- PERT:
- The Project Evaluation and Review Technique (PERT) is a model for project management designed to analyze and represent the tasks involved in completing a given project.
- PERT
is used to:
- find the minimum time
needed to complete the total project.
- identify projects on
a critical path
Projects on the critical path must be completed in time or else, the duration of the project will increase
- find the minimum time
needed to complete the total project.
- Example: Custom automotive assembly business
- Activities
to accomplish the ordering of a
custom automtive frame
and the time
needed to finish
the activity:
- (A): initial paper work
- (B): build body of car
- (C): build frame of car
- (D): finish body
- (E): finish frame
- (F): final paperwork
- (G): mount body to frame
- (H): room washdown
- 3
- 3
- 2
- 3
- 7
- 3
- 6
- 2
Activities Completion Time
- Dependency
of the various activities:
Note:
- The meaning of A → B is:
- Activity B cannot begin until activity A has been completed
- The meaning of A → B is:
- Activities
to accomplish the ordering of a
custom automtive frame
and the time
needed to finish
the activity:
- Terminolgy:
- Earliest Start Time (ES) =
the earliest time that an
activity can begin
- Earliest Finish Time (EF) =
the earliest time that an
activity can be completed
- EF = ES + duration of activity
- Lastest Start Time (LS) =
the latest time that an
activity can begin
without lengthening the
minimum project duration
- Latest Finish Time (LF) =
the earliest time than an
activity can be completed
without lengthening the
minimum project duration
- LF = LS + duration of activity
- Duration of the project =
the difference between
the maximum value of the
"lastest finish time" of projects and
the minimum value of the
"earliest start time" of projects
Project duration = max(LF) - min(ES)
- Slack =
the amount of time that a project
can be delayed
without increasing
the duration of the project
- Critical activity =
an activity in the project with
slack = 0
I.e.: critical activities have no slack, when such project is delayed, the duration of the project will increase
- Earliest Start Time (ES) =
the earliest time that an
activity can begin
- CPM:
- The Critical Path Method is
a (simple) analysis technique
used to find:
- Compute ES,
EF, LS
and LF in
a PERT network
- Identify the critical activities
- Compute ES,
EF, LS
and LF in
a PERT network
- The Critical Path Method is
a (simple) analysis technique
used to find:
- ES and EF are computed by
a forward pass through
the PERT network
- Example:
- Initial PERT network:
- ES(A) = 0 and
EF(A) = 0 + 3 = 3:
- ES(B) = EF(A) = 3 and
EF(B) = EF(B) + 3 = 6
ES(C) = EF(A) = 3 and EF(C) = EF(C) + 2 = 5
- Note:
ES(F) =
max(EF(B), EF(C)) = 6 and
EF(F) = EF(F) + 3 = 9
- Note:
ES(G) =
max(EF(D), EF(E)) = 12 and
EF(F) = EF(F) + 6 = 18
- Initial PERT network:
- Duration of the project:
Project duration = max(LF) - min(ES) = 18 - 0 = 18
- LS and LF are
computed by a
backward pass through the
PERT network
- Example:
- Initial PERT network:
- The latest time that
F, G and H
can finish without
lengthening the duration of the project =
18
Therefore:
- LF(F) = 18
- LF(G) = 18
- LF(H) = 18
That means that the latest time that G and H can start without lengthening the duration of the project are:
- EF(F) = 18 − 3 = 15
- EF(G) = 18 − 6 = 12
- EF(H) = 18 − 2 = 16
Therefore:
- The latest time that G must
start = 12
Therefore: the latest time that D must finish without pushing the start of G further = 12
Therefore:
- LF(D) = 12
That means that the latest time that D must start without lengthening the duration of the project is:
- EF(D) = 12 − 3 = 9
(Similar reasoning hold for activity E)
Therefore:
- The latest time that:
- D must start = 9
- F must start = 15
Therefore: the latest time that B must finish without pushing the start of D or F further = 9 !!!
Therefore:
- LF(B) = 9
That means that the latest time that D must start without lengthening the duration of the project is:
- EF(D) = 9 − 3 = 6
(Similar reasoning hold for activity C)
Therefore:
- The latest time that:
- B must start = 6
- C must start = 3
Therefore: the latest time that A must finish without pushing the start of B or C further = 3 !!!
Therefore:
- LF(A) = 3
That means that the latest time that D must start without lengthening the duration of the project is:
- EF(A) = 3 − 3 = 0
Result:
- Initial PERT network:
- Example:
Notes:
- Activity B:
- Earliest Start time = 3
- Lastest Start time = 6 (without causing project delay)
Activity B can start any time between [3..6] without causing project delay
We say that:
- Activity B has slack = 3
- Activity E:
- Earliest Start time = 5
- Lastest Start time = 5 (without causing project delay)
Activity E can start any time between [5..5] without causing project delay
We say that:
- Activity B has slack = 0
Such an activity is called citical
- Activity B:
- The critical activities in
the PERT example are:
- The critical activities form a (critical) path through the PERT network