Question 3 of 6: Project Control

Question 3: Project Control (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.

(a) The S-curve and why it has that shape

An S-curve is the cumulative plot of a project variable — most often budgeted cost, but equally labour-hours, quantities placed or earned value — against time, obtained by scheduling every activity, spreading its budget over its duration, and summing across the project. Read as a control document it is the project’s baseline: at any date it states what should have been spent or accomplished, and the vertical distance between the plan and the actual record is the control signal.

The characteristic shape follows directly from how resources build up on a site. Early in the job only a few activities can proceed — mobilisation, site preparation, submittals, long-lead procurement — so the rate of expenditure, which is the slope of the curve, is small and the curve is nearly flat. As the network opens up, many activities run in parallel at full crew strength, the monthly expenditure reaches its maximum, and the curve rises steeply and almost linearly through the middle of the project. Towards the end the remaining work is punch list, testing, commissioning and demobilisation, carried out by shrinking crews, so the slope falls away again and the curve flattens as it approaches the budget at completion. A curve that is flat, steep, then flat is by definition S-shaped; equivalently, the S-curve is the integral of the familiar bell-shaped resource histogram.

Two practical readings follow. First, a project whose actual curve rises faster than the baseline early on is usually not ahead of schedule but front-end loaded or over-resourced, and the difference matters; earned value, discussed in part (c), is what separates the two. Second, the curve drawn on the early schedule and the curve drawn on the late schedule bracket a band, and any plan that stays inside that band is feasible — a banana curve, and one of the few graphical tools that shows float at the project level.

(b) Expenses against expected payments

The sketch carries two curves because a contractor lives on cash, not on cost. Expenses are incurred as the work proceeds — payroll weekly, equipment monthly, materials on delivery — whereas payment arrives only after the month closes, the consultant certifies the progress claim, and the owner pays within the contractual period, typically 30 days from certification. That sequence displaces the payment curve to the right by roughly a month and a half on a normal Canadian job. On top of the lag, the owner retains a holdback under the provincial builders lien legislation (10 per cent in British Columbia), released only after substantial performance and the expiry of the lien period, so the payment curve is also compressed vertically and does not meet the cost curve until well after the last activity is complete.

The area between the two curves is the contractor’s working-capital requirement: the money that must be financed from the contractor’s own resources or an operating line. It peaks near mid-project, exactly where the expenditure rate is highest, which is why a contractor with a healthy backlog can still fail on a cash-flow basis. The practical responses are all visible on the diagram: an unbalanced but defensible front-end schedule of values, prompt and complete monthly claims, negotiation of mobilisation payments or material-on-site payments, and early release of holdback on completed subtrades.

(c) Performance indices for schedule and cost control

Comparing spend against budget alone cannot distinguish a project that is under-spent because it is efficient from one that is under-spent because it is behind. Earned value analysis resolves this by measuring three quantities in the same units of currency at the same data date: the planned value PV (budgeted cost of work scheduled), the earned value EV (budgeted cost of work performed — the budget of what has actually been built), and the actual cost AC. From these come two variances and two indices.

Given. A worked illustration at the six-month data date of a project whose budget at completion is BAC = $4,200,000: PV = $1,850,000, EV = $1,665,000 and AC = $1,776,000.

Find. The schedule and cost variances, the two performance indices, and the forecast cost at completion.

1. Variances answer “how much” in dollars. $$\begin{aligned} SV &= EV - PV = 1{,}665{,}000 - 1{,}850{,}000 = -185{,}000\\ CV &= EV - AC = 1{,}665{,}000 - 1{,}776{,}000 = -111{,}000 \end{aligned}$$ Both are negative, so the project has performed less work than planned and has spent more than that work was worth. A schedule variance expressed in dollars is a genuine oddity of the method and is one reason it is usually converted to an index or to a time equivalent.
2. Indices answer “how efficiently” and are dimensionless. $$\begin{aligned} SPI &= \frac{EV}{PV} = \frac{1{,}665{,}000}{1{,}850{,}000} = 0.900\\ CPI &= \frac{EV}{AC} = \frac{1{,}665{,}000}{1{,}776{,}000} = 0.9375 \end{aligned}$$ $$\boxed{\begin{aligned} SPI &= 0.900 \quad (\text{10 per cent behind schedule})\\ CPI &= 0.9375 \quad (\text{6.7 per cent over cost}) \end{aligned}}$$ An index of 1.00 is on plan, above 1.00 is favourable, below 1.00 unfavourable. Because they are ratios they can be compared across activities, across projects and across time, which variances cannot.
3. Forecast from the index, not from the variance. If the efficiency observed to date persists, the estimate at completion is $$EAC = \frac{BAC}{CPI} = \frac{4{,}200{,}000}{0.9375} = 4{,}480{,}000$$ a variance at completion of $280,000 over budget. The alternative assumption, that the overrun to date is a one-off and the remaining work will run to budget, gives $EAC = AC + (BAC - EV)$; quoting both brackets the forecast honestly.

Two refinements complete the picture. The to-complete performance index, $TCPI = (BAC - EV)/(BAC - AC)$, states the efficiency the remaining work must achieve to finish within budget, and a TCPI far above the CPI already being achieved is the clearest available evidence that the budget is no longer credible. And because SPI is measured in dollars of work, it drifts towards 1.00 as a late project approaches completion — every remaining dollar is eventually earned — so schedule control must always be read alongside the critical path, never from the index alone.