7.3 Critical Path Calculations, Float & Schedule Compression
Key Takeaways
- The forward pass computes early start and early finish and yields the project duration; the backward pass computes late start and late finish.
- Total float equals late start minus early start, or late finish minus early finish, and activities with zero total float form the critical path.
- Crashing shortens critical-path activities by adding labor or overtime, raising direct cost without changing the sequence of work.
- Fast-tracking overlaps activities that were planned sequentially, which adds no direct cost but creates coordination risk and potential rework.
- Shortening a non-critical activity never shortens the project, and crashing one critical path can expose a second path that becomes critical.
Critical Path Method (CPM) Calculations
In an Activity-on-Node (AON) CPM diagram, each activity is represented as a node with four critical timing values derived through forward and backward passes:
+---------------+---------------+
| Early Start | Early Finish |
| (ES) | (EF) |
+---------------+---------------+
| Activity Name |
| (Duration) |
+---------------+---------------+
| Late Start | Late Finish |
| (LS) | (LF) |
+---------------+---------------+
The Forward Pass (Early Dates & Project Duration)
The forward pass determines the earliest possible dates an activity can begin and conclude based on logical network predecessors:
- Early Start (ES): The earliest time an activity can begin. For the initial project activity, $\text{ES} = 0$. For any subsequent activity with multiple predecessors, Early Start equals the maximum of the Early Finish dates of all its immediate predecessors:
- Early Finish (EF): The earliest time an activity can finish:
The Backward Pass (Late Dates & Float Calculation)
Once the forward pass calculates the total project duration, the backward pass determines the latest possible dates activities can occur without delaying the overall project completion date:
- Late Finish (LF): For the final activity, Late Finish equals its Early Finish ($\text{LF} = \text{EF}$). For any preceding activity with multiple successors, Late Finish equals the minimum of the Late Start dates of all its immediate successors:
- Late Start (LS): The latest time an activity can begin without delaying the project:
Understanding Float (Slack)
- Total Float (TF): The total amount of time an activity can be delayed from its Early Start without delaying the contractual project completion date:
- Free Float (FF): The amount of time an activity can be delayed without delaying the Early Start of any immediate successor activity:
The Critical Path
The Critical Path is the continuous sequence of dependent activities through the network with Total Float = 0. It represents the longest duration path through the project. Any delay to an activity situated on the critical path directly delays the project completion date by an identical amount of time. Activities with positive float can experience delays up to their float threshold without affecting the project completion date.
Schedule Compression Techniques: Crashing vs. Fast-Tracking
When an owner demands that an architectural team accelerate project delivery—or when project delays must be recovered—project managers deploy two primary schedule compression techniques:
| Feature | Schedule Crashing | Fast-Tracking |
|---|---|---|
| Operational Definition | Adding labor resources or authorized overtime to critical path tasks to shorten duration | Executing tasks concurrently that were originally planned in sequential order |
| Primary Mechanism | Overtime hours, reassigning senior staff, hiring outside drafting consultants | Overlapping phases (e.g., starting CDs during DD; issuing foundation permits early) |
| Cost Impact | Significantly increases direct project cost (overtime premiums, outside consultant fees) | Minimal upfront labor cost addition; fee remains theoretically constant |
| Risk Profile | Low-to-moderate technical risk; design logic and review sequences remain intact | High project risk; creates severe potential for coordination clashes and rework |
| Diminishing Returns | Brooks's Law: Adding manpower to late software/design projects can make them later | Revisions to upstream design alter already-documented or constructed foundations |
1. Schedule Crashing
Crashing focuses strictly on critical path activities where additional labor can compress duration. Crashing non-critical activities wastes money because it merely increases unused float. While crashing guarantees the logical sequence of work remains intact, it incurs diminishing marginal returns: staff fatigue from excessive overtime leads to increased coordination errors, and bringing new personnel onto an active drawing set requires training time that diverts senior staff.
2. Fast-Tracking
Fast-tracking compresses schedules by taking sequential activities and performing them in parallel. A classic architectural example is issuing early bid/permit packages for site excavation and concrete foundations while the architectural superstructure and MEP building enclosure drawings are still undergoing Design Development.
While fast-tracking can cut months from a project timeline without increasing initial labor fees, it introduces immense operational risk. If subsequent structural wind analyses or interior layout modifications require shifting shear walls or column grid lines, already-poured footings or fabricated steel must be demolished or modified via costly construction change orders. Under AIA B101, the architect must warn the owner in writing of the increased risks of rework inherent in fast-tracked project delivery.
An architectural project manager is planning the design schedule for a mixed-use commercial development using the Critical Path Method (CPM). The early phases of the project consist of five sequential and parallel activities:
A developer client demands that the project team accelerate the delivery schedule to complete Construction Documents six weeks ahead of the contractual deadline. The project manager considers schedule compression techniques. Which statement accurately describes the operational difference and risk profile between 'Crashing' and 'Fast-Tracking' the project schedule?