Overview

Master project planning for the PE Civil exam including CPM scheduling, earned value management, cost estimation, and activity network diagrams.

This topic accounts for 4 out of 40 questions on the PE Civil Civil Breadth (AM) exam.

Key Concepts

Critical Path Method (CPM)

CPM identifies the longest sequence of dependent activities that determines the minimum project duration. The critical path has zero total float. To find it: (1) Forward pass to calculate Early Start (ES) and Early Finish (EF), (2) Backward pass to calculate Late Start (LS) and Late Finish (LF), (3) Total Float = LS - ES = LF - EF. Activities with TF = 0 are on the critical path.

Total Float Tf Early Finish Ef Late Start Ls Free Float Ff

Earned Value Management (EVM)

EVM integrates scope, schedule, and cost to measure project performance. Key metrics: PV (Planned Value) = budgeted cost of scheduled work, EV (Earned Value) = budgeted cost of completed work, AC (Actual Cost) = actual cost of completed work. CPI = EV/AC (cost efficiency), SPI = EV/PV (schedule efficiency). CPI < 1 means over budget; SPI < 1 means behind schedule. EAC = BAC/CPI estimates final cost.

Cost Performance Index Cpi Schedule Performance Index Spi Estimate At Completion Eac Cost Variance Cv Schedule Variance Sv Estimate To Complete Etc Variance At Completion Vac

PERT Estimation

Program Evaluation and Review Technique uses three time estimates for each activity: Optimistic (O), Most Likely (M), and Pessimistic (P). Expected time = (O + 4M + P)/6. Standard deviation = (P - O)/6. Variance = [(P - O)/6]^2. The variance of the critical path equals the sum of variances of critical activities.

Pert Expected Activity Time

Quantity Takeoff and Cost Estimation

Cost estimation methods include: Analogous (top-down using historical data), Parametric (statistical models), Bottom-up (detailed quantity takeoff). For earthwork: Average End Area method V = L(A1+A2)/2 converted to cubic yards by dividing by 27. For concrete: calculate volume in cubic yards. Material costs = quantity x unit price + waste factor (typically 5-10%).

Average End Area Method Break Even Point

Common Exam Question Types

Calculate total float for an activity in a network diagram
Determine the critical path and project duration
Calculate EVM metrics (CPI, SPI, EAC, ETC)
Estimate activity duration using PERT
Compute earthwork volumes from cross-sections

Exam Tips & Strategies

For CPM problems, always do the forward pass first (ES, EF), then backward pass (LS, LF)

Remember: CPI = EV/AC, SPI = EV/PV. Both should be > 1 for good performance

EAC = BAC/CPI is the most commonly tested EVM formula

Total Float = 0 defines the critical path. Free Float only affects the immediate successor

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