Critical path in Python

pmcontrols.cpm takes a list of activities, each with an id, its predecessors, and a duration. It runs the forward and backward pass and returns earliest/latest start and finish, total slack, and the critical path (the activities with zero slack).

import pmcontrols as pm

r = pm.cpm([
    {"id": "A", "predecessors": [],         "duration": 2},
    {"id": "B", "predecessors": [],         "duration": 3},
    {"id": "C", "predecessors": ["A"],      "duration": 2},
    {"id": "D", "predecessors": ["B"],      "duration": 4},
    {"id": "E", "predecessors": ["C"],      "duration": 4},
    {"id": "F", "predecessors": ["C"],      "duration": 3},
    {"id": "G", "predecessors": ["D", "E"], "duration": 5},
    {"id": "H", "predecessors": ["F", "G"], "duration": 2},
])

r.stats["project_duration"]      # 15.0
r.meta["critical_activities"]    # ['A', 'C', 'E', 'G', 'H']
print(r.table.to_string(index=False))

activity  duration   es   ef   ls   lf  slack  critical
       A       2.0  0.0  2.0  0.0  2.0    0.0      True
       B       3.0  0.0  3.0  1.0  4.0    1.0     False
       C       2.0  2.0  4.0  2.0  4.0    0.0      True
       D       4.0  3.0  7.0  4.0  8.0    1.0     False
       E       4.0  4.0  8.0  4.0  8.0    0.0      True
       F       3.0  4.0  7.0 10.0 13.0    6.0     False
       G       5.0  8.0 13.0  8.0 13.0    0.0      True
       H       2.0 13.0 15.0 13.0 15.0    0.0      True

This is the textbook General Foundry network. The critical path is A-C-E-G-H at 15 periods, with B and D carrying one period of slack and F carrying six. The whole schedule is reproduced to the digit in the validation suite.

Input

• predecessors may be a list (["A", "B"]) or a comma-separated string ("A, B"). An activity with no predecessors starts at time zero.
• duration is the field name by default; pass duration="dur" to read a differently named column.
• Activity ids are stringified, so integer ids work too.

What you get back

A single Result:

• r.stats: project_duration, n_activities, n_critical.
• r.table: one row per activity with es, ef, ls, lf, slack, critical.
• r.meta["critical_activities"]: the critical path in topological order.

The identity slack = LS - ES = LF - EF holds for every activity and is asserted in the test suite.

Errors

A precedence cycle raises a ValueError that names the cycle. An activity that lists an unknown predecessor raises a ValueError naming both, and a negative duration is rejected. You get a clear message instead of a silently wrong schedule.

The forward/backward pass follows the standard activity-on-node formulation (Render, Stair & Hanna, Quantitative Analysis for Management; PMBOK).