Question 6 of 6: Project Control

Question 6: 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.

Given. Three tasks with budgets totalling $100,000 and a planned-versus-actual bar chart annotated with cumulative percentage complete at each week end.

Find. (a) The planned and actual cumulative cost curves; (b) a comparison of actual against planned progress at the end of week 3; (c) the total expenditure at the end of week 4 measured against the planned amount at that date.

Approach. Convert each percentage complete into dollars by multiplying it by the task budget, sum across tasks to obtain the cumulative planned value (BCWS) and the cumulative earned/expended value at each week end, plot both against time to give the two S-curves, and read the schedule and cost comparisons off the resulting table.

1. Convert percentage complete into dollars, task by task. With cost assumed to accrue in proportion to work performed — the standard simplification for a bar-chart control exercise — $$\text{value}_{i}(t) = \text{budget}_i \times \%\text{complete}_i(t)$$ For task A (budget $30,000): planned values of $6,000, $18,000 and $30,000 at the ends of weeks 1, 2 and 3, against actuals of $3,000, $15,000, $27,000 and $30,000 at the ends of weeks 1 to 4. For task B (budget $20,000): planned $2,000, $16,000 and $20,000, against actuals of nil, $14,000 and $20,000. For task C (budget $50,000): planned $10,000 at the end of week 3, $35,000 at the end of week 4 and $50,000 at the end of week 5, against actuals of $25,000 at the end of week 3 and $50,000 at the end of week 4.
2. Accumulate across tasks to build the planned curve (BCWS). Summing the three planned columns at each week end, $$\begin{aligned} \text{wk }1:&\quad 6{,}000 + 2{,}000 + 0 = \$8{,}000\\ \text{wk }2:&\quad 18{,}000 + 16{,}000 + 0 = \$34{,}000\\ \text{wk }3:&\quad 30{,}000 + 20{,}000 + 10{,}000 = \$60{,}000\\ \text{wk }4:&\quad 30{,}000 + 20{,}000 + 35{,}000 = \$85{,}000\\ \text{wk }5:&\quad 30{,}000 + 20{,}000 + 50{,}000 = \$100{,}000 \end{aligned}$$ The curve closes on the full $100,000 budget at the end of week 5, which is the planned completion of the project and the first check that the reading of the chart is self-consistent.
3. Accumulate the actual curve (ACWP / BCWP). $$\begin{aligned} \text{wk }1:&\quad 3{,}000 + 0 + 0 = \$3{,}000\\ \text{wk }2:&\quad 15{,}000 + 14{,}000 + 0 = \$29{,}000\\ \text{wk }3:&\quad 27{,}000 + 20{,}000 + 25{,}000 = \$72{,}000\\ \text{wk }4:&\quad 30{,}000 + 20{,}000 + 50{,}000 = \$100{,}000 \end{aligned}$$ The actual curve reaches the full budget at the end of week 4, a week earlier than planned.
4. (a) Draw the two S-curves. Plotting the two accumulations against week number gives the characteristic lazy-S shape — shallow at the start while the site is being established, steep through the middle when several tasks overlap, and flattening as the work is completed:
   Figure 6.1 — planned (BCWS) and actual cumulative cost curves. The two curves cross between weeks 2 and 3: the project starts behind plan and finishes ahead of it. The vertical line at week 4 is the data date.
5. (b) Comment on progress at the end of week 3. At the end of week 3 the planned value is $\$60{,}000$ and the value actually earned is $\$72{,}000$, so $$SV = BCWP - BCWS = 72{,}000 - 60{,}000$$ $$\boxed{SV = +\$12{,}000 \text{ ahead of schedule, } SPI = \tfrac{72{,}000}{60{,}000} = 1.20}$$ The aggregate figure conceals two opposite movements, and a useful comment must break it down. Task A is behind: 90 % complete against a planned 100 %, worth $\text{EV}-\text{PV} = 27{,}000-30{,}000 = -\$3{,}000$, and it started half a week late. Task B is on plan in completion terms — it finished in mid-week 3 exactly as scheduled — although it started a half-week late and had to recover. Task C is well ahead: 50 % complete against a planned 20 %, worth $\text{EV}-\text{PV} = 25{,}000-10{,}000 = +\$15{,}000$, because it was begun at the start of week 3 rather than the middle. So the project is ahead overall only because C was started early and pushed hard; the finishing trade on A is lagging, and if A is a predecessor of any remaining work the favourable aggregate is misleading. Because the same percentages generate both the earned and the expended figures here, the cost variance is identically zero and the exercise is measuring schedule performance only.
6. (c) Total expenditure at the end of week 4 versus plan. Reading the two accumulations at the week-4 data date, $$\text{expenditure} = \$100{,}000, \qquad \text{planned} = \$85{,}000$$ $$\Delta = 100{,}000 - 85{,}000$$ $$\boxed{\Delta = +\$15{,}000 \text{ spent above the planned amount } (17.6\% \text{ above plan})}$$ The interpretation matters as much as the arithmetic. The extra $15,000 is not a cost overrun: the full $100,000 budget has been spent because the whole $100,000 of work has been completed, a week ahead of the planned finish. The correct statement is that the project is ahead of schedule and on budget — $SPI = 100{,}000/85{,}000 = 1.18$ and $CPI = 1.00$ — and that the owner should expect the cash requirement to be pulled forward by about one week, with the final account unchanged at $100,000. Had the same $15,000 excess appeared without the corresponding extra work being complete, it would have been a genuine cost overrun; distinguishing the two is exactly what earned-value analysis exists to do, and it is why an S-curve of expenditure alone is never a sufficient control document.