8.1 Precedence Diagramming Method (PDM) & Dependency Relationships

8.1 Precedence Diagramming Method (PDM) & Dependency Relationships

In the Total Cost Management (TCM) Framework established by AACE International, the Critical Path Method (CPM) serves as the primary quantitative modeling engine for project time management, resource allocation, cash flow forecasting, and forensic delay analysis. At the core of CPM is the network diagram—a mathematical graph that models the technological, physical, and managerial interdependencies among discrete project activities.

For Certified Cost Professional (CCP) candidates, mastering the Precedence Diagramming Method (PDM) and understanding how dependency types, leads, lags, and network constraints govern schedule calculation is fundamental to establishing defensible baselines and analyzing project delay claims.

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1. Evolution of Network Scheduling: PDM (AON) vs. Legacy ADM (AOA)

Network scheduling originated in the late 1950s with two independent methodologies:

1. CPM (Critical Path Method): Developed in 1957 by Morgan R. Walker (DuPont) and James E. Kelley Jr. (Remington Rand) for chemical plant shutdowns.
2. PERT (Program Evaluation and Review Technique): Developed in 1958 by the U.S. Navy Special Projects Office with Booz Allen Hamilton for the Polaris submarine missile program.

Both early systems utilized the Arrow Diagramming Method (ADM), also known as Activity on Arrow (AOA). In the 1960s, Professor John W. Fondahl developed the Precedence Diagramming Method (PDM), also known as Activity on Node (AON), which today represents the universal standard in all enterprise project scheduling software (e.g., Oracle Primavera P6, Microsoft Project, Asta Powerproject).

+-----------------------------------------------------------------------------------------+
|                   COMPARISON: ARROW DIAGRAMMING (ADM) VS. PRECEDENCE (PDM)             |
|                                                                                         |
|   1. ARROW DIAGRAMMING METHOD (ADM / AOA):                                              |
|      - Activity on Arrow; Nodes represent instantaneous events (i-node and j-node).     |
|      - Only supports Finish-to-Start (FS) relationships.                                |
|      - REQUIRES "Dummy Activities" (zero duration, dotted lines) to:                     |
|        (a) Uniquely identify parallel activities between the same two event nodes.      |
|        (b) Transmit logic without creating false dependency loops.                      |
|                                                                                         |
|          (Node 10) -------- Activity A (5d) -------> (Node 20)                          |
|              \                                           ^                              |
|               \                                         / (Dummy - 0d)                  |
|                \---> (Node 15) --- Activity B (3d) ----/                                |
|                                                                                         |
|   2. PRECEDENCE DIAGRAMMING METHOD (PDM / AON):                                         |
|      - Activity on Node; Nodes contain full activity data blocks.                       |
|      - Directional arrows represent pure logical dependencies.                          |
|      - Supports 4 dependency types (FS, SS, FF, SF) and positive/negative lags.         |
|      - COMPLETELY ELIMINATES DUMMY ACTIVITIES.                                          |
|                                                                                         |
|          +---------------+      FS (0 lag)      +---------------+                       |
|          |  Activity A   |--------------------->|  Activity B   |                       |
|          |   (5 days)    |                      |   (3 days)    |                       |
|          +---------------+                      +---------------+                       |
+-----------------------------------------------------------------------------------------+

Systematic Comparison Matrix:

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2. The Four Logical Dependency Types

In PDM, dependencies define the sequence and constraints between a predecessor activity (which logically precedes another) and a successor activity (which logically follows). PDM defines four distinct relationship types:

+-----------------------------------------------------------------------------------------+
|                            THE FOUR PDM DEPENDENCY RELATIONSHIPS                        |
|                                                                                         |
|   1. FINISH-TO-START (FS)                2. START-TO-START (SS)                         |
|      [ Predecessor ]                        [ Predecessor ]                             |
|             |                                      |                                    |
|             +----------->[ Successor ]             +----------->[ Successor ]           |
|      Rule: ES(Succ) >= EF(Pred) + Lag       Rule: ES(Succ) >= ES(Pred) + Lag            |
|                                                                                         |
|   3. FINISH-TO-FINISH (FF)               4. START-TO-FINISH (SF)                        |
|      [ Predecessor ]                        [ Predecessor ]                             |
|             |                                      |                                    |
|             +----------->[ Successor ]             +----------->[ Successor ]           |
|      Rule: EF(Succ) >= EF(Pred) + Lag       Rule: EF(Succ) >= ES(Pred) + Lag            |
+-----------------------------------------------------------------------------------------+

1. Finish-to-Start (FS)

• Definition: The successor activity cannot start until the predecessor activity finishes.
• Mathematical Boundary: $ES_{\text{successor}} \ge EF_{\text{predecessor}} + \text{Lag}$
• Application: The default and most fundamental relationship in project scheduling ($>90%$ of all network ties). Example: "Excavate Footing" (Pred) $\xrightarrow{\text{FS}}$ "Pour Concrete Footing" (Succ).

2. Start-to-Start (SS)

• Definition: The successor activity cannot start until the predecessor activity has started.
• Mathematical Boundary: $ES_{\text{successor}} \ge ES_{\text{predecessor}} + \text{Lag}$
• Application: Used to model parallel or staged operations (fast-tracking). Example: "Lay Pipeline Trench" (Pred) $\xrightarrow{\text{SS + 3d}}$ "Install Pipe in Trench" (Succ). The pipe installation crew can start 3 days after trenching begins without waiting for the entire 30-day trenching activity to complete.

3. Finish-to-Finish (FF)

• Definition: The successor activity cannot finish until the predecessor activity finishes.
• Mathematical Boundary: $EF_{\text{successor}} \ge EF_{\text{predecessor}} + \text{Lag}$
• Application: Used to coordinate joint completion of overlapping tasks. Example: "Install Electrical Conduit" (Pred) $\xrightarrow{\text{FF + 2d}}$ "Pull Electrical Cables" (Succ). Cable pulling cannot wrap up until 2 days after conduit installation is 100% complete.

4. Start-to-Finish (SF)

• Definition: The successor activity cannot finish until the predecessor activity has started.
• Mathematical Boundary: $EF_{\text{successor}} \ge ES_{\text{predecessor}} + \text{Lag}$
• Application: Extremely rare in practice ($<0.1%$ of relationships). Typically applied in operational turnover, continuous shift handovers, or just-in-time system replacements. Example: "Commission New Power Substation" (Pred) $\xrightarrow{\text{SF}}$ "Decommission Old Substation" (Succ). The old substation must remain energized and cannot finish operation until the new substation begins operating.
• AACE Guidance & Warning: Industry best practices (e.g., DCMA 14-Point Assessment) strongly discourage SF relationships because they create non-intuitive backward pass logic, invert float consumption, and confuse site execution teams.

Combination / Paired Logic (Laddering):

In construction scheduling, activities are frequently paired using SS and FF relationships simultaneously between the same two activities (e.g., Excavate Trench $\xrightarrow{\text{SS+3d}}$ Lay Pipe AND Excavate Trench $\xrightarrow{\text{FF+2d}}$ Lay Pipe). This technique, called laddering, bounds both the start and finish of the downstream activity, ensuring continuous crew workflow without introducing open ends.

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3. Lead Time (Negative Lag) & Lag Time (Positive Delay)

In PDM scheduling, relationships can be modified by adding a duration value to the logic tie:

+-----------------------------------------------------------------------------------------+
|                                 LEADS VS. LAGS IN PDM LOGIC                             |
|                                                                                         |
|   LAG (+L): Forced waiting buffer inserted between predecessor and successor.           |
|   [ Predecessor (Concrete Pour) ] === (Lag: +7 Days Curing) ===> [ Successor (Strip) ]  |
|                                                                                         |
|   LEAD (-L): Negative lag; advances successor start prior to predecessor finish.        |
|   [ Predecessor (Design Drawings) ]                                                     |
|             [ (-3 Days Lead) ===> Successor (Procurement Order) ]                       |
+-----------------------------------------------------------------------------------------+

1. Lag Time (Positive Lag, $+L$)

• Function: A mandatory delay or waiting buffer between activities that consumes calendar time but requires no direct labor or equipment resources.
• Valid Technical Uses:
  • Physical processes: Concrete curing (e.g., 7 or 28 days), paint/grout drying, grout settling.
  • Regulatory/Contractual review periods: Submittal review by engineer (14 days), permit approval waiting periods.
  • Environmental cooling or thermal dissipation cycles.
• Abusive/Poor Scheduling Practice: Using arbitrary positive lags as placeholders for unmodeled physical work (e.g., using an FS + 45d lag instead of creating a discrete activity called "Manufacture and Deliver High-Pressure Pump"). Unmodeled lags distort resource curves and hide risk.

2. Lead Time (Negative Lag, $-L$)

• Function: Accelerates the successor activity by allowing it to start before the predecessor activity has completed ($ES_{\text{succ}} = EF_{\text{pred}} - \text{Lead}$). Often referred to as negative lag.
• Risks and Schedule Degradation:
  • Logic Distortion: Negative lags imply that work starts before predecessor milestones are achieved, creating risks of rework if the predecessor changes.
  • DCMA 14-Point Rule: Strict 0% threshold. The Defense Contract Management Agency (DCMA) guidelines and AACE Recommended Practices strictly prohibit negative lags in baseline schedules.
  • Remediation: Instead of using "Design Review" $\xrightarrow{\text{FS - 5d}}$ "Procurement", the cost professional should subdivide the predecessor into "Design 80% Complete" and "Final Design Approval", linking procurement cleanly with a positive FS logic tie.

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4. Classification of Dependencies (Mandatory, Discretionary, External, Internal)

Every logic link in a project network falls into a two-dimensional taxonomy based on its origin and control:

+-----------------------------------------------------------------------------------------+
|                          2x2 MATRIX OF DEPENDENCY CLASSIFICATIONS                       |
|                                                                                         |
|                           MANDATORY ("Hard Logic")     DISCRETIONARY ("Soft Logic")      |
|                        +----------------------------+-----------------------------+     |
|   INTERNAL             | Physical / Technological   | Preferential sequencing     |     |
|   (Within Project Team | necessity inside scope.    | strategy, crew balancing,   |     |
|    Control)            | Example: Erect Steel AFTER | equipment sharing.          |     |
|                        | Foundation Concrete cures. | Example: Build Tank A       |     |
|                        |                            | before Tank B with 1 crew.  |     |
|                        +----------------------------+-----------------------------+     |
|   EXTERNAL             | Non-project contractual or | Preferred alignment with    |     |
|   (Outside Project     | regulatory requirements.   | external stakeholder events |     |
|    Team Control)       | Example: Building Permit   | Example: Schedule tie-in    |     |
|                        | issuance by City before    | during municipal highway    |     |
|                        | Site Excavation begins.    | holiday shutdown.           |     |
|                        +----------------------------+-----------------------------+     |
+-----------------------------------------------------------------------------------------+

Critical Principles for Cost Engineers:

1. Mandatory Dependencies (Hard Logic): Imposed by the physical nature of the work or basic laws of physics. Cannot be altered during schedule compression without changing project scope or technology.
2. Discretionary Dependencies (Soft Logic / Preferential Logic): Defined by the project team based on preferred practices, resource sharing, or economic optimization (e.g., routing a specialized welding rig sequentially across three process units).
3. Forensic Delay & Compression Impact (AACE RP 29R-03): In schedule compression (crashing/fast-tracking) or forensic delay claim defense, discretionary logic must be relaxed or restructured before claiming compensable project delays. If a contractor claims a delay on Tank A impacted Tank B, but Tank B was sequenced after Tank A solely due to preferential crew assignment, the owner may argue that the contractor could have mobilized a second crew to mitigate the delay.

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5. Network Integrity: Dangling Logic, Redundant Links & Open Ends

A healthy CPM schedule network must form a completely closed, continuous mathematical loop from the Project Start milestone to the Project Finish milestone.

+-----------------------------------------------------------------------------------------+
|                                SCHEDULE INTEGRITY ANOMALIES                             |
|                                                                                         |
|   1. OPEN END (Missing Predecessor or Successor):                                       |
|      [ Start ] ---> [ Activity A ] ---> [ Activity B (NO SUCCESSOR!) ]                  |
|                                                                                         |
|   2. DANGLING LOGIC (Start Dangle & Finish Dangle):                                     |
|      [ Pred ] --- SS ---> [ Activity X (Finish floats unconstrained!) ]                 |
|      [ Activity Y (Start floats unconstrained!) ] --- FF ---> [ Succ ]                  |
|                                                                                         |
|   3. REDUNDANT RELATIONSHIP (Transitive Bypass):                                        |
|      [ Activity A ] ------------------ FS (REDUNDANT) -----------------> [ Activity C ] |
|             |                                                                 ^         |
|             +---- FS ----> [ Activity B ] ------------------- FS -------------+         |
+-----------------------------------------------------------------------------------------+

1. Open Ends

• Definition: Any activity lacking at least one predecessor (except the project start milestone) or lacking at least one successor (except the project completion milestone).
• Flaw: Prevents backward pass calculations from flowing through the activity, resulting in artificially infinite Total Float and preventing accurate critical path identification.

2. Dangling Logic (Half-Open Nodes)

• Start Dangle: An activity with only a Finish-to-Finish (FF) predecessor. Its finish date is constrained, but its start date is free to float backward in time unconstrained.
• Finish Dangle: An activity with only a Start-to-Start (SS) predecessor. Its start date is constrained, but its finish date is uncoupled from upstream logic. If its duration expands, it does not push downstream work, creating false float.
• Standard Rule: Every activity must have at least one logic tie driving its Start (an incoming FS or SS) and at least one logic tie driving its Finish (an outgoing FS or FF).

3. Redundant Logic (Transitive Bypasses)

• Definition: If Activity A precedes Activity B (A $\rightarrow$ B) and Activity B precedes Activity C (B $\rightarrow$ C), adding an explicit relationship from Activity A to Activity C (A $\rightarrow$ C) is redundant.
• Impact: While mathematically benign in simple networks, having thousands of redundant ties clutters the database, slows calculation speeds, and creates severe confusion when adjusting logic during project execution.

4. Schedule Calculation Modes: Retained Logic vs. Progress Override

When work is executed out of sequence (e.g., a successor starts before its predecessor finishes):

• Retained Logic (Industry Standard): The scheduling software respects the original network logic. The remaining duration of the successor cannot finish until the predecessor completes its remaining duration.
• Progress Override: The software treats the out-of-sequence work as an override, ignoring the predecessor logic and allowing the successor to finish as soon as its remaining duration elapses. AACE recommends Retained Logic for baseline control.

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[!IMPORTANT] AACE CCP Exam Alert — PDM Best Practices:

• Modern CPM relies exclusively on PDM (AON); ADM (AOA) is obsolete and required dummy activities.
• The 4 dependency types are FS (predominant), SS (concurrent start), FF (concurrent finish), and SF (handover - avoid).
• Negative lags (leads) are strictly prohibited under DCMA and AACE quality standards; decompose activities instead.
• Every discrete activity must have both a start driver and a finish driver to eliminate dangling logic.