# Assignment Problems

Document Sample

```					         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
–   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)
• 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