Dependencies & Critical Path Method

Task dependencies in Critical Path are modeled as a Directed Acyclic Graph (DAG).

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Adding Dependencies

A dependency indicates that a target task depends on a source task (the prerequisite).

await engine.addDependency({
  projectId: 'proj-1',
  sourceTaskId: 'task-wireframes',
  targetTaskId: 'task-frontend-ui',
  type: 'finish_to_start',
  lagHours: 0,
});

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Cycle Detection & Prevention

Circular dependencies cause infinite loops and project deadlocks (e.g. Task A depends on Task B, which depends on Task A).

Critical Path performs an automatic topological cycle check before adding or updating any dependency edge:

try {
  // If task-a already depends on task-b:
  await engine.addDependency({
    projectId: 'proj-1',
    sourceTaskId: 'task-b',
    targetTaskId: 'task-a',
    type: 'finish_to_start',
  });
} catch (error) {
  console.error(error.message);
  // Throws: "Circular dependency detected: task-a -> task-b -> task-a"
}

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The Critical Path Method (CPM)

The Critical Path is the sequence of dependent tasks that determines the minimum total time required to complete the project. Any delay on the critical path directly pushes back the project deadline.

Algorithm Steps:

1. Forward Pass: Calculates the earliest possible start time (earlyStart) and finish time (earlyFinish) for every task.
2. Backward Pass: Calculates the latest allowable start time (lateStart) and finish time (lateFinish) without delaying project completion.
3. Total Slack: The difference between lateFinish and earlyFinish (slack = lateFinish - earlyFinish).
4. Critical Path Identification: Tasks with totalSlack === 0 form the Critical Path.

const result = await engine.calculateCriticalPath('proj-1');

console.log(`Project Completion Time: ${result.totalDurationHours} hours`);
console.log(`Bottleneck Tasks:`, result.criticalTaskIds);