SkarpChapter 7 of 20
Scheduling Predictive Projects: Network Diagrams and Critical Path Method
See how activities become a realistic schedule by sequencing work, estimating durations, and using the critical path method to reveal where delays really matter.
From WBS to Schedule: Activities in Predictive Projects
Linking Scope to Time
In predictive projects, you cannot manage time until you turn scope into activities. You move from WBS deliverables to a detailed activity list that can be placed on a calendar.
Key Baseline Inputs
The scope baseline includes the scope statement, the work breakdown structure, and the WBS dictionary. These define what must be delivered and guide which activities are needed.
From Work Package to Activities
A work package is the lowest WBS level for which cost and duration are estimated. For scheduling, each work package is decomposed into smaller, verb-based activities you can assign and track.
Example Decomposition
Work package "Design website homepage" might become: gather requirements, create wireframe, review wireframe, produce visual design, approve final design.
Exam Watch
On CAPM, watch for confusion between deliverables (nouns in the WBS) and activities (verbs in the schedule). Activities come from work packages, not directly from vague ideas.
Defining and Classifying Dependencies
Why Sequence Activities?
After listing activities, you must decide which comes before which. Sequencing creates the logical order of work and is the basis for the schedule network diagram.
Four Relationship Types
Know these: Finish-to-Start (FS), Finish-to-Finish (FF), Start-to-Start (SS), Start-to-Finish (SF). FS is most common, SF is rare and often used for shift changes.
FS and SS Examples
FS: "Code module" must finish before "Test module" starts. SS: "Start excavation" and "Start dewatering" may begin together once site access starts.
FF and SF Examples
FF: "Finalize content" must finish before "Finish layout" finishes. SF: A night shift cannot finish until the day shift starts; rare in exam scenarios.
Mandatory vs Discretionary
Mandatory dependencies are hard logic (e.g., build then test). Discretionary are chosen preferences (e.g., design all screens before coding). Mandatory are harder to change.
Network Diagrams: Visualizing the Schedule Logic
What Is a Network Diagram?
A schedule network diagram shows activities as boxes and dependencies as arrows. It makes the logic of the schedule visible and is built using the Precedence Diagramming Method.
Inside an Activity Node
Each node usually includes an ID, a short activity name, and its duration. For exam problems, assume Finish-to-Start relationships with no lag unless told otherwise.
Sample Workshop Project
Example: A Define objectives, B Design slides, C Develop exercises, D Review materials, E Finalize pack. A precedes B and C; B and C precede D; D precedes E.
Parallel vs Sequential Paths
In the example, B and C run in parallel after A. Parallel paths reveal where work can overlap and where the longest route from start to finish might be.
Why It Matters for CAPM
You must be able to read these diagrams, identify predecessors and successors, and later compute early/late dates and float along each path.
Critical Path Method: Core Concepts and Notation
What CPM Tells You
Critical Path Method calculates earliest and latest start/finish dates for activities, their total float, and the critical path that sets the project duration.
Key CPM Values
Each activity has ES (Early Start), EF (Early Finish), LS (Late Start), and LF (Late Finish). These are time positions on a notional project timeline.
Total Float Defined
Total float is how long an activity can be delayed without delaying the project finish: TF = LS − ES or TF = LF − EF. Zero float means no flexibility.
Critical Path Defined
The critical path is the longest path in duration through the network. Activities on it have zero total float; any delay on them delays the project.
Exam Expectations
Expect to compute ES, EF, LS, LF, and float from a small network diagram, then identify the critical path based on zero-float activities.
Worked Example: Forward Pass (Early Start and Early Finish)
Example Network Setup
Activities: A=2d, B=4d, C=3d, D=2d, E=3d. A precedes B and C; B and C precede D; D precedes E. Assume project starts at time 0.
Forward Pass Rules
First activity: ES=0, EF=ES+Duration. Successor with one predecessor: ES=pred EF. With multiple predecessors: ES=max of predecessor EFs.
Calculating A, B, C
A: ES 0, EF 2. B: ES 2, EF 6. C: ES 2, EF 5. B and C can run in parallel once A finishes.
Calculating D and E
D depends on B and C: ES=max(6,5)=6, EF=8. E depends on D: ES=8, EF=11. Earliest project finish is time 11.
Candidate Critical Path
Path A–B–D–E totals 11; A–C–D–E totals 10. The longer path is the candidate critical path; we confirm after the backward pass.
Worked Example: Backward Pass, Float, and Critical Path
Backward Pass Rules
Start from the last activity: LF=its EF, LS=LF−Duration. For predecessors, LF equals the minimum LS of their successors; LS=LF−Duration.
Applying to E and D
E: LF 11, LS 8. D (predecessor of E): LF=LS of E=8, LS=6. These match D’s ES=6 from the forward pass.
Applying to B and C
B and C precede D, whose LS is 6. So LF of B and C is 6. B: LS 2; C: LS 3. Note C can start later than its ES without delay.
Calculating for A
A precedes B and C. LF of A is the minimum of LS(B)=2 and LS(C)=3, so LF=2, LS=0. This matches the project start.
Float and Critical Path
Total float TF=LS−ES: A,B,D,E have TF 0; C has TF 1. The critical path is A–B–D–E with duration 11 days.
Float/Slack and Where Delays Really Matter
What Is Total Float?
Total float is how long you can delay an activity without delaying the project finish. Formula: TF = LS − ES = LF − EF. Zero float means no slack.
Using Float in Our Example
Activity C had 1 day of total float, so it could start one day later or run longer by one day without changing the project end date of day 11.
Critical vs Non-critical
Critical activities (TF = 0) directly control the finish date and need tight monitoring. Non-critical activities (TF > 0) have some flexibility but can become critical if float is used up.
Float vs Lag
Float is emergent flexibility from the network. Lag is a planned waiting time you add to a dependency. Do not confuse them on exam questions.
Exam Tip
If a question asks which activity can slip without affecting project completion, select the one with positive total float, based on CPM results.
Lags, Leads, and Hard Logic in Schedule Modeling
What Are Lags and Leads?
Lag is a planned wait between activities; lead is a planned overlap where the successor starts before the predecessor fully finishes.
Lag Example
After "Pour concrete," you must wait 3 days before framing. Model as: Pour concrete FS+3d Start framing. The lag extends the project timeline.
Lead Example
You can start testing 2 days before coding ends: Coding FS−2d Testing. The lead overlaps work and can shorten the schedule.
Hard Logic
Hard logic is mandatory dependency that cannot be broken, such as building before testing. Leads and lags must still respect this hard logic.
Exam Connection
On CAPM, translate text like "wait 5 days" or "start early" into FS+lag or FS−lead relationships when reasoning about the schedule.
Schedule Compression: Fast Tracking vs Crashing
Why Compress the Schedule?
After finding the critical path, sponsors may ask to finish earlier. You then consider schedule compression techniques without changing scope.
Fast Tracking
Fast tracking overlaps activities that were sequential, using SS or FS−lead relationships. It can shorten the schedule but increases risk and rework.
Crashing
Crashing adds resources or cost to critical activities to shorten their duration, like paying overtime or adding staff. It increases cost and sometimes risk.
Focus on the Critical Path
Compress only critical path activities; shortening non-critical work usually just increases float, not the overall project speed.
Exam Distinctions
Fast tracking vs crashing are schedule compression. Reducing scope or quality are different strategies, not schedule compression techniques.
Quick Check: Dependencies and Critical Path
Test your understanding of dependencies and critical path basics.
Activity X has ES=5, EF=9, LS=7, LF=11. What is the total float of Activity X, and is it on the critical path?
- Total float is 0; Activity X is on the critical path
- Total float is 2; Activity X is not on the critical path
- Total float is 4; Activity X is not on the critical path
- Total float is 2; Activity X is on the critical path
Show Answer
Answer: B) Total float is 2; Activity X is not on the critical path
Total float TF = LS − ES = 7 − 5 = 2 (or LF − EF = 11 − 9 = 2). Because total float is greater than zero, Activity X is not on the critical path. Critical path activities have total float of zero.
Quick Check: Schedule Compression Techniques
Apply what you learned about fast tracking and crashing.
Your project must finish 2 weeks earlier. The sponsor will not reduce scope or quality. One critical activity can be done with overtime at higher cost; another can partially overlap with its predecessor but increases rework risk. Which pair correctly labels these options?
- Overtime is fast tracking; overlap is crashing
- Overtime is crashing; overlap is fast tracking
- Both are crashing techniques
- Both are fast tracking techniques
Show Answer
Answer: B) Overtime is crashing; overlap is fast tracking
Adding overtime (increasing resources/cost to shorten duration) is crashing. Overlapping activities that were sequential is fast tracking. Only these two are schedule compression techniques for a fixed scope.
Thought Exercise: Build a Mini Network Diagram
Practice turning a WBS fragment into a simple precedence network. Do this on paper or in a notes app.
Scenario: You are planning a small predictive project to create a course handout PDF.
Work packages (from your WBS):
- WP1: Draft content
- WP2: Design layout
- WP3: Review and approve
- WP4: Finalize and export PDF
- List activities (break each work package into at least one activity):
- A: Draft content (3 days)
- B: Edit and refine content (2 days)
- C: Design layout template (2 days)
- D: Apply layout to content (2 days)
- E: Internal review (2 days)
- F: Client approval (3 days)
- G: Final corrections and export PDF (1 day)
- Define logical dependencies (think: what must finish before what):
- Draft content must finish before editing.
- Editing must finish before layout is applied.
- Layout template must exist before layout is applied.
- Layout must be applied before internal review.
- Internal review must finish before client approval.
- Client approval must finish before final corrections/export.
- On your paper:
- Draw each activity as a box labeled A–G with duration.
- Add arrows for dependencies.
- Challenge yourself:
- Identify any parallel paths (hint: content work vs layout template).
- Guess which path might be critical before doing full CPM math.
When you take the next Skarp diagnostic or mock exam, you will see similar small networks. The more you practice sketching them, the faster CPM questions will feel.
Key Terms Review: Network Diagrams and CPM
Flip through these cards to reinforce core concepts before moving on.
- Precedence Diagramming Method (PDM)
- A method of constructing a schedule network diagram where activities are represented by nodes and are graphically linked by one or more logical relationships (dependencies) to show the sequence in which the activities are to be performed.
- Finish-to-Start (FS) relationship
- A logical relationship in which a successor activity cannot start until a predecessor activity has finished. It is the most common dependency type in predictive schedules.
- Mandatory dependency (hard logic)
- A relationship that is legally or contractually required or inherent in the nature of the work. It cannot be changed without changing the work itself.
- Discretionary dependency (soft logic)
- A relationship that is based on best practices, preferences, or convenience. It can be changed if needed, for example to compress the schedule.
- Early Start (ES) and Early Finish (EF)
- ES is the earliest time an activity can start given its predecessors. EF is the earliest time it can finish, calculated as ES plus its duration.
- Late Start (LS) and Late Finish (LF)
- LS is the latest time an activity can start without delaying the project finish. LF is the latest time it can finish without delaying the project finish.
- Total float (total slack)
- The amount of time an activity can be delayed without delaying the project finish date. Calculated as LS − ES or LF − EF.
- Critical path
- The sequence of activities that represents the longest path through a project, which determines the shortest possible project duration. Activities on the critical path have zero total float.
- Lag vs Lead
- Lag is a waiting period inserted between activities (e.g., FS+3d). Lead is an overlap where a successor starts before the predecessor finishes (e.g., FS−2d).
- Fast tracking
- A schedule compression technique that involves performing activities in parallel or overlapping them that were originally planned in sequence, often increasing risk and rework.
- Crashing
- A schedule compression technique that involves adding or adjusting resources to critical path activities to shorten their durations without changing scope, usually increasing cost.
Key Terms
- lag
- A waiting period inserted between a predecessor and successor activity in a schedule network diagram.
- lead
- An overlap between activities in which a successor activity starts before the predecessor activity has finished.
- crashing
- A schedule compression technique that adds or adjusts resources to critical path activities to shorten their durations without changing project scope, usually increasing cost.
- total float
- The amount of time an activity can be delayed without delaying the project finish date, calculated as LS − ES or LF − EF.
- work package
- The work defined at the lowest level of the work breakdown structure for which cost and duration are estimated and managed.
- critical path
- The sequence of activities that represents the longest path through a project, which determines the shortest possible project duration. Activities on the critical path have zero total float.
- fast tracking
- A schedule compression technique that overlaps activities that were originally planned to be done in sequence, often increasing risk and rework.
- schedule network diagram
- A graphical representation of the logical relationships among project schedule activities, often built using the Precedence Diagramming Method.
- work breakdown structure
- 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.
- Precedence Diagramming Method (PDM)
- A method of constructing a schedule network diagram where activities are represented by nodes and are graphically linked by one or more logical relationships to show sequence.