Critical tasks have zero total float. Total float is latest start minus earliest start: the available scheduling flexibility without extending project completion, subject to the other relationships.

Finish-to-start (FS): the successor cannot start before the predecessor finishes, adjusted by lead or lag.

Start-to-start (SS): the successor cannot start before the predecessor starts, adjusted by lead or lag.

Finish-to-finish (FF): the successor cannot finish before the predecessor finishes, adjusted by lead or lag.

Start-to-finish (SF): the successor cannot finish before the predecessor starts, adjusted by lead or lag.

A positive lag adds waiting time. A negative lag introduces lead. For example, FS +3 means wait three days after the predecessor finishes; FS −3 permits three days of overlap. Other dependencies can still prevent that earlier start.

Relationships define earliest permitted events, not compulsory exact times. With SS, FF and SF constraints, shortening a critical task does not necessarily shorten the project one-for-one.

The engine uses forward and backward precedence calculations. Every task must finish before project completion, including tasks disconnected by an edit. No task may start before Day 0. Circular dependencies are rejected.

Assumptions: unlimited resources, uniform days, no weekends or holidays, no imposed deadlines and no resource levelling. Durations and lead/lag are limited to 365 days in this teaching tool.

Practical caution: these are illustrative plans, not production estimates or instructions to bypass approvals, inspections, safety controls or quality gates. Lead is appropriate only when usable partial outputs genuinely support downstream work. Model substantial waits and staged handoffs explicitly when managing a real project.