Scheduling Computation , Critical Path Method. (CPM)

The basic scheduling computation consists of three distinct sequences:
i. The forward pass through the network,
ii. The backward pass through the network,
iii. Calculation of slack or float and determination of critical path.

Forward Pass Computation
The forward pass through the network is made by computing the earliest expected occurrence dates for every other event and the earliest completion dates for the activities. In case there is more than one activity merging at a point, the maximum of the completion times is taken as the earliest completion time. Starts should be chosen as it fulfills the condition that no activity can begin until all its constraining activities are complete. The forward pass procedure proceeds event to event along each node of the network until the end event has been reached. The expected duration time will be longest sequence of activities through the network i.e. the earliest completion time of the last event.

Backward Pass Computation
The planner establishes the latest allowable occurrence date for each event (TL) and latest allowable start at completion date for the event. In the backward pass the planner employs the path tracing procedure characteristic of the forward path in reverse starting with the last event and proceeding backwards along each path to the baseline or the beginning event.

In the backward pass a latest allowable occurrence time is set for the end event corresponding to the scheduled or expected completion date for the project. In the absence of a scheduled end later the earliest expected completion date is automatically set as the latest allowable date.

Slack Computation
Slack is defined as the difference between an earliest possible occurrence time for an event and its latest allowable occurrence time. This difference expressed in time units indicates how the occurrence of the event can be delayed without delaying the end event in the network.

Identification of Critical Path
Once we have determined the slack values attached to various events and activities in the network, the critical path is identified. Critical path can be defined as the longest sequence of activities leading to the end objective. It is the path with the lowest slack value. When a network contains negative slack, the path with the most negative slack is identified as the critical path.

There are many types of slack defined in literature but the two most important ones are Total Slack and Free Slack.
Total Slack: It is the amount of time an activity could be delayed without affecting the overall project duration.
Free Slack: It is the amount of time an activity could be delayed without delaying subsequent activities. It is equal to the difference between the earliest start time of the successor activity and the early finish time of the activity in question.

The Problem of Uncertainty
The project network is the basis of both the PERT and the CPM technique. The notions of the critical path and activity slack are common to each. But these models were developed independently and in somewhat distinct problem settings.

PERT was developed for and has been used most frequently research and development types of programmes. The technologies are rapidly changing and their products are nonstandard. CPM on the other hand, has most frequently been applied to construction projects. The activities in these projects use standard materials whose properties are well known. They employ long-developed and well-seasoned components, and they are based on a more or less stable technology. The PERT technique assumes that the activities and their network relationships have been well defined, but it allows for uncertainties in the activity times.

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