3.2 Advanced Logic Modeling: Ladders and Fragnets

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:

1. 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).
2. 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.

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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: $\text{Total Duration} = 30 + 30 + 30 = \mathbf{90\text{ working days}}$

[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 $\xrightarrow{\text{SS + 3 days}}$ Activity B
• Activity A $\xrightarrow{\text{FF + 3 days}}$ 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: $\text{Project Start} = \text{Day } 0$ $ES_B = ES_A + \text{Lag}_{SS} = 0 + 3 = \text{Day } 3$ $ES_C = ES_B + \text{Lag}_{SS} = 3 + 3 = \text{Day } 6$ $EF_A = 0 + 30 = \text{Day } 30$ $EF_B = \max(ES_B + D_B, EF_A + \text{Lag}_{FF}) = \max(3 + 30, 30 + 3) = \text{Day } 33$ $EF_C = \max(ES_C + D_C, EF_B + \text{Lag}_{FF}) = \max(6 + 30, 33 + 3) = \mathbf{Day\ 36}$

The project duration drops from 90 days to 36 days, accurately capturing the fast-track continuous linear production train.

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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 ($D_{\text{pred}} > D_{\text{succ}}$)

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 $\text{SS} = +3$ and $\text{FF} = +3$.

• Forward Pass Calculation:
  • $ES_A = 0$; $EF_A = 20$.
  • Via SS Link: $ES_B \ge ES_A + 3 = 0 + 3 = 3$.
  • If Activity B starts on Day 3 with a 10-day duration, its early finish would be $3 + 10 = \text{Day } 13$.
  • Via FF Link: $EF_B \ge EF_A + 3 = 20 + 3 = \mathbf{Day\ 23}$.
  • To finish on Day 23 with a 10-day duration, Activity B cannot start until $23 - 10 = \mathbf{Day\ 13}$!

Case 2: Predecessor is Faster than Successor ($D_{\text{pred}} < D_{\text{succ}}$)

Suppose Activity A (Excavation) takes 10 days, while Activity B (Pipe Laying) takes 20 days (a slower operation). The network has $\text{SS} = +3$ and $\text{FF} = +3$.

• Forward Pass Calculation:
  • $ES_A = 0$; $EF_A = 10$.
  • Via SS Link: $ES_B \ge ES_A + 3 = 0 + 3 = \mathbf{Day\ 3}$.
  • Early Finish based on start: $EF_B = 3 + 20 = \mathbf{Day\ 23}$.
  • Via FF Link: $EF_B \ge EF_A + 3 = 10 + 3 = \text{Day } 13$.
  • The SS link forces $EF_B = 23$, which easily satisfies the FF requirement ($23 \ge 13$).

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Continuous vs. Discontinuous Activity Modeling & Ladder Collapse

Commercial CPM software engines handle ladder relationships under two distinct calculation paradigms:

1. 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).
2. 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 $\xrightarrow{\text{FS}}$ Welding Sec 1 $\xrightarrow{\text{FS}}$ Backfill Sec 1
  • Excavation Sec 1 $\xrightarrow{\text{FS}}$ Excavation Sec 2 $\xrightarrow{\text{FS}}$ 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.

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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)  │
└─────────────────┴──────────────────┴──────────────────┴─────────────────┴──────────────┘

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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:

$\mathbf{\Delta\text{Project Completion} = \text{Completion Date}_{\text{Post-Fragnet}} - \text{Completion Date}_{\text{Pre-Fragnet}}}$

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.