ENGI5003 · Professional Engineering Management
Budgeting: Cost Estimation, Slack & Crashing
Budgeting turns the WBS and schedule into money: you estimate each work package's cost, spread it over the Gantt to get a cumulative-cost S-curve, then manage the time-cost trade-off by levelling cash flow within slack or crashing the critical path to buy time. This is the quantitative spine of the ENGI 5003 exam — the closed-book paper reliably tests cost estimation, slack levelling, and a multi-step crashing calculation where you must re-check the critical path after every cut.
What this chapter covers
- 01Direct vs indirect (overhead) costs
- 02Top-down, bottom-up and apportioning estimation
- 03Budget on the Gantt: early-start vs late-start
- 04Periodic cost and the cumulative-cost S-curve
- 05Slack management: levelling cash flow
- 06The time-cost trade-off
- 07Cost slope = $ per period crashed
- 08Crashing procedure and parallel critical paths
Crash a project the cheapest way to save 2 weeks
- +1Confirm the critical path and list crashable critical activities with their cost slopes: Q is cheapest at $9k/wk, then S at $14k/wk, then P at $15k/wk (R is not crashable).
- +1Step 1 — crash the cheapest critical activity, Q, by 1 week ($9k). P-Q-R-S drops 20→19; now P-T-R-S also = 19, so a second critical path appears. Running extra cost = $9k.
- +1Re-check the paths before the next cut: both P-Q-R-S and P-T-R-S sit at 19 weeks, so any further cut must shorten BOTH paths together.
- +1Step 2 — to drop both paths, either crash a SHARED activity (here S, $14k/wk, shared by both paths) or one activity on each path. S alone ($14k) beats crashing Q-on-one-path + T-on-the-other; Q is already at its 1-week limit anyway. Crash S 1 week. Both paths → 18 weeks. Running extra cost = $9k + $14k = $23k.
- +1State the result: 20 → 18 weeks (saved 2) for $23k extra direct cost — the cheapest feasible 2-week compression. Note any indirect/overhead saved over the 2 fewer weeks can offset this.
Key terms
- Direct cost
- A cost traceable to one activity or work package — labour (hours × rate), materials and equipment, and subcontractors. These are the costs placed on the Gantt and changed when an activity is crashed.
- Indirect cost
- A cost that cannot be tied to a single task — overhead (site, supervision, plant hire), general and administrative (G&A), and contingency. Indirect costs typically accrue per unit of time, so finishing sooner reduces them.
- Apportioning method
- A top-down estimating technique that allocates a known total budget across WBS elements by each element's percentage significance; the percentages must sum to 100%. Used when a project closely resembles a past one.
- Cumulative-cost S-curve
- The running total of periodic (per-period) project spend plotted against time. The early-start schedule traces the upper envelope (spend early) and the late-start schedule the lower envelope; a feasible plan lies between them.
- Slack management
- Levelling the periodic cost or resource profile by shifting activities only within their slack, with the due date held fixed. Shift order: non-critical with free slack first, then non-critical with total slack, then critical only if a later end date is accepted.
- Cost slope
- The added direct cost per period saved when crashing an activity: (crash cost − normal cost) / (normal time − crash time). The critical activity with the smallest cost slope is crashed first because it buys a period most cheaply.
Budgeting: Cost Estimation, Slack & Crashing FAQ
What is the difference between direct and indirect costs in project budgeting?
Direct costs (labour, materials, subcontractors) are traceable to a specific activity and go on the Gantt. Indirect costs (overhead, G&A, contingency) cannot be tied to one task and usually accrue per unit time, which is why crashing raises direct cost but cuts indirect cost.
How do I calculate the cost slope for crashing?
Cost slope = (crash cost − normal cost) ÷ (normal time − crash time). It is the extra direct cost per period saved. When crashing, pick the critical activity with the smallest cost slope first (Rule 1); if slopes tie, crash the one that can be crashed earliest (Rule 2).
Why do early-start and late-start budgets give the same total?
ES and LS schedules spend the same total budget — only the timing differs. ES front-loads spend (activities start as soon as allowed); LS back-loads it (each non-critical activity waits out its slack). Drawing both shows the feasible cash-flow envelope and where the periodic-cost peak sits.
Why must I re-check the critical path after every crash step?
Crashing the original critical path shortens it until it ties the length of a parallel path. Once a second critical path appears, crashing the first alone no longer shortens the project; you must crash a shared activity or one activity on each path. Forgetting this re-check is the classic exam error.
Does slack management change the project duration or total cost?
No. Slack management only re-shapes when money is spent — cutting the periodic peak and raising the trough — by shifting activities within their slack. The project total and the due date are unchanged. The moment you would need to move a critical activity you have left levelling and entered a schedule trade-off (crashing or accepting a delay).
Exam move
Treat this chapter as three linked drills, not theory. First, lock the cost-estimation vocabulary (direct vs indirect, top-down/bottom-up/apportioning) because Part-A short answers test recognition. Then practise the full crashing algorithm until it is automatic: (1) find the critical path and list every path's length, (2) compute each crashable critical activity's cost slope, (3) crash the cheapest critical activity one period and add its slope to a running total, (4) re-list path lengths and, if a second path ties, crash a shared activity or one on each path, (5) repeat to the target and report weeks saved plus total extra cost. The marks are won by the step-4 re-check and lost when students keep crashing one path after a parallel path has caught up. Keep the cost-slope formula and the slack-shift order on your single A4 note sheet, and rehearse stating the final line ("X weeks saved for $Y extra direct cost") so you bank the result mark.
