Total slack is calculated as the smaller value of the Late Finish minus the Early Finish field, and the Late Start minus the Early Start field.
Total slack, also known as total float, represents the maximum amount of time a task can be delayed from its Early Start without delaying the project finish date or violating a project constraint. It's a crucial metric in project management, especially when using methods like the Critical Path Method (CPM).
What is Total Slack?
Essentially, total slack is the buffer time available for a specific task. If a task has zero total slack, it is considered a critical task, meaning any delay in this task will directly impact the project's overall completion date.
Key Terms in Total Slack Calculation
To calculate total slack, you need four key time values for each task:
- Early Start (ES): The earliest possible time a task can begin, based on the project's schedule network logic and any constraints.
- Early Finish (EF): The earliest possible time a task can be completed, calculated as Early Start plus the task's duration.
- Late Start (LS): The latest possible time a task can begin without delaying the project's finish date or violating a constraint.
- Late Finish (LF): The latest possible time a task can be completed without delaying the project's finish date or violating a constraint.
These values are typically determined during the schedule network analysis process, involving forward pass (to find ES and EF) and backward pass (to find LS and LF) calculations.
The Formula for Total Slack
Based on the reference provided, total slack is determined by finding the smaller of two differences:
- The difference between the task's Late Finish and Early Finish (LF - EF).
- The difference between the task's Late Start and Early Start (LS - ES).
Therefore, the formula can be written as:
Total Slack = Minimum (Late Finish - Early Finish, Late Start - Early Start)
Or using abbreviations:
TS = Min (LF - EF, LS - ES)
Example Calculation
Let's consider a hypothetical task with the following schedule dates:
- Early Start (ES): Day 5
- Early Finish (EF): Day 10
- Late Start (LS): Day 7
- Late Finish (LF): Day 12
Now, let's apply the formula:
- Calculate LF - EF: 12 - 10 = 2
- Calculate LS - ES: 7 - 5 = 2
Comparing the two results (2 and 2), the smaller value is 2.
So, the Total Slack for this task is 2 days. This means the task can be delayed by up to 2 days without impacting the project finish date.
Here's a table summarizing the example:
| Metric | Value |
|---|---|
| Early Start | Day 5 |
| Early Finish | Day 10 |
| Late Start | Day 7 |
| Late Finish | Day 12 |
Calculation:
- LF - EF = 12 - 10 = 2
- LS - ES = 7 - 5 = 2
Total Slack = Min (2, 2) = 2 days
Let's consider another example where the values are different:
- Early Start (ES): Day 8
- Early Finish (EF): Day 15
- Late Start (LS): Day 12
- Late Finish (LF): Day 19
Calculation:
- Calculate LF - EF: 19 - 15 = 4
- Calculate LS - ES: 12 - 8 = 4
Total Slack = Min (4, 4) = 4 days.
One more example:
- Early Start (ES): Day 3
- Early Finish (EF): Day 8
- Late Start (LS): Day 5
- Late Finish (LF): Day 11
Calculation:
- Calculate LF - EF: 11 - 8 = 3
- Calculate LS - ES: 5 - 3 = 2
Total Slack = Min (3, 2) = 2 days.
In this last example, even though LF - EF was 3, the smaller value from LS - ES (which was 2) determined the total slack.
Why Calculate Total Slack?
Calculating total slack is essential for several project management activities:
- Identifying the Critical Path: Tasks with zero total slack lie on the critical path.
- Prioritizing Tasks: Tasks with less slack require closer monitoring.
- Resource Leveling: Slack provides flexibility in scheduling tasks to optimize resource allocation.
- Managing Risk: Understanding slack helps assess the impact of potential delays.
By correctly calculating total slack using the Early Start, Early Finish, Late Start, and Late Finish dates, project managers gain valuable insight into schedule flexibility and critical activities.
