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

Minimize 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

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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 utilization:

Demand now ranges from 1 to 3 workers, compared to the original peak of 4.

infoNote

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

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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.

infoNote

Key Formulas

Total Float:

\text{Float} = \text{LFT} - \text{EST} - \text{Duration}

Worker Demand:

\text{Total workers at time \( t \)} = \sum \text{workers required for all active activities at \( t \)}

Levelling Constraint:

\text{Total workers at any time} \leq \text{Available workers}

Non-critical Activity Adjustment: Adjust start times within float to reduce resource peaks while maintaining dependencies.

Resource Levelling Simplified Revision Notes for A-Level Edexcel Further Maths Decision Maths 1

11.1.6 Resource Levelling

Introduction

Key Concepts

Critical and Non-Critical Activities

Objectives of Resource Levelling

Adjusting Activity Start Times

Worked Examples

Example 1: Levelling a Simple Resource Histogram

Example 2: Levelling with Resource Constraints

Note Summary

Common Mistakes

Key Formulas

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