CVEN9702 Chap.6 Line of Balance and PERT
Line of Balance and PERT
Line-of-balance charts represent repeated work across locations or units and make production rate, buffer and interference visible. PERT addresses a different scheduling problem: uncertain activity time. It uses optimistic, most likely and pessimistic estimates to derive an expected duration and variance. Both methods retain structure that a single deterministic bar chart hides.
What this chapter covers
- 01
Read line slope as a repeated-work production rate
- 02
Use start buffers to prevent activity interference
- 03
Distinguish a shifted start from a changed production rate
- 04
Calculate a PERT expected duration from three estimates
- 05
Calculate activity and path variance with correct units
- 06
Recognise independence and normal-approximation limits
Worked example · free
Calculate a PERT activity mean and variance
- +1Expected duration is (3+4×5+9)/6=32/6=5.33 days.
- +1The duration range used for standard deviation is 9-3=6 days.
- +1Standard deviation is 6/6=1 day.
- +1Variance is the square, 1 day squared, ready to add with independent path variances.
Key terms
- Line of balance
- A time-location chart representing production progress for repeated activities across units or work areas.
- Production buffer
- The planned separation between predecessor and follower work that prevents spatial or temporal interference.
- Optimistic time
- The activity duration expected when conditions proceed well, distinct from a deliberately crashed duration.
- Most likely time
- The modal activity duration judged most plausible under the stated working method and conditions.
- PERT variance
- The squared uncertainty measure derived from the pessimistic and optimistic duration range.
Line of Balance and PERT FAQ
What does a crossing line mean in line of balance?
It signals that one activity catches another across time or location, creating interference or an impossible sequence. Change the start buffer, production rate, crew arrangement or method so the follower remains safely separated.
Is the PERT optimistic time a crash time?
No. It is a plausible duration when the activity proceeds well under the defined method. Crash time belongs to an accelerated method with its own resource and cost assumptions. Mixing them understates uncertainty and confuses two different models.
Why are path variances added instead of standard deviations?
Under the independence assumption, variances of activity durations add along a path. The path standard deviation is the square root of that total variance. Adding standard deviations directly overstates or misstates dispersion.
Where should a line-of-balance buffer be checked?
Check separation at the first unit, last unit and every production-rate change. Converging activity lines may begin safely yet create a later workface conflict between crews.
Exam move
For line of balance, sketch axes first and label which direction represents time and which represents location or units. Draw two activities with the same slope and a safe buffer, then change the follower slope until the lines cross. Explain whether the problem comes from start timing or production rate. For PERT, memorise the mean and variance formulas through repeated calculation rather than isolated recall.
Build small paths, add expected durations and variances, then convert a deadline into a standard score only after checking the assumptions. Keep optimistic time separate from crash time. Revise the limitations: activity dependence, competing paths and too few summed durations can weaken the simple normal approximation.
In a written answer, state both the numerical result and which project assumption is most likely to determine whether that result is credible. Create a time-location dataset for six repeated units and calculate the production rate of each trade from the line slope. Identify the minimum separation needed for access, curing or safety, then test the buffer at both the first and last unit.
Parallel lines preserve separation; converging lines predict a future clash even when the first unit appears safe. Compare three remedies: delay the follower, change crew productivity or divide the work into zones. State how each affects continuity and completion. For PERT, build a calculation table with optimistic, most likely and pessimistic times, expected duration, standard deviation and variance.
Add expected durations and variances along the selected path, not standard deviations. Convert the deadline to a standard score using the path mean and square root of total variance, then describe the probability in words. Test a second near-critical path rather than assuming one path always controls. Ask whether activity durations share weather or access drivers, because dependence weakens simple addition.
Explain that an optimistic estimate is a plausible low duration under favourable conditions, not a crash duration purchased through extra resources. Finish by stating the approximation limits and one better next step, such as simulation when paths compete or distributions are materially skewed.
