Project Scheduling Basics

Project scheduling is a core competency tested on the PE Civil Transportation exam. Understanding activity relationships, precedence types, network formats, and basic scheduling terms is essential before performing full Critical Path Method (CPM) analyses.

Elements of a Schedule

A project schedule is a model that translates project activities, durations, resources, and constraints into a time-based plan.

Activity (Task): A cohesive unit of work that consumes time and resources.
Milestone: A significant event or point in time. It has zero duration and consumes no resources.
Duration ($d$): The estimated time required to complete an activity (usually measured in working days).
Predecessor: An activity that must start or finish before another activity can begin or complete.
Successor: An activity that cannot start or finish until another activity has started or completed.

Precedence Relationships

Activities are linked using logical dependencies. There are four types of relationships, which can be modified by lags or leads.

flowchart TD
    subgraph FS ["1. Finish-to-Start (FS)"]
        direction TB
        A1[A] -->|FS| B1[B]
    end
    subgraph SS ["2. Start-to-Start (SS)"]
        direction TB
        A2[A] -->|SS| B2[B]
    end
    subgraph FF ["3. Finish-to-Finish (FF)"]
        direction TB
        A3[A] -->|FF| B3[B]
    end
    subgraph SF ["4. Start-to-Finish (SF)"]
        direction TB
        A4[A] -->|SF| B4[B]
    end

1. Finish-to-Start (FS)

The successor activity cannot start until the predecessor activity finishes. This is the most common relationship.

Equation: $ES_B \ge EF_A$
With Lag ($L$): $ES_B \ge EF_A + L$ (Activity B can start $L$ days after Activity A finishes).

2. Start-to-Start (SS)

The successor activity cannot start until the predecessor activity starts.

Equation: $ES_B \ge ES_A$
With Lag ($L$): $ES_B \ge ES_A + L$ (Activity B can start $L$ days after Activity A starts). Common for overlapping tasks like excavation and pipe laying.

3. Finish-to-Finish (FF)

The successor activity cannot finish until the predecessor activity finishes.

Equation: $EF_B \ge EF_A$
With Lag ($L$): $EF_B \ge EF_A + L$ (Activity B can finish $L$ days after Activity A finishes).

4. Start-to-Finish (SF)

The successor activity cannot finish until the predecessor activity starts. This is rarely used in construction.

Equation: $EF_B \ge ES_A$
With Lag ($L$): $EF_B \ge ES_A + L$

Lag and Lead Times

Lag Time: A directed delay that requires an activity to wait a specified time after its predecessor’s start/finish before starting/finishing itself (positive value). Example: Pour concrete (Activity A) must cure for 5 days before building forms (Activity B). This is a Finish-to-Start relationship with a 5-day lag (FS + 5).
Lead Time: A negative lag that allows a successor to begin before the predecessor is completely finished (negative value). Example: Lay asphalt (Activity B) can start 2 days before subgrade prep (Activity A) completes (FS - 2).

Network Diagram Formats

There are two primary styles of scheduling network diagrams. The PE Civil exam almost exclusively uses AON.

1. Activity-on-Node (AON)

Activities are represented by geometric shapes (nodes/boxes), and dependencies are represented by arrows connecting the nodes.

Advantage: Easy to represent all four precedence types and lags.
Node Anatomy: A typical AON node contains key scheduling variables:

2. Activity-on-Arrow (AOA)

Activities are represented by arrows, and nodes (circles) represent events (the start or finish of activities).

Advantage: Clear visual representation of events.
Disadvantage: Can only represent Finish-to-Start relationships without lags. Requires the use of dummy activities (dashed arrows with zero duration) to maintain logic.

Worked Example: Precedence and Lag Calculations

Problem:
Activity X (duration = 6 days) begins at Day 0. It is connected to Activity Y (duration = 4 days) and Activity Z (duration = 5 days) under the following rules:

Activity Y has a Start-to-Start relationship with Activity X with a 2-day lag (SS + 2).
Activity Z has a Finish-to-Start relationship with Activity X with a 3-day lag (FS + 3).

Calculate the Early Start (ES) and Early Finish (EF) for Activities X, Y, and Z.

Solution:

Note: We will use the 0-based scheduling convention where the project begins at Day 0.

Step 1: Calculate Activity X

$ES_X = 0$
$EF_X = ES_X + d_X = 0 + 6 = 6\text{ days}$

Step 2: Calculate Activity Y (SS + 2 with X)

Relationship: $ES_Y = ES_X + \text{Lag} = 0 + 2 = 2\text{ days}$
$EF_Y = ES_Y + d_Y = 2 + 4 = 6\text{ days}$

Step 3: Calculate Activity Z (FS + 3 with X)

Relationship: $ES_Z = EF_X + \text{Lag} = 6 + 3 = 9\text{ days}$
$EF_Z = ES_Z + d_Z = 9 + 5 = 14\text{ days}$

Schedule Compression Overview

When a schedule exceeds its allowable duration, it must be compressed. This can be achieved through two primary techniques:

Fast-Tracking: Performing activities in parallel that would normally be done in sequence.
- Pros: No additional direct cost.
- Cons: Increases risk, coordination complexity, and potential for rework.
Crashing: Shortening the duration of activities on the critical path by adding resources (overtime, extra equipment, labor).
- Pros: Safely compresses duration.
- Cons: Increases direct costs.

Crucial Pitfalls and Exam Traps

0-Based vs. 1-Based Systems:
- In a 0-based system, if Activity A finishes at day 4, the next Finish-to-Start Activity B starts at day 4. (Formula: $EF = ES + d$).
- In a 1-based system (often used in project management textbooks), if Activity A finishes at day 4, Activity B starts at day 5. (Formula: $EF = ES + d - 1$).
- Exam Strategy: Check the answer choices or NCEES handbook. If the NCEES handbook uses $EF = ES + t$, it is using the 0-based system. The 0-based system is significantly less error-prone when dealing with lags.
Applying Lags to the Wrong Dates: Read the relationship carefully. A Start-to-Start lag adds to the Early Start of the predecessor. A Finish-to-Start lag adds to the Early Finish. Misapplying this is a major source of calculation errors.