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Strategic Cost Management · Network Analysis - PERT, CPM

Resource Levelling, Smoothing and Updating of Networks

Updated 11 October 2026 · Fact-checked

Resource levelling and smoothing rearrange non-critical activities, using their float, so that daily resource demand becomes even. Smoothing keeps the project duration fixed. Levelling accepts a longer duration if resources are capped. Updating revises the network with actual progress and re-computes the critical path and completion date.

Understand Resource Levelling, Updating and Applications

A network gives you a time schedule. It does not tell you whether you have enough labour, machines or cash to follow it. If the earliest-start schedule puts many activities in the same week, resource demand spikes and then falls. Peaks mean overtime, hiring and idle capacity later.

Resource smoothing (time-limited scheduling) keeps the project duration unchanged. You shift non-critical activities within their total float so that demand is more even. Critical activities are never moved, because moving them delays the project.

Resource levelling (resource-limited scheduling) applies when the resource has a hard cap, such as only 10 fitters. You schedule activities so that the cap is never exceeded. If the cap forces activities to wait beyond their float, the project duration increases.

A simple way to remember the difference: smoothing protects time, levelling protects the resource limit.

Updating is done during execution. Actual start and finish dates, changed estimates, added or dropped activities and revised resource availability are fed into the network. You recompute earliest and latest times for the remaining work. The critical path may change, as a non-critical activity that has overrun its float becomes critical. Management then decides on crashing, reallocation or revised commitments.

PERT/CPM are used for planning, scheduling and control of large, non-repetitive projects such as construction, plant installation, shutdown maintenance and product launches. They also have limits, which you must be able to state.

Key rules to remember

Total float
Total float = LST − EST = LFT − EFT
Float is the room available to shift an activity without delaying project completion. Critical activities have zero total float.
Free float
Free float = Earliest start of succeeding activity − EFT of this activity
Use free float to shift an activity without affecting even the next activity's earliest start.
Resource demand per period
Demand in a period = Σ resource units of all activities scheduled in that period
Build this row from a time-scaled bar chart and compare it with the cap or the average.
Average resource requirement
Average = Total resource-days ÷ Project duration
Smoothing aims to bring daily demand close to this figure.
Updated completion time
Revised completion = Elapsed time + Longest remaining path from the status date
Recompute with remaining durations only for incomplete activities.

How to solve Resource Levelling, Updating and Applications questions

Use this order for any levelling, smoothing or updating question.

  1. 1Draw the network and compute EST, EFT, LST, LFT and total float for each activity. Mark the critical path.
  2. 2Draw a time-scaled bar chart with every activity at its earliest start. Write each activity's resource units on its bar.
  3. 3Total the resource demand for each period. Note the peaks, and the cap if one is given.
  4. 4Keep critical activities fixed. Shift non-critical activities, within their float, from peak periods to low periods. Respect precedence.
  5. 5Recompute the demand row. For smoothing, stop when demand is as even as float permits. For levelling, check that the cap is met in every period.
  6. 6If the cap cannot be met within the floats, delay activities further and state the new project duration.
  7. 7For updating, replace completed work with actuals, use revised durations for the remaining activities, recompute the forward and backward pass from the status date, and name the new critical path.
  8. 8State a conclusion: the schedule, the peak demand, and the effect on project duration.

Quickest way: Float-first shifting on a bar chart

When to use it: Use this when the question gives resource units per activity and asks for a smoothed or levelled schedule.

  1. Find the critical path and float first. This tells you which activities can move.
  2. Plot all activities at earliest start and total the demand row.
  3. Pick the non-critical activity with the largest float that sits in the peak period.
  4. Move it later by as many periods as its float and precedence allow, and re-total.
  5. Repeat until the peak is at or below the cap, or no float remains.
  6. Write the final demand row and the project duration in one line.

Common mistakes in Resource Levelling, Updating and Applications

  • Shifting a critical activity to reduce a peak.

    The peak looks easy to cut, and the student forgets that critical activities have no float.

    Fix: Mark critical activities first and treat them as fixed. Only non-critical activities may move, and only within float.

  • Treating smoothing and levelling as the same thing.

    Both flatten resource demand, so the labels get mixed up.

    Fix: Smoothing holds the project duration. Levelling holds the resource cap and may extend duration. Say which one the question asks for.

  • Moving an activity by its total float without checking successors.

    Total float is shared along a chain of activities. Using all of it on one activity can remove the float of the next.

    Fix: Check the successor's earliest start. Use free float when you want no knock-on effect, and recompute float after each shift.

  • Not recomputing the critical path while updating.

    Students simply add the delay to the old completion date.

    Fix: Rerun the forward and backward pass on the remaining activities. A delayed non-critical activity can use up its float and create a new critical path.

  • Listing only advantages of PERT/CPM, or stating limits vaguely.

    Students memorise the benefits and skip the limitations.

    Fix: Give both sides with a reason each, for example that PERT's three time estimates are subjective and the method assumes a fixed logic of activities.

Worked examples

Example 1

A (2 days, 4 workers) and B (2 days, 4 workers) have no predecessor. C (2 days, 3 workers) follows A only. B has no successor, so it only needs to finish by the end of the project. Project ends when all activities finish. Compute project duration and show how smoothing can reduce the peak demand.

Show the solution
  1. Forward pass: A runs 0 to 2, B runs 0 to 2, C runs 2 to 4. Project duration is 4 days (path A-C).
  2. Backward pass: C has latest finish 4 and latest start 2. A has latest finish 2 and latest start 0. B has no successor, so its latest finish is the project end, day 4, and its latest start is 2. Critical path is A-C. B has total float = LST − EST = 2 − 0 = 2 days.
  3. Earliest-start demand: days 1 and 2 = A 4 + B 4 = 8 workers. Days 3 and 4 = C 3 workers. Demand row is 8, 8, 3, 3. Peak is 8.
  4. Average requirement = total resource-days ÷ duration = (4×2 + 4×2 + 3×2) ÷ 4 = 22 ÷ 4 = 5.5 workers a day.
  5. Smoothing: keep critical activities A and C fixed. Shift B by its full float of 2 days, so B works on days 3 and 4. This is allowed because B has no successor and finishes on day 4, which is its latest finish.
  6. New demand: day 1 = A 4 = 4, day 2 = A 4 = 4, day 3 = B 4 + C 3 = 7, day 4 = B 4 + C 3 = 7. Demand row is 4, 4, 7, 7. A shift of only 1 day would give 4, 8, 7, 3, which keeps the peak at 8.
  7. Compare using the sum of squared deviations from the average of 5.5. Original row (8, 8, 3, 3): 2.5² × 4 = 25. One-day shift (4, 8, 7, 3): 1.5² + 2.5² + 1.5² + 2.5² = 17. Full two-day shift (4, 4, 7, 7): 1.5² × 4 = 9. The full shift gives the lowest peak (7) and the smallest spread around the average, so it is the better choice here. The project duration stays at 4 days.

Answer: Duration is 4 days (critical path A-C). B has 2 days of float. Shifting B by its full float, to days 3 and 4, changes demand from 8, 8, 3, 3 to 4, 4, 7, 7. The peak falls from 8 to 7 workers, the sum of squared deviations from the average of 5.5 falls from 25 to 9, and the duration is unchanged at 4 days.

Example 2

A project has 100 resource-days of work to be done over a 20-day critical path. State the average daily requirement. The earliest-start schedule peaks at 9 workers. Only 6 workers are available. Explain what you will do and what the likely effect on duration is.

Show the solution
  1. Average requirement = 100 ÷ 20 = 5 workers per day.
  2. The earliest-start peak of 9 exceeds the cap of 6, so demand must be cut by at least 3 workers in the peak periods.
  3. Check the critical activities first. They have no float and cannot move without delaying the project. If the critical activities alone need more than 6 workers in any period, the cap of 6 cannot be met within 20 days, and the duration extends beyond 20 days. The problem does not give this data.
  4. First step: shift non-critical activities within their total float, keeping critical activities fixed and respecting precedence. This is smoothing-type shifting, and the duration stays at 20 days.
  5. If demand still exceeds 6 in some period after all the float is used, activities must be delayed beyond their float. This is resource-limited scheduling, that is, levelling, and the project duration extends beyond 20 days.
  6. Lower bound from the cap: 100 ÷ 6 = 16.67 days, which is below 20. So the cap does not by itself force the duration beyond 20 days. But this is only a lower bound. It does not show that a 6-worker schedule is feasible within 20 days. That depends on the critical activities' demand and the available floats.
  7. Result: the duration stays at 20 days only if the critical activities alone never exceed 6 workers in any period and the floats allow a rescheduling that brings demand to 6 or below throughout. Otherwise the duration extends beyond 20 days. You cannot say which without the activity-wise resource and float data.

Answer: Average demand is 5 workers a day. The cap of 6 is feasible within 20 days only if the critical activities alone never need more than 6 workers in any period and the floats permit a rescheduling that keeps demand at 6 or below. First shift non-critical activities within float, keeping critical activities fixed. If demand still exceeds 6, you must delay activities beyond float (levelling), and the project will take longer than 20 days.

Exam tips

  • Read the question for the key words. 'Fixed duration' means smoothing. 'Limited resources' means levelling.
  • Always show the float table before moving any activity. Examiners award marks for the correct choice of which activities can move.
  • For theory, give advantages and limitations in two separate bullets lists, with a reason for each point, and add one practical use such as construction or maintenance shutdown.
  • In updating questions, state the status date, the remaining durations, the new critical path and the revised completion date in that order.
  • End application answers with a clear recommendation, such as where to add resources or which activity to watch.

Practice questions from Network Analysis - PERT, CPM

Resource Levelling, Updating and Applications in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Resource Levelling, Updating and Applications: frequently asked questions

What is the difference between resource smoothing and resource levelling?

Smoothing keeps the project duration fixed and shifts non-critical activities within their float to even out demand. Levelling keeps a resource limit fixed and may extend the project duration if the limit forces delays.

What are the advantages and limitations of PERT and CPM?

They give a clear view of activity sequence, the critical path, float and expected completion, and help in control and resource planning. Limitations are that they need clear activity logic, rely on time estimates that can be subjective, are costly for small projects, and do not by themselves handle resource limits unless levelling is added.

How is a PERT network updated during execution?

You record actual progress, revise durations or logic for the remaining work, and recompute earliest and latest times from the status date. You then find the new critical path and completion date. Management uses this to decide on corrective action.

Can the critical path change after updating?

Yes. If a non-critical activity overruns beyond its float, or a critical activity finishes early, another path can become the longest. That is why you must redo the calculation rather than add the delay to the old date.