Page 245 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes 12.3.1 Time Estimates: Earliest Time and Latest Time

Before the critical path in a network is determined, it is necessary to find the earliest and latest
time of each event to know the earliest expected time (T ) at which the activities originating
E
from the event can be started and to know the latest allowable time (T ) at which activities
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terminating at the event can be completed.
Forward Pass Computations (to calculate Earliest, Time T )
E

Procedure

Step 1: Begin from the start event and move towards the end event.
Step 2: Put T = 0 for the start event.
E
Step 3: Go to the next event (i.e. node 2) if there is an incoming activity for event 2, add
calculate T of previous event (i.e. event 1) and activity time. Note: If there are more
E
than one incoming activities, calculate T for all incoming activities and take the
E
maximum value. This value is the T for event 2.
E
Step 4: Repeat the same procedure from step 3 till the end event.
Backward Pass Computations (to calculate Latest Time T )
L

Procedure

Step 1: Begin from end event and move towards the start event. Assume that the direction
of arrows is reversed.
Step 2: Latest Time T for the last event is the earliest time. T of the last event.
L E
Step 3: Go to the next event, if there is an incoming activity, subtract the value of T of
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previous event from the activity duration time. The arrived value is T for that
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event. If there are more than one incoming activities, take the minimum T value.
E
Step 4: Repeat the same procedure from step 2 till the start event.
Determination of Float and Slack Times

As discussed earlier, the non-critical activities have some slack or float. The float of an activity
is the amount of time available by which it is possible to delay its completion time without
extending the overall project completion time.

For an activity i = j, let
t = duration of activity
ij
T = earliest expected time
E
T = latest allowable time
L
ES = earliest start time of the activity
ij
EF = earliest finish time of the activity
ij
LS = latest start time of the activity
ij
LF = latest finish time of the activity
ij

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