16-Civ-B8 Management of Construction · May 2015

Question 3 of 6: Estimating and bidding — trenching machine production and unit cost

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. National Exams, May 2015 — 98-Civ-B8 Management of Construction (the paper now catalogued as 16-Civ-B8). Three hours, closed book; one of two approved calculator models permitted. Six questions of equal value (20 marks each); the rubric states that any five constitute a complete paper and that only the first five presented in the answer book will be marked. All six are worked here, because this set is a study resource rather than an exam script. The paper is three calculation questions (1, 3, 4) and three discussion questions (2, 5, 6).

Source note. The two side tables on page 2 — the activity/duration/predecessor list in Question 1 and the trenching-machine production table in Question 3 — are given in full in the Given blocks below. The final activity in the Question 1 table is printed as a two-character label that reads QI; it is a closing activity of one day's duration following V and S, and the answer does not depend on how the label is read.

Reference texts.

Halpin, D. W. and Senior, B. A., Construction Management, 4th ed., Wiley — Ch. 9–11 (network scheduling, activity-on-arrow networks, float), Ch. 4 (project delivery methods), Ch. 13–14 (equipment production and cost estimating).
Hendrickson, C. and Au, T., Project Management for Construction, 2nd ed. — Ch. 8 (construction contracts and risk allocation), Ch. 10 (fundamental scheduling procedures, critical path and float), Ch. 5 (cost estimation, productivity).
Peurifoy, R. L., Schexnayder, C. J., Shapira, A. and Schmitt, R., Construction Planning, Equipment, and Methods, 9th ed., McGraw-Hill — Ch. on trenching and excavating machinery (ladder- and wheel-type trenchers, production tables, operating-efficiency factors).
Fraser, N. M., Jewkes, E. M. et al., Global Engineering Economics: Financial Decision Making for Engineers, Canadian ed., Pearson — Ch. 3 (compound-interest factors), Ch. 4 (present worth), Ch. 5 (comparison of alternatives).
Canadian Construction Documents Committee, CCDC 2 — Stipulated Price Contract, CCDC 14 — Design-Build Stipulated Price Contract; and the Canadian Construction Association Guide to Calling Bids and Awarding Contracts.
Hinze, J. W., Construction Safety, 2nd ed.; WorkSafeBC, Occupational Health and Safety Regulation (Parts 3, 4, 5, 8, 11, 12, 13, 18, 20) and the Canadian Centre for Occupational Health and Safety (CCOHS) fact sheets.
Construction Industry Institute and the U.S. Business Roundtable productivity studies, as summarised in Halpin & Senior Ch. 15 (labour productivity, work sampling, the five-minute rating).

Question 3: Estimating and bidding — trenching machine production and unit cost (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. A single trench of uniform section excavated by one ladder-type trencher with a three-person crew — operator, labourer and foreman — the machine's digging speed read from the manufacturer's table for the applicable depth and width band.

Given data for the trench excavation estimate
Item	Value
Trench length	2,940 ft
Trench width	30 in. (2.5 ft)
Average trench depth	7 ft
Material	common earth
Table digging speed, depth 6–8 ft and width 30–36 in.	25 to 50 ft/hr
Operating efficiency	45 productive min per 60-min hour
Trenching machine	$87/hr
Machine operator	$25/hr
Labourer	$20/hr
Foreman	$20/hr

Find. The total cost of the trench excavation and the cost per linear foot of trench.

Section through the trench: 30 in. (2.5 ft) wide by 7 ft average depth in common earth. This depth-and-width combination selects the 25–50 ft/hr row of the production table.

Approach. Enter the production table with the trench's depth and width to obtain the ideal digging speed, correct it for operating efficiency to get an achievable production rate, divide the length by that rate to get machine hours, and multiply by the assembled hourly cost of the machine and crew.

Select the correct row of the production table. The trench is 7 ft deep on average and 30 in. wide, which places it in the 6–8 ft depth band and, within that band, in the 30, 32, 36 in. width group. The tabulated digging speed for that combination is 25 to 50 ft/hr. Selecting the row is the step that carries the most estimating judgement, because moving one band up in width or depth would roughly double the assumed production, and every later number scales inversely with it.
Take a representative ideal speed. The table gives a range rather than a value, so in the absence of a stated soil condition the midpoint is the defensible estimate for common earth, which is the average of the materials the range is meant to cover: $$v_{\text{ideal}}=\frac{25+50}{2}=37.5\ \text{ft/hr}$$ The lower end of the range corresponds to tight, stony or wet ground and the upper end to loose, free-digging soil; the sensitivity of the answer to this choice is quantified at the end.
Convert the operating efficiency into a factor. An efficiency stated as 45 productive minutes per hour accounts for the time the machine is not cutting: repositioning, spoil handling, minor adjustments, operator breaks and crew delays. $$E=\frac{45\ \text{min}}{60\ \text{min}}=0.75$$
Compute the achievable production rate. Multiplying the ideal speed by the efficiency factor gives the rate that should be used for estimating: $$P=v_{\text{ideal}}\cdot E=37.5\times0.75=\boxed{28.125\ \text{ft/hr}}$$ This is the number that would be quoted to the superintendent as the daily target — roughly 225 ft in an eight-hour shift.
Convert the quantity of work into machine hours. Dividing the length of trench by the production rate, $$t=\frac{L}{P}=\frac{2{,}940\ \text{ft}}{28.125\ \text{ft/hr}}=104.53\ \text{hr}$$ which at eight hours per shift is a little over thirteen working days for the trenching operation alone.
Assemble the hourly cost of the operation. The machine and the whole crew are charged for every hour the operation is on site, because the labourer and the foreman cannot be released while the trencher is working: $$C_{\text{hr}}=87+25+20+20=\boxed{\$152\ \text{per hour}}$$
Compute the total cost and the unit cost. Multiplying the duration by the hourly cost, $$C_{\text{total}}=t\cdot C_{\text{hr}}=104.53\times152=\boxed{\$15{,}889}$$ and dividing by the length of trench, $$C_{\text{ft}}=\frac{15{,}889}{2{,}940}=\boxed{\$5.40\ \text{per linear foot}}$$ A useful check is that the unit cost can be obtained directly, without the duration, as the hourly cost divided by the production rate: $C_{\text{hr}}/P=152/28.125=\$5.40$ per foot, which agrees.
Cross-check against a volumetric rate. Estimators normally sanity-check a linear price against the volume it moves. The bank volume excavated is $$V=\frac{2{,}940\times2.5\times7}{27}=1{,}906\ \text{bank yd}^3$$ so the operation costs $C_{\text{total}}/V=\$8.34$ per bank cubic yard, which is a plausible order of magnitude for machine trenching in common earth and confirms that no factor-of-twelve unit slip has crept into the width conversion.

Quantify the sensitivity to the tabulated range. Because the table spans a factor of two, the estimate should be reported with its range rather than as a single number:

Sensitivity of the estimate to the digging speed assumed
Ideal speed	Production at E = 0.75	Duration	Total cost	Cost per linear foot
25 ft/hr (tight ground)	18.75 ft/hr	156.8 hr	$23,834	$8.11
37.5 ft/hr (mid-range, adopted)	28.125 ft/hr	104.5 hr	$15,889	$5.40
50 ft/hr (free-digging)	37.5 ft/hr	78.4 hr	$11,917	$4.05

A bidder would price the mid-range figure and carry the difference to the low-production case as a contingency, or investigate the ground further before committing.

Check: the estimate assumes (i) the mid-range digging speed of 37.5 ft/hr, since the paper states only "common earth" and gives a two-to-one range; (ii) that the labourer and foreman are charged for the full duration of the trenching operation rather than part-time; and (iii) that the cost asked for is the direct cost of excavation only — no mobilisation, bedding, shoring, dewatering, backfill, compaction, overhead or profit is included, none of which the question supplies data for. Trench boxes or sloping would be mandatory at this depth under WorkSafeBC OHS Regulation Part 20, and their cost would be added in a real bid.

Question 3 — final results
Quantity	Value
Table digging speed selected (6–8 ft deep, 30–36 in. wide)	25 to 50 ft/hr, midpoint 37.5 ft/hr
Operating efficiency factor	0.75
Achievable production rate	28.125 ft/hr
Duration of the trenching operation	104.5 hr (about 13 eight-hour shifts)
Assembled hourly cost, machine plus crew	$152/hr
Total cost of excavation	$15,889
Cost per linear foot	$5.40/ft
Equivalent volumetric cost	$8.34 per bank cubic yard (1,906 bank yd³)

Topic. Equipment production estimating — converting a manufacturer's ideal output into a priced unit rate.

Key relations. Production $P=v_{\text{ideal}}\cdot E$ where $E$ is the operating-efficiency factor; duration $t=L/P$; assembled hourly cost $C_{\text{hr}}=\sum(\text{machine rates})+\sum(\text{crew rates})$; total cost $C=t\cdot C_{\text{hr}}$; unit cost $C_{\text{unit}}=C_{\text{hr}}/P$; trench volume $V=L\cdot w\cdot d/27$ for dimensions in feet giving cubic yards.

Why this works. Every equipment estimate is the same three-line calculation: how fast can the machine work, how much of the hour does it actually work, and what does an hour cost. The manufacturer's table gives an ideal rate measured under favourable conditions; the efficiency factor is the estimator's admission that a 60-minute hour never happens on a construction site, and 45 minutes per hour is the conventional value for reasonably well-managed work. The identity $C_{\text{unit}}=C_{\text{hr}}/P$ is worth internalising because it shows that unit price depends only on the hourly cost and the production rate, not on the quantity — the quantity merely scales the total. That is also why an estimator's greatest exposure is the production rate: halving it doubles the unit price, whereas a ten per cent error across the labour rates — $65 of the $152 hourly cost — moves the price by about four per cent.

Common pitfall. The first classic error is forgetting to convert the 30 in. width to 2.5 ft in the volume cross-check, which produces a volume twelve times too large and a nonsensically cheap unit rate. The second is charging only the machine and operator for the full duration while treating the labourer and foreman as incidental; with a three-person crew behind one machine that omission removes 26 per cent of the hourly cost and under-prices the bid by the same fraction. A third is applying the efficiency factor to the cost rather than to the production — a mistake that moves the answer in the wrong direction entirely.

Source. Peurifoy, Schexnayder, Shapira & Schmitt, Construction Planning, Equipment, and Methods, 9th ed. — trenching and excavating machinery, production tables and operating-efficiency factors; Halpin & Senior, Construction Management, 4th ed., Ch. 13–14 (equipment cost and production estimating).

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