Question 5 of 6: Project Control — The S-Curve and the Earned Value Method

Question 5: Project Control — The S-Curve and the Earned Value Method (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — the S-curve and why it has that shape

The S-curve is the plot of cumulative quantity against time, where the quantity may be cost, labour-hours, physical progress or percentage complete. It is obtained by integrating the period-by-period expenditure implied by the schedule, so the baseline S-curve is a direct product of the CPM programme and the cost loading of its activities, not an independent document. Its slope at any instant is the current burn rate, and its final ordinate is the budget at completion.

The shape follows from the way construction resources build and release. In the opening phase only a few activities are available to start, because the network fans out from a single beginning: mobilisation, site establishment, submittals, procurement and permits consume calendar time while consuming very little cost, so the curve rises slowly. In the middle phase the network is at its widest, many activities run in parallel, manpower and plant are at their peak, and the major permanent works are being installed; the curve is steep and close to linear. In the closing phase the network converges again, trades leave the site, and what remains is commissioning, testing, deficiency correction, demobilisation and documentation, which take time but very little money, so the curve flattens. The compounding of these three effects — a widening then narrowing activity population multiplied by a rising then falling resource level — is what produces the characteristic elongated S.

In practice two S-curves are drawn rather than one: an earliest-start curve, obtained by starting every activity at its early start, and a latest-start curve, obtained from the late starts. Together they bound a lens-shaped region often called the banana or float envelope, and any physically achievable progress curve must lie inside it. Progress above the early-start curve is impossible, progress below the late-start curve means the completion date has already been lost. The envelope has direct commercial uses: the owner reads it as a funding forecast and a basis for the drawdown schedule, the contractor reads it as a cash-flow forecast and prices the financing gap between expenditure and progress payments net of holdback, and both read the actual curve against the planned one as the coarsest possible measure of whether the project is on track.

That last use is also the S-curve’s limitation, and it is what makes part (b) necessary. A cumulative cost curve running below plan is ambiguous: the project may be behind schedule, or it may be exactly on schedule and spending less than budgeted. The curve of money spent cannot separate the two, because it contains no measure of what has actually been built.

Part (b) — earned value as the control instrument

Earned value resolves the ambiguity by adding a third curve. The planned value (PV, historically BCWS) is the budgeted cost of the work scheduled to be complete by the data date — the baseline S-curve. The actual cost (AC, historically ACWP) is what has been spent. The earned value (EV, historically BCWP) is the budgeted cost of the work actually performed, that is, physical progress valued at baseline rates. Because EV is measured in the same units as both of the others, it can be differenced against each, and the two differences separate the schedule question from the cost question.

Given. To make the indices concrete, take a project with a budget at completion of $2,400,000 whose status at the data date is a planned value of $1,200,000, an earned value of $960,000 and an actual cost of $1,150,000, with 9,600 budgeted labour-hours earned against 11,000 hours actually expended.

Find. The cost and schedule variances, the two performance indices, the forecast cost at completion and a productivity measure for the labour.

1. Compute the two variances. Subtracting in the order that makes a negative result unfavourable,$$CV = EV - AC = 960{,}000 - 1{,}150{,}000 = -190{,}000$$$$SV = EV - PV = 960{,}000 - 1{,}200{,}000 = -240{,}000$$Both are negative, so the project has spent 190,000 dollars more than the work performed was worth and has performed 240,000 dollars less work than it planned to.
2. Express the same information as dimensionless indices. Ratios are preferred for trending because they are independent of project size:$$CPI = \frac{EV}{AC} = \frac{960{,}000}{1{,}150{,}000} = \boxed{0.835}$$$$SPI = \frac{EV}{PV} = \frac{960{,}000}{1{,}200{,}000} = \boxed{0.800}$$A CPI of 0.835 means the project earns 83.5 cents of budgeted work for every dollar it spends; an SPI of 0.800 means it is achieving four-fifths of the planned rate of progress.
3. Forecast the outturn cost. Assuming the cost performance observed to date persists over the remaining work,$$EAC = \frac{BAC}{CPI} = \frac{2{,}400{,}000}{0.835} = \boxed{2{,}875{,}000}$$giving a variance at completion of $VAC = BAC - EAC = -475{,}000$ dollars. The to-complete performance index needed to recover the budget, $(BAC-EV)/(BAC-AC) = 1{,}440{,}000/1{,}250{,}000 = 1.152$, tells the project manager that the remaining work would have to be executed 15 per cent more efficiently than budget, which is a far more useful statement than the raw variance.
4. Measure productivity in labour-hours rather than dollars. The same construction applied to hours isolates crew performance from wage rates and material prices:$$PF = \frac{\text{earned labour-hours}}{\text{actual labour-hours}} = \frac{9{,}600}{11{,}000} = \boxed{0.873}$$so the crews are achieving 87.3 per cent of the estimated productivity. Comparing this with the CPI of 0.835 shows that roughly three-quarters of the cost overrun is genuine loss of productivity and the balance comes from prices, which points the corrective action at the right department.

Used this way, earned value controls all three of the quantities the question names. It controls time because the schedule variance and SPI say whether the physical work is keeping pace, and because the SPI applied to the remaining duration gives a first estimate of the forecast completion date — although the schedule variance must always be read alongside the critical path, since progress on activities with float can mask a delay on critical ones. It controls cost because the cost variance, the CPI and the estimate at completion convert a report of expenditure into a forecast of outturn early enough to act on. And it controls productivity because the same arithmetic performed in labour-hours at the work-package level, reported weekly against each cost account in the work breakdown structure, identifies which crews and which items are losing hours while the work is still in progress.