4
Earliest Start
and
Earliest Finish Times E 24
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38. St. Adolf’s Hospital Latest Start and Latest Finish Times Project15 A 12 F 10 K 6 C 10 G 35
Start
Finish
In much the same fashion, late start and late finish times can be calculated working backward through the network. This is Example 4.3 in the text.
This slide advances automatically. B 9 D 10 H 40 J 4
Project
finish
Time = 63
Latest Start
and
Latest Finish Times E 24
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39. St. Adolf’s Hospital Latest Start and Latest Finish Times Latest15 A 12 F 10 K 6
Latest
finish
time C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Latest
finish
time
Latest Start
and
Latest Finish Times 63 E 24
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40. St. Adolf’s Hospital Latest Start and Latest Finish Times Latest start15 A 12 F 10
Latest
start
time K 6
Latest
finish
time C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Latest Start
and
Latest Finish Times
Latest start
time E 24
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41. St. Adolf’s Hospital Latest Start and Latest Finish Times Start Finish15 A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Latest Start
and
Latest Finish Times E 24
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42. St. Adolf’s Hospital Latest Start and Latest Finish Times Start Finish15 A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Latest Start
and
Latest Finish Times E 24
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43. St. Adolf’s Hospital Latest Start and Latest Finish Times Start Finish15 A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Latest Start
and
Latest Finish Times E 24
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44. St. Adolf’s Hospital Latest Start and Latest Finish Times15
Earliest start time
Earliest finish time
Latest start time
Latest finish time A 12 F 10 K 6 C 10 G 35
Start
Finish
Critical path B 9 D 10 H 40 J 4
Latest Start
and
Latest Finish Times E 24
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45. St. Adolf’s Hospital Activity Slack Analysis Start Finish I 15 A 12 F A 12 F 10 K 6 C 10 G 35
Start
Finish
Having these sets of times it is possible to analyze slack for the network. This starts the presentation of Example 4.4. The series first shows the manual development of activity slack and then presents the screen shot of the Project output, Figure 4.9.
This slide advances automatically. B 9 D 10 H 40 J 4
Activity Slack Analysis E 24
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46. St. Adolf’s Hospital Activity Slack Analysis Activity Slack Finish I15 A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Activity Slack Analysis E 24
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47. St. Adolf’s Hospital Activity Slack Analysis Activity Slack15
Slack = LS – ES or
Slack = LF – EF A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Activity Slack Analysis E 24
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48. St. Adolf’s Hospital Activity Slack Analysis Activity Slack15
SlackK = 57 – 27 = 30 or
SlackK = 63 – 33 = 30 A 12 F 10 K 6 C 10 G 35
Start
Finish
Using either the ES/LS or EF/LF pairs results in the same analysis. B 9 D 10 H 40 J 4
Activity Slack Analysis E 24
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49. St. Adolf’s Hospital Activity Slack Analysis Node Duration ES LS Slack15 A 12 F 10 K 6 C 10 G 35
Start
Finish
Completing the analysis for the entire network, these are the results. B 9 D 10 H 40 J 4
Activity Slack Analysis E 24
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50. St. Adolf’s Hospital Activity Slack Analysis Node Duration ES LS SlackB C D E F G H I J K I 15 A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4
Activity Slack Analysis E 24
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51. St. Adolf’s Hospital Critical Path Node Duration ES LS SlackB C D E F G H I J K I 15 F 10 K 6 C 10 G 35
Finish
The critical path will be the path with zero slack. B 9 D 10 H 40 J 4 E 24
Critical Path
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52. St. Adolf’s Hospital Critical Path Start Finish I 15 A 12 F 10 K 6 C A 12 F 10 K 6 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4 E 24
Critical Path
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53. St. Adolf’s Hospital Cost-Time Relationships in Cost Analysis 8000 —
7000 —
6000 —
5000 —
4000 —
3000 —
0 —
Direct cost (dollars)
| | | | | |
Time (weeks)
Crash cost (CC)
Normal cost (NC)
Linear cost assumption
Estimated costs for a 2-week reduction, from 10 weeks to
8 weeks
5200
This slide advances automatically.
(Crash time)
(Normal time)
Figure 8.11
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54. St. Adolf’s Hospital
TABLE 8.1 DIRECT COST AND TIME DATA FOR THE ST. ADOLF’S HOSPITAL PROJECT
A 12 $ 12, $ 13,000 1 $ 1,000
B 9 50, , ,000
C 10 4, ,
D 10 16, , ,000
E , , ,000
F 10 10, , ,500
G , , ,000
H 40 1,200, ,260, ,000
I 15 40, , ,500
J 4 10, , ,000
K 6 30, , ,000
Totals $1,992,000 $2,209,000
Maximum
Normal Normal Crash Crash Time Cost of
Time Cost Time Cost Reduction Crashing per
Activity (NT) (NC) (CT) (CC) (wk) Week
This slide presents Table 4.1 with all the necessary cost data.
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55. St. Adolf’s Hospital Modeling project schedule in Excel
Forward schedule (Earliest time)
ES = EF of predecessor, if only one predecessor
ES = Max(EF of predecessors), if more than one
EF = ES + Activity duration
Backward schedule (Latest time)
LF = LS of successor, if only one successor
ES = Min(LS of successors), if more than one
LS = LF - Activity duration
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56. St. Adolf’s Hospital Optimal crashing using Excel Solver
Target cell = Cost or project completion time
Changing cells = Crashing time
Constraints = Crashing time <= MTR
Options:
Non-negative
Tolerance
Estimates, derivative, search
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57. St. Adolf’s Hospital Pert = Project Evaluation Review Technique
Finding probability for project completion time
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58. Probabilistic Time Estimates
Probability
Mean m a b
Figure 8.12 (a) Beta Distribution
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59. ( ) St. Adolf’s Hospital te = 2 = Probabilistic Time Estimates MeanK
te =
a + 4m + b 6
Mean
Start C G
Finish B D H J
Often referred to as the PERT technique, the use of probabilistic time estimates allows for additional analysis of the project network.
2 =
( )
b – a 6 2
Variance E
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60. St. Adolf’s Hospital Probabilistic Time Estimates Activity B MostK
Activity B
Most
Optimistic Likely Pessimistic
(a) (m) (b)
7 8 15
Start C G
Finish B D H J
Often referred to as the PERT technique, the use of probabilistic time estimates allows for additional analysis of the project network. E
Example 8.6
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61. ( ) St. Adolf’s Hospital te = = 9 weeks 2 = = 1.78
Probabilistic Time Estimates I A F K
Activity B
Most
Optimistic Likely Pessimistic
(a) (m) (b)
7 8 15
Start C G
Finish B D H J
te = = 9 weeks
7 + 4(8) + 15 6
2 = = 1.78
( )
15 - 7 2 E
Example 8.6
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62. St. Adolf’s Hospital Time Estimates (wk) Activity Statistics
Optimistic Likely Pessimistic Expected Variance
Activity (a) (m) (b) Time (te ) (2 )
Time Estimates (wk) Activity Statistics A B C D E F G H I J K
This table shows all the expected task times and variances for use in the probabilistic calculations.
Example 8.6
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63. St. Adolf’s Hospital 2 =  (variances of critical path activities)
What is the probability the project will be completed in 65 weeks?
Critical Path = B - D - H - J
TE = = 63 weeks
2 =  (variances of critical path activities)
This slide advances automatically.
2 = = 11.78
 = = 3.432
Example 8.7
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64. St. Adolf’s Hospital T – TE  Probabilities
Critical Path = B - D - H - J
T = 65 days TE = 63 days s = 3.432
T – TE 
65 – 63
3.432
z = =
= 0.58
From Normal table in page 807,
for z = 0.58, the table area =
The probability that the project will be
Completed within 65 days is 71.9%
Example 8.7
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65. St. Adolf’s Hospital Normal distribution: Mean = 63 weeks;
Probability of meeting the schedule is
Length of critical path
Probability of exceeding 65 weeks is 63 65
Project duration (weeks)
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66. St. Adolf’s Hospital T = 63 + 2.055 (3.432) = 70.05 weeks
Expected project completion time with 98% probability
Critical Path = B - D - H - J
T = TE + z s
Normal table for 98%, z = 2.055
T = (3.432) = weeks
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67. St. Adolf’s Hospital 2 =  (variances of activities)
Probabilities
Path = A - C - G – J Find probability for T = 65 days
TE = = 61 days
2 =  (variances of activities)
2 = = 15.44
z =
T – TE
2
z = = 1.02
65 – 61
15.44
From Appendix 2
Pz = .8461
Example 8.7
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