11.1.5 Resource Histograms

Introduction

A resource histogram is a bar chart used to visually represent the number of workers (or resources) required over the duration of a project. This tool helps to assess the workforce demands and ensures that the necessary resources are available at the right times.

In A-Level Further Maths, constructing resource histograms involves:

Allocating workers to specific activities.
Using the project timeline (e.g., derived from a Gantt chart) to determine the number of workers required at each time interval.

Steps to Construct a Resource Histogram

Understand the Problem
Collect Key Information
Build the Histogram

1. Understand the Problem

Each activity has a start time, duration, and number of workers required.
Use the timeline of activities (e.g., from a Gantt chart) to calculate the total number of workers needed at each time step.

2. Collect Key Information

For each activity, note:

Start and finish times.
Number of workers required.
Duration of the activity.

3. Build the Histogram

Divide the timeline into units (e.g., days, weeks).
For each unit, sum the workers needed across all activities in progress.
Draw a bar for each time interval representing the total workforce.

Worked Example

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Example 1: Construct a Resource Histogram

Step 1: Given Information

Activity	Start Time	Duration (days)	Workers Required
A	0	3	2
B	2	4	3
C	4	2	4
D	5	3	1

Step 2: Analyse Overlaps

Activity A runs from day 0 to day 2.
Activity B starts at day 2 and overlaps with Activity A for 1 day.
Activity C starts at day 4, overlaps with Activity B for 1 day, and then continues independently.
Activity D starts at day 5, overlaps with Activity C for 2 days.

Step 3: Calculate Workers at Each Day

Day	Workers from A	Workers from B	Workers from C	Workers from D	Total Workers
0	2	0	0	0	2
1	2	0	0	0	2
2	2	3	0	0	5
3	0	3	0	0	3
4	0	3	4	0	7
5	0	0	4	1	5
6	0	0	4	1	5
7	0	0	0	1	1

Step 4: Draw the Resource Histogram

The resource histogram can be represented as follows:

Day:       0   1   2   3   4   5   6   7
Workers:   ██  ██  █████  ███  ███████ █████  █████  █

Key:

The height of each bar represents the total workers needed for that day.
Activities contributing to each total are determined from the table.

infoNote

Example 2: Histogram with Non-Uniform Durations

Step 1: Given Information

Activity	Start Time	Duration (weeks)	Workers Required
A	0	2	5
B	1	3	4
C	3	2	6

Step 2: Analyse Overlaps

Activity A runs from week 0 to week 1.
Activity B starts at week 1, overlaps with Activity A in week 1, and continues until week 3.
Activity C starts at week 3, overlaps with Activity B in week 3, and then continues independently.

Step 3: Calculate Workers at Each Week

Week	Workers from A	Workers from B	Workers from C	Total Workers
0	5	0	0	5
1	5	4	0	9
2	0	4	0	4
3	0	4	6	10
4	0	0	6	6

Step 4: Draw the Resource Histogram

Week:      0   1   2   3   4
Workers:   █████  █████████ ████ ██████████ ██████

Key:

Bars clearly show workforce demand by week.
Overlaps of activities result in taller bars.

Note Summary

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Common Mistakes

Forgetting overlaps: Not summing workers from activities that occur simultaneously.
Incorrect time intervals: Misaligning activities with the timeline.
Misinterpreting durations: Confusing start and finish times with durations.
Omitting zero contributions: Failing to account for periods when no workers are required.
Poor visualization: Drawing inconsistent or unclear bars in the histogram.

infoNote

Key Formulas

Resource calculation: Total workers = sum of workers for overlapping activities.
Start and finish times:

Finish time = start time + duration.

Histogram representation:

Height of the bar = total workers required at each time step.

Overlaps:

Add contributions from all activities running during the same time interval.

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

11.1.5 Resource Histograms

Introduction

Steps to Construct a Resource Histogram

1. Understand the Problem

2. Collect Key Information

3. Build the Histogram

Worked Example

Example 1: Construct a Resource Histogram

Example 2: Histogram with Non-Uniform Durations

Note Summary

Common Mistakes

Key Formulas

500K+ Students Use These Powerful Tools to Master Resource Histograms For their A-Level Exams.

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