2.2 Construction Scheduling and Project Control

1.2 Construction Scheduling and Project Control

Construction scheduling is the process of planning, sequencing, and allocating time and resources to project activities to ensure successful completion within specified constraints. On the Professional Engineering (PE) Civil exam, scheduling questions focus heavily on the mathematical principles of the Critical Path Method (CPM), activity relationships, float analysis, and resource leveling.

Precedence Diagramming Method (PDM) and Activity Relationships

The Precedence Diagramming Method (PDM) represents activities as nodes connected by arrows that define the logical sequence and dependencies between tasks. In modern project management, there are four standard types of precedence relationships:

1. Finish-to-Start (FS): The successor activity cannot begin until the predecessor activity has completed. This is the most common relationship in construction. For example, you must finish placing reinforcing steel (predecessor) before you can start pouring concrete (successor).
2. Start-to-Start (SS): The successor activity cannot start until the predecessor activity has started. This is used for overlapping activities. For example, as soon as trenching (predecessor) starts, laying pipe (successor) can begin, allowing both to proceed concurrently.
3. Finish-to-Finish (FF activity relationship): The successor activity cannot finish until the predecessor activity finishes. For example, backfilling (successor) cannot finish until pipe inspection (predecessor) is finished.
4. Start-to-Finish (SF): The successor activity cannot finish until the predecessor activity starts. This relationship is rarely used in construction. An example is the startup of a new traffic bypass system (successor) that cannot be completed until the decommissioning of the old road system (predecessor) begins.

Dependencies can be modified using lead or lag values:

• Lag is a direct delay added to the start or finish of a successor activity. For example, an FS relationship with a 7-day lag (FS + 7 days) means the successor must wait 7 days after the predecessor finishes, commonly used to represent concrete curing time.
• Lead (negative lag) allows a successor activity to begin before the predecessor is fully finished.

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The Critical Path Method (CPM) Calculations

CPM is an analytical technique used to calculate the project duration and identify the sequence of activities that controls the project finish date. The method involves two computational passes: the forward pass and the backward pass.

Notation of a Node

Each activity node contains:

• Activity ID and Duration (D)
• Early Start (ES): The earliest possible time the activity can start.
• Early Finish (EF): The earliest possible time the activity can complete.
• Late Start (LS): The latest possible time the activity can start without delaying the project.
• Late Finish (LF): The latest possible time the activity can complete without delaying the project.

The Forward Pass (Early Times)

The forward pass begins at the start node (usually day 0 or day 1) and moves chronologically forward through the network.

1. The early start of the initial activity is 0.
2. The early finish for any activity is: EF = ES + Duration
3. For subsequent activities, the early start is determined by its predecessors: ES_successor = Max(EF_predecessors) (for simple FS relationships) If a lag is present: ES_successor = Max(EF_predecessor + Lag)

The maximum early finish of the final activity represents the minimum total project duration.

The Backward Pass (Late Times)

The backward pass begins at the final activity and moves backward through the network to calculate the latest times activities can occur without extending the project duration.

1. Set the late finish (LF) of the final activity equal to its early finish (EF) (or the target project deadline).
2. The late start for any activity is: LS = LF - Duration
3. For preceding activities, the late finish is determined by its successors: LF_predecessor = Min(LS_successors) (for simple FS relationships) If a lag is present: LF_predecessor = Min(LS_successor - Lag)

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Float Analysis

Float represents the scheduling flexibility of an activity. There are two primary types of float:

1. Total Float (TF)

Total float is the amount of time an activity can be delayed from its early start without delaying the project completion date. It is shared along a path of activities. Delaying an activity by more than its total float will push out the final project completion date. Total Float is calculated as: TF = LF - EF = LS - ES

2. Free Float (FF)

Free float is the amount of time an activity can be delayed without delaying the early start of any immediate successor activity. Free float belongs solely to that specific activity and is not shared. Free Float is calculated as: FF = Min(ES_successors) - EF - Lag

The Critical Path

The critical path is the longest continuous path of dependent activities through the network from start to finish. Activities on this path are critical activities and have the minimum total float (typically zero). Any delay to an activity on the critical path directly increases the overall project duration. A project can have multiple, parallel critical paths.

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Gantt Charts

A Gantt chart is a bar chart that visually represents the project schedule. The vertical axis lists the activities, and the horizontal axis represents time. Horizontal bars represent the duration of each activity, with their left edge at the early start and right edge at the early finish. Gantt charts are effective for:

• Visualizing overlapping tasks and parallel paths.
• Displaying total float as a dashed line or extension of the bar, showing how much a task can slide before affecting the schedule.
• Identifying resource loading over time by stacking daily resource demands beneath the timeline.

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Resource Allocation: Leveling vs. Smoothing

Construction activities require labor, equipment, and materials. Simply scheduling activities at their earliest start times can lead to highly fluctuating resource demands, which is inefficient and costly.

Resource Leveling

Resource leveling is used when resources are limited or capped. If the daily demand for a resource exceeds the available limit, non-critical activities are shifted within their float to reduce the peak demand. If resource constraints are severe and cannot be resolved using float, activities must be delayed further, which will extend the critical path and increase the project duration.

Resource Smoothing

Resource smoothing is used when the project duration is fixed (cannot be extended), but the estimator wishes to minimize fluctuations in resource demand. Activities are shifted only within their available total float. As a result, the peak resource demands are reduced, but the overall project completion date remains unchanged.

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Schedule Crashing and Project Acceleration

Project managers are frequently required to shorten (crash) the project duration to meet a deadline or respond to delays. Crashing refers to adding additional resources (overtime, extra shifts, larger equipment) to critical activities to reduce their durations.

Because crashing adds resources, it increases the direct cost of the activity. However, shortening the project reduces indirect costs (overhead, supervision, site utilities, and liquidated damages). The goal of project crashing is to achieve the target duration at the minimum total cost.

Incremental Crash Cost Slope

To crash a project economically, we must identify the activity on the critical path that is the cheapest to shorten. The cost per unit time to shorten an activity is the crash cost slope:

Crash Cost Slope = (Crash Cost - Normal Cost) / (Normal Duration - Crash Duration)

Step-by-Step Crashing Procedure:

1. Identify the current critical path(s) and project duration.
2. Determine which critical activities can be crashed (i.e., they have not yet reached their minimum crash duration).
3. Select the critical activity with the lowest crash cost slope.
4. Crash that activity by 1 day (or the maximum possible increment before another path becomes critical or the activity is fully crashed).
5. Recalculate the project network. If a new critical path is created (parallel critical paths), future crashing must shorten all critical paths simultaneously.
6. Repeat the process until the target duration is met or all critical activities are crashed.