2.2Schedule development & the critical path

When a PM receives a status report saying "a certain activity is running 2 days late," the first question to ask is: "is that activity on the critical path, or does it have slack (float)?" Failing to answer this immediately leads to judgment errors—overestimating the deadline impact and incurring unnecessary extra cost, or underestimating it and delaying action until it is too late. This section covers how to identify the critical path, compute float, and diagnose the overall impact of a delay.

2.2.1CPM and identifying the critical path

• CPM (critical path method) computes the total duration along every path from start to finish, deriving earliest start/finish (forward pass) and latest start/finish (backward pass) to identify the paths with no slack. The critical path is the path from start to finish with the longest total duration; activities on it have zero float, so a delay of even one day on any of them delays the entire project's completion date by the same amount.
• When a project has multiple paths, only the path with the longest total duration is the critical path; activities on shorter paths have slack (float). Whether an activity is on the critical path must never be judged by impressions—"the assignee looks busy" or "the work looks difficult"—it must always be identified through path calculation.

2.2.2Total float and free float

• Total float is the maximum number of days an activity can slip without delaying the overall project completion date; activities on the critical path have zero total float. Free float is the maximum number of days an activity can slip without delaying the earliest start date of its immediate successor, and it is always less than or equal to total float (free float <= total float).
• Confusing the two leads to a misleading report—"there is free float, so the overall deadline has slack too" is wrong (free float only measures the impact on the immediate successor). Total float is the indicator that determines the impact on the overall deadline.

A PM's project has two paths from start to finish. Path 1 is "Activity A (3 days) -> Activity B (5 days) -> Activity D (4 days)," totaling 12 days; Path 2 is "Activity A (3 days) -> Activity C (6 days) -> Activity D (4 days)," totaling 13 days. Comparing durations, Path 2 is longer, so the critical path is Path 2 (A->C->D, 13 days total), and Activity B has total float = 13 - 12 = 1 day. At one week's status meeting, Activity B's assignee reports a 1-day delay due to illness. Since Activity B is not on the critical path and has 1 day of float, this 1-day delay falls within the total float, and the PM can diagnose that it does not affect the overall project completion date. Even so, the PM should not simply relax—if Activity B slips by one more day, it would exhaust its float and merge into the critical path, so this needs to be watched. In a different week, Activity C's assignee reports a 2-day delay due to unexpectedly complex requirements. Because Activity C is on the critical path (A->C->D) with total float = 0, the PM can immediately conclude that this 2-day delay directly pushes the overall project completion date back by 2 days. In this case, the PM must not just receive the report but promptly communicate the impact to the successor Activity D and other related teams, and begin considering shortening measures such as crashing or fast tracking, covered in the next section. The core point of this section is that the same "2-day delay" report calls for entirely different responses depending on whether the activity is on the critical path.

2.2.3Section summary

• The critical path is the longest-duration path with zero float. Identify it via path calculation, never by impression
• Total float shows the impact on the overall deadline; free float shows only the impact on the immediate successor (free float <= total float)
• On receiving a delay report, first identify whether the activity is on the critical path, then judge the overall impact before responding