Mathematics of the Forward

1
Mathematics of the Forward Backward Pass

• Nodes must be numbered uniquely
• No two activities can have the same start and end
  node
• Notation
• Let ESi represent the Earliest Start Time for
  Node i
• Let LCi represent the Latest Completion Time for
  Node i
• Let Dij represent the duration of activity (i,j)

2
Forward PassMathematics

• Let i0 and in represent the project start and
  finish nodes, respectively
• Set ES0 0 (or a known/assumed start date)
• Proceed forward through the network calculating
  ES for each node using
• ESj max ESi Dij
• for all activities (i,j) terminating at node j
• The forward pass is complete when ESn has been
  determined

3
Backward PassMathematics

• Set LCn ESn
• Proceed backward through the network calculating
  LC for each node using
• LCi min LCj - Dij
• for all activities (i,j) initiating at node i
• The backward pass is complete when LC0 has been
  determined