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A schedule is a model of how work will unfold, not a wish. Building one means four things in order:
define the activities, sequence them, estimate how long each takes, then develop the schedule model that
falls out of those decisions. Everything else (compression, leveling, forecasting) is manipulation of
that model. On the exam, schedule questions are heavy on network logic and float arithmetic, so the
mechanics below are worth knowing cold.
Two parallel paths connect activity A to activity D. The lower path through C is longer, so
it sets the 23-day project duration and carries zero float; the upper path through B has 4 days of total
float and can slip that much without delaying the finish.
Sequencing: dependency types and modifiers
Type
Meaning
GCHS example
Finish-to-start (FS)
Predecessor must finish before successor starts.
By far the most common.
Demolition must finish before framing starts.
Start-to-start (SS)
Successor cannot start until predecessor starts.
Debris hauling starts two days after demolition starts (SS + 2).
Finish-to-finish (FF)
Successor cannot finish until predecessor
finishes.
Final punch cannot finish until final cleaning finishes.
Start-to-finish (SF)
Successor cannot finish until predecessor starts.
Rare, usually a shift-handover pattern.
The temporary heater stays running until the new
HVAC system starts up.
Two modifiers adjust the relationship. A lag is required waiting time: concrete must
cure five days before framing, so that is FS with a 5-day lag. A lead is
overlap, allowing a successor to begin before the predecessor is complete: starting trim work three days
before painting finishes is FS with a 3-day lead. Leads compress; lags stretch.
Dependencies are also classified by where they come from. Mandatory (hard logic) is
physically or contractually unavoidable: you cannot drywall before rough-in inspection.
Discretionary (preferred or soft logic) reflects best practice and can be changed: painting before flooring because the crew prefers it that way. External dependencies sit
outside the project team's control, such as a county permit. Internal ones are inside the
team's control. Only discretionary logic is safely available for fast-tracking.
Critical path method: the arithmetic
The critical path is the longest path through the network, and therefore the
shortest possible project duration. Suppose the network runs Start → A(5) → B(8) →
D(6) → Finish, and also Start → A(5) → C(12) → D(6) → Finish. Path A-B-D is 19
days; path A-C-D is 23 days. The critical path is A-C-D at 23 days, and B carries 23 − 19 = 4 days of
total float.
The forward pass moves left to right and computes early start (ES) and
early finish (EF): the earliest each activity can happen. The backward
pass moves right to left and computes late start (LS) and late finish
(LF): the latest each activity can happen without delaying the project.
Term
Formula
Plain meaning
Total float
LS − ES, or LF − EF
How long this
activity can slip without delaying the project finish date
Free float
ES of the earliest successor − EF of this
activity
How long this activity can slip without delaying the early start of any
successor
Critical path
Longest path; total float normally zero
The
sequence that sets the project duration
Negative float
Total float below zero
The schedule is already
behind an imposed constraint: the plan is infeasible as drawn
Key points
Free float is always less than or equal to total float, never more.
A project can have more than one critical path, which raises risk, because there are more ways to
slip.
Negative float is not a curiosity; it is a signal that you must compress, reduce scope, or move
the date, and that a change request is probably coming.
Delaying a non-critical activity by less than its total float does not delay the
project.
Compressing the schedule
Crashing
Fast-tracking
What you do
Add resources to critical path activities to shorten them
Perform
activities in parallel that were planned in sequence
Main cost
Money: more crew, overtime, premium delivery
Risk: rework, coordination errors
Best when
Budget exists and risk tolerance is low
Budget is fixed and the logic
is discretionary rather than mandatory
Watch out for
Diminishing returns; adding people to a crowded bathroom slows it down
Overlapping mandatory logic: you cannot inspect rough-in that has been covered
Two disciplines apply to both: only compress activities on the critical path (crashing a non-critical activity costs money and changes the finish date by zero) and choose the
lowest cost per day saved first. If activity X crashes 3 days for 6,000 dollars (2,000 per day)
and activity Y crashes 2 days for 3,000 dollars (1,500 per day), you crash Y first, provided both are
critical.
Watch for this on the exam
A question that offers a very cheap crash option on an activity that is not on the critical
path is a trap. So is compressing before you have confirmed the finish date can even be recovered: the
tested sequence is analyze impact, evaluate options, recommend, then process the change.
Resources: leveling versus smoothing
Both adjust the schedule around resource availability, and the difference is exactly one thing: whether the critical path may move.
Resource leveling is applied when resources are over-allocated or only available in
limited quantities. It can change the critical path and can extend the project
duration. If GCHS has one certified lead-safe renovator and three units need him at once, leveling
is what you do, and the finish date probably moves.
Resource smoothing adjusts activities only within their available float.
The critical path is not changed and the completion date is not delayed. It evens out peaks and
valleys in resource demand but cannot fix a genuine over-allocation.
Rolling wave planning is the progressive-elaboration answer to uncertainty: plan the
near-term work in fine detail and leave later work at a higher level, refining it as it approaches. It is
legitimate planning, not laziness, and it is common in hybrid programs where the first three months are
known and month nine is not.
Adaptive scheduling: cadence, velocity, and burn charts
Adaptive projects invert the constraint. Instead of fixing scope and letting the date move, they
fix the timebox and let scope vary. The unit of planning is the iteration, and the
forecasting tool is velocity: the number of story points a team actually completes per
iteration, averaged over recent iterations. If a team completed 24, 30, 27, and 31 points, its average
velocity is 112 / 4 = 28 points per iteration. With 168 points remaining in the release backlog, the
forecast is 168 / 28 = 6 more iterations.
Iteration burndown: work remaining in the current iteration, trending toward
zero.
Release burndown: remaining work across the whole release; when scope is added the
chart can go up, which honestly shows the effect of new requests.
Burnup chart: plots work completed against a separate total-scope line, which
makes scope growth visible as a rising ceiling rather than hiding it inside the remaining-work line.
This is why many teams prefer burnup for stakeholder conversations.
Release planning: mapping which features are likely to land in which iterations,
refreshed as velocity data accumulates.
Velocity is a forecasting tool for one team, not a performance score and never a cross-team comparison.
Story points are relative to a single team's estimating baseline; comparing them across teams is
meaningless and drives point inflation.
Do not do this
Do not update the schedule baseline just because reality diverged from it. The baseline changes only
through approved change control. Update the schedule with actuals and forecasts, keep the
baseline as the measuring stick, and if the date truly must move, raise a change request with
the analysis behind it.
Practice Questions
1. A network has two paths: A(5 days) to B(8 days) to D(6 days), and A(5 days) to C(12 days) to D(6 days). What is the critical path duration?
42 days
19 days
23 days
31 days
Answer: c. Path A-B-D is 5 + 8 + 6 = 19 days and path A-C-D is 5 + 12 + 6 = 23 days. The critical path is the longest path, so the project duration is 23 days. The 19-day answer picks the shorter path, which would be the shortest path rather than the longest.
2. Using the same network, A(5)-B(8)-D(6) at 19 days and A(5)-C(12)-D(6) at 23 days, how much total float does activity B have?
8 days
0 days
4 days
6 days
Answer: c. Total float on the non-critical path equals the difference between the critical path and that path: 23 - 19 = 4 days. Activity B can slip up to 4 days without moving the project finish date; a fifth day would make its path 24 days and push the finish out.
3. An activity has ES = 10, EF = 16, LS = 13, and LF = 19. What is its total float?
0 days
3 days
6 days
9 days
Answer: b. Total float = LS - ES = 13 - 10 = 3, and the cross-check LF - EF = 19 - 16 = 3 agrees. The 6-day answer is the activity's duration (EF - ES), and 9 comes from subtracting ES from LF, which mixes an early value with a late value and is not a valid float calculation.
4. Activity D has an early finish of day 22. Its two successors have early starts of day 26 and day 24. What is D's free float?
0 days
6 days
4 days
2 days
Answer: d. Free float = the earliest of the successors' early starts minus this activity's early finish = 24 - 22 = 2 days. The 4-day answer uses the later successor, but delaying D by 4 days would push the successor starting on day 24: exactly what free float is defined to protect.
5. Which definition of total float is correct?
The amount of time added to an estimate as a buffer
The time an activity can be delayed without delaying the early start of any successor
The time an activity can be delayed without delaying the project finish date
The difference between the budget and the actual cost
Answer: c. Total float is measured against the project finish date; the definition tied to a successor's early start is free float. Free float is always less than or equal to total float, since protecting the immediate successor is a tighter constraint than protecting the project end.
6. Which statement about the critical path is correct?
It always contains the activities with the highest cost, so its length is set by the most expensive work packages
A project can only ever have one critical path
It is the shortest path through the network and represents the longest possible duration
It is the longest path through the network and represents the shortest possible project duration
Answer: d. The critical path is the longest sequence of dependent activities, and because every activity on it must occur in order, its length is the shortest time the project can possibly take. Projects can have multiple critical paths, which raises risk because there are more ways for the finish date to slip.
7. A GCHS crew estimates lead-safe abatement in a single unit at an optimistic 6 days, a most likely 9 days, and a pessimistic 18 days. Using the PERT (beta) formula, what is the estimated duration?
10 days
11 days
13 days
9 days
Answer: a. PERT = (O + 4M + P) / 6 = (6 + 4(9) + 18) / 6 = (6 + 36 + 18) / 6 = 60 / 6 = 10 days. The 9-day answer is only the most likely estimate on its own, which ignores the optimistic and pessimistic data the formula is designed to weigh in.
8. Framing on a GCHS unit cannot start until 5 days after demolition finishes, to let dust settle and allow an inspection. What is this relationship?
Finish-to-start with a 5-day lead
Finish-to-start with a 5-day lag
Start-to-start with a 5-day lag
Finish-to-finish with a 5-day lag
Answer: b. The successor cannot start until the predecessor finishes, which is finish-to-start logic, and the 5 days of required waiting time is a lag, not an overlap. A lead would let framing begin before demolition finished, the opposite of what is described.
9. A GCHS renovation budget is fixed, but the finish date must be pulled in. The logic between two activities is discretionary rather than mandatory. What should the project manager do?
Crash the critical path activities
Apply resource leveling
Apply resource smoothing
Fast-track the discretionary logic by overlapping the activities
Answer: d. Fast-tracking overlaps activities that were planned in sequence and costs risk rather than money, which fits a fixed budget, and it is only safe on discretionary logic. Crashing would add cost, which the fixed budget rules out.
10. Two critical-path activities can each be crashed: Activity M saves 4 days for 8,000 dollars, and Activity N saves 2 days for 3,000 dollars. Which should be crashed first, and why?
Activity M, because it saves more total days
Both at the same time, to save the most total time
Activity N, because its cost per day saved (1,500 dollars) is lower than M's (2,000 dollars)
Neither, since crashing always changes the critical path
Answer: c. Crashing should always start with the lowest cost per day saved among critical activities: M is 8,000 / 4 = 2,000 per day, N is 3,000 / 2 = 1,500 per day, so N is more efficient. Saving more total days is irrelevant if it costs more per day gained.
11. GCHS has one certified lead-safe renovator who is needed on three units at the same time. Leveling his schedule across the units will most likely do what?
Eliminate the need to schedule him at all
Extend the project duration and potentially change the critical path
Have no effect on the schedule at all
Only change float, never the finish date
Answer: b. Resource leveling is used precisely when a resource is over-allocated, and because it resequences work around a real constraint, it can push out the finish date and shift which path is critical. Resource smoothing, not leveling, is the technique limited to using only existing float.
12. A hybrid GCHS program plans the next three months of work in detail and keeps month nine at a high level, refining it as it gets closer. What is this technique called?
Decomposition
Rolling wave planning
Critical path method
Resource smoothing
Answer: b. Rolling wave planning elaborates near-term work in detail while leaving distant work at a summary level until it approaches, which is legitimate planning under uncertainty rather than a shortcut. Decomposition breaks scope into smaller pieces but does not itself describe this near-term-versus-later distinction.
13. An agile team completed 18, 20, 19, and 23 story points in its last four iterations, and 140 points remain in the release backlog. Using average velocity, how many more iterations should the team forecast?
7 iterations
8 iterations
5 iterations
6 iterations
Answer: a. Average velocity is (18 + 20 + 19 + 23) / 4 = 80 / 4 = 20 points per iteration, and 140 / 20 = 7 more iterations. This forecast is only valid for this one team, since story points are not comparable across teams.
14. Stakeholders on an adaptive GCHS project want a chart that shows completed work against total scope, so that scope growth is visible rather than hidden. Which chart should the team use?
Burnup chart
Iteration burndown
Release burndown
Cumulative flow diagram
Answer: a. A burnup chart plots completed work against a separate total-scope line, so when scope is added the ceiling visibly rises instead of the remaining-work line simply failing to shrink. A burndown chart can go up when scope is added, which is confusing rather than clarifying for stakeholders.
Glossary
Total float
The amount of time an activity can be delayed without delaying the project finish date; LS minus ES or LF minus EF.
Free float
The amount of time an activity can be delayed without delaying the early start of any successor activity.
Critical path
The longest path through the network diagram, which sets the shortest possible project duration.
Crashing
A compression technique that adds resources to critical path activities to shorten duration, at added cost.
Fast-tracking
A compression technique that performs activities in parallel that were originally planned in sequence, at added risk.
Resource leveling
Adjusting the schedule to resolve resource over-allocation, which can change the critical path and extend duration.
Resource smoothing
Adjusting activities only within their available float so the critical path and finish date do not change.
Velocity
The average number of story points a team completes per iteration, used to forecast remaining iterations.