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Time Calculations in Network

. TIME CALCULATIONS IN NETWORK

 

Let t ij be the duration of an activity (i, j).

 

(a) Earliest Start Ti me (ES) . This is the earliest occurrence time of the event from which the activity emanates.

 

For the beginning event, ES 1 = 0 and let ES i = ES of all the activities emanating from node i. Then

ES j = Max { ES i + tij }

i

(b) Earliest Finish/Completion Time (EF) . This is the ES plus the activity duration

EF I = ES i+ t ij

 

For example, Consider a part of the network.

ES j = max  .{ ES l + t lj , ES 2 +T 2J} =Max { 3+2+1 } =5

EF l = 3+2 =5, EF 2 = 1+3 =4

 

 

(c) Latest Finish/Completion Time (LF). This is the latest occurrence time of the event at which the activity terminates.

 

LF i = Min j{LF1. – t ij }

 

For example, consider a part of the network

Then                                      

LF I =MIN { LF l – t il , LF 2 –T i2 }

= min { 8-3 ,7-4 } =3

 

(d) Latest Start Time (LS). This is the last time at which the event can occur without delaying  the completing of the project.

 

(e) Total Floats (TF). It is a time duration in which an activity can be delayed without affecting the project completion time.

 

 

TF ij = LFj – ES i -  t ij

= LF j - (ES; + tii)

=LFj – EF ij.

Also                             TF ij = LS ij – ES i

= (LF j – t ij) – ES i

 

(f ) Free Floats (FF). It is a time duration in which the activity completion time can be delayed without affecting the earliest start time of immediate successor activities in the network.

 

EF ij = ES j – ES i  t ij

= ES j - (ES i + t ii)

= ES j – EF ij.

 

An activity (i, j) is said to be critical if all the following conditions are satisfied :

 

ES i = LF i , ES j = = LF j ES j – ES j = LF j – LF j = t ij.

 

Thus any critical activity will have zero total float and zero free float.

 

(g) Independent Floats. It is defined as the difference between the free float and the tail slack.

 

Note. Slack is with reference to an event and float is with respect to an activity. Slack is generally used with PERT and float with CPM, but they may be used interchangeably used.