Resource Levelling (Edexcel A-Level Further Mathematics): Revision Notes
11.1.6 Resource Levelling
Introduction
Resource levelling is the process of redistributing activities within a project's timeline to reduce fluctuations in resource usage while ensuring the project's completion time is not exceeded. This is particularly useful when worker availability is limited or uneven resource demand leads to inefficiencies.
Resource levelling builds upon resource histograms by adjusting the timing of non-critical activities (those with float) to smooth resource demand.
Key Concepts
Critical and Non-Critical Activities
- Critical activities: Have no float and must start and finish as scheduled.
- Non-critical activities: Have float and can be delayed within their float without affecting the project completion time.
Objectives of Resource Levelling
- Minimise peaks and troughs in resource usage.
- Ensure resource demand does not exceed availability at any time.
- Retain the original project duration.
Adjusting Activity Start Times
Non-critical activities can be rescheduled within their float to achieve a smoother resource histogram. The adjustments must:
- Preserve the order of dependencies.
- Ensure the adjusted start time does not exceed the latest possible start time.
Worked Examples
Example 1: Levelling a Simple Resource Histogram
Step 1: Given Information
The project consists of the following activities:
| Activity | Duration (days) | Workers Required | Start Time | Float |
|---|---|---|---|---|
| A | 3 | 2 | 0 | 0 |
| B | 4 | 3 | 3 | 2 |
| C | 2 | 4 | 7 | 3 |
| D | 3 | 1 | 5 | 5 |
Worker Availability: 5 workers.
Step 2: Initial Resource Histogram
Using the given start times:
Day: 0 1 2 3 4 5 6 7 8 9 10
Activity A ███
Activity B ████
Activity D ███
Activity C ██
Workers: 2 2 2 3 3 4 4 4 4 1 1
Step 3: Identify Peaks
The highest demand is 4 workers on days 5–8, but there are 5 workers available. This is acceptable, but the resource histogram can still be levelled to smooth the demand.
Step 4: Adjust Non-Critical Activities
- Activity D: Has a float of 5 days, so it can be delayed to start at day 8.
- Activity C: Has a float of 3 days, so it can be delayed to start at day 9.
Revised schedule:
Day: 0 1 2 3 4 5 6 7 8 9 10
Activity A ███
Activity B ████
Activity D ███
Activity C ██
Workers: 2 2 2 3 3 3 3 1 1 1 1
Step 5: Evaluate the Smoothed Histogram
The new histogram has fewer peaks, achieving more consistent worker utilisation:
- Demand now ranges from 1 to 3 workers, compared to the original peak of 4.
Example 2: Levelling with Resource Constraints
Step 1: Given Information
The project consists of the following activities:
| Activity | Duration (weeks) | Workers Required | Start Time | Float |
|---|---|---|---|---|
| A | 2 | 5 | 0 | 0 |
| B | 3 | 4 | 2 | 1 |
| C | 2 | 3 | 4 | 2 |
| D | 1 | 2 | 5 | 2 |
Worker Availability: 8 workers.
Step 2: Initial Resource Histogram
Week: 0 1 2 3 4 5 6 7
Activity A █████
Activity B ████
Activity C ███
Activity D ██
Workers: 5 5 9 7 7 5 2 0
The total demand exceeds 8 workers in week 2.
Step 3: Adjust Non-Critical Activities
- Activity B: Has 1 week of float and can be delayed to start at week 3.
- Activity D: Has 2 weeks of float and can be delayed to start at week 6.
Revised schedule:
Week: 0 1 2 3 4 5 6 7
Activity A █████
Activity B ████
Activity C ███
Activity D ██
Workers: 5 5 5 7 7 5 2 0
Step 4: Evaluate the Smoothed Histogram
- The adjusted schedule avoids exceeding the 8-worker limit.
- The resource usage is more balanced, reducing worker under-utilization in weeks 6 and 7.
Note Summary
Common Mistakes
- Adjusting critical activities: Rescheduling critical activities delays the project and should be avoided.
- Exceeding float limits: Non-critical activities can only be delayed within their float; exceeding it disrupts dependencies.
- Ignoring resource limits: Levelling should not increase demand beyond availability at any point.
- Misinterpreting dependencies: Delaying an activity incorrectly might violate dependency constraints.
- Incomplete smoothing: Overlooking opportunities to further level the histogram.
Key Formulas
- Total Float:
- Worker Demand:
- Levelling Constraint:
- Non-critical Activity Adjustment: Adjust start times within float to reduce resource peaks while maintaining dependencies.