You are an expert in calculating critical path project timelines using PERT/CPM (Program Evaluation and Review Technique / Critical Path Method) methodology with integration of statutory deadlines for expropriation projects.
Granular Focus
Project timeline calculation and critical path analysis (complementary to deadline tracking). This skill provides quantitative schedule analysis - NOT operational deadline monitoring.
When to Use This Skill
Use this skill when you need to:
- Calculate project duration using critical path method (CPM)
- Identify critical path tasks (zero float tasks that drive project duration)
- Perform PERT analysis (optimistic/most_likely/pessimistic time estimates)
- Assess timeline risks (statutory deadline compliance, float analysis)
- Calculate resource requirements (staff, consultants, budget by phase)
- Optimize project schedule (identify bottlenecks, dependency chains)
- Generate Gantt charts for visualization and communication
Critical Path Method (CPM) Fundamentals
What is Critical Path?
Critical path: Longest sequence of dependent tasks that determines minimum project duration.
Critical tasks: Tasks with zero total float (any delay directly extends project completion).
Total float: Amount of time a task can be delayed without extending project duration.
- Critical path tasks: Total float = 0 days
- Non-critical tasks: Total float > 0 days (schedule flexibility)
Free float: Amount of time a task can be delayed without delaying any successor.
Forward Pass & Backward Pass
Forward pass: Calculate earliest start/finish times
- Start with day 0
- Early start = max(predecessor early finishes)
- Early finish = early start + duration
Backward pass: Calculate latest start/finish times
- Start with project end date
- Late finish = min(successor late starts)
- Late start = late finish - duration
Float calculation:
- Total float = late start - early start (or late finish - early finish)
- Free float = min(successor early starts) - early finish
Example Calculation
Tasks:
- A: Duration 10 days (no predecessors)
- B: Duration 20 days (after A)
- C: Duration 15 days (after A)
- D: Duration 5 days (after B and C)
Forward pass:
- A: ES=0, EF=10
- B: ES=10, EF=30
- C: ES=10, EF=25
- D: ES=30 (max of B and C), EF=35
Backward pass:
- D: LS=30, LF=35
- B: LS=10, LF=30
- C: LS=15, LF=30
- A: LS=0, LF=10
Float:
- A: 0 (critical)
- B: 0 (critical)
- C: 5 days (LS 15 - ES 10)
- D: 0 (critical)
Critical path: A → B → D (35 days)
PERT Analysis
Three-Point Estimates
PERT uses three time estimates to account for uncertainty:
- Optimistic (O): Best-case scenario (everything goes perfectly)
- Most Likely (M): Realistic scenario (normal conditions)
- Pessimistic (P): Worst-case scenario (significant problems)
PERT Formulas
Expected time (weighted average):
TE = (O + 4M + P) / 6Standard deviation:
σ = (P - O) / 6Variance:
σ² = ((P - O) / 6)²Project variance (sum of critical path task variances):
Project σ² = Σ(critical path task variances)Project standard deviation:
Project σ = √(Project σ²)Confidence Intervals
90% confidence interval (Z = 1.645):
Lower bound = Expected duration - 1.645 × Project σ
Upper bound = Expected duration + 1.645 × Project σ95% confidence interval (Z = 1.960):
Lower bound = Expected duration - 1.960 × Project σ
Upper bound = Expected duration + 1.960 × Project σExample PERT Calculation
Task: Prepare expropriation plan
- Optimistic: 14 days
- Most Likely: 21 days
- Pessimistic: 35 days
Expected time:
TE = (14 + 4×21 + 35) / 6 = (14 + 84 + 35) / 6 = 133 / 6 = 22.2 daysStandard deviation:
σ = (35 - 14) / 6 = 21 / 6 = 3.5 daysVariance:
σ² = 3.5² = 12.25Interpretation: Task will take approximately 22 days, with ±3.5 days variability.
Integration with OEA Statutory Deadlines
Statutory Deadline Constraints
3-Month Registration Deadline (OEA s.9(2)):
- Expropriation plan must be registered within 90 days of approval
- Deadline is absolute (approval expires if missed)
- Critical path must complete plan registration by day 85 (5-day buffer)
Form 2 Service (Best Practice):
- Serve Notice of Application 30 days before registration
- Not statutory, but reduces procedural challenges
Form 7 Service (OEA s.11):
- Serve Notice of Expropriation at least 30 days before possession
- Statutory minimum (can give more time)
Deadline Risk Assessment
Buffer analysis:
Buffer = Statutory deadline - Task late finishRisk levels:
- CRITICAL: Buffer < 0 (task finishes AFTER deadline)
- HIGH: Buffer 0-5 days (insufficient buffer)
- MEDIUM: Buffer 5-10 days (below minimum buffer)
- LOW: Buffer > 10 days (adequate buffer)
Example:
- Statutory deadline: Day 90 (registration)
- Task late finish: Day 91 (plan registration)
- Buffer: 90 - 91 = -1 day (CRITICAL risk - misses deadline)
Calculator Usage
Input Format
JSON input structure:
{
"project_name": "Transit Station Property Acquisition",
"approval_date": "2025-03-15",
"tasks": [
{
"id": "A",
"name": "Obtain approval",
"duration": 30,
"optimistic": 20,
"most_likely": 30,
"pessimistic": 45,
"resources": {
"staff": 2,
"consultants": {"legal": 1},
"budget": 15000
}
}
],
"dependencies": [
["A", "B"]
],
"statutory_deadlines": {
"G": 90
},
"buffer_days": 10
}Command Line Usage
Basic calculation:
python project_timeline_calculator.py sample_1_simple_acquisition.jsonSpecify output location:
python project_timeline_calculator.py input.json -o Reports/timeline_analysis.mdJSON output format:
python project_timeline_calculator.py input.json -f json -o results.jsonVerbose output:
python project_timeline_calculator.py input.json -vOutput Report
Markdown report includes:
- Executive Summary: Project duration, critical path percentage, risk summary
- Critical Path Analysis: Sequence of critical tasks with schedule
- Statutory Deadlines: OEA milestone dates and compliance status
- Risk Assessment: Timeline risks by severity (critical/high/medium/low)
- Task Details Table: All tasks with early/late dates, float, criticality
- Gantt Chart: Text-based visualization of timeline
- Resource Requirements: Total and peak resource needs
- Dependency Analysis: Complexity metrics and bottleneck identification
Resource Requirements Analysis
Resource Calculation
For each task, specify:
- Staff: Number of staff required (concurrent)
- Consultants: Number by type (legal, surveyor, appraiser, etc.)
- Budget: Cost allocated to task
Calculator computes:
- Total staff-days: Σ(staff × duration)
- Total consultant-days: Σ(consultants × duration) by type
- Total budget: Σ(task budgets)
- Peak resources: Maximum concurrent staff/consultants at any point
Resource Leveling
Identify resource bottlenecks:
- Tasks with peak resource requirements (> 5 concurrent staff)
- Critical path tasks with high resource needs (no flexibility)
- Resource conflicts (multiple tasks requiring same consultant)
Mitigation strategies:
- Delay non-critical tasks (use available float)
- Increase resources during peak periods
- Outsource specialist work (appraisals, surveys)
Dependency Analysis
Dependency Complexity Metrics
Total dependencies: Number of predecessor-successor relationships
Average dependencies per task: Total dependencies ÷ Total tasks
- Simple project: < 1.5 dependencies/task
- Moderate complexity: 1.5 - 2.5 dependencies/task
- High complexity: > 2.5 dependencies/task
Dependency density: Total dependencies ÷ (Total tasks)²
- Measures interconnectedness
- Higher density = more complex, rigid schedule
Bottleneck tasks: Tasks with 3+ dependencies (predecessors or successors)
- High risk: Any delay cascades through project
- Monitor closely, allocate extra resources
Dependency Types
Finish-to-Start (FS): Successor starts after predecessor finishes
- Example: "Prepare plan" → "Review plan"
- Most common dependency type
Start-to-Start (SS): Tasks start together
- Example: "Negotiation" starts when "Appraisal" starts
- Used for parallel work streams
Finish-to-Finish (FF): Tasks finish together
- Example: "Legal review" finishes when "Plan preparation" finishes
- Used for coordinated completions
Start-to-Finish (SF): Rare, successor finishes when predecessor starts
- Uncommon in expropriation projects
Note: Current calculator supports Finish-to-Start only. For other types, model as multiple FS dependencies.
Risk Assessment
Timeline Risk Categories
1. Statutory Deadline Risk:
- Task late finish exceeds statutory deadline
- Severity: CRITICAL (approval expires)
- Mitigation: Crash critical path, expedite reviews, obtain second approval
2. Critical Path No-Float Risk:
- Critical path task with zero schedule flexibility
- Severity: MEDIUM
- Mitigation: Add buffer time, parallel work streams, increase resources
3. Long Duration Risk:
- Task duration > 60 days (potential for unforeseen delays)
- Severity: LOW
- Mitigation: Break into sub-tasks, weekly monitoring
4. Dependency Bottleneck Risk:
- Task with 3+ dependencies (delays cascade)
- Severity: MEDIUM
- Mitigation: Early coordination, dedicated resources
Risk Mitigation Strategies
Crashing the schedule (reduce critical path duration):
- Add resources to critical path tasks
- Work overtime / weekends
- Outsource work to expedite
- Fast-track (overlap dependent tasks if possible)
Fast-tracking:
- Start successor before predecessor 100% complete
- Risk: Rework if predecessor output changes
- Example: Start plan review while plan preparation 80% complete
Buffering:
- Add contingency time to critical path
- Project buffer: 10-15% of critical path duration
- Feeding buffers: Protect critical path from non-critical delays
Worked Example
Sample Input
Project: Transit station property acquisition (see samples/sample_1_simple_acquisition.json)
Key tasks:
- A: Obtain approval (30 days)
- B: Prepare plan (21 days) - after A
- C: Plan review (7 days) - after B
- D: Corrections (10 days) - after C
- E: Solicitor approval (7 days) - after D
- F: Registry scheduling (15 days) - after E
- G: Plan registration (1 day) - after F
- H: Appraisal (30 days) - after A, parallel to B-G
- I: Prepare Form 2 (5 days) - after A
- J: Serve Form 2 (1 day) - after I
Statutory deadline: Task G (registration) must complete by day 90.
Critical Path Analysis
Critical path: A → B → C → D → E → F → G
Project duration: 30 + 21 + 7 + 10 + 7 + 15 + 1 = 91 days
Problem: Critical path (91 days) exceeds statutory deadline (90 days) by 1 day!
Buffer: 90 - 91 = -1 day (CRITICAL risk)
PERT Analysis
Task B (Prepare plan):
- Optimistic: 14 days
- Most Likely: 21 days
- Pessimistic: 35 days
Expected time: (14 + 4×21 + 35) / 6 = 22.2 days (vs. 21 deterministic)
Standard deviation: (35 - 14) / 6 = 3.5 days
Project with PERT estimates: ~92 days (expected)
- 90% confidence interval: 86 - 98 days
- Probability of meeting 90-day deadline: ~30% (not acceptable)
Risk Mitigation
Option 1: Crash critical path
- Reduce Task B (plan preparation) from 21 → 18 days (add surveyor)
- Reduce Task C (plan review) from 7 → 5 days (priority review)
- New duration: 88 days (2-day buffer)
Option 2: Fast-track
- Start Task C (review) when Task B is 90% complete (overlap 2 days)
- Start Task F (registry scheduling) during Task E (parallel booking)
- New duration: 87 days (3-day buffer)
Option 3: Parallel work streams
- Split plan preparation into multiple parcels
- Register parcels as ready (rolling registration)
- Risk: Complex coordination, higher legal costs
Recommended: Combination of Options 1 and 2 to achieve 85-day completion (5-day buffer).
Integration with Other Skills
Complementary skills:
- expropriation-statutory-deadline-tracking:
- Operational deadline monitoring (weekly checks, escalation) - This skill: Quantitative schedule calculation
- expropriation-compensation-entitlement-analysis:
- Legal entitlement to compensation components - This skill: Timeline for compensation calculation tasks
- land-assembly-expert:
- Multi-property acquisition strategy - This skill: Timeline for land assembly projects
Automated Workflow
Calculator follows PDF → JSON → Python → Report pattern:
- Input: User creates JSON file with tasks, dependencies, deadlines
- Validation: Schema validation ensures data integrity
- Calculation: PERT/CPM analysis computes critical path
- Risk Assessment: Identifies deadline compliance and timeline risks
- Output: Markdown report with Gantt chart, JSON data export
No manual intervention required - fully automated from input to report.
Limitations
Current implementation:
- Supports Finish-to-Start (FS) dependencies only
- Assumes deterministic resource availability
- Does not optimize resource allocation (requires manual leveling)
- Weekends/holidays not modeled (calendar days only)
For advanced features:
- Use project management software (Microsoft Project, Primavera P6)
- Resource optimization algorithms
- Monte Carlo simulation (10,000+ scenarios)
- Earned value analysis (budget vs. actual tracking)
This skill activates when you:
- Calculate project critical path and duration
- Perform PERT analysis with three-point estimates
- Identify timeline risks and statutory deadline compliance
- Calculate resource requirements by phase
- Generate Gantt charts for visualization
- Analyze dependency complexity and bottlenecks
- Optimize project schedule through crashing or fast-tracking