Project Controls: Earned Value, CPM Scheduling and Resources

NCEES FE Civil spec: Construction Engineering, C. Project controls (e.g., earned value, scheduling, allocation of resources, activity relationships). FE Reference Handbook: Civil Engineering chapter, Construction section (CPM and Earned-Value Analysis).

What the FE Civil Spec Covers

Subtopic C, project controls, includes earned value, scheduling, allocation of resources and activity relationships. It is the most calculation-heavy part of Construction Engineering, and it shows up reliably: find the critical path, find float, or compute a performance index.

Key Concepts

Critical path method (CPM)

A network lists activities, durations and dependencies. The forward pass finds early start (ES) and early finish (EF); the backward pass finds late finish (LF) and late start (LS). The critical path is the longest path through the network, and every activity on it has zero total float (for a project whose required finish equals its early finish).

Activity relationships

Finish-to-start (FS) is the default: B starts after A finishes. Start-to-start (SS) and finish-to-finish (FF) tie starts or finishes together, often with a lag. Start-to-finish (SF) is rare.

Resource allocation

Resource leveling shifts noncritical activities within their float to smooth crew or equipment demand without extending the project. If float runs out, leveling lengthens the schedule.

Earned value

Earned value compares three numbers at a status date: planned value (PV or BCWS), earned value (EV or BCWP) and actual cost (AC or ACWP).

Core Formulas

E F = E S + D L S = L F - D

E S = max (E F of predecessors) L F = min (L S of successors)

T F = L S - E S = L F - E F F F = min (E S_{successors}) - E F

C V = E V - A C S V = E V - P V C P I = \frac{E V}{A C} S P I = \frac{E V}{P V}

E T C = \frac{B A C - E V}{C P I} E A C = A C + E T C V A C = B A C - E A C

With the CPI-based forecast, $E A C = B A C / C P I$ gives the same answer.

Where It Is in the FE Reference Handbook

The Construction section at the end of the Civil Engineering chapter shows activity-on-node and activity-on-arrow notation, the ES/EF/LS/LF definitions, and the earned value variances, indices and forecasting terms. Search for "Earned-Value" to jump there.

Worked Example 1: CPM Network

Activity	Duration (days)	Predecessors	ES	EF	LS	LF	TF	FF
A	4	none	0	4	0	4	0	0
B	6	A	4	10	4	10	0	0
C	3	A	4	7	5	8	1	0
D	5	B	10	15	10	15	0	0
E	7	C	7	14	8	15	1	1
F	2	D, E	15	17	15	17	0	0

Forward pass: F waits for the later of D (EF 15) and E (EF 14), so F starts on day 15 and the project takes 17 days. Backward pass: start with LF = 17 at F. E must finish by 15, so its LS is 8; C must finish by 8, so its LS is 5. A must finish by the smaller of B's LS (4) and C's LS (5), which is 4.

The critical path is A, B, D, F (4 + 6 + 5 + 2 = 17 days). C and E share 1 day of total float. C has zero free float because any delay pushes E's early start; E has 1 day of free float because F does not start until day 15 anyway.

Worked Example 2: Earned Value

A project has BAC = $500,000. At the status date, PV = $200,000, EV = $180,000 and AC = $225,000.

C V = 180, 000 - 225, 000 = - $45, 000 S V = 180, 000 - 200, 000 = - $20, 000

C P I = \frac{180 , 000}{225 , 000} = 0.80 S P I = \frac{180 , 000}{200 , 000} = 0.90

E T C = \frac{500 , 000 - 180 , 000}{0.80} = $400, 000 E A C = 225, 000 + 400, 000 = $625, 000

The project is over budget and behind schedule, and at the current cost efficiency it will finish $V A C = 500, 000 - 625, 000 = - $125, 000$ over budget.

Common Mistakes

Taking the shortest path as critical. The critical path is the longest one.
Using the minimum predecessor EF in the forward pass. ES is the maximum predecessor EF.
Reporting free float as total float for activities that feed a noncritical chain.
Inverting the indices. Earned value is always on top: CPI = EV/AC, SPI = EV/PV.
Reading a negative CV as under budget. Negative variance means over budget or behind schedule.

Practice Problems

Try these from the free PolyCalc FE Civil problem bank. Each one has a full worked solution.

A project has two complete paths: A-B-C takes 4 + 6 + 3 days, and A-D-C takes 4 + 9 + 3 days. Assuming activities B and D can run in parallel, what is the project duration? See the worked solution or practice the Construction & Scheduling deck
An activity has early start ES = 5 days and late start LS = 8 days. What is its total float? See the worked solution or practice the Construction & Scheduling deck
An activity-on-node schedule has activity A (6 days) followed by both B (4 days) and C (3 days). B is followed by D (5 days) and C is followed by E (2 days). Both D and E precede F (4 days), which is followed by G (2 days). The critical path duration is most nearly: See the worked solution or practice the Construction & Scheduling deck
A project has activities A (3 days), B (5 days, after A), C (4 days, after A) and D (2 days, after both B and C). The total float of activity C is: See the worked solution or practice the Construction & Scheduling deck
At a progress review, a project reports a budgeted cost of work performed of $180,000, an actual cost of work performed of $210,000, and a budgeted cost of work scheduled of $200,000. The project status is best described as: See the worked solution or practice the Construction & Scheduling deck
At a status date a project has earned value $450,000, actual cost $500,000 and planned value $480,000. The cost performance index is most nearly: See the worked solution or practice the Construction & Scheduling deck

Related Calculators and Examples

Frequently Asked Questions

What is the difference between total float and free float?

Total float is how long an activity can slip without delaying the project finish (LS minus ES). Free float is how long it can slip without delaying the early start of any successor (earliest successor ES minus the activity EF). Free float is never larger than total float.

What does a CPI below 1.0 mean?

The project is over budget: each dollar spent has earned less than a dollar of budgeted work. A CPI of 0.80 means 80 cents of planned work for every dollar of actual cost.

Are BCWP and earned value the same thing?

Yes. BCWP (budgeted cost of work performed) is earned value, BCWS (budgeted cost of work scheduled) is planned value, and ACWP (actual cost of work performed) is actual cost. The FE handbook uses the BCWP, BCWS and ACWP names.

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