Critical Path in Network Analysis
Basic Scheduling Computations
The notations used are
(i, j) is Activity with tail event i and head event j
Ei is Earliest occurrence time of event i
Lj is Latest allowable occurrence time of event j
Dij is Estimated completion time of activity (i, j)
(Es)ij is Earliest starting time of activity (i, j)
(Ef)ij is Earliest finishing time of activity (i, j)
(Ls)ij is Latest starting time of activity (i, j)
(Lf)ij is Latest finishing time of activity (i, j)
The process is as follows
The calculation commences from the start node and goes towards the end node. For easiness, the forward pass computation begins by assuming the first occurrence time of zero for the first project event.
i. Earliest starting time of activity (i, j) is also the earliest event time of the tail end event, that is (Es)ij = Ei
ii. Earliest finish time of activity (i, j) is also the earliest starting time + the activity time, that is (Ef)ij = (Es)ij + Dij or (Ef)ij = Ei + Dij
iii. Earliest event time for event j is the maximum of the earliest finish times of each and every activities end in to that event, that is Ej = max [(Ef)ij for all immediate predecessor of (i, j)] or Ej =max [Ei + Dij]
For end event suppose E = L. Remember that all E's have been calculated by forward pass computations.
Latest finish time for activity (i, j) is equivalent to the latest event time of event j, that is (Lf)ij = Lj
Latest starting time of activity (i, j) is equal to the latest completion time of (i, j) - the activity time or (Ls)ij =(Lf)ij - Dij or (Ls)ij = Lj - Dij
Latest event time for event 'i' is the least of the latest start time of all activities originating from that event, that is Li = min [(Ls)ij for all immediate successor of (i, j)] = min [(Lf)ij - Dij] = min [Lj - Dij]
There are three types of floats
(Tf)ij = (Latest start - Earliest start) for activity ( i - j)
(Tf)ij = (Ls)ij - (Es)ij or (Tf)ij = (Lj - Dij) - Ei
(Ff)ij = (Earliest time for event j - Earliest time for event i) - Activity time for ( i, j)
(Ff)ij = (Ej - Ei) - Dij
(If)ij = (Ej - Li) - Dij
The negative independent float is always considered as zero.
Head event slack = Lj - Ej, Tail event slack = Li - Ei
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