CPM Algebraic Representation

where

Explanation

  1. Earliest start of Event 0 (first node - project start time) is set to 0
  2. Moving forward through the network. The earliest time of Event j is equal to the earliest time of Event i plus the duration of (i,j). The maximum is over i where Arc (i,j) exists.
  3. Latest start of Event n (last node - project finish time) is set to the earliest start of Event n.
  4. Moving backward through the network. The latest time of Event i is equal to the latest start time Event j minus the duration of (i,j). The minimum is over j where Arc (i,j) exists.
  5. Total slack calculation for each Activity (i,j).

For each activity in the network the earliest (latest) start time and the earliest (latest) finish times are defined as follows:

where