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"variance": 0, "es": 3, "ef": 4, "lf": 4, "ls": 3, "float": 0, "critical": "Yes" }, { "id": "L4A", "name": "Equal parallel work L4A", "optimistic": 1, "likely": 1, "pessimistic": 1, "predecessors": [ "L3A", "L3B" ], "expectedDuration": 1, "variance": 0, "es": 4, "ef": 5, "lf": 5, "ls": 4, "float": 0, "critical": "Yes" }, { "id": "L4B", "name": "Equal parallel work L4B", "optimistic": 1, "likely": 1, "pessimistic": 1, "predecessors": [ "L3A", "L3B" ], "expectedDuration": 1, "variance": 0, "es": 4, "ef": 5, "lf": 5, "ls": 4, "float": 0, "critical": "Yes" }, { "id": "L5A", "name": "Equal parallel work L5A", "optimistic": 1, "likely": 1, "pessimistic": 1, "predecessors": [ "L4A", "L4B" ], "expectedDuration": 1, "variance": 0, "es": 5, "ef": 6, "lf": 6, "ls": 5, "float": 0, "critical": "Yes" }, { "id": "L5B", "name": "Equal parallel work L5B", "optimistic": 1, "likely": 1, "pessimistic": 1, "predecessors": [ "L4A", "L4B" ], "expectedDuration": 1, "variance": 0, "es": 5, "ef": 6, "lf": 6, "ls": 5, "float": 0, "critical": "Yes" }, { "id": "FINISH", "name": "Finish acceptance", "optimistic": 0, "likely": 0, "pessimistic": 0, "predecessors": [ "L5A", "L5B" ], "expectedDuration": 0, "variance": 0, "es": 6, "ef": 6, "lf": 6, "ls": 6, "float": 0, "critical": "Yes" } ] }, { "title": "Critical path assumptions", "columns": [ { "key": "path", "label": "Path", "unit": "" }, { "key": "activities", "label": "Activity IDs", "unit": "" }, { "key": "duration", "label": "Duration", "unit": "weeks" }, { "key": "variance", "label": "Path variance", "unit": "weeks²" }, { "key": "used", "label": "Deadline approximation", "unit": "" } ], "rows": [ { "path": 1, "activities": "START → L0A → L1A → L2A → L3A → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Selected path" }, { "path": 2, "activities": "START → L0A → L1A → L2A → L3A → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 3, "activities": "START → L0A → L1A → L2A → L3A → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 4, "activities": "START → L0A → L1A → L2A → L3A → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 5, "activities": "START → L0A → L1A → L2A → L3B → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 6, "activities": "START → L0A → L1A → L2A → L3B → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 7, "activities": "START → L0A → L1A → L2A → L3B → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 8, "activities": "START → L0A → L1A → L2A → L3B → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 9, "activities": "START → L0A → L1A → L2B → L3A → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 10, "activities": "START → L0A → L1A → L2B → L3A → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 11, "activities": "START → L0A → L1A → L2B → L3A → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 12, "activities": "START → L0A → L1A → L2B → L3A → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 13, "activities": "START → L0A → L1A → L2B → L3B → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 14, "activities": "START → L0A → L1A → L2B → L3B → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 15, "activities": "START → L0A → L1A → L2B → L3B → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 16, "activities": "START → L0A → L1A → L2B → L3B → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 17, "activities": "START → L0A → L1B → L2A → L3A → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 18, "activities": "START → L0A → L1B → L2A → L3A → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 19, "activities": "START → L0A → L1B → L2A → L3A → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 20, "activities": "START → L0A → L1B → L2A → L3A → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 21, "activities": "START → L0A → L1B → L2A → L3B → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 22, "activities": "START → L0A → L1B → L2A → L3B → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 23, "activities": "START → L0A → L1B → L2A → L3B → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 24, "activities": "START → L0A → L1B → L2A → L3B → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 25, "activities": "START → L0A → L1B → L2B → L3A → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 26, "activities": "START → L0A → L1B → L2B → L3A → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 27, "activities": "START → L0A → L1B → L2B → L3A → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 28, "activities": "START → L0A → L1B → L2B → L3A → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 29, "activities": "START → L0A → L1B → L2B → L3B → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 30, "activities": "START → L0A → L1B → L2B → L3B → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 31, "activities": "START → L0A → L1B → L2B → L3B → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 32, "activities": "START → L0A → L1B → L2B → L3B → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 33, "activities": "START → L0B → L1A → L2A → L3A → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 34, "activities": "START → L0B → L1A → L2A → L3A → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 35, "activities": "START → L0B → L1A → L2A → L3A → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 36, "activities": "START → L0B → L1A → L2A → L3A → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 37, "activities": "START → L0B → L1A → L2A → L3B → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 38, "activities": "START → L0B → L1A → L2A → L3B → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 39, "activities": "START → L0B → L1A → L2A → L3B → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 40, "activities": "START → L0B → L1A → L2A → L3B → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 41, "activities": "START → L0B → L1A → L2B → L3A → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 42, "activities": "START → L0B → L1A → L2B → L3A → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 43, "activities": "START → L0B → L1A → L2B → L3A → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 44, "activities": "START → L0B → L1A → L2B → L3A → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 45, "activities": "START → L0B → L1A → L2B → L3B → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 46, "activities": "START → L0B → L1A → L2B → L3B → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 47, "activities": "START → L0B → L1A → L2B → L3B → L4B → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 48, "activities": "START → L0B → L1A → L2B → L3B → L4B → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 49, "activities": "START → L0B → L1B → L2A → L3A → L4A → L5A → FINISH", "duration": 6, "variance": 0, "used": "Not included" }, { "path": 50, "activities": "START → L0B → L1B → L2A → L3A → L4A → L5B → FINISH", "duration": 6, "variance": 0, "used": "Not included" } ] }, { "title": "Whole-schedule duration scenarios", "columns": [ { "key": "case", "label": "Duration assumption", "unit": "" }, { "key": "duration", "label": "Schedule duration", "unit": "weeks" } ], "rows": [ { "case": "optimistic", "duration": 6 }, { "case": "expected", "duration": 6 }, { "case": "pessimistic", "duration": 6 } ] } ], "warnings": [ "The deadline metric is a normal approximation for one selected critical path. It is not the probability that the entire dependency graph finishes by the target. Independent task durations and a stable critical path are assumed.", "64 critical paths exist. Parallel path uncertainty and path switching are omitted from the selected-path approximation.", "Only the first 50 critical paths are displayed; the total count is shown.", "The selected path has zero variance. Its deadline result is deterministic under the supplied durations." ], "summary": "The dependency schedule takes 6 weeks under PERT means. 64 critical paths have no total float. The first displayed path contains 8 activities and has a 100% selected-path deadline approximation for week 10; this does not quantify full-DAG deadline confidence.", "methods": [ "PERT mean = (optimistic + 4 × most likely + pessimistic) / 6. Variance = ((pessimistic − optimistic) / 6)^2.", "Forward CPM gives earliest start/finish; backward CPM gives latest start/finish; total float = latest start − earliest start.", "Every critical path is a start-to-finish path of zero-float activities with contiguous earliest times. At most 50 are displayed.", "Deadline probability uses a normal approximation with variance summed on the first displayed critical path.", "PERT means, CPM dates, float and path membership use exact rational arithmetic for canonical decimal inputs. Positive float remains positive at every supported scale." ], "limitations": [ "No resource levelling, calendars, correlated durations, uncertainty simulation or contract completion warranty.", "Normal approximation ignores competing near-critical paths and path switching. Multiple critical paths make the probability especially limited.", "Standard deviation and the selected-path normal CDF use numerical approximation. Arithmetic exactness does not remove omitted paths, correlations or uncertainty in duration inputs.", "Numerical input precision: use zero or absolute values of at least 0.000000001. Smaller nonzero inputs are rejected explicitly." ] }