Chapter 20 Exercises — Labor, Productivity, and the Construction Workforce

These exercises are meant to be done with a pencil, a calculator, and the chapter open. Several of them produce artifacts you should keep in your Willow Street notebook.

Difficulty legend: ⭐ basic · ⭐⭐ applied · ⭐⭐⭐ advanced judgment · ⭐⭐⭐⭐ research and extension

Selected answers appear in Appendix J. Where a numeric answer is given here, it is inside a <details> block — do the work before you open it.

Part A — Conceptual Understanding ⭐

A1. State the unit-cost formula from Chapter 12 and identify which of its three terms a project team can meaningfully change after Notice to Proceed. In one sentence, say why that matters for how you spend your attention in the field.

A2. Define unit rate and production rate, give the units of each, and write the formula that converts between them. Then explain in two sentences why man-hours per unit is the more stable measure for building a cost database.

A3. Write the formula for the productivity factor. What does a PF of 0.88 mean in plain English to a foreman who has never heard the term?

A4. List the ten components of a fully burdened labor rate in the order the chapter builds them. Which components are percentages of wage and which are flat dollars per person? Why does that distinction change the burden multiplier for a low-wage classification?

A5. Explain the difference between a prevailing wage requirement and a worker classification (employee versus independent contractor) issue. Both are called "classification" problems in casual conversation; say precisely what each one actually is.

A6. What is a wage determination, who publishes it, and what two numbers does it give you for each labor classification?

A7. Name the six categories used in a work-sampling study and give one example of an observation that falls into each.

A8. Why is a subcontractor's manpower loading curve an earlier warning than their schedule update? Answer with arithmetic, not with an assertion.

A9. Give three mechanisms — not three restatements — by which sustained overtime reduces output per hour.

A10. Explain what an experience modification factor does to a contractor's labor cost, and why it is one of the few places where safety performance appears as a visible line item.

Part B — Applied Analysis ⭐⭐

B1. A drywall subcontractor's foreman tells you his crew is "about 70 percent done" with the level-3 partitions. Your cost report shows 78 percent of the budgeted hours spent. Write down four things you would do before concluding anything, in order, and say what each one would rule in or out.

B2. Your interior framing crew grew from eight to fourteen people over three weeks because the superintendent wanted "more bodies on it." Production went from 640 linear feet a day to 790. Describe what has probably happened in terms of the optimum-crew curve, and name two observations you could make on a walk-through that would confirm it.

B3. Kestrel is bidding two jobs in the same week: a $9M municipal library (prevailing wage, public) and a $9M private office fit-out. Explain, in a short paragraph each, why Kestrel would approach the labor side of these two bids differently, and identify which cost components change and which do not.

B4. A superintendent proposes running a second shift on the interior finishes to recover three weeks. List the productivity, cost, quality, safety, and coordination consequences you would want quantified before approving it — at least two items under each heading.

B5. Your masonry subcontractor has a stable crew of twelve who have been on the job seven months. They tell you they are rotating four of them to another project for six weeks and bringing in four replacements. Estimate, in words and rough numbers, what that costs you, and say which cost code it will show up in.

B6. A work-sampling study on your job returns: direct work 29%, preparatory 12%, tools and material handling 22%, travel 24%, waiting 9%, idle 4%. Rank the three management interventions you would pursue, in order of expected return, and name who owns each.

B7. The same activity is being performed by two crews on two floors of the same building. Crew A: 6 people, 420 SF/day. Crew B: 9 people, 590 SF/day. Which crew is more productive? Show the arithmetic, then explain why the question as asked is incomplete.

B8. Explain to a first-year field engineer why a cost code without a unit of measure attached to it can never produce a productivity factor, and what that means for how a cost-code structure should be designed. (See Chapter 28.)

Part C — Calculations and Deliverables ⭐⭐–⭐⭐⭐

C1 — Build a burdened rate. Build the fully burdened hourly rate for a journeyman electrician using this data. Show every line and compute the multiplier.

Then answer: is this multiplier higher or lower than the carpenter's 1.59 in §20.5, and give the two reasons why.

C2 — Productivity factor and forecast. An activity has a budget of 3,600 man-hours. At the week-14 update, 48 percent of the quantity is installed and 1,980 man-hours have been charged. The burdened rate is $58.00/hr.

1. Compute the PF.
2. Forecast man-hours at completion, by two independent methods.
3. Compute the variance in hours and dollars.
4. Compute the PF the remaining work must achieve to finish on budget, and say whether you would believe a foreman who promised it.

C3 — The overtime decision. A crew of 12 is going to a 10-hour, six-day schedule for five weeks. Base wage $36.00/hr; fully burdened straight-time rate $56.50/hr; statutory loading on wages 21.5%. Use efficiency factors of 1.00, 0.96, 0.91, 0.87, 0.85 for weeks 1 through 5.

1. Compute the correctly loaded cost of one overtime hour.
2. Compute the five-week cost of the 10×6 schedule and the five-week cost of a 40-hour baseline.
3. Compute effective (productive-equivalent) hours for each.
4. Compute cost per effective hour for each, and the marginal cost per extra effective hour.
5. Write the two-sentence recommendation you would give your project executive.

C4 — The optimum crew. Using the burdened rates from §20.5 (foreman $63.32, journeyman $54.12, apprentice $40.70, laborer $41.51) and these production figures for a metal-stud framing operation on 10-hour days, build the full table — MH/day, unit rate in MH/LF, crew cost per day, and unit labor cost per LF — and identify the optimum crew.

Then compute the marginal cost per linear foot for each step up, and identify the crew size at which the marginal cost exceeds the optimum's average cost. State in one sentence when you would nevertheless staff past the optimum.

C5 — Certified payroll. Using the illustrative wage determination in §20.4, prepare the weekly certified payroll line for a worker who works 32 hours as an ironworker and 12 hours as a laborer, Group 1 in the same week, with the overtime premium computed on the applicable basic rate for the hours in excess of 40. Show straight time by classification, the overtime computation, fringe, and gross. Then answer: what contemporaneous record must exist to support the 32/12 split, and who is responsible for creating it?

C6 — Apprentice ratio compliance. A crew of 14 carpenters on a prevailing-wage job contains 8 journeymen and 6 registered apprentices. The program permits 1 apprentice per 4 journey-level workers. Journeyman package $52.05; apprentice package $35.80. Compute the weekly (40-hour) back-wage exposure. Then propose two different compliant crew configurations and state the cost difference between them.

C7 — Learning curve. A production builder frames houses. The first house takes 710 man-hours. Assume a 88 percent learning curve.

1. Compute the unit hours for houses 2, 4, 8, 16, and 32.
2. Estimate the total framing hours for 30 houses with and without the learning effect, and value the difference at $48/hr burdened.
3. The framing subcontractor proposes rotating in a fresh crew at house 15 to serve another subdivision. Explain, with numbers, what you would tell them.

C8 — The Thursday diagnosis, from scratch. A concrete crew of 9 works a 10-hour day and places 74 CY. The budgeted unit rate is 1.15 MH/CY and the burdened rate is $54.00/hr.

1. Compute the day's unit rate, production rate in CY per hour, PF, and labor variance in hours and dollars.
2. The following day, the same crew places 74 CY again — but with eight people, because one called in sick. Compute the same four figures and explain why the second day looks better on paper.
3. State what that comparison tells you about using a single day's PF as a management signal, and what you would use instead.

C9 — Blended prevailing-wage rate. Using the illustrative wage determination in §20.4, compute the blended hourly package for a nine-person crew of 1 carpenter foreman (carpenter package plus a $3.10 foreman differential), 4 carpenters, 2 cement masons, and 2 laborers, Group 1. Then compute the crew's cost for a 10-hour day, and the unit labor cost per SFCA if the crew produces 780 SFCA. Finally: state one change to the crew composition that would reduce unit labor cost, and one that would reduce total daily cost but raise unit labor cost — and explain the difference between those two objectives.

Part D — Judgment and Ethics ⭐⭐⭐

D1. Your superintendent tells a subcontractor's foreman, "I need the north wing framed by Friday, I don't care how." No written directive, no added resources, no schedule revision. Nothing illegal has happened. Explain what has happened, using the third finding of the scaffold near-miss investigation, and write the two sentences the superintendent should have said instead.

D2. A subcontractor bids your job 18 percent below the next bidder. In the scope review you learn that their field crews are paid as 1099 independent contractors through a crew leader. Walk through: what you would ask, what you would verify, what you would require in the subcontract, and under what circumstances you would decline to use them. Then state honestly what you would do if they were the only bidder who could staff the work.

D3. Your safety incentive program pays each crew a bonus for every month with no recordable injuries. Your recordable rate has dropped 40 percent in a year and your near-miss reports have dropped 70 percent. Interpret those two numbers together. What would you change, and what would you say to the crews about why?

D4. You are three weeks from substantial completion. Your project executive asks you to move 400 man-hours of punch-list labor from the (overrunning) drywall cost code to a general-conditions code so that the trade-level cost report looks clean at close. Nobody is being paid less; no invoice changes. Is this a problem? Argue it from three positions: the company's, the owner's under a cost-reimbursable arrangement, and your own five years from now when you are trying to estimate a job from this cost history.

D5. Your open-shop crews include several workers whose first language is not English, and your toolbox talks, JHAs, and orientation are English-only. Nobody has complained and there have been no incidents. Frame this as a business and risk problem rather than a values problem, name the specific exposures, and price the fix.

Part M — Mixed and Interleaved Practice ⭐⭐–⭐⭐⭐

M1 — with Chapter 14 (CPM) and Chapter 19. An activity has a duration of 20 work days built on a crew of 10 at a unit rate of 0.42 MH/SF for 38,000 SF. At the week-4 update, the subcontractor is staffing 6. Compute the implied new duration, determine whether the activity's total float (7 days) absorbs it, and write the four-sentence email you would send. Then say which is the earlier signal — the manpower count or the schedule update — and by roughly how many weeks.

M2 — with Chapter 12 and Chapter 13. You are pricing 22,000 SF of interior metal-stud framing at a base unit rate of 0.038 MH/SF. The work will be performed in an occupied wing with infection-control barriers, on a second shift, with two other trades in the area. Using the adjustment-factor table in §20.7, produce a defensible adjusted unit rate. Then write the two sentences you would put in the estimate's basis-of-estimate narrative explaining and hedging your factor. (Your narrative matters more than your number.)

M3 — with Chapter 30. Take the C2 data and express it as earned value in dollars: PV assuming linear planned progress at week 14 of a 26-week activity, EV, AC, CV, SV, CPI, and SPI. Then explain in two sentences why the CPI equals the productivity factor here and under what condition it would not.

M4 — with Chapter 24 and Chapter 29. Build a one-page recovery plan for a 12-day slip that includes an explicit safety impact section. For each recovery measure, state the productivity assumption, the cost, the days recovered, and the specific hazard the measure introduces along with its control. Then rank the measures by cost per recovered day and by hazard introduced, and note where the two rankings disagree.

M5 — with Chapter 27. Work sampling on your job shows waiting at 16 percent and travel at 21 percent. Design a six-week look-ahead and constraint-log process aimed specifically at those two categories. Name the constraints you would track, who removes each, and the one metric you would report weekly to know it is working.

M6 — with Chapter 33. Your subcontractor submits a disruption claim supported entirely by a published productivity-factor table applied to their bid hours. Write the three-paragraph response: what is wrong with the methodology, what evidence you would accept instead, and what you are willing to do about the portion of their loss you believe is real but unproven.

Part E — Research and Extension ⭐⭐⭐⭐

E1. Find the current prevailing-wage requirements that would apply to a $6.8 million municipal community center in your jurisdiction. Determine: whether a state prevailing-wage law applies and at what threshold; whether the project would instead or additionally be covered by federal Davis-Bacon requirements and why; where the applicable wage determination is published; the classification and rate for a carpenter and for a laborer; the certified payroll submission method and frequency; and the apprentice ratio rules. Write it as a one-page memo with the source and the date you verified each item — and include a re-verification date. Do not use any number from this book.

E2. Interview a working foreman, superintendent, or craft worker with at least ten years in the trades. Ask four questions: what wastes the most time on a typical day; what a good general contractor does that a bad one does not; what would have made them leave the trade early in their career; and what kept them. Write 800 words on what you heard, and specifically identify anything that contradicted this chapter. Contradictions are the valuable part.

E3. Locate a registered apprenticeship program in your area — union joint apprenticeship committee, open-shop association program, or community college partnership. Document the program length, the classroom and on-the-job hour requirements, the wage progression by period, the ratio requirements, the cost to the apprentice, and the completion rate if it is published. Then write half a page on what a contractor gets for the per-hour training contribution, and whether you would pay it voluntarily if it were optional.