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Critical Path, Float and Schedule Analysis

Critical path, float and schedule analysis · Construction Planning, Scheduling and Project Control

Course review
StandardInternational undergraduate curriculum synthesis with GAO schedule-quality practice; verify the governing contract, calendar, constraints and project procedures
Source2 source files
Review stateTechnical and publication gates pending
LEARNING OUTCOMES

After this chapter, you should be able to

  • Translate a simple construction work breakdown into logically connected activities.
  • Distinguish duration, milestone, relationship, lag, calendar, constraint, critical path, near-critical path, total float and free float.
  • Complete forward- and backward-pass calculations using a declared day-zero convention.
  • Calculate and interpret total float and free float without treating either as an unconditional entitlement.
  • Identify a continuous critical path and recognise activities that can become critical after a small change.
  • Test a duration change and explain the resulting management response using traceable schedule evidence.
  • Identify logic, calendar, constraint and progress-data issues that can make a schedule forecast unreliable.

The decision: what truly controls completion?Source §Planning and scheduling · Decision-led lesson opening

A construction team may have hundreds of activities in progress, but not every delay moves the forecast completion date. The manager’s immediate task is to identify the connected sequence that controls completion, the nearby sequences with little remaining flexibility, and the evidence behind that conclusion. A critical-path calculation supports that decision only when the logic, durations, calendars, constraints and status information are credible.

Prerequisite checkSource §Learning sequence · Prior knowledge check

Before calculating dates, check that you can read a predecessor statement and add whole-day durations. Answer mentally, then reveal the feedback.

SELF CHECK

Precedence and elapsed time

An activity starts at time zero, lasts two working days and has a finish-to-start successor. When may the successor start under this lesson’s convention?

  • At time one
  • At time two
  • At time three
Reveal answer and feedbackAt time two

Early finish equals early start plus duration. The successor may start at its predecessor’s early finish when no lag or different calendar is present.

Turn the work plan into a logic modelSource §Activity networks · Network fundamentals

A bar chart communicates when activities are expected to occur. A logic network also records why an activity may start or finish. That dependency structure is what allows the schedule to forecast the effect of change rather than merely display dates.

Activity
A defined piece of work with a duration, owner and measurable completion condition.
Milestone
A zero-duration control point used to mark an event, approval or hand-off. The teaching network uses a one-day handover activity rather than a milestone so every activity follows the same arithmetic.
Predecessor
An activity whose logic relationship controls when another activity may start or finish.
Calendar
The working and non-working time rules applied to an activity or project.
Constraint
A date condition that can override or restrict dates calculated from network logic.
Data date
The status boundary separating recorded progress from forecast work in an updated schedule.
Common precedence relationships
RelationshipMeaningConstruction interpretationControl note
Finish to startSuccessor starts after predecessor finishesEnvelope work follows completion of its supporting frame areaUse for the base network because it makes the calculation transparent
Start to startSuccessor starts after predecessor startsServices rough-in follows released work frontsAdd a justified lag or work-front rule; avoid vague overlap
Finish to finishSuccessor finishes after predecessor finishesTesting completion follows installation completionCheck that start logic is also complete
Start to finishSuccessor finishes after predecessor startsRare transition logicUse only with a clear operational reason
Relationship choice should describe a real hand-off, access condition, approval or production dependency—not force a preferred date.
  • Give every non-start activity at least one credible predecessor.
  • Give every non-finish activity at least one credible successor.
  • Use activity names that describe measurable work, location or hand-off.
  • Keep durations consistent with scope, productivity, access and the assigned calendar.
  • Use lags and constraints sparingly and record the reason, owner and revision.
Original activity-on-node network for the teaching case. Solid double-line treatment identifies the calculated controlling sequence; dashed branches retain float.Original STRUCTURA review diagram · technical sign-off pending
SELF CHECK

Read a merge

Services rough-in has two predecessors. Which predecessor date controls its early start?

  • The earlier predecessor finish
  • The later predecessor finish
  • The average predecessor finish
Reveal answer and feedbackThe later predecessor finish

A finish-to-start successor cannot begin until every predecessor is complete, so the forward pass takes the maximum predecessor early finish.

Declare the time conventionSource §Time convention · Calculation basis

The base case uses day zero, whole working-day durations and one project calendar. An activity that starts at zero and lasts two working days finishes at two. Its finish-to-start successor may start at two. This convention avoids the inclusive-date ambiguity that appears when learners mix elapsed-time coordinates with labelled calendar days.

Forward pass: find the earliest datesSource §Forward pass · Early-date calculation

Early finish
EF = ES + duration

For a finish-to-start successor, early start is the maximum early finish of its immediate predecessors.

Early start at a merge
ESsuccessor = maximum(EFpredecessors)

The merge waits for the last required predecessor. Using an average or minimum would forecast work before every required hand-off is complete.

At the Services rough-in merge, the later predecessor finish controls the earliest feasible start.Original STRUCTURA review diagram · technical sign-off pending
  • Place all start activities at early start zero.
  • Add duration to obtain each early finish.
  • Move through the network in dependency order.
  • At a merge, select the maximum predecessor early finish.
  • The largest terminal early finish is the earliest project completion for this model.

Backward pass: find the latest datesSource §Backward pass · Late-date calculation

Late start
LS = LF − duration

Set terminal late finish to the calculated project duration, then move backward through the network.

Late finish at a branch
LFpredecessor = minimum(LSsuccessors)

The predecessor must finish soon enough to protect every successor, so the most restrictive successor late start controls.

At the Structural frame branch, the smaller successor late start controls the predecessor’s late finish.Original STRUCTURA review diagram · technical sign-off pending

Float: interpret schedule flexibilitySource §Float · Float calculation and meaning

Total float
TF = LS − ES = LF − EF

In this unconstrained teaching network, total float is the time an activity may move before the calculated project finish moves. Activities along a path share this flexibility.

Free float
FF = minimum(ESsuccessors) − EF

Free float is the delay available before the earliest start of an immediate successor moves. It is normally no greater than total float in this model.

Total float protects the forecast finish; free float protects immediate successor dates. The diagram uses separate line patterns so the distinction does not depend on colour.Original STRUCTURA review diagram · technical sign-off pending
Critical path
A continuous start-to-finish sequence with the least calculated total float that controls the modelled completion date.
Near-critical path
A sequence with little remaining float that can become controlling after a small duration, logic or progress change.
Longest path
The continuous logic sequence from the status boundary to the completion milestone with the greatest calculated duration; complex constraints can cause zero-float activities to differ from the true driving path.
SELF CHECK

Total float versus free float

An activity has total float but zero free float. What happens if it is delayed within its total float?

  • Nothing else changes
  • Its immediate successor date moves but project completion need not move
  • Project completion must move
Reveal answer and feedbackIts immediate successor date moves but project completion need not move

Zero free float means the successor has no local protection. Total float may still protect the final completion date, but using it changes downstream timing and can disturb resource plans.

Worked construction networkSource §Worked network · Manual calculation

Base construction activity data
ActivityConstruction activityDuration (working days)Immediate predecessor
ASite establishment2—
BFoundations4A
CLong-lead procurement5A
DStructural frame6B
EServices rough-in3C and D
FBuilding envelope4D
GInternal finishes5E and F
HHandover milestone activities1G
All relationships are finish to start with zero lag on one project working-day calendar.
WORKED EXAMPLE

Calculate the base-case finish and float

Complete a forward pass, set the terminal late finish to the project duration, complete the backward pass, then calculate total and free float.

  1. Forward pass through the frame

    A: ES 0, EF 0 + 2 = 2; B: ES 2, EF 2 + 4 = 6; D: ES 6, EF 6 + 6 = 12

    The frame finishes at time 12.
  2. Forward-pass merges

    E: ES max(7, 12) = 12, EF 15; G: ES max(15, 16) = 16, EF 21

    H finishes at time 22, so project duration is 22 working days.
  3. Backward pass through the branch

    H: LF 22, LS 21; G: LF 21, LS 16; F: LF 16, LS 12; E: LF 16, LS 13; D: LF min(13, 12) = 12, LS 6

    The envelope branch is more restrictive than Services rough-in in the base case.
  4. Float

    C: TF 8 − 2 = 6 and FF 12 − 7 = 5; E: TF 13 − 12 = 1 and FF 16 − 15 = 1

    E is near-critical; C has more total than free float.
  5. Reasonableness check

    Zero-total-float activities connect continuously from A to H

    A–B–D–F–G–H is the controlling path.

Result. Project duration = 22 working days. Critical path = A–B–D–F–G–H. Services rough-in has one working day of total float.

Verified base-case CPM results
ActivityESEFLSLFTotal floatFree float
A020200
B262600
C2781365
D61261200
E1215131611
F1216121600
G1621162100
H2122212200
ES = early start; EF = early finish; LS = late start; LF = late finish. Results are independently covered by deterministic tests.

Predict, test, check and reflectSource §Interactive learning · Simulation sequence

First predict whether changing a duration will move completion or change the controlling path. Then change one or more bounded durations, inspect the recomputed network and table, check your prediction, and explain which management action the evidence supports.

IMPLEMENTED REVIEW SIMULATION

Critical Path and Float Explorer

Test how bounded duration changes alter early dates, late dates, float, the critical path and the forecast project duration.

Learning sequence
Record a completion and path prediction before checking. · Change one duration at a time before testing combinations. · Use the results table to verify the visual network. · Write a management interpretation that states the changed assumption.
Assumptions
Day-zero elapsed-time convention · Whole working-day durations from one to twenty · One project calendar · Finish-to-start relationships with zero lag · No constraints, progress, resource levelling or probabilistic durations
States
Base case · Changed duration · Prediction checked · Invalid input · Reset
Validation
Implemented against deterministic teaching cases; independent technical approval pending
INTERACTIVE REVIEW SIMULATION

Critical Path and Float Explorer

Predict first. Change bounded durations. Check the recomputed network, dates and management meaning.

Technical approval pending
Day-zero conventionOne working-day calendarFinish to start · zero lagWhole days onlyNo constraints or resources
PREDICT

What will your change do?

Adjust activity durationsEnter a whole number from 1 to 20. Results recalculate after each accepted value.
Base case loaded. Record a prediction, then change a duration.
Forecast duration22working days
Controlling pathA–B–D–F–G–Hzero-total-float sequence
Near-criticalEone or two days total float
Recalculated construction critical path networkEight activity blocks show durations, early dates and total float. Double solid connectors and labelled critical blocks identify the controlling path; dashed connectors identify non-controlling branches.ASite establishmentES 0 · EF 2TF 0 · 2dCRITBFoundationsES 2 · EF 6TF 0 · 4dCRITCLong-lead procurem…ES 2 · EF 7TF 6 · 5dFLEXDStructural frameES 6 · EF 12TF 0 · 6dCRITEServices rough-inES 12 · EF 15TF 1 · 3dNEARFBuilding envelopeES 12 · EF 16TF 0 · 4dCRITGInternal finishesES 16 · EF 21TF 0 · 5dCRITHHandover milestone…ES 21 · EF 22TF 0 · 1dCRIT
Critical: zero total floatNear-critical: one or two daysFlexible branch
MANAGEMENT INTERPRETATION

The model still forecasts 22 working days. Manage A–B–D–F–G–H as the controlling sequence and review E as near-critical.

Recalculated early dates, late dates and float
ActivityWorkDurationESEFLSLFTotal floatFree floatState
ASite establishment2020200Critical
BFoundations4262600Critical
CLong-lead procurement52781365Flexible
DStructural frame661261200Critical
EServices rough-in31215131611Near-critical
FBuilding envelope41216121600Critical
GInternal finishes51621162100Critical
HHandover milestone activities12122212200Critical
The table contains the same results as the visual network and remains the authoritative accessible fallback for this teaching simulation.
Reflect before continuing

Which changed assumption moved the forecast? Which path now controls completion? What site, design, procurement or resource evidence would you check before issuing a schedule revision?

SELF CHECK

Services rough-in sensitivity

Before testing, predict what happens when Services rough-in increases from three to five working days.

  • Completion remains at 22 and the path is unchanged
  • Completion becomes 23 and the controlling path passes through Services rough-in
  • Completion becomes 24 and both branches remain critical
Reveal answer and feedbackCompletion becomes 23 and the controlling path passes through Services rough-in

The longer Services rough-in finishes at 17, one day after the envelope. Internal finishes then start at 17, project completion becomes 23, and the controlling sequence changes to A–B–D–E–G–H.

Use the result as a management signalSource §Schedule control · Management interpretation

The schedule does not decide the response. It identifies where a changed assumption affects the forecast. The team must then verify work-front access, design release, procurement status, production rates, resources, interfaces and constraints before selecting an action. A responsible update records the data date, evidence, owner, revision and decision.

A controlled schedule update connects status evidence, logic review, forecast calculation, management decision and an authorised revision.Original STRUCTURA review diagram · technical sign-off pending
Schedule-quality issues and management checks
IssueWhy it distorts the forecastManagement check
Open endsMissing predecessor or successor logic creates artificial flexibilityTrace every activity from start to completion
Excessive lagsElapsed time is hidden outside measurable workReplace with explicit work or record the justified basis
Hard constraintsCalculated dates and float may reflect imposed dates rather than the driving logicReview the constraint type, owner and reason
Unrealistic calendarsDuration and float are calculated against the wrong working timeConfirm shifts, holidays and activity-calendar assignment
Out-of-sequence progressActual work no longer follows the planned relationshipApply the approved progress rule and repair future logic where authorised
Very high floatA missing dependency or distant completion link may be presentTrace the path and test whether the flexibility is real
Nearly all activities criticalThe network may be over-serial, constrained or resource-drivenReview logic detail, constraints and resource assumptions
These checks support review; they do not replace the project’s accepted scheduling procedure.

Guided and independent practiceSource §Practice · Application exercises

SELF CHECK

Complete a missing late date

In the base case, Building envelope finishes early at 16 and its successor Internal finishes has late start 16. What are the envelope late finish, late start and total float?

  • LF 16, LS 12, TF 0
  • LF 17, LS 13, TF 1
  • LF 21, LS 17, TF 5
Reveal answer and feedbackLF 16, LS 12, TF 0

The successor late start sets the predecessor late finish. Subtract the four-day duration to obtain late start 12; late and early starts are equal, so total float is zero.

WORKED EXAMPLE

Independent mini-network

Temporary access lasts two days. Excavation and off-site steel detailing then take four and six days respectively. Base preparation takes three days after excavation. Erection takes five days after both base preparation and detailing. Determine the project duration, controlling path and float on the shorter branch.

  1. Attempt before revealing

    Draw the network and complete both passes on paper.

    State the time convention and every predecessor.
  2. Forward-pass check

    Access EF 2; Excavation EF 6; Base preparation EF 9; Detailing EF 8; Erection ES max(9, 8) = 9 and EF 14

    Project duration is 14 working days.
  3. Path check

    Access–Excavation–Base preparation–Erection = 14; Access–Detailing–Erection = 13

    The excavation and base-preparation branch controls; detailing has one working day of float.

Result. Duration 14 working days; controlling path through excavation and base preparation; off-site detailing has one working day of float.

Lesson summarySource §Summary · Key learning

Key points

  • A logic network explains why dates move; a bar chart alone may only display when work is planned.
  • The forward pass uses maximum predecessor early finish at a merge; the backward pass uses minimum successor late start at a branch.
  • Total float protects the modelled finish, while free float protects immediate successor dates under the stated assumptions.
  • The base case finishes at 22 working days along A–B–D–F–G–H; Services rough-in is near-critical with one day of float.
  • Criticality can change after a small duration, logic, calendar, constraint or progress update.
  • A credible management interpretation records source, calendar, data date, revision, owner, assumptions, checks and limitations.

Source references recorded by the supplied chapter

  • Chartered Institute of Building — Accreditation and Education Framework: https://www.ciob.org/learning-providers/accreditation-education-framework
  • Loughborough University — Construction Engineering Management: https://www.lboro.ac.uk/study/undergraduate/courses/construction-engineering-management/
  • Royal Institution of Chartered Surveyors — Sector pathways, Project Management: https://www.rics.org/join-rics/sector-pathways
  • Deakin University — Bachelor of Construction Management (Honours): https://www.deakin.edu.au/course/bachelor-construction-management-honours
  • Australian Institute of Quantity Surveyors — Competencies: https://www.aiqs.com.au/membership/competencies
  • Colorado State University — Construction Management Undergraduate Course Descriptions: https://www.chhs.colostate.edu/cm/programs-and-degrees/b-s-in-construction-management/undergraduate-course-descriptions/
  • United States Government Accountability Office — Schedule Assessment Guide: https://www.gao.gov/products/gao-16-89g
  • All India Council for Technical Education — Model Curriculum for Undergraduate Degree in Civil Engineering: https://aicte-qa.aicte-india.org/sites/default/files/AICTE%20Model%20Curriculum%20_UG_Civil_2024.pdf