Relationships                 between Activities• A project is a sequence of activities.   – Large projects have interrela...
Step 2           Develop a Network Model• A Network Diagram visually displays the interrelated  activities using nodes (ci...
Two Types              of Network Models       Activity-on-Arc (AOA)Time                  Time                Time       A...
What AON Nodes look like.                                                                 Slack (S) is the difference, if ...
Precedent                                                  Relationships          Precedent relationships determine a seq...
Activity RelationshipsS & T must be completed    T & U cannot begin until Sbefore U can be started.   has been completed. ...
Activity Relationships                                U cannot begin until S & T have beenU & V can’t begin until S & T   ...
Activity RelationshipsT & U cannot begin until S has beencompleted; V cannot begin until both T & Uhave been completed.   ...
St. Adolf’s Hospital                                      (A sample project)                                              ...
St. Adolf’s Hospital                               Diagramming the Network             Activity Times             (wks) Im...
St. Adolf’s Hospital                                                I Paths are sequences of activities between a project’...
St. Adolf’s Hospital       The longest path is the critical path!                                                    IPath...
3. Develop the schedule• Now we insert the time estimates.  – This is where we distinguish between PERT & CPM.• CPM is use...
Using PERT       • PERT is used when activity times are uncertain.             – Decision making under risk (“P” for proba...
St. Adolf’s Hospital                         Developing the schedule• Earliest Start Time (ES) for an activity is the earl...
Earliest Start and Earliest Finish Times                                               12                                 ...
Earliest Start and Earliest Finish Times Path                Time (wks)                                               12  ...
Latest Start and Latest Finish Times                        (Working from the last activity toward the first activity)    ...
Node   Duration   ES   LS   Slack                                        Slack is the difference between LS A       12    ...
Sample GanttChart Printout
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Es 08 pert final

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Es 08 pert final

  1. 1. Relationships between Activities• A project is a sequence of activities. – Large projects have interrelated sequences.• These are called Precedent activities – They must be defined before the project begins.
  2. 2. Step 2 Develop a Network Model• A Network Diagram visually displays the interrelated activities using nodes (circles) and arcs (arrows) that depict the relationships between activities.• It is a graphical diagram.• Two types of Graphical Network Models – Activity On Arc (AOA) – Activity On Node (AON) (We will use AON)
  3. 3. Two Types of Network Models Activity-on-Arc (AOA)Time Time Time Activity D Activity E Activity-on-Node (AON) Activity Activity We will use D E this! Link
  4. 4. What AON Nodes look like. Slack (S) is the difference, if any, The is the earliest you can start an between the early start (ES) and late activity. It is determined by the early start times (LS) or the early finish (EF) finish time of the precedent activity. If and late finish (EF) times. there are two or more precedent activities, this time is the same as S = LS - ES or S = LF - EF precedent activity with the latest “Early Slack Finish” time. The earliest you can complete an activity--determined by adding the Activity activity time (duration) to the early Early Early start time. Start Finish Late Late This is the latest you can finish an Start Activity Finish Duration activity without delaying project This is the Late-Finish completion. It is the same as the time minus the activity Late Start time of the next activity. duration. If there are two or more subsequent activities, this time is the same as the earliest of those “Late Start” times.© 2011 Lew Hofmann
  5. 5. Precedent Relationships Precedent relationships determine a sequence for accomplishing activities. They specify that any given activity cannot start until its preceding activity or activities have been completed. Activity On Node approach In our AON approach, the nodes (circles) represent activities, and the arcs AON represent the sequential relationships between them. S T UNodes are simplified in the following examples. “S” precedes “T” which precedes “U”
  6. 6. Activity RelationshipsS & T must be completed T & U cannot begin until Sbefore U can be started. has been completed. S T U S T U
  7. 7. Activity Relationships U cannot begin until S & T have beenU & V can’t begin until S & T completed. V cannot begin until T hashave been completed. been completed. S U S U T V T V
  8. 8. Activity RelationshipsT & U cannot begin until S has beencompleted; V cannot begin until both T & Uhave been completed. S T V U
  9. 9. St. Adolf’s Hospital (A sample project) 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 & 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*We won’t be using the “Responsibility” data, but it is important in project management.
  10. 10. St. Adolf’s Hospital Diagramming the Network Activity Times (wks) Immediate IPredecessorsA – 12 A F KB – 9C A 10D B 10 Start C G FinishE B 24F A 10G C 35 B D H JH D 40I A 15J E,G,H 4 EK F,I,J 6
  11. 11. St. Adolf’s Hospital I Paths are sequences of activities between a project’s start and finish. A F KPath Time (wks) Start C G FinishA-I-K33A-F-K28 B D H JA-C-G-J-K 67B-D-H-J-K 69B-E-J-K 43 E
  12. 12. St. Adolf’s Hospital The longest path is the critical path! IPath Time (wks) A F KA-I-K33A-F-K28 Start C G FinishA-C-G-J-K 67B-D-H-J-K 69B-E-J-K 43 B D H JProject ExpectedTime is 69 wks. E
  13. 13. 3. Develop the schedule• Now we insert the time estimates. – This is where we distinguish between PERT & CPM.• CPM is used when activity times are Certain. • It is Decision making under Certainty • You are certain of the time each activity will require to complete.• PERT is used when activity times are not certain. (Decision making under risk)
  14. 14. Using PERT • PERT is used when activity times are uncertain. – Decision making under risk (“P” for probabilistic) – Three time estimates are required for each activity. • OPTIMISTIC TIME: Best time if everything goes perfectly • REALISTIC TIME: Most likely time • PESSIMISTIC TIME: A worst-case situation B + 4M + P Expected Time = ------------------- 6In this example, the most likely time is given a weight of 4, and the other two times (pessimisticand optimistic) are each given weights of 1. Software allows you to change these as needed, butthe denominator must be the total of the weights given.
  15. 15. St. Adolf’s Hospital Developing the schedule• Earliest Start Time (ES) for an activity is the earliest finish time of the immediately preceding activity.• Earliest Finish Time (EF) for an activity is its earliest start time plus how long it takes to do it (estimated duration).• Latest Start Time (LS) is the latest you can finish the activity minus the activity’s estimated duration.• Latest Finish Time (LF) is the latest start time of the activity that immediately follows it. (Latest start and finish times for each activity are computed starting at the project’s last activity completion time and working forward.)
  16. 16. Earliest Start and Earliest Finish Times 12 I 27 Earliest start time 15 Earliest finish time A 12 K 69 0 12 F 22 63 12 10 6 12 C 22 22 G57 Start Finish 10 35 0 B9 9 D 19 19 H59 59 J 63 9 10 40 4 9 E 33 24© 2012 Lew Hofmann
  17. 17. Earliest Start and Earliest Finish Times Path Time (wks) 12 I 27 The Critical Path takes A-I-K33 15 69 weeks A-F-K28 A-C-G-J-K 67 A K 69 B-D-H-J-K 69 0 12 12 F 22 63 B-E-J-K 43 12 10 6 12 C 22 22 G57 Start Finish 10 35 0 B9 9 D 19 19 H59 59 J 63 Critical Path 9 10 40 4 9 E 33 24© 2012 Lew Hofmann
  18. 18. Latest Start and Latest Finish Times (Working from the last activity toward the first activity) 12 I27 48 1563 A K 0 12 12 F 22 Latest 63 69 Latest 2 1214 53 1063 start 63 6 69 finish time time C 12 22 22 G 57 Start Finish 14 1024 24 59 35 0 B9 9 D 19 19 H 59 59 J 63 0 9 9 9 1019 19 4059 59 4 63 9 E 33 35 2459© 2012 Lew Hofmann
  19. 19. Node Duration ES LS Slack Slack is the difference between LS A 12 0 2 2 and ES or the EF and LF. B 9 0 0 0 C 10 12 14 2 12 I27 D 10 9 9 0 E 24 9 35 26 48 1563 F 10 12 53 41 G 35 22 24 2 A K H 40 19 19 0 0 12 12 F 22 63 69 I 15 12 48 36 2 12 14 53 1063 63 6 69 J 4 59 59 0 K 6 63 63 0 C 12 22 22 G 57 Start Finish 14 1024 24 59 35 0 B9 9 D 19 19 H59 59 J 63 Activity Slack 0 9 9 9 1019 19 4059 59 4 63 Analysis 9 E 33 35 2459© 2012 Lew Hofmann
  20. 20. Sample GanttChart Printout

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