Separate observed labor-contribution movement across output, realization, productivity, and labor rate, then test whether a planned productivity improvement becomes demand capacity, capturable labor cost, or stranded capacity once output growth and labor commitments are included.
About this interactive
The observed bridge compares two operating periods using the same output and productive-labor definitions. Contribution is decomposed across output, revenue per unit, productivity, and labor rate using every possible driver ordering, so interaction effects are shared rather than assigned by a fixed sequence. The forward analysis then starts from Period B and phases in an entered productivity improvement while output grows toward the entered horizon requirement. Productivity-created hours are divided between output growth that would otherwise require additional labor, surplus that can be converted into lower labor-cost capacity after the entered flex date, and capacity left stranded by timing or labor commitment. Labor-cost equivalents are valued at the Period B average labor rate; they are not treated as realized cash savings unless the entered flexibility can actually reduce paid labor cost. For more information, visit our Labor Cost Optimization practice.
Observed periods
Forward productivity capacity
Observed contribution movement
The contribution equation is evaluated through every ordering of output, revenue per unit, productivity, and labor rate. Each driver receives its average marginal contribution effect, so interactions reconcile without depending on which mechanism is applied first.
Forward labor capacity
The white line is the hours required if Period B productivity never improves. The blue line includes the entered productivity improvement. The dashed line is the Period B productive-hour base.
Capacity disposition
Created hours first offset output growth that would otherwise require hours above the Period B base. Remaining hours are surplus; only the flexible share can be converted into lower labor-cost capacity after the entered flex-start month.
Productivity capacity value
These values all use the Period B average labor rate. Demand absorption is labor requirement avoided as output grows; capturable surplus represents hours the entered labor flexibility permits to move out of the labor requirement; stranded surplus remains economically present but not captured.
Operating thresholds
The thresholds keep the other forward assumptions fixed and solve for the productivity, labor-commitment, or output-growth condition that changes the capacity result.
What changed
LABOR PRODUCTIVITY BRIDGE: ILLUSTRATIVE DEFAULT RECORD OBSERVED PERIOD INPUTS Period A output: 100,000 Period B output: 112,000 Period A productive labor hours: 50,000 Period B productive labor hours: 52,000 Period A revenue: $20,000,000 Period B revenue: $23,000,000 Period A labor cost: $4,000,000 Period B labor cost: $4,680,000 OBSERVED ECONOMICS Period A productivity: 2.000 units/hr Period B productivity: 2.154 units/hr Productivity change: 7.7% Period A revenue per unit: $200.00 Period B revenue per unit: $205.36 Period A labor rate: $80.00/hr Period B labor rate: $90.00/hr Period A labor contribution: $16,000,000 Period B labor contribution: $18,320,000 Net labor-contribution movement: +$2,320,000 SEQUENCE-NEUTRAL OBSERVED CONTRIBUTION ATTRIBUTION Output effect: +$1,940,714 Revenue-per-unit effect: +$567,857 Productivity effect: +$322,143 Labor-rate effect: −$510,714 Reconciled contribution movement: +$2,320,000 FORWARD CAPACITY ASSUMPTIONS Planned productivity improvement vs Period B: 5.0% Full productivity improvement realized by: M2 End-of-horizon output growth vs Period B: 3.0% Labor committed share: 98.0% Labor flex start: M3 Planning horizon: 6 months FORWARD CAPACITY RESULT Full planned productivity: 2.262 units/hr Productivity-created labor requirement avoided: 13,903 hrs Equivalent labor value at Period B labor rate: $1,251,289 Hours used to absorb output growth: 5,460 hrs Demand-absorption value at Period B labor rate: $491,400 Productivity-created surplus hours: 8,443 hrs Capturable surplus after commitment and timing: 4,110 hrs Capturable labor-cost equivalent: $369,943 Stranded surplus hours: 4,333 hrs Stranded labor-cost equivalent: $389,946 OPERATING THRESHOLDS Minimum productivity gain required to absorb entered end-horizon output growth without exceeding Period B hours: 3.0% Maximum committed labor share that still permits full capture of all surplus after the entered flex-start month: 96.7% Maximum end-horizon output growth absorbable at full planned productivity without exceeding Period B hours: 5.0% First month additional hours are required without planned productivity: M1 First month additional hours are required with planned productivity: None inside horizon MONTHLY FORWARD PATH M1: output 112,560 | planned productivity 2.208 units/hr | hours at B productivity 52,260 | hours at planned productivity 50,985 | demand absorption 260 hrs | capturable surplus 0 hrs | stranded surplus 1,015 hrs M2: output 113,120 | planned productivity 2.262 units/hr | hours at B productivity 52,520 | hours at planned productivity 50,019 | demand absorption 520 hrs | capturable surplus 0 hrs | stranded surplus 1,981 hrs M3: output 113,680 | planned productivity 2.262 units/hr | hours at B productivity 52,780 | hours at planned productivity 50,267 | demand absorption 780 hrs | capturable surplus 1,040 hrs | stranded surplus 693 hrs M4: output 114,240 | planned productivity 2.262 units/hr | hours at B productivity 53,040 | hours at planned productivity 50,514 | demand absorption 1,040 hrs | capturable surplus 1,040 hrs | stranded surplus 446 hrs M5: output 114,800 | planned productivity 2.262 units/hr | hours at B productivity 53,300 | hours at planned productivity 50,762 | demand absorption 1,300 hrs | capturable surplus 1,040 hrs | stranded surplus 198 hrs M6: output 115,360 | planned productivity 2.262 units/hr | hours at B productivity 53,560 | hours at planned productivity 51,010 | demand absorption 1,560 hrs | capturable surplus 990 hrs | stranded surplus 0 hrs FINDING Observed labor contribution increased by $2,320,000. Sequence-neutral attribution assigns $1,940,714 to higher output, $567,857 to revenue per unit, $322,143 to productivity, and $510,714 of absorption to the higher labor rate. In the forward case, the planned productivity improvement avoids 13,903 labor hours relative to holding Period B productivity constant. 5,460 of those hours absorb the entered output growth, 4,110 become capturable labor-cost capacity under the entered commitment and flex timing, and 4,333 remain stranded. At the Period B labor rate, the capturable amount is $369,943 and the stranded amount is $389,946. The entered 3.0% end-horizon output growth requires at least a 3.0% productivity improvement to remain inside Period B hours, while the entered 5.0% productivity improvement can absorb up to 5.0% output growth once fully realized. METHOD STATUS Management-entered assumptions. Labor contribution equals revenue less labor cost. The observed bridge expresses contribution as output multiplied by revenue per unit less output divided by productivity multiplied by labor rate. Output, revenue per unit, productivity, and labor rate are moved from Period A to Period B in every possible ordering and each driver’s marginal contribution effect is averaged across all orderings. This shares interaction effects without choosing a preferred calculation sequence and reconciles exactly to the Period B less Period A labor-contribution movement. The forward capacity analysis starts from Period B productivity, productive hours, output, and labor rate. Output grows linearly from the Period B run rate to the entered end-of-horizon growth rate. Planned productivity improvement phases in linearly through the entered realization month and then remains at the full entered improvement. Productivity-created hours equal the labor hours that the forward output path would require at Period B productivity less the hours required at planned productivity. Those created hours are first assigned to output growth that would otherwise require labor above Period B productive hours. Any remainder is productivity-created surplus. Before the entered flex-start month no surplus is treated as capturable. After that month, capturable surplus is limited to the flexible share of Period B productive hours, with the remainder classified as stranded. Labor-cost equivalents value hours at the Period B average labor rate and do not assert that accounting payroll cash will fall unless the entered labor flexibility can actually be converted into lower paid labor cost. No external productivity, staffing, wage, output-growth, or utilization benchmark is used.
Continue your analyses, email calculation records, and return to your work from one account.
By creating an account, you agree to the Terms of Use and acknowledge the Privacy Policy.
Enter the 6-digit code sent to .
