Calculate critical path, total float, and free float for project activities with early/late start-finish analysis.
A precedence network turns activity durations and dependencies into a project schedule. Enter each activity, its duration, and its immediate predecessors to obtain early start, early finish, late start, late finish, total float, free float, and the critical path. The common surprise is that total float and free float are different: total float measures movement available before project completion moves, while free float measures movement available before an immediate successor's earliest start moves.
A concrete input and expected output from the current implementation.
Input
A: duration 3, predecessors none B: duration 2, predecessors A C: duration 4, predecessors A D: duration 1, predecessors B, C
Expected output
Project duration: 8 units. Critical path: A -> C -> D. A: ES 0, EF 3, LS 0, LF 3, total float 0, free float 0. B: ES 3, EF 5, LS 5, LF 7, total float 2, free float 2. C: ES 3, EF 7, LS 3, LF 7, total float 0, free float 0. D: ES 7, EF 8, LS 7, LF 8, total float 0, free float 0.
C runs until time 7, so D cannot start when B finishes at time 5. B therefore has 2 units of float, while A, C, and D form the zero-float route controlling the 8-unit completion.
Starting at time zero, an activity without predecessors has early start 0 and early finish equal to its duration. Every other activity starts at the largest early finish among its immediate predecessors. Adding its duration gives early finish. The largest finish among terminal activities is the calculated project duration.
Working backward from project completion, late start equals late finish minus duration, and a predecessor's late finish is the smallest late start of its successors. Total float is late start minus early start. Free float is the earliest successor start minus early finish, with project completion acting as the finish milestone for terminal work. Zero total float marks critical activities.
Yes. An activity can have an immediate successor scheduled to start as soon as that activity finishes, giving zero free float, while the entire branch still has room before it affects project completion. In that case delaying the activity moves its successor, but a limited delay does not move the project's finish.
No. Zero total float means the current schedule provides no delay allowance for that activity without moving the calculated completion, assuming all other durations and dependencies remain unchanged. It says nothing by itself about actual progress. Several routes can tie for the longest duration, producing multiple critical paths.
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