Latest start time

As explained in Statistics Every Programmer Needs

A latest start time is the latest point at which a project activity can begin without delaying the project's completion.

A latest start time (LS) is the latest point at which an activity can begin without delaying the project’s completion. It is determined during a backward pass through the project network. section 13.3 section 13.3.2

Calculate and interpret LS values as follows:

• Set the final activity’s latest finish time to the planned project completion time. section 13.3.2
• Subtract the activity duration from its latest finish time: LS = LF − duration. section 13.3.2
• For an activity with multiple successors, use the smallest successor latest start time as its latest finish time. section 13.3.2
• Compare LS with earliest start time to calculate slack; zero slack identifies a critical-path activity. section 13.3.3

Automated reporting tool project

The project finishes at week 29. Activity L has a two-week duration, so its latest start time is 29 − 2 = 27 weeks. Activity K must finish when L starts, at week 27; with a three-week duration, K has an LS of 24 weeks. section 13.3.2

Figure 13.3 A second visual representation of the automated reporting tool project plan. The new three-digit sequence for each activity represents, in order, the latest start time, the expected duration, and the latest finish time. A quick and easy way of distinguishing critical tasks from noncritical tasks is to compare the three-digit sequences: critical tasks have similar three-digit sequences, whereas noncritical tasks do not.

Compare each activity’s latest-start, duration, and latest-finish sequence to distinguish critical tasks from noncritical tasks. section 13.3.2

How Statistics Every Programmer Needs covers it

How deep it goes

Explains the subtraction formula, successor rule, worked values, and slack interpretation, but does not provide software implementation.

Examples

Uses activities K and L in an automated reporting tool project and represents values in a network diagram and CPM table.

What it assumes

Assumes a project network with activity dependencies, expected durations, and a known completion time.

What you can do after

Apply the backward pass to calculate activity deadlines and identify critical tasks through zero slack.

How it connects

Connects latest start time with latest finish time, backward pass, earliest start time, slack, and the critical path.

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Related concepts

• expected activity timeused by · An expected activity time is the estimated duration assigned to a project activity after combining its optimistic, pessimistic, and most-likely duration estimates.
• latest finish timeused by · A latest finish time is the latest point at which a project activity can be completed without delaying the project's completion.
• earliest start timecontrasts with · An earliest start time is the earliest point at which a project activity can begin while respecting its predecessor dependencies.

This explainer was generated by Manning's knowledge graph from the text of Statistics Every Programmer Needs. The section links point to the parts of the book it draws on.