The sequence of activities that represents the longest path through a project, determining the shortest possible project duration and having zero total float.

total float (total slack)

The amount of time an activity can be delayed without delaying the project finish date (or a specified completion date), under the current schedule network and dates.

A schedule compression technique that shortens the schedule duration for the least incremental cost by adding resources or increasing effort on critical-path activities.

The amount of time an activity can be delayed without delaying the earliest start date of any of its immediate successor activities.

The amount of time an activity can be delayed without delaying the project finish date (or a specified completion date), under the current schedule network and dates.

Scheduling in Predictive Projects: Networks, Durations, and Critical Path Method — CAPM Mastery: Comprehensive Exam-Ready Preparation for the 2023+ CAPM Blueprint

From WBS to Activities: What Are We Scheduling?

From WBS to Activities

Scheduling builds on the WBS, which is "A hierarchical decomposition of the total scope of work to be carried out by the project team to accomplish the project objectives and create the required deliverables."

The lowest WBS level is the work package: "The work defined at the lowest level of the work breakdown structure for which cost and duration are estimated and managed."

For scheduling, work packages are decomposed into activities: specific tasks with clear starts/finishes that can be estimated and sequenced on a schedule.

Example work package "Develop user manual" becomes activities: draft outline, write content, peer review, edit and format, final approval.

Typical planning flow: 1) Scope and WBS, 2) Identify activities, 3) Sequence activities, 4) Estimate durations, 5) Build network, find critical path, 6) Approve schedule baseline.

Activity Lists and Attributes: Building the Raw Material

Activity List

The activity list is a complete list of all schedule activities, each with a unique ID and clear name. It is the bridge between the WBS and the schedule.

Activity Attributes

Activity attributes add detail: predecessors/successors, leads/lags, resources, constraints, assumptions, and the WBS element the activity belongs to.

Example: A-10 "Draft user manual outline" with attributes: WBS 3.2.1, predecessor A-05, duration 2 days, resource technical writer, cannot start before contract signed.

Exam clue: If a question says "a complete list of activities that need to be scheduled", think activity list. This must exist before reliable duration estimates or sequencing.

Dependencies and Precedence Relationships

Four Relationship Types

PDM uses four main relationships: Finish-to-Start (FS), Start-to-Start (SS), Finish-to-Finish (FF), and Start-to-Finish (SF) between activities.

FS: Successor cannot start until predecessor finishes (most common). SS: Successor cannot start until predecessor starts (can overlap).

FF: Successor cannot finish until predecessor finishes. SF: Successor cannot finish until predecessor starts (rare, like shift handovers).

Dependency Categories

Mandatory (hard logic), Discretionary (preferred logic), External (outside project), Internal (within project).

Exam tip: For schedule compression, discretionary dependencies are the ones you typically adjust; mandatory and external are usually fixed.

Building a Simple Network Diagram (AON Style)

Activity-on-Node (AON)

In AON diagrams, each activity is a box with its duration. Arrows show dependencies, forming a network that represents the project logic.

Mini-Project Example

Activities: A Book room (2d), B Prepare slides (3d), C Print handouts (1d), D Deliver training (1d).

Dependencies: B → C (FS); A → D, B → D, C → D (all FS). A and B can start in parallel; C waits for B; D waits for A, B, and C.

Visually: four boxes A, B, C, D. Arrows from A to D, B to C, B to D, C to D. This is a simple precedence diagram.

Quick check: Which activities can start at time zero? A and B. Which are dependent? C depends on B, D depends on A, B, and C.

Critical Path Method: Core Logic, Not Just Math

What CPM Does

Critical Path Method (CPM) finds the longest path through the network, the shortest possible project duration, and the float for each activity.

Critical Path & Float

The critical path is the sequence that determines the project finish. Total float is how long an activity can slip without delaying the project finish.

Forward & Backward Pass

CPM uses a forward pass (earliest start/finish) and a backward pass (latest start/finish) to compute float and identify critical-path activities.

CPM uses single-point duration estimates, matching a predictive life cycle where scope, time, and cost are determined early.

Exam angle: Expect small networks or tables, and questions about which path is critical or how a change affects the critical path and float.

Worked CPM Example: Forward and Backward Pass

Network Setup

Activities: A(3) → B(4) → D(5) → F(2); A(3) → C(2) → E(3) → F(2). All are Finish-to-Start. A starts the project; F finishes it.

Forward Pass

Forward pass: A ES 0 EF 3; B ES 3 EF 7; C ES 3 EF 5; D ES 7 EF 12; E ES 5 EF 8; F ES 12 EF 14. Project earliest finish = 14 days.

Backward Pass

Backward pass: F LF 14 LS 12; D LF 12 LS 7; E LF 12 LS 9; B LF 7 LS 3; C LF 9 LS 7; A LF 3 LS 0.

Total Float

Total float TF = LS-ES: A 0, B 0, C 4, D 0, E 4, F 0. Zero-float activities form the critical path.

Critical Path Result

Critical path = A-B-D-F, duration 14 days. Non-critical path A-C-E-F has 4 days of float on C and E.

Float/Slack: Total, Free, and Common Exam Traps

Types of Float

Total float: delay allowed without delaying project finish. Free float: delay allowed without delaying earliest start of successors.

Example: If C finishes at day 5 and its successor E can start at day 5, free float is 0. But if C could slip to day 9 without delaying project finish, total float is 4.

Exam Traps

Traps: assuming all non-critical activities have same float, treating float as "extra" time to waste, and ignoring negative float when deadlines are tighter than CPM results.

Critical path can change when durations or logic change. Always re-evaluate which path now has zero total float and longest duration.

Memory hook: Critical path = path of zero total float, not necessarily the one with the most activities or resources.

Schedule Baseline and Monitoring Performance

What Is the Schedule Baseline?

The schedule baseline is the approved version of the schedule model used to measure and control schedule performance, including key dates and project finish.

It is part of the performance measurement baseline, along with the scope baseline (scope statement, WBS, WBS dictionary) and the cost baseline.

Monitoring Performance

You compare actual dates to the baseline and, in EVM, use schedule variance: "A measure of schedule performance expressed as the difference between earned value and planned value."

Change Control

The baseline changes only via formal change control. Corrective actions try to bring work back in line; major approved changes may trigger re-baselining.

Remember: The baseline is the yardstick. Forecasts can move, but the baseline stays fixed unless the project is officially redefined.

Schedule Compression: Crashing vs Fast Tracking

Why Compress the Schedule?

If the CPM finish is later than the required date, you use schedule compression to shorten the project without changing scope.

Crashing

Crashing: Add resources or cost to shorten durations of critical-path activities. Often raises cost and sometimes risk; crash the least expensive options first.

Fast Tracking

Fast tracking: Change logic so activities overlap or run in parallel. Increases risk and potential rework but may not increase direct cost.

Exam Focus

Compress critical-path work only. Fast tracking mainly increases risk; crashing increases cost and risk. Scope is unchanged; only timing and approach shift.

Thought Exercise: Spot the Critical Path and Float

Use this exercise to practice reasoning without doing full calculations.

Network (all Finish-to-Start):

A: 2 days, starts project
B: 5 days, depends on A
C: 3 days, depends on A
D: 4 days, depends on B
E: 2 days, depends on C
F: 1 day, depends on D and E (final)

1) Identify possible paths from start to finish

Path 1: A → B → D → F
Path 2: A → C → E → F

2) Estimate path lengths (do this mentally):

Path 1 duration = 2 + 5 + 4 + 1 = 12 days
Path 2 duration = 2 + 3 + 2 + 1 = 8 days

3) Questions for you:

a) Which is the critical path? Why?
b) Which activities definitely have zero total float?
c) Does activity C have any total float? Roughly how much?

Pause and answer before reading the reasoning.

Reasoning

Critical path is the longest: A-B-D-F (12 days). Any delay here delays the project.
Activities on this path (A, B, D, F) have zero total float.
The shorter path A-C-E-F is 4 days shorter (8 vs 12), so C and E together have 4 days of shared total float. Roughly, each could slip some amount as long as the path stays ≤ 12 days.

On the exam, even if you do not compute exact ES/EF/LS/LF, you can often answer float and critical-path questions by comparing path lengths and remembering that only non-critical paths have positive total float.

Quick Check: Dependencies and Compression

Test your understanding of dependency types and schedule compression.

A project manager wants to shorten the schedule without increasing cost. They decide to overlap design and development, which were originally in strict finish-to-start sequence. Which statement best describes what they are doing and what type of dependency they are most likely changing?

They are crashing the schedule by changing a mandatory dependency.
They are fast tracking the schedule by changing a discretionary dependency.
They are fast tracking the schedule by changing an external dependency.
They are crashing the schedule by changing an internal dependency.

Show Answer

Answer: B) They are fast tracking the schedule by changing a discretionary dependency.

Overlapping activities that were previously in strict finish-to-start sequence is **fast tracking**. Changing how design and development overlap is typically a matter of team preference, so it is a **discretionary dependency**. Crashing would involve adding resources or cost; external dependencies involve parties outside the project.

Quick Check: Critical Path and Float

Apply CPM logic to a small scenario.

In a small project, there are two complete paths from start to finish. Path 1 has a duration of 18 days. Path 2 has a duration of 15 days. There are no other paths. Which statement is most accurate?

Path 1 is the critical path, and activities on Path 2 have a total float of 3 days.
Path 2 is the critical path, and activities on Path 1 have a total float of 3 days.
Both paths are critical, so all activities have zero total float.
Path 1 is the critical path, and activities on Path 2 have a total float of 15 days.