Question 6 of 6: Estimating

Question 6: Estimating (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) Duration and cost of each activity

Given. Five sequential highway activities with their quantities, nominal crew production rates and unit prices, and an expectation that crews will achieve only 70 per cent of the nominal rate.

Find. The expected duration in working days and the direct cost of each activity at 70 per cent productivity, and the totals for the project.

Approach. Reduce each nominal production rate to the rate actually expected, divide the quantity by it to obtain a duration, round up to a whole working day for scheduling, and price the work at the given unit rate.

1. Convert the nominal rate to an expected rate. A productivity factor is a straight multiplier on output: $$R_{\text{eff}} = f \times R_{\text{nom}}, \quad f = 0.70$$ so, activity by activity, $742 \rightarrow 519.4$, $394 \rightarrow 275.8$, $600 \rightarrow 420.0$, $5{,}305 \rightarrow 3{,}713.5$ and $8{,}842 \rightarrow 6{,}189.4$ units per day.
2. Duration is quantity divided by the expected rate. $$t = \frac{Q}{R_{\text{eff}}} = \frac{Q}{f\,R_{\text{nom}}}$$ For the base course, for example, $t = 12{,}000/420.0 = 28.57$ days, which is scheduled as 29 working days. Because the factor divides, a 30 per cent shortfall in output does not cost 30 per cent more time but $1/0.70 = 1.43$ times the time — a 43 per cent extension, and the single most useful sanity check on this question.
3. Cost follows the tendered unit price. $$C = Q \times c_u$$ so excavation is $4{,}200 \times 10 = 42{,}000$ and the base course is $12{,}000 \times 12 = 144{,}000$ dollars, and so on. The unit prices are given per unit of finished work, not per crew-day, so the direct cost of each activity is fixed by the quantity and is unaffected by how many days the crew takes.
4. Assemble the estimate. Collecting the five results:

   Activity estimate at 70 per cent productivity

   Activity	Quantity	Effective rate/day	Duration (days)	Scheduled (days)	Cost (CAD)
   1. Excavation	4,200 m3	519.4	8.09	9	42,000
   2. Sub-base	1,200 m2	275.8	4.35	5	1,560
   3. Base	12,000 m2	420.0	28.57	29	144,000
   4. Binder	12,000 m2	3,713.5	3.23	4	60,000
   5. Asphalt	7,200 m2	6,189.4	1.16	2	28,800
   Totals			45.40	49	276,360

5. State the project totals. $$\boxed{\begin{aligned} \sum t &= 45.4\ \text{working days (49 when each activity is rounded up)}\\ \sum C &= \text{CAD } 276{,}360 \end{aligned}}$$ At full nominal productivity the same five activities would occupy 31.8 working days, so the 70 per cent factor costs the project 13.6 days — six working weeks becomes nine.

(b) Factors that affect crew productivity

Productivity is output per crew-hour, and it is depressed by anything that keeps a crew from working steadily at what it is trained to do. The influences group naturally under five headings.

Project and site conditions. Weather and temperature (cold-weather concreting and winter paving are the classic Canadian penalties), site access and haul distance, congestion and working room, ground and groundwater conditions, restricted or night-time working under traffic, and the physical repetition available — a long uninterrupted paving run is far more productive per square metre than the same area in short intermittent sections.

Management and planning. The largest recoverable losses are usually here: waiting for materials, drawings, inspection or equipment; poorly sequenced work that leaves crews idle or stacked; late or unclear instructions; rework caused by defective work or by design change; and inadequate supervision. Learning-curve effects work in the opposite direction, so a crew repeating a cycle for the tenth time may be a third more productive than on the first.

Labour force. Skill, experience and training; crew size and composition, since adding workers to a fixed work face yields diminishing and eventually negative returns; turnover and absenteeism; motivation, incentive schemes and morale; overtime, which raises output per day but lowers output per hour and, sustained beyond a few weeks, can lower both; and shift work, where a night shift typically produces 10 to 15 per cent less than the day shift.

Equipment and materials. Suitability and capacity of plant, its condition and availability, the balance of the fleet (a paver waiting on trucks is a productivity loss that no paving crew can recover), fuel and maintenance support, and the timely supply of conforming materials.

External constraints. Regulatory and permit conditions, traffic management requirements, environmental restrictions and seasonal windows, labour relations and jurisdictional disputes, and public or third-party interference. The practical estimating lesson is that a productivity factor such as the 70 per cent in this question is not a fudge: it is the estimator converting a known set of these conditions into a number, and it should be supported by the company’s own historical output records for comparable work rather than borrowed from a published table.