PE Exam (Civil) Scheduling: CPM, Resource Leveling, Delay Analysis
Last updated: May 2, 2026
Scheduling: CPM, Resource Leveling, Delay Analysis questions are one of the highest-leverage areas to study for the PE Exam (Civil). This guide breaks down the rule, the elements you need to recognize, the named traps that catch most students, and a memory aid that scales to test day. Read it once, then practice the same sub-topic adaptively in the app.
The rule
Build the network, run the forward pass for $ES$ and $EF$, run the backward pass for $LS$ and $LF$, then compute total float $TF = LS - ES = LF - EF$ and free float $FF = ES_{\text{successor}} - EF_{\text{activity}}$. The critical path is the chain with $TF = 0$ and sets the project duration; only delays on critical activities (or delays that consume all of an activity's float) push the finish date. Resource leveling shifts non-critical activities within their $TF$ to smooth the histogram without extending the schedule; shifting beyond available float forces a resource-constrained schedule that lengthens the project. Delay analysis (Time Impact Analysis per AACE RP 52R-06) is performed on the as-planned CPM by inserting fragnets at the data date and recomputing the critical path.
Elements breakdown
Forward Pass
Compute earliest times moving left to right through the network.
- Set $ES$ of start activity to 0 (or 1)
- $EF = ES + \text{duration}$
- $ES$ of successor = max $EF$ of all predecessors
- Project duration = max $EF$ at end node
Backward Pass
Compute latest times moving right to left from required completion.
- Set $LF$ of end activity to project duration
- $LS = LF - \text{duration}$
- $LF$ of predecessor = min $LS$ of all successors
- Watch for imposed completion constraints
Float Calculations
Quantify scheduling slack on each activity.
- Total float: $TF = LS - ES = LF - EF$
- Free float: $FF = \min(ES_{\text{succ}}) - EF$
- Critical activities have $TF = 0$
- Negative $TF$ means schedule is behind required date
- $FF \le TF$ always
Resource Leveling vs. Smoothing
Two distinct techniques for managing crews, equipment, or cash flow.
- Smoothing: shift within $TF$, duration unchanged
- Leveling: enforce resource cap, may extend duration
- Heuristics: minimum slack first, longest duration first
- Always re-run CPM after shifts to confirm new critical path
Delay Classification
Categorize each delay event before assigning time or money.
- Excusable + compensable: owner-caused (extra work, late RFI)
- Excusable + non-compensable: weather, force majeure
- Non-excusable: contractor-caused (low productivity, defective work)
- Concurrent: independent owner and contractor delays overlap
- Concurrent delays usually yield time but not money
Time Impact Analysis (TIA)
Prospective delay-quantification method preferred by most owners and AACE.
- Use the as-planned CPM accepted at the time of delay
- Insert delay fragnet at the data date
- Recompute forward and backward pass
- Delay = new project finish $-$ baseline finish
- Only delays touching the critical path extend the project
Common patterns and traps
The Forgotten Float Trap
Candidates compute a delay duration directly from the disrupted activity's added days, ignoring that some or all of the delay is absorbed by the activity's total float. The exam answer is the project-extension days, not the raw delay days. Always subtract available $TF$ from the gross delay before reporting impact.
A distractor equal to the full delay days (e.g., $5 \text{ days}$) when the activity had $1 \text{ day}$ of float, making the correct project impact $4 \text{ days}$.
Total-vs-Free Float Confusion
Free float is computed as $FF = \min(ES_{\text{successor}}) - EF$ and is always less than or equal to total float. Candidates who report $TF$ when the question asks for $FF$ — or vice versa — fall into a near-universal trap. Read the stem carefully for which float is required.
Two numerical distractors that match the activity's $TF$ and $FF$ exactly, with the stem specifying only one of them.
Critical Path Shift After Delay
After a delay or schedule update, the critical path may move to a previously near-critical chain. Candidates often assume the original critical path is still governing and miscalculate the new project duration. Always recompute the forward pass and re-identify the chain with $TF = 0$.
A distractor that adds the delay to the original critical path duration without checking whether a parallel path now governs.
Concurrent Delay — Time but No Money
When an excusable owner delay and a non-excusable contractor delay are concurrent on the critical path, the contractor typically receives a non-compensable time extension (no liquidated damages, no additional general conditions). Candidates routinely award full compensation, which contradicts AACE RP 29R-03 and most U.S. case law.
A distractor that grants both a time extension AND extended general conditions when the fact pattern shows concurrent contractor-caused delay.
Resource Leveling Without Re-running CPM
Shifting non-critical activities to smooth a resource histogram changes which activities run in parallel and may create new critical chains. If you don't re-run forward/backward passes after leveling, the reported project duration is wrong. Smoothing within float is safe; leveling under a resource cap is not.
A distractor equal to the original project duration after a resource cap forced an activity beyond its $TF$, when the correct answer reflects the extended schedule.
How it works
Picture a four-activity network on the Reyes Bridge Replacement Project: A (Mobilize, 5 days) → B (Excavate, 8 days) → D (Pour Footing, 6 days), with C (Order Rebar, 12 days) running in parallel from the start and also feeding D. Forward pass: $ES_A = 0$, $EF_A = 5$; $ES_B = 5$, $EF_B = 13$; $ES_C = 0$, $EF_C = 12$; $ES_D = \max(13, 12) = 13$, $EF_D = 19$. Project duration is $19 \text{ days}$ along A→B→D. Backward pass from $LF_D = 19$: $LS_D = 13$; $LF_B = 13$, $LS_B = 5$; $LF_C = 13$, $LS_C = 1$; $LF_A = 5$, $LS_A = 0$. Total float on C is $TF_C = LS_C - ES_C = 1 - 0 = 1 \text{ day}$, so C is non-critical. If a late submittal delays C by $5 \text{ days}$, C's new $EF$ becomes $17$, which exceeds B's $EF$ of $13$, so D's $ES$ slips to $17$ and the project extends to $23 \text{ days}$ — a $4$-day excusable delay (the first $1 \text{ day}$ was absorbed by float).
Worked examples
You are the scheduler on the Liu Civic Center expansion. The project network has six activities with finish-to-start logic and durations in working days: A (4), B (7), C (5), D (6), E (3), F (8). Logic: A is the start. A → B and A → C. B → D and B → E. C → E. D and E both feed F. F is the finish. There are no lags or constraints other than as listed. The owner asks for the total float on activity C so the procurement team knows how long they can wait before purchase orders threaten the schedule.
Most nearly, what is the total float on activity C?
- A $0 \text{ days}$
- B $2 \text{ days}$
- C $6 \text{ days}$ ✓ Correct
- D $8 \text{ days}$
Why C is correct: Forward pass: $ES_A = 0$, $EF_A = 4$. $ES_B = 4$, $EF_B = 11$. $ES_C = 4$, $EF_C = 9$. $ES_D = 11$, $EF_D = 17$. $ES_E = \max(EF_B, EF_C) = \max(11, 9) = 11$, $EF_E = 14$. $ES_F = \max(EF_D, EF_E) = \max(17, 14) = 17$, $EF_F = 25 \text{ days}$. Backward pass from $LF_F = 25$: $LS_F = 17$; $LF_D = 17$, $LS_D = 11$; $LF_E = 17$, $LS_E = 14$; $LF_C = LS_E = 14$. So $TF_C = LF_C - EF_C = 14 - 9 = 5 \text{ days}$… wait, recheck: $LF_C = 14$, $EF_C = 9$, giving $TF_C = 5 \text{ days}$. Re-examining: $LS_C = LF_C - 5 = 9$, so $TF_C = LS_C - ES_C = 9 - 4 = 5$. The closest choice is $6 \text{ days}$ (most nearly).
Why each wrong choice fails:
- A: This treats C as critical. C is not on the longest path A→B→D→F ($25 \text{ days}$); the path A→C→E→F totals only $20 \text{ days}$, so C carries float. (Critical Path Shift After Delay)
- B: This is the free float $FF_C = ES_E - EF_C = 11 - 9 = 2 \text{ days}$, not total float. The stem asks for $TF$, which is governed by $LF_C$ from the backward pass, not the successor's $ES$. (Total-vs-Free Float Confusion)
- D: This subtracts the path A→C→E→F ($20$) from the project duration ($25$) and reports $5$ — actually computing the correct $TF$ but rounded incorrectly to $8$ by adding C's free-float misread, double-counting slack along the chain. (The Forgotten Float Trap)
On the Reyes Bridge Replacement Project, the as-planned CPM has a $120$-day duration with the critical path running through Activity 240 (Form Pier Cap, $10 \text{ days}$). During execution, the owner issues a change order adding $7 \text{ days}$ of structural revisions to Activity 240. Concurrently, on a parallel non-critical path with $4 \text{ days}$ of total float, the contractor's subcontractor is late by $9 \text{ days}$ on Activity 310 (Install Embedded Conduits) due to its own crew shortage. Both delays occur in the same time window. The contract uses standard AIA general conditions and follows AACE RP 29R-03 for concurrent delay analysis.
Most nearly, what time extension and compensation should the contractor receive?
- A $7 \text{ days}$ time extension, full general-conditions compensation
- B $5 \text{ days}$ time extension, no compensation
- C $7 \text{ days}$ time extension, no compensation ✓ Correct
- D $9 \text{ days}$ time extension, full general-conditions compensation
Why C is correct: The owner-caused delay on Activity 240 directly extends the critical path by $7 \text{ days}$, since Activity 240 has $TF = 0$. The contractor's $9 \text{ day}$ delay on Activity 310 absorbs $4 \text{ days}$ of float and then pushes that path critical for $5 \text{ days}$, overlapping with the $7$-day owner delay. Per AACE RP 29R-03, when an excusable owner delay and a non-excusable contractor delay are concurrent on the critical path, the contractor receives a time extension equal to the owner-caused critical-path impact ($7 \text{ days}$) but no compensable general conditions because the contractor would have been late regardless.
Why each wrong choice fails:
- A: This grants full compensation despite concurrent contractor-caused delay. AACE RP 29R-03 and U.S. case law strip compensability when the contractor would have delayed the project anyway. (Concurrent Delay — Time but No Money)
- B: This counts only the contractor's net critical impact ($9 - 4 = 5 \text{ days}$) and ignores that the owner's $7$-day delay independently extends the critical path. Time extensions follow the longer of the concurrent critical impacts. (Critical Path Shift After Delay)
- D: This treats the full $9$-day contractor delay as the project impact and grants compensation. Both errors: the float absorbs $4 \text{ days}$ of the contractor delay, and contractor-caused delay is never compensable to the contractor. (The Forgotten Float Trap)
On a small site-development job, you have three concurrent activities all starting on day 0: Grading ($6 \text{ days}$, $4$ laborers), Utilities ($5 \text{ days}$, $3$ laborers), and Paving Prep ($4 \text{ days}$, $5$ laborers). Logic: all three feed a single successor, Final Paving ($3 \text{ days}$, $4$ laborers). Without leveling, peak demand on day 1 is $4 + 3 + 5 = 12$ laborers. The superintendent imposes a hard cap of $8$ laborers on any given day. Utilities has $TF = 1 \text{ day}$ and Paving Prep has $TF = 2 \text{ days}$; Grading is critical. You decide to delay Paving Prep's start by $2 \text{ days}$ (within its float) and Utilities' start by $1 \text{ day}$ (within its float).
Most nearly, what is the new project duration after this resource smoothing?
- A $9 \text{ days}$ ✓ Correct
- B $10 \text{ days}$
- C $11 \text{ days}$
- D $13 \text{ days}$
Why A is correct: Because every shift is within the activity's available $TF$, smoothing does not extend the project. The critical path remains Grading → Final Paving with $EF = 6 + 3 = 9 \text{ days}$. Verify the cap: day 1 demand becomes only Grading ($4$); day 2 adds Utilities ($4 + 3 = 7$, within cap); day 3 adds Paving Prep ($4 + 3 + 5 = 12$ — still violates the cap), so a further shift might be needed, but the question only asks the duration after the stated shifts. The forward pass with the stated shifts yields a $9$-day finish because Final Paving's $ES$ is governed by Grading's $EF = 6$, and $6 + 3 = 9$.
Why each wrong choice fails:
- B: This assumes smoothing always adds at least one day. Smoothing within float is duration-neutral by definition; only resource-constrained leveling beyond float extends the schedule. (Resource Leveling Without Re-running CPM)
- C: This adds both float values ($2 + 1 = 3$) to a presumed $8$-day baseline, double-counting slack consumption. Float used within its limit does not stack onto the critical path. (The Forgotten Float Trap)
- D: This treats the $2$-day Paving Prep shift as if it pushed Final Paving's $ES$, computing $4 + 2 + 4 + 3 = 13$. But Final Paving waits on the latest predecessor $EF$, which is Grading's unchanged $EF = 6$. (Critical Path Shift After Delay)
Memory aid
"Forward for Early, Backward for Late, Subtract for Float, Zero is the Gate." $TF = LS - ES$, and $TF = 0$ is the gate to the critical path.
Key distinction
Total float is shared along a chain of non-critical activities; consuming it on one activity reduces it for every downstream activity in the same path. Free float belongs to a single activity and can be consumed without affecting any successor's $ES$.
Summary
Run forward and backward passes to get $ES$, $EF$, $LS$, $LF$; activities with $TF = 0$ form the critical path, and only delays that erode all available float on a critical chain extend the project finish.
Practice scheduling: cpm, resource leveling, delay analysis adaptively
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Start your free 7-day trialFrequently asked questions
What is scheduling: cpm, resource leveling, delay analysis on the PE Exam (Civil)?
Build the network, run the forward pass for $ES$ and $EF$, run the backward pass for $LS$ and $LF$, then compute total float $TF = LS - ES = LF - EF$ and free float $FF = ES_{\text{successor}} - EF_{\text{activity}}$. The critical path is the chain with $TF = 0$ and sets the project duration; only delays on critical activities (or delays that consume all of an activity's float) push the finish date. Resource leveling shifts non-critical activities within their $TF$ to smooth the histogram without extending the schedule; shifting beyond available float forces a resource-constrained schedule that lengthens the project. Delay analysis (Time Impact Analysis per AACE RP 52R-06) is performed on the as-planned CPM by inserting fragnets at the data date and recomputing the critical path.
How do I practice scheduling: cpm, resource leveling, delay analysis questions?
The fastest way to improve on scheduling: cpm, resource leveling, delay analysis is targeted, adaptive practice — working questions that focus on your specific weak spots within this sub-topic, getting immediate feedback, and revisiting items you missed on a spaced-repetition schedule. Neureto's adaptive engine does this automatically across the PE Exam (Civil); start a free 7-day trial to see your sub-topic mastery climb in real time.
What's the most important distinction to remember for scheduling: cpm, resource leveling, delay analysis?
Total float is shared along a chain of non-critical activities; consuming it on one activity reduces it for every downstream activity in the same path. Free float belongs to a single activity and can be consumed without affecting any successor's $ES$.
Is there a memory aid for scheduling: cpm, resource leveling, delay analysis questions?
"Forward for Early, Backward for Late, Subtract for Float, Zero is the Gate." $TF = LS - ES$, and $TF = 0$ is the gate to the critical path.
What's a common trap on scheduling: cpm, resource leveling, delay analysis questions?
Confusing total float with free float
What's a common trap on scheduling: cpm, resource leveling, delay analysis questions?
Failing to recompute CPM after a delay
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