CPM Algebraic Representation

where

Explanation

- Earliest start of Event 0 (first node - project start time) is set to 0
- 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. - Latest start of Event
*n*(last node - project finish time) is set to the earliest start of Event*n*. - 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. - 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