Planning with Network, PERT,

1
Planning with Network, PERT, CPM

• We use a Network of tasks to show the
  relationship among tasks
• interdependencies among tasks
• A task requires time and resources
• major use of network is for scheduling

2
Relevant Characteristics of Tasks

• For each Task (or Activity)
• its predecessor tasks
• tasks that must be completed before it
• its successor tasks
• tasks that can not begin until it is completed
• its parallel tasks
• tasks that are independent and may be performed
  simultaneously with it

3
Tasks and Immediate Predecessors Table
Duration
Immediate Predecessors
Tasks
A
-
20 time units
B
A
25
C
B
10
D
C
15
E
C
40
F
25
E, D
4
Activity-on-Arrow Representation
Task Z , 25 time units
Task and the duration are represented as an arrow
between two nodes, which represent the beginning
and end of a task
5
Activity-on-Node Representation
Task Z (25 time units)
The task and the duration are both represented
in the Node
We will be using this notation
6
Activity-on-Node Representation of the 6 Tasks
from the Previous Table
D 15
A 20
B 25
C 10
F 25
E 40
7
Using the Network in Project Planning

• Major usage is for determining how long the
  project will take .
• The longest path through the network is the
  expected project duration.
• It is also called the CRITICAL Path
• Note that if there is a delay in any of the tasks
  on a critical path, the result would be a delay
  in the completion of the overall project.

8
Critical Path of the Previous Network
D 15
A 20
B 25
C 10
F 25
E 40
Tasks, A,B,C,E, and F are on the CRITICAL Path
9
Earliest Start(ES) and Earliest Finish(EF) of
Tasks by Taking a Forward Pass through the
Network, starting at Task A
D 15
A 20
B 25
C 10
F 25
Task
ES
EF
E 40
20
A
0
B
20
45
C
45
55
D
55
70
Note that EF (early finish) of task E is 95,
which forces ES (early start) of task F to be 95.
E
55
95
F
95
120
10
Late Start(LS) and Late Finish(LF) of Tasks by
Taking a Backward Pass through the Network,
starting at task F
D 15
A 20
B 25
C 10
F 25
Task
LS
LF
E 40
20
A
0
B
20
45
C
45
55
D
80
95
Note that LS of task D is 80 because it
needs only 15 time units to complete the
task. But you cant use it as Cs late
finish time.
E
55
95
F
95
120
11
Slack Time

• Note that for Task D in the previous example
• ES is 55 and EF is 70
• LS is 80 and LF is 95
• so, we can actually take the LS as the actual
  start time and not affect the over-all project
  schedule !
• Total slack of an activity is defined as the
  difference in start time between when a
  (non-critical) task must start at the latest and
  when it can start at the earliest
• Slack Time (LS ES) or (LF EF)
• in the above case slack time is 80-55 25 time
  units

12
Free Slack

• We are interested in slack time that allows us to
  delay the start of an activity without impacting
  the start time of its successor.
• Free Slack of Task x
• ES (of the earliest successor of Task
  x) EF
• For Task D of the previous example
• Free Slack 95 - 70 25
• In this case, Slack time is the same as Free
  Slack so the start of activity D can be delayed
  by 25 time units and there is no impact.

13
Another Example
D 3
B 5
F 5
A 10
E 5
-Activities A,C, F are on the Critical
Path. -Next longest path is A,B,E,F
C 15
Act.
ES
EF
LS
LF.
For Activity B (a non-critical activity)
-slack time LS - ES 15 - 10 5 -free
slack earliest ES - EF 15 -15 0 -this
says even if there is a 5 unit of slack time,
there is no free time For Activity D (a
non-critical activity) -slack time LS -ES
22 - 15 7 -free slack earliest ES -EF 25
- 18 7 - this says we can delay activity D by
7 units without hurting the successor activity
A
10
0
10
0
B
10
15
20
15
C
10
25
25
10
D
15
18
25
22
E
15
20
25
20
F
25
30
30
25
14
Program Evaluation Review Technique(PERT)

• PERT is based on the critical path that was
  addressed in the Network technique, except the
  task time is estimated using expected time
• Expected task time (e-t-t)for each of the tasks
  on the critical path is computed as follows
• e-t-t (Optimistic-time 4Most-likely-time
  Pessimistic-time)/6
• Expected Project time (EP) is the sum of all the
  e-t-ts on the critical path.

15
Critical Path Method (CPM)

• CPM is concerned with the relationship of cost to
  schedule.
• Given a time duration, T, and a cost, C, for a
  task, what would be the shortest time duration,
  Ts, if the associated cost, Cs, is allowed to
  increase? (Be very careful with this because
  thousands of software managers have been burned
  with this temptation!)
• The cost slope for each task on the critical path
  may be defined as follows
• cost slope for task i (Ci - Csi) / (Ti-
  Tsi)

We use absolute value to evade negative slopes
COST
(Tsi , Csi)
Csi
(Ti , Ci)
Ci
TIME
Ti
Tsi
16
CPM (cont.)

• Compute the task slope(s) of all the tasks.
• The lowest or smallest cost slope is the most
  effective time/cost trade-off task however, the
  most effective one for the project would be the
  lowest cost slope of the task residing on the
  critical path.
• We would apply more resources to that task to
  shorten the critical path, thus shortening the
  total project duration then go on to look at the
  next lowest cost slope of tasks on the critical
  path.
• One would stop this process when the desired
  schedule and the affordable cost is reached.