Crew Productivity and Labor Estimating

Crew Productivity and Labor Estimating

Crew Productivity and Labor Estimating

What the tool does

A labor estimate turns a take-off quantity into hours and money through a productivity: how much of the work a crew installs in an hour. The tool takes a work breakdown of tasks, each with a quantity, a crew and an output per crew-hour (or labor hours per unit), builds the cost of a crew-hour from the trades and equipment of the crew, adjusts the hours for the conditions under which the work will actually be done, prices the overtime, chains the tasks into a schedule with its labor histogram and cumulative curves, and, once work starts, compares the hours actually spent with the hours earned to forecast the hours at completion. The method is the crew-based unit pricing that the Corps of Engineers' cost engineering regulation requires for its detailed estimates (ER 1110-2-1302: unit costs computed by estimating the equipment, labor, material and production rates of each element) and that the Navy's Seabee planners teach in NAVEDTRA 14043 and NAVFAC P-405.

Crew-hours and labor hours

For one crew under average conditions the crew-hours of a task are H_b = Q / R, the quantity over the output per crew-hour, or, when the estimate is kept in labor hours per unit as in the P-405 tables, H_b = Q u / m with u the labor hours per unit and m the number of workers in the crew. The labor hours are H = m H_c and the equipment hours are the crew-hours themselves. Several identical crews split the duration, not the hours: D = H_c / (N_c h_d) working days for N_c crews at h_d hours a day. The man-day arithmetic of NAVEDTRA 14043 is the same: 100 man-hours of effort for a crew of four at 8 hours a day is 100 / (4 × 8) = 3.1 days of lapse time, at 10 hours a day 2.5 days.

Production conditions

Estimating tables give an average production. The Seabee handbooks adjust it with a production efficiency rating: eight elements (work load, site area, labor, supervision, job conditions, weather, equipment, tactical and logistical support) are each rated between 25 and 100 percent against the descriptions of Table 9-2, the average is the production efficiency, and the graph of Figure 9-7 converts it to a delay factor that multiplies the man-hours of the tables. The handbook's own tables sit at 67 percent (delay factor 1.00), peak production at 100 percent is 0.66, and the printed example reads 0.80 at 87 percent, so 6 man-hours per unit become 6 × 0.8 = 4.8. The tool holds the graph as a piecewise-linear function between its labelled rows (digitized from the 1993 edition, with the three printed values taken as printed) and applies the factor to every task.

The other conditions are entered multipliers on the crew-hours, task by task: weather, congestion (trade stacking, a restricted site: the DOE Cost Estimating Guide's example applies 10 percent to the labor hours of work in a congested area, DOE G 430.1-1 chapter 15), shift work (UFC 3-740-05 5-4 notes that the second and third shifts produce less than the day shift), and an other factor for altitude, heat, protective clothing, radiation areas or security. The DOE guide's rule is followed throughout: a site productivity factor is built into the labor hours before they are multiplied by the labor rate. The combined factor is k = DF × k_w × k_c × k_s × k_o × k_L / k_OT, so a factor above one is more hours and the overtime efficiency, a productivity, divides.

Overtime: premium and efficiency

Two things happen when a crew works more than 40 hours a week. The first is arithmetic: the hours beyond 40 are paid at a premium. UFC 3-740-05 5-4.1 computes it as the hours paid over the hours worked: 40 hours straight time plus 8 at time and a half pays 52 hours for 48 worked, a premium of 8.33 percent on the base wage. The tool applies the same rule to each task's hours per day and days per week with the first 40 hours straight time, the weekday hours beyond 40 at the weekday multiple, Saturday and Sunday at their own multiples, in the three schemes of the UFC's Table 5-1 (1.5× with Sunday at 2×; 1.5× with Saturday and Sunday at 2×; 2× all overtime). The closed form reproduces the one-shift block of that table except three cells that are misprints in the 2010 edition (the 5-day 12-hour 1.5× cells print 13.37 for 16.67, the 6-day 9-hour row prints 70 regular hours for 40 and 21.33 for 21.30, and the 7-day 12-hour 2×-weekend cell prints 40.68 for 40.48). The UFC applies taxes and insurance to the premium but not fringes; the tool applies the one burden percentage to the premium as well, a simplification that slightly overstates it.

The second is physical: after a few weeks of extended hours the output per hour falls. The Business Roundtable's 1980 study, the Corps of Engineers' Modification Impact Evaluation Guide (EP 415-1-3, 1979, which reproduced those curves and was rescinded in 1996), the Construction Industry Institute's and Hanna, Taylor and Sullivan's 2005 regression on 88 projects all give the productivity of a 50- or 60-hour week relative to a 40-hour week as a function of the hours and the number of consecutive weeks. Those curves are copyrighted or withdrawn, and the claims literature (Braimah, Ndekugri and Gameson 2006; AACE Recommended Practice 25R-03) warns that every one of them rests on a narrow data set, so the tool does not ship any: the overtime efficiency is an entered input, either per task or as a curve of hours per week against efficiency that is interpolated at each task's week. The crew-hours are divided by it.

Learning

When a task is a run of identical repetitions (footings, floors, bays) and the entered rate is the first repetition's, the unit learning curve of DOE G 430.1-1 chapter 21 (Wright's law in Crawford's unit form) gives the effort of the n-th repetition as T₁ n^b with b = ln(s) / ln 2 for a slope s (a 90 percent curve takes 90 percent of the hours per unit at every doubling). The factor on the total hours of N repetitions is the cumulative average over the first unit, k_L = (1/N) Σ n^b, which the tool evaluates as the exact sum. The Cost Estimating tool fits the slope from unit or lot data and projects lots; its unit-theory total for N units is the same sum.

The crew-hour cost build-up

The straight-time cost of a crew-hour is Σ count × wage × (1 + burden) over the labor lines plus Σ units × hourly rate over the equipment. The wage is the base rate (the Davis-Bacon or prevailing rate, UFC 3-740-05 5-2); the burden collects the payroll taxes and insurance that the UFC builds up in its Example 5-2 (workman's compensation, state and federal unemployment, social security, 19.25 percent in its illustration) and the fringes of its Example 5-3. The task cost is C = H_c [c_lab (1 + p_OT) + c_eq], the unit cost C / Q, and the labor hours per unit H / Q are the number an estimator compares with the published rates. Materials, field overhead, home office and profit are outside the tool.

Equipment rates

The hourly rate of a piece of equipment is built up as the Corps of Engineers' pamphlet EP 1110-1-8 prescribes for contract pricing: the ownership cost is the straight-line depreciation of the total equipment value (list price less discount, plus sales tax and freight) less salvage and tires over the economic life in hours, plus the facilities capital cost of money on the average value, TEV × AVF × CMR / WHPY with AVF = [(N − 1)(1 + SLV) + 2] / (2N) for a depreciation period of N = LIFE / WHPY years; the operating cost is the fuel of each engine (fuel factor in gallons per brake-horsepower-hour × horsepower × price), filters, oil and grease as a share of the fuel cost times the regional labor factor, repair as a share of the value less tires over the life (repair cost factor × economic adjustment × labor factor), tire wear as 1.5 × tire cost / (1.8 × wear factor × maximum life) for one recap, and tire repair at 15 percent of the wear. The standby rate is half the depreciation plus the cost of money, and a week longer than 40 hours spreads the cost of money over the hours worked. The advanced-mode build-up carries the pamphlet's Figure 2-1 example as its default (a 150-ton lattice-boom truck crane in Region I, 2016: ownership 70.58, operating 106.99, total 177.57 per hour) and reproduces every line of it; the operator is a labor line of the crew, as the pamphlet excludes operating labor from the rate.

Schedule, histogram and curves

The tasks are chained finish-to-start by the task numbers in the After column: a task starts when the last of its predecessors finishes, and one with no predecessor starts at day 0. No other network logic is applied (the Project Schedule tool takes lags, overlaps, float and the critical path; Resource Leveling takes the resource limits). The bar chart shows the chain, the histogram sums crews × workers × hours per day over the tasks running on each day (a partial day pro rata), and the cumulative labor hours and cost against working days are the time-phased baseline of the chain, the planned value of earned value management for this scope.

Tracking: earned hours and the estimate at completion

Once a task is under way, the installed quantity and the actual labor hours give the earned hours (budget hours × fraction installed) and the productivity factor PF = earned / actual, which is the actual output per labor hour over the estimated one: above 1.00 the crew beats the estimate. The estimate at completion of the task's hours is EAC = actual + (budget − earned) / PF, the remaining work at the productivity achieved so far; over the whole estimate the tool reports both the EAC with only the tracked tasks finished at their PF and the EAC with every remaining hour at it. An actual rate measured over a period free of disruption is the measured mile that the Delay and Claims Analysis tool uses to quantify a loss of productivity; the DCAA's audit manual (12-808) lists extended overtime, stacking of trades and weather among the causes it expects such a claim to isolate.

Sources and limits

Every number the tool computes comes from a closed form or from the public documents named above (NAVEDTRA 14043, NAVFAC P-405, UFC 3-740-05, EP 1110-1-8, ER 1110-2-1302, DOE G 430.1-1); no production-rate table is shipped, and RSMeans, Walker's and the AACE recommended practices are cited for the user's own rates. The default case is an illustrative five-task concrete foundation with an excavation crew and a concrete crew; its rates and wages are round numbers, not a published estimate. Not covered: materials, overhead and profit, calendar dates and holidays, resource limits across tasks, multi-shift calendars, and the weeks-in-a-row dependence of the overtime curves (enter the efficiency the contract or agency accepts for the planned duration).