PERT (Programme Evaluation and Review Technique)
- PERT was developed in 1956–58 by a research team to help in the planning and scheduling of the US Navy’s Polaris Nuclear Submarine Missile project involving thousands of activities.
- This technique has proved to be useful for projects that have an element of uncertainty in the estimation of activity duration.
CPM (Critical Path Method)
- CPM was developed by E.I. DuPont company along with Remington Rand Corporation almost at the same time, 1956-58.
- This technique has proved to be useful for developing time-cost trade-off for projects that involve activities of repetitive nature.
- In Project Planning phase, identify various activities (tasks or work packages/elements) to be performed in the project, that is, develop a breakdown structure.
DIFFERENCE BETWEEN PERT AND CPM
| S.No. | PERT | CPM |
|---|---|---|
| 1. | PERT is that technique of project management which is used to manage uncertain (i.e., time is not known) activities of any project. | CPM is that technique of project management which is used to manage only certain (i.e., time is known) activities of any project. |
| 2. | It is event-oriented technique which means that network is constructed on the basis of event. | It is activity-oriented technique which means that network is constructed on the basis of activities. |
| 3. | It is a probabilistic model. | It is a deterministic model. |
| 4. | It majorly focuses on time as meeting time target or estimation of percent completion is more important. | It majorly focuses on Time-cost trade off as minimizing cost is more important. |
| 5. | It has non-repetitive nature of job. | It has repetitive nature of job. |
Activities
- Activities in the network diagram represent project operations (or tasks) to be conducted.
- Each activity except dummy activity requires resources and takes a certain amount of time for completion.
- An arrow is commonly used to represent an activity.
- The activities can be further classified into the following three categories:
- Predecessor Activity: An activity which must be completed before one or more other activities start is known as predecessor activity.
- Successor Activity: An activity which starts immediately after one or more of other activities are completed is known as successor activity.
- Dummy Activity: An activity which does not consume either any resource and/or time is known as dummy activity.
Fulkerson’s Rule – Numbering of events
- The initial event which all outgoing arrows with no incoming arrow is numbered ‘a’.
- Delete all the arrows coming out from node ‘1’.
- Delete all the arrows going out from these numbered events to create more initial events.
- Continue until the final or terminal node which has all arrows coming in, with no arrow going out is numbered.
The objective of critical path analysis is to estimate the total project duration and to assign starting and
finishing times to all activities involved in the project.
The duration of individual activities may be uniquely determined (in case of CPM) or may involve the
three-time estimates (in case of PERT).
Critical path is the 1ongest path through the project network.
The activities on the path are the critical activities,
Therefore, any delay in their completion must be avoided to prevent delay in project completion.
For calculating the earliest occurrence and latest allowable times for events, following two methods:
Forward Pass method and Backward Pass method are used.
Forward Pass Method (For Earliest Start Time)
The method may be summarized as follows:
- Set the earliest occurrence time of initial event 1 to zero. That is, E1 = 0, for i = 1.
- Calculate the earliest start time for each activity that begins at event i (= 1). This is equal to the earliest occurrence time of event, i (tail event). That is:
ESij = Ei , for all activities (i, j) starting at event i.
3. Calculate the earliest finish time of each activity that begins at event i. This is equal to the earliest start time of the activity plus the duration of the activity. That is:
EFij = ESij + tij = Ei + tij , for all activities (i, j) beginning at event i.
4. Proceed to the next event, say j; j > i.
5. Calculate the earliest occurrence time for the event j. This is the maximum of the earliest finish times of all activities ending into that event, that is,
Ej = Max {EFij} = Max {Ei + tij }, for all immediate predecessor activities.
6. If j = N (final event), then earliest finish time for the project, that is, the earliest occurrence time EN for the final event is given by
EN = Max { EFij} = Max {EN – 1 + tij}, for all terminal activities
Backward Pass Method (For Latest Finish Time)
In this method, calculations begin from the final event N. The method may be summarized as follows:
1. Set the latest occurrence time of last event, N equal to its earliest occurrence time (known from forward pass method). That is, LN = EN , j = N.
2. Calculate the latest finish time of each activity which ends at event j. This is equal to latest occurrence time of final event. That is:
LFij = Li, for all activities (i, j) ending at event j.
3. Calculate the latest start times of all activities ending at j. This is obtained by subtracting the duration of the activity from the latest finish time of the activity. That is:
LFij = Lj and LSij = LFij – tij = Lj – tij, for all activity (i, j) ending at event j.
4. Proceed backward to the event in the sequence, that decreases j by 1.
5. Calculate the latest occurrence time of event i (i < j). This is the minimum of the latest start times of all activities from the event. That is:
Li = Min {LSij} = Min {Lj – tij}, for all immediate successor activities.
6. If j = 1 (initial event), then the latest finish time for project, i.e. latest occurrence time L1 for the initial event is given by:
L1 = Min {LSij} = Min {Lj – 1 – tij}, for all immediate successor activities.
Float (Slack) of an Activity and Event
The float (slack) or free time is the length of time in which a non-critical activity and/or an event can be delayed or extended without delaying the total project completion time.
PROJECT SCHEDULING WITH UNCERTAIN ACTIVITY TIMES
PERT was developed to handle projects where the time duration for each activity is not known with certainty.
The three-time estimates that are required are as under.
(i) Optimistic time (to or a) The shortest possible time (duration) in which an activity can be performed assuming that everything goes well.(ii) Pessimistic time (tp or b ) The longest possible time required to perform an activity under extremely bad conditions.(iii) Most likely time ( tm or m ) The time that would occur most often to complete an activity, if the activity was repeated under exactly the same conditions many times. Obviously, it is the completion time that would occur most frequently (i.e., model value).
Slack (Float) of an Activity
It is the amount of activity time that can be increased or delayed without delaying project completion time.
Types of Float
There are 4 types of floats:
- Total float
- Free float
- Independent float
- Interfering float
Total float simply called as the float is the amount of time an activity can be delayed without delaying the project completion date.
Total Float or Float = LS – ES or LF – EF
Total float = Latest start - Earliest start or Latest Finish - Earliest Finish
Free float
Free float is the amount of time that a task can be delayed without impacting the subsequent task
Free float = ((Ej – Ei ) – t ij
Independent float
This is the length of time by which completion time of any non-critical activity
(i, j) can be delayed without causing any delay in its predecessor or the successor activities.
Independent Float = Total Float – Tail Event Slack
Note: In case negative value is obtained, it is taken as zero.
Interfering Float
Interfering Float is the amount of time a schedule activity can be delayed or extended from its early start date without delaying the project finish date.
Interfering Float = Total Float – Free Float
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