The amount of time an activity can be delayed without delaying the project finish date (or a specified completion date). Calculated as TF = LS − ES or TF = LF − EF.

The amount of time an activity can be delayed without delaying the early start of any immediate successor. FF = min(ES of successors) − EF of this activity.

The sequence of activities that determines the earliest possible completion date of the project. In a simple network, activities on this path have total float = 0.

A schedule compression technique that involves performing activities in parallel or overlapping them that were originally planned in sequence, often increasing rework and risk.

A schedule compression technique that involves adding resources to critical path activities to shorten their duration, which always increases cost.

Schedule compression by adding resources to critical path activities to reduce their duration, which increases cost.

The amount of time an activity can be delayed without delaying the early start of any immediate successor. Calculated as min(ES of successors) − EF of the activity.

The amount of time an activity can be delayed without delaying the project finish date (or a specified completion date). Calculated as LS − ES or LF − EF.

Predictive Scheduling II: Float, Compression, and Schedule Performance — CAPM Mastery: Comprehensive Exam-Ready Prep for the Modern CAPM (PMI)

Q: In a network, Activity X has ES=5, EF=9, LS=8, LF=12. Its only successor, Activity Y, has ES=12. What are X's total float and free float?

Total float = 3, Free float = 3. Total float = LS − ES = 8 − 5 = 3 (or LF − EF = 12 − 9 = 3). Free float = ES(successor) − EF(X) = 12 − 9 = 3. So both total and free float are 3 days.

From Network Diagram to Float and Performance

Why This Module Matters

You already know how to build a predictive schedule. Now the focus shifts to analyzing and controlling that schedule: float, compression, resources, and performance.

Exam Context

These skills sit mainly in Predictive (Plan-Based) Methodologies and Project Management Fundamentals and Core Concepts. Expect numeric questions and scenario trade‑offs.

What You Will Be Able To Do

You will calculate total/free float, choose between fast tracking and crashing, distinguish resource leveling vs smoothing, read resource charts, and compute schedule variance.

Total Float and Free Float: Concepts and Formulas

ES, EF, LS, LF Refresher

ES/EF are the earliest an activity can start/finish. LS/LF are the latest it can start/finish without delaying the project finish date.

Total Float

Total float (TF) is how long you can delay an activity without delaying the project finish date. `TF = LS − ES` or `TF = LF − EF`.

Free Float

Free float (FF) is how long you can delay an activity without delaying any immediate successor: `FF = min(ES of successors) − EF of this activity`.

Exam Traps

Look for multiple critical paths, negative float from tight constraints, and wording like "without affecting successors" (that points to free float).

Worked Example: Calculating Total and Free Float

Network Setup

Network: A → B → D and A → C → D. Durations: A=4, B=3, C=5, D=2. All finish‑to‑start, no lags, start at day 0.

Forward and Backward Pass

Forward: A(0–4), B(4–7), C(4–9), D(9–11). Backward: D(9–11), B(6–9), C(4–9), A(0–4).

Total Float Results

Total float: A=0, B=2, C=0, D=0. Critical path is A → C → D. B has 2 days of total float.

Free Float Results

Free float: B: 9 − 7 = 2, C: 9 − 9 = 0. B can slip 2 days without affecting D’s ES; C cannot slip at all.

Quiz: Total vs Free Float

Use the scenario carefully; this is similar to CAPM numeric items.

In a network, Activity X has ES=5, EF=9, LS=8, LF=12. Its only successor, Activity Y, has ES=12. What are X's total float and free float?

Total float = 3, Free float = 3
Total float = 4, Free float = 3
Total float = 3, Free float = 4
Total float = 4, Free float = 4

Show Answer

Answer: A) Total float = 3, Free float = 3

Total float = LS − ES = 8 − 5 = 3 (or LF − EF = 12 − 9 = 3). Free float = ES(successor) − EF(X) = 12 − 9 = 3. So both total and free float are 3 days.

Schedule Compression: Fast Tracking vs Crashing

What Is Schedule Compression?

Schedule compression shortens the schedule without changing scope. The two main techniques: fast tracking and crashing.

Fast Tracking

Fast tracking overlaps activities that were sequential. It may shorten time with little extra cost but increases rework and coordination risk.

Crashing

Crashing adds resources to critical path activities to finish sooner. It always increases cost and can raise risk from overcrowding.

Choosing Between Them

If possible, fast track first when risk is acceptable. Crash when you must spend money to save time, and only on critical path work.

Quiz: Pick the Right Compression Technique

Identify the best response based on the scenario.

Your project is 2 weeks behind schedule. The sponsor will pay more to recover time but wants the lowest additional risk of rework. Which is the BEST option?

Fast track design and testing to run fully in parallel.
Crash selected critical path activities using experienced contractors.
Fast track all remaining activities, including integration and user training.
Crash non‑critical activities to build schedule buffer.

Show Answer

Answer: B) Crash selected critical path activities using experienced contractors.

The sponsor is willing to increase cost but wants lower rework risk. Crashing critical path activities (especially with experienced resources) adds cost but less rework risk than aggressive fast tracking. Crashing non‑critical work does not help the finish date.

Resource Optimization: Leveling vs Smoothing

Why Optimize Resources?

Your initial schedule may over‑allocate people or equipment. Resource optimization adjusts the plan to be realistic.

Resource Leveling

Leveling respects resource limits by delaying or splitting work. It can change the critical path and extend the project end date.

Resource Smoothing

Smoothing moves activities only within their float to even out resource use, without changing the end date.

Key Distinction

Leveling: schedule may slip. Smoothing: end date must stay fixed; you only use available float on non‑critical work.

Resource Artifacts: RBS, Histogram, and Calendar

Resource Breakdown Structure (RBS)

The RBS is a hierarchical breakdown of resources by category and type (for example, role, location, or skill). It shows who/what is used.

Resource Histogram

A resource histogram is a bar chart of resource usage over time. Peaks reveal over‑allocation; valleys show under‑use.

Resource Calendar

A resource calendar defines when each resource is available: working days, shifts, holidays, and part‑time patterns.

Using These Artifacts

Together, RBS, histograms, and calendars let you spot over‑allocation and decide where to level or smooth resources.

Schedule Baseline, Milestones, and Progress Tracking

Schedule Baseline

The schedule baseline is the approved schedule with set start/finish dates. It is the reference for measuring schedule performance.

Milestones and Charts

Milestones are zero‑duration key events. Milestone charts show only these events and dates, ideal for senior stakeholder communication.

Tracking Progress

You record actuals, update the schedule, and compare forecasts against the baseline to spot variances and control the project.

Schedule Variance and Schedule Health

Canonical Definition

schedule variance is "A measure of schedule performance expressed as the difference between earned value and planned value."

SV and SPI Formulas

SV = EV − PV. SPI = EV / PV. Both compare earned value to what was planned to be earned by now.

Interpreting Results

SV>0 or SPI>1: ahead of schedule. SV=0 or SPI=1: on schedule. SV<0 or SPI<1: behind schedule.

Link to Network

SV/SPI are value‑based indicators. Use them with your network, float, and forecasts to understand actual dates and critical path impact.

Thought Exercise: Reading Schedule Health

Use this exercise to connect numbers and diagrams the way the CAPM wants you to think.

Imagine this situation halfway through a 6‑month predictive project:

Planned Value (PV) by now: 200,000
Earned Value (EV) by now: 170,000
Actual Cost (AC) by now: 180,000

Also, your updated schedule shows that several non‑critical activities have used up most of their float, but the critical path is only 5 days behind the baseline finish date.

Reflect and answer mentally (or jot on scratch paper):

Compute SV and SPI

What is `SV = EV − PV`?
What is `SPI = EV / PV` (to two decimals)?

Schedule interpretation

Based on SV and SPI, is the project ahead or behind schedule in value terms?
How does that relate to the 5‑day slip on the critical path?

Control actions

Would you consider schedule compression? If so, where would you look first: critical or non‑critical activities? Why?
How could resource leveling vs smoothing change your options?

Pause for 1–2 minutes and reason through it. Then compare with this reference reasoning:

SV = 170,000 − 200,000 = −30,000 (behind schedule in value terms).
SPI ≈ 170,000 / 200,000 = 0.85 (only 85% of planned value earned).
You are behind both in value terms and in days on the critical path. Compression should target critical path activities, while also preventing further float erosion on near‑critical paths.

Key Term Flashcards: Float, Compression, and Performance

Use these flashcards to reinforce critical definitions and distinctions.

Total float (TF): The amount of time an activity can be delayed without delaying the project finish date (or a specified completion date). Calculated as TF = LS − ES or TF = LF − EF.
Free float (FF): The amount of time an activity can be delayed without delaying the early start of any immediate successor. FF = min(ES of successors) − EF of this activity.
Critical path: The sequence of activities that determines the earliest possible completion date of the project. In a simple network, activities on this path have total float = 0.
Fast tracking: A schedule compression technique that involves performing activities in parallel or overlapping them that were originally planned in sequence, often increasing rework and risk.
Crashing: A schedule compression technique that involves adding resources to critical path activities to shorten their duration, which always increases cost.
Resource leveling: A resource optimization technique that adjusts activity start/finish dates based on resource constraints, which may change the critical path and extend the project end date.
Resource smoothing: A resource optimization technique that adjusts activities within their float to smooth resource usage without changing the project end date.
Resource breakdown structure (RBS): A hierarchical decomposition of project resources by category and type (for example, role, location, or skill), similar in form to a WBS but focused on resources.
Resource histogram: A bar chart that shows the number of resources required over time, used to identify over‑allocation and under‑utilization.
Resource calendar: A calendar that specifies the working days, shifts, holidays, and availability patterns for specific resources or resource types.
Schedule baseline: The approved version of the schedule model that is used as a basis for comparison to actual results and can be changed only through formal change control.
schedule variance (SV) definition: "A measure of schedule performance expressed as the difference between earned value and planned value."
Schedule Variance formula: SV = EV − PV. SV > 0: ahead of schedule; SV = 0: on schedule; SV < 0: behind schedule (in value terms).
Schedule Performance Index (SPI): SPI = EV / PV. SPI > 1: ahead of schedule; SPI = 1: on schedule; SPI < 1: behind schedule.
Milestone chart: A schedule representation that shows only key events (milestones) and their planned dates, used to communicate major events to stakeholders.

Key Terms

Crashing: Schedule compression by adding resources to critical path activities to reduce their duration, which increases cost.
Free float: The amount of time an activity can be delayed without delaying the early start of any immediate successor. Calculated as min(ES of successors) − EF of the activity.
Total float: The amount of time an activity can be delayed without delaying the project finish date (or a specified completion date). Calculated as LS − ES or LF − EF.
Critical path: The sequence of activities that determines the earliest possible completion date of the project; in a simple network, activities on this path have zero total float.
Fast tracking: Schedule compression by overlapping or parallelizing activities that were originally planned in sequence, increasing coordination and rework risk.
Milestone chart: A simplified schedule view that shows major milestones and their planned dates, without all underlying activities.
Earned Value (EV): The measure of work performed expressed in terms of the budget authorized for that work.
Resource calendar: A calendar specifying working and non‑working time for resources, used to calculate realistic activity dates.
Resource leveling: Resource optimization that delays or splits activities to respect resource constraints, potentially changing the critical path and extending the end date.
Schedule baseline: The approved schedule model used as a basis for comparison with actual results; changes require formal change control.
schedule variance: A measure of schedule performance expressed as the difference between earned value and planned value.
Planned Value (PV): The authorized budget assigned to scheduled work up to a given point in time.
Resource histogram: A bar chart that displays resource usage over time to highlight periods of over‑allocation or under‑utilization.
Resource smoothing: Resource optimization that adjusts activities within their float to reduce resource peaks without changing the project end date.
Resource breakdown structure: A hierarchical decomposition of project resources by category and type, used to organize and plan resource usage.
Schedule Performance Index (SPI): An index of schedule efficiency calculated as EV divided by PV. Values above 1 indicate ahead of schedule; below 1 indicate behind schedule.