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CPM Network Computation


                       Activity
                                                     Depends on   t
             AOA                  AON
              1-2                  A                      ─       3
              2-3                  B                      A       4




Spring 2008,                        Activity on Node                  1
King Saud University              Dr. Khalid Al-Gahtani
AOA                                                           A ct ivit y N a m e


       1                                               3
                       A
                                             B

                       3
                                             4
                             2                             A ct ivit y D urat io n


 AON
           3                                       4

           A                                       B




Spring 2008,                 Activity on Node                                        2
King Saud University       Dr. Khalid Al-Gahtani
Drawing CPM Networks
•        Prerequisites: Before drawing a CPM
         network, we must have:
     –      List of all activities comprising the project
     –      Order of precedence of each activity
     –      Duration estimate of each activity




Spring 2008,                 Activity on Node               3
King Saud University       Dr. Khalid Al-Gahtani
Example:
                             Depends on                    Duration (Day)
   Activity
                       (Immediate Predecessor(s))         (Time to perform)
        a                          ─                             14
        b                          ─                              3
        c                          ─                              7
        d                         a, b                            4
        e                         b, c                           10




Spring 2008,                        Activity on Node                          4
King Saud University              Dr. Khalid Al-Gahtani
Activity on arrow Solution

                       a
                                                            d


                       b                           D um m y




                       c
                                                        e




Spring 2008,                 Activity on Node                   5
King Saud University       Dr. Khalid Al-Gahtani
Activity-on-node Solution
                       a



                                                   d



   ST A RT             b                               F IN IS H



                                                   e



                       c




Spring 2008,                 Activity on Node                      6
King Saud University       Dr. Khalid Al-Gahtani
Class work#1:
Draw AON Network for the fowling project:

                    Activity   Depends upon              Activity   Depends upon
                      A                                    G              F
                       B             A                      I             F
                       F             A                      J             H
                      H              A                     K           I, J, F
                       C            B, A                    L         G, D, E
                      D              B                     M              K
                       E             C                     N            L, M




 Spring 2008,                      Activity on Node                            7
 King Saud University            Dr. Khalid Al-Gahtani
“Activity on Node”
• Nodes = Activities
• Links = Precedence Relationships
• Dummy activities are not required


                       ES      t    ES
                        Activity Name
                       LS     TF    LF
Spring 2008,                  Activity on Node      8
King Saud University        Dr. Khalid Al-Gahtani
Example
           Activity     Depends on             Duration (Days)
             A                                        5
              B                A                     15
              C                A                     10
             D                 B                     15
              E               B, C                   10
              F               D, E                    5




Spring 2008,             Activity on Node                        9
King Saud University   Dr. Khalid Al-Gahtani
AON
                                                       ES     t      EF

                                                            N am e


                            B                 D        LS    TF      LF




                                                   F                 FIN ISH
ST A R T               A




                            C                  E




Spring 2008,                 Activity on Node                             10
King Saud University       Dr. Khalid Al-Gahtani
AON
                                                                            ES     t        EF

                                                                                 N am e
                               5      15   20      20   15   35

                                      B                 D                   LS    TF        LF


                               5           20      20        35



                                                                  35   5   40          40        0    40
0      0       0   0   5   5
                                                                       F                    FIN ISH
    ST A R T           A

                                                                  35       40          40             40
0              0   0       5




                               5      10   15      20   10   30

                                      C                 E

                               15          25      25        35




Spring 2008,                          Activity on Node                                               11
King Saud University                Dr. Khalid Al-Gahtani
Constraints with Lead/lag time




Spring 2008,             Activity on Node      12
King Saud University   Dr. Khalid Al-Gahtani
Finish-to-Start (FSij):
• FSij is equal to the minimum number of
  time units that must transpire from the
  completion of the predecessor (i) prior to
  the start of the successor (j).
• The time between the finish of one activity
  and the start of its successor is called
  “Lag”.


Spring 2008,               Activity on Node      13
King Saud University     Dr. Khalid Al-Gahtani
Finish-to-Start (FSij):
• If the relationship is not listed on the
  dependency arrow, FS is assumed with
  Lag= 0.
• Example: a planner may wish to have an
  activity of removing formwork from a new
  building component follow the concrete
  pour by some pre-defined lag period to
  allow setting.

Spring 2008,               Activity on Node      14
King Saud University     Dr. Khalid Al-Gahtani
Start-to-Start (SSij):
• SSij is equal to the minimum number of
  time units that must be complete on the
  preceding activity (i) prior to the start of the
  successor (j).




Spring 2008,                Activity on Node      15
King Saud University      Dr. Khalid Al-Gahtani
Start-to-Start (SSij):
• “Lag” is always applied to SS relation.
• Example: parallel in starting of Installing
  and Finishing the walls activity of 100
  rooms on a project must be 10 days
  difference (SS=10 days).
     – You don’t have to wait installing 100 wall’s
       room to start doing the finishing work.



Spring 2008,                Activity on Node          16
King Saud University      Dr. Khalid Al-Gahtani
Finish-to-Finish (FFij):
• FFij is equal to the minimum number of
  time units that must remain to be
  completed on the successor (j) after the
  completion of the predecessor (i).
• It is applied as productivity control.




Spring 2008,              Activity on Node      17
King Saud University    Dr. Khalid Al-Gahtani
Finish-to-Finish (FFij):
• The finish date of Installing and Finishing
  walls’ activity of 100 rooms on a project
  must have 10 days difference in order to
  control productivity (FF=10 days).
     – In this example, the productivity of installing
       the walls’ activity might be less than finishing
       the rooms’ activity.
• “Lag” is always applied to FF relation as
  buffer between the two activities.
Spring 2008,             Activity on Node                 18
King Saud University   Dr. Khalid Al-Gahtani
Start-to-Finish (SFij):
• SFij is equal to the minimum number of
  time units that must transpire from the
  start of the predecessor (i) to the
  completion of the successor (j).
• It is applied also for controlling productivity




Spring 2008,               Activity on Node      19
King Saud University     Dr. Khalid Al-Gahtani
Start-to-Finish (SFij):
  Example: The start date of Installing 100
  rooms’ wall’s activity and the finish date of
  Finishing same walls’ activity of a project
  must maintain 30 days difference to
  control productivity (SF=30 days).
  “Lag” is always applied to SF relation as
  buffer between the two activities.
• It is not recommended to use by planner.
Spring 2008,               Activity on Node      20
King Saud University     Dr. Khalid Al-Gahtani
Start-to-Start and Finish-to-Finish
                  (ZZij):
• ZZij is a combination of two constraints.
  i.e., a start-to-start and finish-to-finish
  relationship. It is written with the SSij time
  units first, followed by the FFij time units.
• These two relations are used combined to
  maintain buffer between the start and
  finish of two activities.


Spring 2008,             Activity on Node      21
King Saud University   Dr. Khalid Al-Gahtani
Forward Pass Computations
                               Initial T im e
                               E Fi        F S ij
        E S j = M ax   all i   ESi         SS ij
                               E Fi        F F ij      Dj
                               ESi         SF ij       Dj


         EFj = ESj + Dj

Spring 2008,                     Activity on Node           22
King Saud University           Dr. Khalid Al-Gahtani
Backward Pass Computation
                                      T erm inal T im e
                                      LS j        F S ij
           L F i = M in   all j       LF j         F Fij
                                      LSi         SS ij    Di
                                      LF j        SFij     Di


           LSi = LFi       Dj

Spring 2008,                        Activity on Node            23
King Saud University              Dr. Khalid Al-Gahtani
Example
                       2                   2                 6
                       B   FS 4            C          SF 5   D
                           SS 3

                                                      FF 1
                                                      SF 5
 4                     1                   3                          6
 A                     F   SF 4            L                          E




                       5                   1                 2   ES D      EF
                       K                   G          FS 4   H    A ctivity
                                                                 LS   F    LF



Spring 2008,                        Activity on Node                  24
King Saud University              Dr. Khalid Al-Gahtani
Example Solution
                           4    2   6            10   2   12           9    6   15
                                B        FS 4         C         SF 5        D
                           5    1   7    SS 3    11   1   13           10   1   16

                                                                FF 1
                                                                SF 5
0     4   4                4    1   5             9   3   12                         16   6    22
      A                         F        SF 4         L                                   E
0     0   4                10   6   11           11   2   14                         16   0    22



                                                                                     ES D      EF
                           4    5   9             9   1   10           14   2   16    A ctivity
                                K                     G         FS 4        H        LS   F    LF
                           4    0   9             9   0   10           14   0   16



    Spring 2008,                              Activity on Node                            25
    King Saud University                    Dr. Khalid Al-Gahtani

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Node

  • 1. CPM Network Computation Activity Depends on t AOA AON 1-2 A ─ 3 2-3 B A 4 Spring 2008, Activity on Node 1 King Saud University Dr. Khalid Al-Gahtani
  • 2. AOA A ct ivit y N a m e 1 3 A B 3 4 2 A ct ivit y D urat io n AON 3 4 A B Spring 2008, Activity on Node 2 King Saud University Dr. Khalid Al-Gahtani
  • 3. Drawing CPM Networks • Prerequisites: Before drawing a CPM network, we must have: – List of all activities comprising the project – Order of precedence of each activity – Duration estimate of each activity Spring 2008, Activity on Node 3 King Saud University Dr. Khalid Al-Gahtani
  • 4. Example: Depends on Duration (Day) Activity (Immediate Predecessor(s)) (Time to perform) a ─ 14 b ─ 3 c ─ 7 d a, b 4 e b, c 10 Spring 2008, Activity on Node 4 King Saud University Dr. Khalid Al-Gahtani
  • 5. Activity on arrow Solution a d b D um m y c e Spring 2008, Activity on Node 5 King Saud University Dr. Khalid Al-Gahtani
  • 6. Activity-on-node Solution a d ST A RT b F IN IS H e c Spring 2008, Activity on Node 6 King Saud University Dr. Khalid Al-Gahtani
  • 7. Class work#1: Draw AON Network for the fowling project: Activity Depends upon Activity Depends upon A G F B A I F F A J H H A K I, J, F C B, A L G, D, E D B M K E C N L, M Spring 2008, Activity on Node 7 King Saud University Dr. Khalid Al-Gahtani
  • 8. “Activity on Node” • Nodes = Activities • Links = Precedence Relationships • Dummy activities are not required ES t ES Activity Name LS TF LF Spring 2008, Activity on Node 8 King Saud University Dr. Khalid Al-Gahtani
  • 9. Example Activity Depends on Duration (Days) A 5 B A 15 C A 10 D B 15 E B, C 10 F D, E 5 Spring 2008, Activity on Node 9 King Saud University Dr. Khalid Al-Gahtani
  • 10. AON ES t EF N am e B D LS TF LF F FIN ISH ST A R T A C E Spring 2008, Activity on Node 10 King Saud University Dr. Khalid Al-Gahtani
  • 11. AON ES t EF N am e 5 15 20 20 15 35 B D LS TF LF 5 20 20 35 35 5 40 40 0 40 0 0 0 0 5 5 F FIN ISH ST A R T A 35 40 40 40 0 0 0 5 5 10 15 20 10 30 C E 15 25 25 35 Spring 2008, Activity on Node 11 King Saud University Dr. Khalid Al-Gahtani
  • 12. Constraints with Lead/lag time Spring 2008, Activity on Node 12 King Saud University Dr. Khalid Al-Gahtani
  • 13. Finish-to-Start (FSij): • FSij is equal to the minimum number of time units that must transpire from the completion of the predecessor (i) prior to the start of the successor (j). • The time between the finish of one activity and the start of its successor is called “Lag”. Spring 2008, Activity on Node 13 King Saud University Dr. Khalid Al-Gahtani
  • 14. Finish-to-Start (FSij): • If the relationship is not listed on the dependency arrow, FS is assumed with Lag= 0. • Example: a planner may wish to have an activity of removing formwork from a new building component follow the concrete pour by some pre-defined lag period to allow setting. Spring 2008, Activity on Node 14 King Saud University Dr. Khalid Al-Gahtani
  • 15. Start-to-Start (SSij): • SSij is equal to the minimum number of time units that must be complete on the preceding activity (i) prior to the start of the successor (j). Spring 2008, Activity on Node 15 King Saud University Dr. Khalid Al-Gahtani
  • 16. Start-to-Start (SSij): • “Lag” is always applied to SS relation. • Example: parallel in starting of Installing and Finishing the walls activity of 100 rooms on a project must be 10 days difference (SS=10 days). – You don’t have to wait installing 100 wall’s room to start doing the finishing work. Spring 2008, Activity on Node 16 King Saud University Dr. Khalid Al-Gahtani
  • 17. Finish-to-Finish (FFij): • FFij is equal to the minimum number of time units that must remain to be completed on the successor (j) after the completion of the predecessor (i). • It is applied as productivity control. Spring 2008, Activity on Node 17 King Saud University Dr. Khalid Al-Gahtani
  • 18. Finish-to-Finish (FFij): • The finish date of Installing and Finishing walls’ activity of 100 rooms on a project must have 10 days difference in order to control productivity (FF=10 days). – In this example, the productivity of installing the walls’ activity might be less than finishing the rooms’ activity. • “Lag” is always applied to FF relation as buffer between the two activities. Spring 2008, Activity on Node 18 King Saud University Dr. Khalid Al-Gahtani
  • 19. Start-to-Finish (SFij): • SFij is equal to the minimum number of time units that must transpire from the start of the predecessor (i) to the completion of the successor (j). • It is applied also for controlling productivity Spring 2008, Activity on Node 19 King Saud University Dr. Khalid Al-Gahtani
  • 20. Start-to-Finish (SFij): Example: The start date of Installing 100 rooms’ wall’s activity and the finish date of Finishing same walls’ activity of a project must maintain 30 days difference to control productivity (SF=30 days). “Lag” is always applied to SF relation as buffer between the two activities. • It is not recommended to use by planner. Spring 2008, Activity on Node 20 King Saud University Dr. Khalid Al-Gahtani
  • 21. Start-to-Start and Finish-to-Finish (ZZij): • ZZij is a combination of two constraints. i.e., a start-to-start and finish-to-finish relationship. It is written with the SSij time units first, followed by the FFij time units. • These two relations are used combined to maintain buffer between the start and finish of two activities. Spring 2008, Activity on Node 21 King Saud University Dr. Khalid Al-Gahtani
  • 22. Forward Pass Computations Initial T im e E Fi F S ij E S j = M ax all i ESi SS ij E Fi F F ij Dj ESi SF ij Dj EFj = ESj + Dj Spring 2008, Activity on Node 22 King Saud University Dr. Khalid Al-Gahtani
  • 23. Backward Pass Computation T erm inal T im e LS j F S ij L F i = M in all j LF j F Fij LSi SS ij Di LF j SFij Di LSi = LFi Dj Spring 2008, Activity on Node 23 King Saud University Dr. Khalid Al-Gahtani
  • 24. Example 2 2 6 B FS 4 C SF 5 D SS 3 FF 1 SF 5 4 1 3 6 A F SF 4 L E 5 1 2 ES D EF K G FS 4 H A ctivity LS F LF Spring 2008, Activity on Node 24 King Saud University Dr. Khalid Al-Gahtani
  • 25. Example Solution 4 2 6 10 2 12 9 6 15 B FS 4 C SF 5 D 5 1 7 SS 3 11 1 13 10 1 16 FF 1 SF 5 0 4 4 4 1 5 9 3 12 16 6 22 A F SF 4 L E 0 0 4 10 6 11 11 2 14 16 0 22 ES D EF 4 5 9 9 1 10 14 2 16 A ctivity K G FS 4 H LS F LF 4 0 9 9 0 10 14 0 16 Spring 2008, Activity on Node 25 King Saud University Dr. Khalid Al-Gahtani