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3.2 Advanced Logic Modeling: Ladders and Fragnets
AACE Planning and Scheduling Professional PSP
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1 Chapter 0: Introduction & AACE PSP Exam Structure
0.1 Current AACE PSP Exam, Eligibility, and Certification Facts 0.2 Planning and Scheduling Professional Roles and Competencies 0.3 Cost Engineering and Scheduling Terminology per RP 10S-90
2 Chapter 1: Scope Definition & Planning Fundamentals
1.1 Work Breakdown Structure (WBS) Architecture & RP 33R-15 1.2 Organization & Resource Breakdown Structures (OBS, RBS, RAM) 1.3 Project Planning and Activity-Logic Development 1.4 Contract Requirements and Delivery Constraints 1.5 Stakeholder Identification, Needs, and Plan Review 1.6 Constructability Methods and Value Engineering 1.7 Resource Identification and Project Variables 1.8 Scope, Goals, Project Plan, and Phase Definition 1.9 Cost Breakdown Structure and Cost Estimate Development 1.10 Phase Relationships, Baseline Plan, Forecasts, and Risk/Recovery Planning
3 Chapter 2: Critical Path Method Mechanics & Network Logic
2.1 Activity Definition and Logic Relationships 2.2 Activity Durations, Productivity, and Work Calendars 2.3 Forward and Backward Pass Mathematical Mechanics 2.4 Float Calculations and Critical-Path Identification
4 Chapter 3: Advanced Network Techniques & Schedule Constraints
3.1 Schedule Constraints and Their Impact on Dates and Float 3.2 Advanced Logic Modeling: Ladders and Fragnets 3.3 Schedule Levels of Detail and Schedule Basis Documentation 3.4 Schedule Scope and Schedule Specification 3.5 Breakdown-Structure Relationships and the Cost Estimate Model 3.6 Stakeholder Feedback and Types of Schedules 3.7 Activities, Milestones, Schedule Quality, and Basis Documentation
5 Chapter 4: Resource Management & Leveling
4.1 Resource Planning, Allocation, and Histograms 4.2 Resource Leveling vs. Resource Smoothing 4.3 Cumulative Resource S-Curves & Productivity Tracking
6 Chapter 5: Baseline Management & Schedule Updating
5.1 Baseline Establishment, Forecasts, and Controlled Revision 5.2 Progress Measurement and Data Date Mechanics 5.3 Out-of-Sequence Logic: Progress Override vs. Retained Logic 5.4 Schedule Update Review and Quality Verification per RP 53R-06 5.5 Cost/Resource Management, Schedule Change, and Feedback 5.6 Acceleration and Recovery Scheduling per RP 54R-07 5.7 Control Schedules, Variance Analysis, Forecasts, and Management Summaries
7 Chapter 6: Schedule Risk Analysis & Monte Carlo Simulation
6.1 Schedule Risk Principles, Risk Drivers, and Three-Point Estimates 6.2 Monte Carlo Simulation, Criticality, Correlation, and Merge Effects 6.3 Risk Outputs, Confidence Dates, Sensitivity, and Contingency
8 Chapter 7: Earned Value & Earned Schedule Management
7.1 Earned Value Foundations: PV, EV, AC, and Variances 7.2 Traditional EV Performance Indices & Late-Project Quirks 7.3 Earned Schedule (ES) Theory, SV(t), and SPI(t) 7.4 Independent Schedule Forecasting & IEAC(t)
9 Chapter 8: Forensic Schedule Analysis & Delay Claims
8.1 Delay Classification, Criticality, and Contract Questions 8.2 RP 29R-03 Taxonomy, Data Validation, and Method Selection 8.3 TIA, Windowed Analysis, and Subtractive Models 8.4 Concurrency, Pacing, and Float: Technical Analysis Before Entitlement
10 Chapter 9: Executive Communication & Practical Scenario Applications
9.1 Official PSP Memo Writing Framework 9.2 Structured Technical Problem-Solving for PSP Scenarios 9.3 Current Exam Strategy and Core Calculation Review
3.2 Advanced Logic Modeling: Ladders and Fragnets
Key Takeaways Explain This Topic AI
Ladder relationships model continuous, overlapping linear production using parallel Start-to-Start (SS) and Finish-to-Finish (FF) dependencies with positive lags.
The pacing and duration ratio between predecessor and successor in a ladder determines whether the Start-to-Start lag or Finish-to-Finish lag is driving the successor.
When a successor in a ladder operates faster than its predecessor, a conventional SS/FF ladder causes activity stretching or discontinuous work unless intermediate buffers or work packages are introduced.
A Fragnet (fragmentary network) is a discrete, localized sub-network inserted into a CPM baseline to model the schedule impact of scope changes, owner delays, or unforeseen field conditions.
The standard fragnet insertion protocol requires establishing uninfluenced predecessor tie-in nodes, estimating fragnet activity durations and internal logic, linking to downstream successor impact nodes, and recalculating the CPM to quantify delay.
Last updated: October 2026
3.2 Advanced Logic Modeling: Ladders and Fragnets
Basic Critical Path Method (CPM) networks rely heavily on discrete, sequential Finish-to-Start (FS) relationships. While FS logic is simple and intuitive, it is often inadequate for modeling complex modern industrial construction. Two specialized network techniques are essential for professional planners and schedulers:
Ladder Networks (Ladder Logic) : Used during baseline development to model continuous, overlapping, repetitive linear production (such as cross-country pipelines, highways, high-rise structural framing, and multi-floor fit-outs).
Fragmentary Networks (Fragnets) : Used during project execution and forensic delay analysis to model the schedule impacts of scope changes, differing site conditions, owner delays, and unexpected work stoppages.
Mastering these advanced network constructs allows the planning professional to create dynamic schedules that reflect real-world site production rates while maintaining forensic defensibility.
Ladder Logic in Linear and Repetitive Construction
A ladder relationship consists of two parallel, overlapping activities linked simultaneously by a Start-to-Start (SS) relationship with lag and a Finish-to-Finish (FF) relationship with lag .
The Linear Production Problem
Consider a 10-mile pipeline installation involving three sequential operations:
- Activity A: "Trench Excavation" (Duration = 30 days)
- Activity B: "Pipe Stringing and Welding" (Duration = 30 days)
- Activity C: "Backfill and Compaction" (Duration = 30 days)
If the scheduler connects these activities using traditional Finish-to-Start (FS = 0) logic, the total duration is: Total Duration = 30 + 30 + 30 = 90 working days \text{Total Duration} = 30 + 30 + 30 = \mathbf{90\text{ working days}} Total Duration = 30 + 30 + 30 = 90 working days [Trench Excavation (30d)] ──(FS=0)──► [Pipe Welding (30d)] ──(FS=0)──► [Backfill (30d)]
|<------------------------------ 90 Working Days ------------------------------>|
In reality, a pipeline contractor does not excavate all 10 miles of trench before laying the first joint of pipe. Once the excavation crew has advanced 3 days ahead, the welding crew immediately mobilizes behind them. Once the pipe is welded and inspected, the backfill crew mobilizes 3 days behind the welders. Work proceeds as an overlapping, continuous production train .
Ladder Network Modeling Mechanics
To model this overlapping workflow, the scheduler creates ladder logic:
Activity A → SS + 3 days \xrightarrow{\text{SS + 3 days}} SS + 3 days Activity B
Activity A → FF + 3 days \xrightarrow{\text{FF + 3 days}} FF + 3 days Activity B [Activity A: Trench Excavation (30d)]
- │ │
- │(SS = +3) │(FF = +3)
- ▼ ▼
- [Activity B: Pipe Welding (30d)]
- │ │
- │(SS = +3) │(FF = +3)
- ▼ ▼
- [Activity C: Backfill & Compaction (30d)]
In this ladder configuration:
Start-to-Start Lag (SS Lag) : Represents the physical lead time or distance buffer required for the predecessor to open sufficient workfront so the successor can operate safely without craft interference.
Finish-to-Finish Lag (FF Lag) : Represents the close-out buffer required for the successor to complete the final segment of work after the predecessor finishes the final stretch.
With 3-day lags, the total project duration is drastically compressed: Project Start = Day 0 \text{Project Start} = \text{Day } 0 Project Start = Day 0 E S B = E S A + Lag S S = 0 + 3 = Day 3 ES_B = ES_A + \text{Lag}_{SS} = 0 + 3 = \text{Day } 3 E S B = E S A + Lag SS = 0 + 3 = Day 3 E S C = E S B + Lag S S = 3 + 3 = Day 6 ES_C = ES_B + \text{Lag}_{SS} = 3 + 3 = \text{Day } 6 E S C = E S B + Lag SS = 3 + 3 = Day 6 E F A = 0 + 30 = Day 30 EF_A = 0 + 30 = \text{Day } 30 E F A = 0 + 30 = Day 30 E F B = max ( E S B + D B , E F A + Lag F F ) = max ( 3 + 30 , 30 + 3 ) = Day 33 EF_B = \max(ES_B + D_B, EF_A + \text{Lag}_{FF}) = \max(3 + 30, 30 + 3) = \text{Day } 33 E F B = max ( E S B + D B , E F A + Lag FF ) = max ( 3 + 30 , 30 + 3 ) = Day 33 E F C = max ( E S C + D C , E F B + Lag F F ) = max ( 6 + 30 , 33 + 3 ) = D a y 36 EF_C = \max(ES_C + D_C, EF_B + \text{Lag}_{FF}) = \max(6 + 30, 33 + 3) = \mathbf{Day\ 36} E F C = max ( E S C + D C , E F B + Lag FF ) = max ( 6 + 30 , 33 + 3 ) = Day 36
The project duration drops from 90 days to 36 days , accurately capturing the fast-track continuous linear production train.
The Pacing Dilemma: Driving Relationships in Ladder Networks
A critical mathematical dynamic tested on the PSP exam is determining which relationship drives the successor when activity durations (production rates) are unequal.
Case 1: Predecessor is Slower than Successor ( D pred > D succ D_{\text{pred}} > D_{\text{succ}} D pred > D succ )
Suppose Activity A (Excavation) takes 20 days , while Activity B (Pipe Laying) is performed by a high-speed crew taking only 10 days . The network has SS = + 3 \text{SS} = +3 SS = + 3 and FF = + 3 \text{FF} = +3 FF = + 3 .
Forward Pass Calculation :
E S A = 0 ES_A = 0 E S A = 0 ; E F A = 20 EF_A = 20 E F A = 20 .
Via SS Link: E S B ≥ E S A + 3 = 0 + 3 = 3 ES_B \ge ES_A + 3 = 0 + 3 = 3 E S B ≥ E S A + 3 = 0 + 3 = 3 .
If Activity B starts on Day 3 with a 10-day duration, its early finish would be 3 + 10 = Day 13 3 + 10 = \text{Day } 13 3 + 10 = Day 13 .
Via FF Link: E F B ≥ E F A + 3 = 20 + 3 = D a y 23 EF_B \ge EF_A + 3 = 20 + 3 = \mathbf{Day\ 23} E F B ≥ E F A + 3 = 20 + 3 = Day 23 .
To finish on Day 23 with a 10-day duration, Activity B cannot start until 23 − 10 = D a y 13 23 - 10 = \mathbf{Day\ 13} 23 − 10 = Day 13 !
Important
The Faster Successor Rule : When the successor is faster than the predecessor ( D succ < D pred D_{\text{succ}} < D_{\text{pred}} D succ < D pred ), the Finish-to-Finish (FF) relationship is driving . If the successor were to start at its earliest SS date (Day 3), it would catch up to the slow predecessor on Day 6 and run out of work front, forcing an uncoordinated work stoppage!
Loading diagram... Ladder Logic Mechanics and Driving Link Determination
Case 2: Predecessor is Faster than Successor ( D pred < D succ D_{\text{pred}} < D_{\text{succ}} D pred < D succ )
Suppose Activity A (Excavation) takes 10 days , while Activity B (Pipe Laying) takes 20 days (a slower operation). The network has SS = + 3 \text{SS} = +3 SS = + 3 and FF = + 3 \text{FF} = +3 FF = + 3 .
Forward Pass Calculation :
E S A = 0 ES_A = 0 E S A = 0 ; E F A = 10 EF_A = 10 E F A = 10 .
Via SS Link: E S B ≥ E S A + 3 = 0 + 3 = D a y 3 ES_B \ge ES_A + 3 = 0 + 3 = \mathbf{Day\ 3} E S B ≥ E S A + 3 = 0 + 3 = Day 3 .
Early Finish based on start: E F B = 3 + 20 = D a y 23 EF_B = 3 + 20 = \mathbf{Day\ 23} E F B = 3 + 20 = Day 23 .
Via FF Link: E F B ≥ E F A + 3 = 10 + 3 = Day 13 EF_B \ge EF_A + 3 = 10 + 3 = \text{Day } 13 E F B ≥ E F A + 3 = 10 + 3 = Day 13 .
The SS link forces E F B = 23 EF_B = 23 E F B = 23 , which easily satisfies the FF requirement ( 23 ≥ 13 23 \ge 13 23 ≥ 13 ).
Note
The Slower Successor Rule : When the successor is slower than the predecessor ( D succ > D pred D_{\text{succ}} > D_{\text{pred}} D succ > D pred ), the Start-to-Start (SS) relationship is driving . The successor starts early and falls further behind the rapid predecessor without risk of work starvation.
Continuous vs. Discontinuous Activity Modeling & Ladder Collapse
Commercial CPM software engines handle ladder relationships under two distinct calculation paradigms:
Contiguous (Continuous) Work Assumption : The software assumes that once an activity starts, it must proceed uninterrupted until completion. If an FF link demands a late finish, the software delays the activity's start date (as demonstrated in Case 1 above).
Interruptible (Discontinuous / Split) Work Assumption : The software allows an activity to begin at its earliest SS date, pause execution when work front is exhausted, and resume later to satisfy the FF date.
The "Ladder Collapse" Phenomenon
During project updates, ladder logic is exceptionally fragile. If actual start and finish dates are entered out of sequence, or if productivity rates deviate from baseline assumptions, the ladder can experience ladder collapse :
If an actual start date is entered for Activity B without progress on Activity A, the software may lock the start date while the backward pass generates anomalous float.
If a scheduler applies positive lags that exceed activity durations (e.g., SS = +15 on a 10-day activity), circular logic or negative float bugs can emerge.
The Segmented Work Package Alternative
To eliminate the calculation anomalies of ladder logic, one transparent alternative is to model repetitive linear projects using geographical or spatial segmentation :
Decompose the 10-mile pipeline into 5 discrete 2-mile sections (Section 1, Section 2, Section 3, Section 4, Section 5).
Link the operations within each section and across adjacent sections using standard Finish-to-Start (FS) logic:
Excavation Sec 1 → FS \xrightarrow{\text{FS}} FS Welding Sec 1 → FS \xrightarrow{\text{FS}} FS Backfill Sec 1
Excavation Sec 1 → FS \xrightarrow{\text{FS}} FS Excavation Sec 2 → FS \xrightarrow{\text{FS}} FS Welding Sec 2
This segmented FS approach can make workfronts, status, and interfaces easier to audit, although its level of detail and logic still require validation.
Fragnets (Fragmentary Networks): Definition & Architecture
A Fragnet (short for fragmentary network ) is a discrete, localized sequence of CPM activities developed to model the detailed schedule impact of a specific project change, unforeseen field condition, owner-directed revision, or delay event.
A fragnet can support prospective change evaluation or time-impact analysis. RP 29R-03 and RP 52R-06 provide technical considerations, but a fragnet result does not by itself prove contractual entitlement.
When a multi-activity fragnet improves transparency
When an owner issues a major design change or a contractor encounters an unforeseen underground obstruction, inexperienced schedulers often attempt to model the delay by simply inflating the duration of an existing baseline activity (e.g., changing "Install Foundations" from 20 days to 55 days). That shortcut may be too coarse for the analysis because:
It obscures the root causes of the delay.
It prevents auditing of concurrent contractor actions.
It fails to delineate between administrative delay, engineering redesign, material procurement, and physical field rework.
When the event has distinct causal stages, a multi-activity fragnet can expose them for review: ┌────────────────────────────────────────────────────────────────────────────────────────┐
- │ ANATOMY OF A PROFESSIONAL FRAGNET │
- ├─────────────────┬──────────────────┬──────────────────┬─────────────────┬──────────────┤
- │ 1. Discovery & │ 2. Owner Review │ 3. Engineering │ 4. Material │ 5. Physical │
- │ Field Notice │ & Direction │ Redesign │ Procurement │ Execution │
- │ (RFI Submitt)│ (RFI Response)│ (Rev Drawings)│ (Long-Lead) │ (Rework) │
- └─────────────────┴──────────────────┴──────────────────┴─────────────────┴──────────────┘
- The Step-by-Step Fragnet Insertion Protocol
To ensure forensic defensibility during a Time Impact Analysis (TIA), the planning professional commonly uses the following traceable workflow, adapted to the contract, purpose, and available records:
Step 1: Select the Contemporaneous Baseline/Update Schedule
Select the appropriate contemporaneous schedule that represents status before the event. Often this is the accepted update immediately preceding the event, but the contract, schedule-of-record provisions, timing, and data quality govern the choice.
Step 2: Establish Fragnet Activities & Estimate Durations
Develop discrete activities representing the delay sequence. Use justified duration estimates supported by the best available scope, vendor information, historical data, or contemporaneous records, and disclose uncertainty.
Step 3: Identify Predecessor Tie-In Points
Identify the specific activities in the CPM schedule that trigger the fragnet. The predecessor tie-in should represent the logical interface that enables the modeled event work (e.g., "Complete Exploratory Potholing").
Step 4: Identify Successor Tie-In Points
Identify the downstream activities whose starts or finishes are physically or contractually prevented until the fragnet work is complete (e.g., "Commence Duct Bank Concrete Pour").
Step 5: Recalculate the CPM Network (Compute Schedule Variance)
Run the forward and backward passes. Compare the project completion milestone date and key intermediate milestone dates before and after fragnet insertion:
Δ Project Completion = Completion Date Post-Fragnet − Completion Date Pre-Fragnet \mathbf{\Delta\text{Project Completion} = \text{Completion Date}_{\text{Post-Fragnet}} - \text{Completion Date}_{\text{Pre-Fragnet}}} Δ Project Completion = Completion Date Post-Fragnet − Completion Date Pre-Fragnet
If the tested completion date shifts outward by 12 working days, the calculation shows a 12-day modeled incremental effect under the schedule, tie-in, duration, status, and calendar assumptions used.
Step 6: Post-Impact Audit & As-Built Reconciliation
During subsequent monthly schedule updates, as the change work is actually executed in the field, replace estimated fragnet durations with actual start and finish dates. This reconciles the prospective model with actual as-built project performance.