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					         2/21 Project Management
•   Roll call/ collect homework
•   Go over homework(?)
•   Project management: Critical Path Method
•   Small groups
•   Assign homework
•   Discuss midterm exam
                  Project Modeling
• Project: build a house.
  – Various tasks to be accomplished to achieve this
    goal:
     •   get permits
     •   pour foundations
     •   install electrical systems
     •   install plumbing systems
     •   connect systems to public systems
     •   frame walls
     •   install flooring
      Project Modeling: CPM
• How to organize? How to plan?
• How long will the entire project take?
• Critical Path Model - Terms
  – Activity on Node
  – predecessor
  – duration
      Project Modeling: CPM
• How to organize? How to plan?
• How long will the entire project take?
• Critical Path Model - Terms
  – Activity on Node
  – predecessor
  – duration
      Project Modeling: CPM
• How to organize? How to plan?
• How long will the entire project take?
• Critical Path Model - Terms As long as the
  – Activity on Node           longest (duration)
                               series of activities
  – predecessor
                               takes -- also call the
  – duration                   CRITICAL PATH.
  Critical Path Method - Terms.
• Activity on Node            Arc: precedence

              A               B
  Start                                    Finish
              6               8


                                   Duration
                                   (EX: hrs.,
          Nodes: activities
                                   days)
   Critical Path Method: Terms
• “Activity A must be done before B can
  begin.” - Activity A is a PREDECESSOR
  of B.
               A               B
   Start                                 Finish
               6               8


                           Arc: precedence
           Nodes: activities
     Critical Path Method: Terms
 • “Activities A and B must be done before C
   can begin.” - A & B are PREDECESSORS
   of C.
                    A
                    6
  Start                    C           Finish
                           5
                    B
                    8
                           Arcs: predecessors
Nodes: activities
           Critical Path Method
• “Activity A must be done before C and B
  can begin.”
                                B
                                8
                   A
 Start             6                       Finish

                                C
                                5
         Nodes: activities
                             Arcs: predecessors
             EX: build a house
• Project tasks:
  –   install landscaping
  –   pour foundations
  –   frame walls
  –   install plumbing systems
  –   get permits
  –   install electrical systems
  –   move in.
EX: build a house: tasks in order
 –   get permits
 –   pour foundations
 –   frame walls
 –   install plumbing systems
 –   install electrical systems
 –   install landscaping
 –   move in.
        EX: build a house: durations
Durations:
   2 – get permits
   6 – pour foundations
   5 – frame walls
   4 – install plumbing systems
   6 – install electrical systems
   9 – install landscaping
   3 – move in.
    EX: build a house: label activities
Durations:
   2 – A: get permits
   6 – B: pour foundations
   5 – C: frame walls
   4 – D: install plumbing
   6 – E: install electrical
   9 – F: install landscaping
   3 – G: move in.
      EX: build a house: create table
Durations:
   2 – A: get permits           Act.   Dur.   Preds.   Post.
   6 – B: pour foundations      A      2      --       D
   5 – C: frame walls           B      6      --       C,F
                                C      5      B        D
   4 – D: install plumb.
                                D      4      A,C      E
   6 – E: install elec.
                                E      6      D        G
   9 – F: install landscaping   F      9      B        G
   3 – G: move in.              G      3      E,F
EX: build a house: create graphic CPM
                                     Act Dur Pre   Post
                                     A   2   -     D
        A                            B   6   -     C,F
                D   E                C   5   B     D
                                     D   4   A,C   E
start       C                        E   6   D     G
                        G   finish
                                     F   9   B     G
        B                            G   3   E,F
            F
   EX: build a house: add in durations
                                         Act Dur Pre   Post
                                         A   2   -     D
            A
                                         B   6   -     C,F
            2
                    D   E                C   5   B     D
                    4   6
                                         D   4   A,C   E
                C
start           5           G            E   6   D     G
                                finish
                            3            F   9   B     G
        B
        6           F                    G   3   E,F
                    9
          But what is the Critical Path?
(We must tell the family when the house will be done -- how soon?)

                  A
                  2             D         E
                                4         6
  start               C
                      5                             G
                                                              finish
                                                    3
              B
              6                     F
                                    9
 The critical path is the path of activities that takes the longest
 amount of time; the path with the activities that cannot be altered
 time-wise without changing the overall project duration.
           What is the Critical Path?
Add up all the paths possible; see what path is the longest. That path
is the critical path.
                                                      A-D-E-G = 12
                   A                                  B-C-D-E-G = 24
                   2             D        E           B-F-G       = 18
                                 4        6
    start              C
                       5                              G
                                                               finish
                                                      3
                 B
                 6                 F
                                   9
    Defining slack, ES, EF, LS, LF
• Slack: how much extra time you have available for a
  particular activity.
• ES -- early start: the earliest possible time you could
  begin a particular activity.
• EF -- early finish: the earliest possible time you could
  finish a particular activity.
• LS -- late start: the latest possible time you could begin
  a particular activity.
• LF -- late finish: the latest possible time you could
  finish a particular activity.
    Calculating slack, ES, EF, LS, LF
•   Slack = (time available) - (duration)
•   ES = (calc. time at the beginning of the node)
•   EF = ES + duration
•   LS = LF - duration
•   LF = (calc. time at the ending of the node)
                       Calculating slack
Any activity on the critical path has NO SLACK.
Any others are based on when they meet the critical path.
EX: Activity A requires two days, but there are 11 days available (
  Activity A meets the critical path at “start” (0) and at D. 11 days
  have passed on the critical path before getting to D (B+C=11).
                   A
                   2             D        E
                                 4        6
  start                  C
                         5                           G
                                                               finish
                                                     3
               B
               6                     F
                                     9
          Calculating ES (Early Start)
Early start is the earliest possible time the activity could start.
EX: Activity A could start (at the earliest) at 0.
    Activity D could start (at the earliest) at 11 (CP – No slack)
    Activity F could start (at the earliest) at 6.

                  A
                  2              D        E
                                 4        6
  start                C
                       5                             G
                                                               finish
                                                     3
              B
              6                      F
                                     9
       Calculating EF (Early Finish)
Early finish is the earliest possible time the activity could finish.
EF = ES + Duration.
EX: Activity A could finish (at the earliest) at 2 (0 + 2).
    Activity D could finish (at the earliest) at 15 (11 + 4) (CP).
    Activity F could finish (at the earliest) at 15 (6 + 9).
                 A
                  2               D         E
                                  4         6
 start                  C
                        5                               G
                                                                 finish
                                                        3
               B
               6                    F
                                    9
        Calculating LF (Late Finish)
Late finish is the latest possible time the activity could finish without
  affecting the overall project time.
EX: Activity A could finish (at the latest) at 11.
    Activity D could finish (at the latest) at 15 (Crit path – no slack).
    Activity F could finish (at the latest) at 21.
                  A
                  2               D         E
                                   4        6
 start                  C
                         5                             G
                                                                 finish
                                                       3
                B
                6                    F
                                     9
         Calculating LS (Late Start)
Late start is the latest possible time the activity could start w/o
  affecting the overall project time.
LS = LF – Duration.
EX: Activity A could start (at the latest) at 9 (11 – 2).
    Activity D could start (at the latest) at 11 (crit. path – no slack).
    Activity F could start (at the latest) at 12 (21 – 9).
                  A
                  2                D        E
                                    4        6
 start                   C
                         5                              G
                                                                  finish
                                                        3
                B
                6                     F
                                      9
                Labeling the CPM
Basic model:
               Activity    ES EF
               Duration    LS LF

         A 0 2
         2 9 11            D 10 15     E 15 21
                           4 10 15     6 15 21
start             C 6 11
                  5 6 11                         G 21 24
                                                           finish
                                                 3 21 24
        B 0 6
                             F 6 15
        6 0 6
                             9 12 21
          Small Group Exercise
• Installation of a computer system comprises
  eight activities.     Activity Immediate    Duration
  Draw the network               Predecessors
  model, calculate      A        -            3
  the ES, EF, LS, LF, B          -            6
  and slack for each    C        A            2
  activity.             D        B, C         5
                         E       D            4
                         F       E            3
                         G       B, C         9
                         H       F, G         3
                  Homework
Ch. 10 #2 (just draw the CPM model in Excel)
Ch. 10 #4 (draw the CPM model in Excel,
 calculate the critical path.)
Ch. 10 #8 (draw the CPM model in Excel,
 calculate and label all activities with ES, EF, LS,
 LF. Calculate the critical path. Calculate the
 slack for each activity.)
Ch. 10 #9 (calculate the critical path, calculate the
 ES, EF, LS, LF, and slack for each activity)
       About the Midterm Exam
• Three versions – make sure you do the right one.
• NO COLLABORATION
  Collaboration=Cheating
• When you open the spreadsheet, click on
  “Enable Macros” (if it comes up).
• The midterm is posted (by 9 p.m. Thursday) at
  http://www.adbook.net/teach022/305/m.htm
• It is due by 9:00 p.m. on Saturday, Feb. 23rd.
• Read the directions very carefully!