Resources
Construction resources are often summarised as the 5 Ms: Manpower, Materials, Machinery, Money and Management (with space/time also treated as resources).
- Renewable resources — available again each period (labour, equipment per day).
- Non-renewable (consumable) resources — used up (materials, money).
Resource planning
- Determine resource requirements of each activity (e.g. 4 masons, 1 mixer).
- Schedule activities (early start schedule from CPM).
- Aggregate resources per time period → resource histogram (resource loading diagram).
- Compare with availability; level or allocate as needed.
Resource histogram
A bar diagram of resource units required versus time. Irregular histograms with high peaks and valleys cause hiring and firing, idle time, overtime and poor productivity.
Resource levelling (smoothing)
Resource levelling reshuffles non-critical activities within their floats so that resource demand becomes as uniform as possible, without changing the project duration.
- Critical activities are not moved.
- Activities are shifted (start delayed) using free float first, then total float (which may affect successors).
- Objective measures: reduce peak demand, reduce fluctuations, minimise the sum of squares of daily resource demand (the total resource-days remain constant, so a smaller sum of squares means a more uniform profile).
Resource allocation (resource-constrained scheduling)
When resources are limited (a maximum available per period), activities are scheduled so that demand never exceeds availability, even if the project duration increases.
Heuristic priority rules for deciding which activity receives resources first:
- Least total float (minimum slack) first.
- Earliest late start / earliest late finish.
- Shortest duration first.
- Activities with most resources or on the critical path first.
Levelling vs allocation
| Aspect |
Resource levelling (smoothing) |
Resource allocation (constrained) |
| Project duration |
Fixed |
May increase |
| Resource limit |
Not fixed; aim is uniformity |
Fixed maximum availability |
| Activities moved |
Only within floats |
Any, as required |
| Objective |
Reduce fluctuations and peaks |
Keep within resource limits |
Worked example — levelling
✎Worked ExampleLevelling within float
| Activity |
Duration (days) |
Workers/day |
Predecessor |
Early start schedule |
| A |
3 |
4 |
— |
days 1–3 (critical) |
| B |
2 |
3 |
— |
days 1–2 (total float 4) |
| C |
3 |
2 |
A |
days 4–6 (critical) |
Project duration = 6 days; total resource-days = 12 + 6 + 6 = 24.
Early start histogram: days 1–2: 4 + 3 = 7; day 3: 4; days 4–6: 2
Peak = 7; sum of squares =49+49+16+4+4+4=126
Levelled — shift B to days 4–5 (using its float): days 1–3: 4; days 4–5: 2 + 3 = 5; day 6: 2
Peak = 5; sum of squares =16×3+25×2+4=102
The project still finishes on day 6, peak demand falls from 7 to 5 and the profile is smoother (lower sum of squares).
✎Worked ExampleResource constraint
In the same project, only 4 workers are available per day. What is the minimum duration?
Solution. A (4 workers) and B (3 workers) cannot run together. A is critical, so schedule A on days 1–3. C (2 workers) and B (3 workers) together need 5 > 4. Schedule C on days 4–6 and B on days 7–8, or B on days 4–5 and C on days 6–8.
Minimum duration = 8 days — the resource limit extends the project by 2 days.
