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Module 3 - Time Management

Day 9: CPM Fundamentals, Float, and the Critical Path

9% of the exam - about 2.5 hours - 14 practice questions

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Reading

Time management questions on the CCM exam are the most mechanical in the entire test. If you can run a forward and backward pass reliably, you will bank points that other candidates lose.

Network logic and relationship types

A CPM schedule is a network of activities connected by logical relationships. Precedence Diagramming Method, which is what virtually all modern scheduling software uses, puts activities in nodes and relationships on the arrows.

Four relationship types appear. Finish-to-Start is the default and most common: B cannot start until A finishes. Start-to-Start means B cannot start until A starts, often with a lag, which is how you model overlapping work like excavation and hauling. Finish-to-Finish means B cannot finish until A finishes. Start-to-Finish is rare and mostly appears on exams to test whether you know it exists.

A lag is imposed waiting time between activities, such as concrete cure before stripping forms. A lead, sometimes written as negative lag, allows an overlap. Heavy use of leads and lags is a warning sign in a real schedule because it hides logic rather than expressing it, and reviewers should question it.

The forward and backward pass

The forward pass computes early dates. Start at the first activity with an Early Start of zero or day one, depending on convention. Early Finish equals Early Start plus duration. For each successor, Early Start equals the latest Early Finish of all its predecessors. Work left to right through the network. The largest Early Finish at the end of the network is the project duration.

The backward pass computes late dates. Start at the end with Late Finish equal to the project duration. Late Start equals Late Finish minus duration. For each predecessor, Late Finish equals the earliest Late Start of all its successors. Work right to left.

Total float equals Late Start minus Early Start, which also equals Late Finish minus Early Finish. It is the amount an activity can slip without delaying project completion.

Free float is the amount an activity can slip without delaying the early start of any successor. Free float equals the earliest Early Start of successors minus the Early Finish of the activity. Free float is always less than or equal to total float.

The critical path is the longest path through the network, and it is the chain of activities with zero total float, assuming no imposed constraints. Delay any activity on it and the project finishes late. On a network with imposed finish dates, float can be negative, which means the schedule as logic-driven cannot meet the constraint, and negative float is a signal to the CM that the plan is already infeasible.

Note the definition carefully. The critical path is the longest path, not the path with the most activities and not the path with the most expensive work. Exam distractors play on that.

A worked example. Five activities. A has duration 4 with no predecessor. B has duration 6 following A. C has duration 3 following A. D has duration 5 following B. E has duration 2 following C and D.

Forward pass. A runs 0 to 4. B runs 4 to 10. C runs 4 to 7. D runs 10 to 15. E takes the later of its predecessors, so E starts at 15 and runs 15 to 17. Project duration is 17.

Backward pass. E has Late Finish 17 and Late Start 15. D has Late Finish 15 and Late Start 10. C has Late Finish 15 and Late Start 12. B has Late Finish 10 and Late Start 4. A has Late Finish 4 and Late Start 0.

CPM network diagram with five activities showing early and late dates and the critical path Activity A, duration 4, runs day 0 to 4 with zero float. A leads to B and C. Activity B, duration 6, runs 4 to 10 with zero float. Activity C, duration 3, runs 4 to 7 with 8 days total float. B leads to D, duration 5, running 10 to 15 with zero float. C and D both lead to E, duration 2, running 15 to 17 with zero float. The critical path is A, B, D, E, totalling 17 days. 0 4 4 A 0 0 4 4 6 10 B 4 0 10 4 3 7 C 12 8 15 10 5 15 D 10 0 15 15 2 17 E 15 0 17 ES DUR EF ACTIVITY LS TF LF Critical path: A → B → D → E = 17 days Red border and thicker arrows mark zero total float. C carries 8 days of float.
Read the top row left to right for the forward pass, the bottom row right to left for the backward pass. Total float sits in the bottom centre of each node. Any activity where late start equals early start has zero float and is on the critical path.
CPM Network: Forward and Backward Pass

Float. A has zero. B has zero. D has zero. E has zero. C has Late Start 12 minus Early Start 4, which is 8 days of total float. The critical path is A, B, D, E, totaling 4 plus 6 plus 5 plus 2, which is 17. C sits off the critical path with 8 days of room.

Bar diagram showing that in this network, Activity C's free float equals its total float Activity C finishes day 7. Its only successor, E, cannot start until day 15, because E also waits on D, which finishes later than C. So C can slide all the way to day 15, the same point at which the project itself would slip, before it delays anything. Free float and total float are both 8 days here. That will not always be true: when an activity's own finish sets its successor's early start, free float can come in lower than total float. Day 4 Day 7 Day 15 Day 17 Activity C 3 days float: 8 days (free = total here) Activity D (the real gate on E) runs day 10 to day 15 E's earliest start (day 15, set by D) project finish Why free float equals total float here C is not the activity holding E back, D is. So slipping C never touches E's start until C's own slip reaches 8 days, the same threshold that delays the project.
Free float is always less than or equal to total float, but they are not always different. Here, because D (not C) is what actually sets E's earliest start, C's free float and total float are the same 8 days. Free float can come in lower than total float only when the activity's own finish is what sets a successor's early start; if that successor has float of its own, the activity's free float is less than its total float.
Total Float versus Free Float

Who owns float

This is heavily tested and frequently misunderstood in the field. Absent contract language to the contrary, the prevailing view is that float belongs to the project, not to the owner and not to the contractor. It is a shared resource consumed by whichever party first needs it. Many modern contracts state this explicitly. Some contracts assign float to the owner, and a few contractors attempt to sequester float by inflating durations or adding fictitious constraints. The CM's job in schedule review is to detect that.

Practically, the consequence is this: a contractor cannot automatically claim a time extension for an owner-caused delay to an activity that still has float remaining, because the project completion date has not moved.

What makes a schedule good, not just mechanically correct

A network can be logically valid and still be a poor schedule. Federal scheduling guidance identifies characteristics that separate a genuinely reliable CPM schedule from one that merely runs without errors, and the exam draws on the same list when it tests schedule review, not just schedule math. A good schedule captures all activities from the project's WBS, so nothing required to finish the work is missing from the plan. It sequences every activity with real logical relationships rather than artificial date constraints, since a schedule built on hard constraints instead of logic cannot correctly show how a delay in one place ripples elsewhere. It assigns the resources each activity actually needs and sets durations that are realistic and short enough to measure progress against, rather than long, vague summary blocks that hide what is really happening inside them.

A reliable schedule is also traceable both horizontally, meaning the hand-offs between activities in different parts of the project are actually linked, and vertically, meaning a summary schedule and its underlying detailed schedule tell the same story. It has a validated critical path and a reasonable total float, since unreasonably high float on an activity is itself a warning sign that logic is missing or wrong, not a comfort. It has been stress-tested with a schedule risk analysis to determine the confidence level behind the finish date, and it is kept current through disciplined updates using actual progress rather than by pushing dates around by feel. Finally, it is managed against a maintained baseline, so that performance is always measured against a fixed, approved target rather than a plan that quietly resets itself every time it slips.

Why this matters for the exam

A scenario describing a schedule with vague, long-duration "summary" activities, missing logic ties, or a float distribution that looks too generous everywhere is testing whether you can recognize a low-quality schedule even though it technically runs a forward and backward pass without error.

Practice Questions

1. Total float equals:

  1. Free float plus lead
  2. Early Finish minus Early Start
  3. Late Start minus Early Start
  4. Duration minus lag

2. The critical path is:

  1. The most expensive path
  2. The path with the most float
  3. The longest path through the network, with zero total float absent constraints
  4. The path containing the most activities, because every added activity lengthens the total duration

3. Free float is:

  1. The delay possible without delaying any successor's early start; never more than total float
  2. Identical to total float on every activity, because both are measured to the project finish, so the two never differ
  3. Only present on the critical path
  4. Always greater than total float

4. A relationship where B cannot start until A starts, commonly used with a lag to model overlapping work, is:

  1. Finish-to-Start
  2. Finish-to-Finish
  3. Start-to-Start
  4. Start-to-Finish

5. Negative float on a schedule indicates:

  1. The project will finish early
  2. Excess contingency built into durations, which the CM should ask the contractor to remove
  3. An error that should be ignored
  4. The logic-driven schedule cannot meet an imposed constraint date

6. Absent contract language to the contrary, float is generally considered to belong to:

  1. The project, as a shared resource
  2. The contractor, because it builds the schedule and controls the sequence of work
  3. The owner
  4. The surety

7. An owner-caused delay consumes 3 days on an activity with 10 days of total float. The contractor's entitlement to a time extension is:

  1. Double, as a penalty
  2. Generally none, because project completion has not moved
  3. Automatic, 3 days, because the owner caused the delay and the contractor is entitled to be made whole
  4. Determined by the architect

8. Heavy use of leads and negative lags in a submitted baseline should prompt the CM to:

  1. Extend the contract time
  2. Approve it as sophisticated scheduling, because leads and lags show the contractor has optimized the sequence
  3. Reject the contractor
  4. Question it, since leads and lags can conceal logic rather than express it

9. A schedule contains several long, vague "summary" activities instead of discrete, measurable work packages. This most directly violates which quality characteristic?

  1. Realistic, short, measurable durations
  2. Vertical traceability only
  3. Baseline maintenance
  4. Nothing; summary activities are always acceptable

10. Horizontal traceability in a schedule refers to:

  1. Whether the schedule fits on one printed page
  2. Whether hand-offs between activities across the project are actually linked by logic
  3. Whether the critical path is colored red
  4. Whether resources are assigned

11. Vertical traceability means:

  1. All activities run top to bottom on the page
  2. The schedule has no float anywhere
  3. The schedule was built using only Finish-to-Start relationships
  4. A summary schedule and its underlying detailed schedule are consistent with each other

12. Unreasonably high total float across many activities in a submitted schedule should be read as:

  1. A possible sign that schedule logic is missing or invalid, warranting review
  2. Evidence the project has too much money
  3. Good news requiring no further review
  4. Proof the contractor is ahead of schedule

13. A schedule risk analysis is best described as:

  1. A deterministic recalculation of the CPM forward and backward pass after each update, used to confirm the single most likely finish date
  2. A statistical simulation using schedule risk data to determine confidence in the completion date and needed time contingency
  3. A tool used only after the project is complete
  4. A synonym for the baseline schedule

14. Why does maintaining a baseline schedule matter, even though the working schedule is updated constantly?

  1. It doesn't; only the current schedule matters
  2. Performance must be measured and reported against a fixed, approved target, not a plan that resets every time it slips
  3. The baseline is only used for billing purposes
  4. Baselines are optional on all but public projects

Micro-Assignment

Build a small network by hand. Use at least seven activities with at least two parallel paths that converge. Run the forward pass, the backward pass, compute total float for every activity, and mark the critical path. Then answer in writing: which single activity, if it slipped by five days, would cause the greatest damage to project completion, and why? Do this on paper, not in software. The exam will not give you software.

Glossary

PDM
Precedence Diagramming Method; activities in nodes, relationships on arrows.
Total Float
Slip available without delaying project completion.
Free Float
Slip available without delaying any successor's early start.
Critical Path
The longest path; zero total float absent constraints.
Lag
Imposed waiting time between activities.
Negative Float
Indicates the schedule cannot meet an imposed constraint.
Horizontal traceability
Hand-offs between sequenced activities across the project are genuinely linked by logic.
Vertical traceability
A summary schedule and its underlying detailed schedule are consistent with each other.
Schedule risk analysis
A statistical simulation over a CPM schedule estimating confidence in the finish date and the time contingency needed.

Progress

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