BACK-SOLVED CAPACITY
Start from the finish line and solve the weekly effort it demands
This model is for partners who know the measurable goal but do not know whether their weekly availability supports it. It subtracts accepted and certain one-off units, adjusts throughput for usable work, solves combined hours, and shows a proportional allocation. The allocation is arithmetic, not a judgment about what either person owes.
| Layer | Basis | Share or rate | Result | Unit |
|---|
Detailed calculation process
Formula, declared symbols, substitutions, intermediate results, and reconciliation
H = (Q − Q0 − x)/(W·r·u); hA = H·a/(a+b); hB = H·b/(a+b)
Remaining units are divided by usable output per hour across the horizon. Required combined hours are allocated by each partner’s share of entered availability.
| Symbol | Meaning | Unit / default |
|---|---|---|
| Q, Q0, x | target, accepted baseline, and documented one-off output | 500, 80, 20 units |
| W, r, u | weeks, accepted units per person-hour, usable fraction | 20; 2.5; 0.80 |
| H | required combined weekly effort | hours/week |
| a, b | entered weekly availability of A and B | 5 and 3 hours/week |
- Remaining recurring scope=500−80−20=400 units.
- Usable output per scheduled person-hour=2.5×0.80=2 units/hour.
- Required horizon effort=400÷2=200 person-hours.
- Required weekly effort H=200÷20=10 hours/week.
- Proportional allocation: A=10×5/(5+3)=6.25; B=3.75 hours/week.
- Final reconciliation: available 8−required 10=−2 hours/week; 20×10×2+80+20=500 units returns the target.
How to back-solve
- Define the accepted finish line.
- Subtract completed units.
- Include only certain one-off units.
- Measure throughput with matching units.
- Apply a realistic usable share.
- Compare solved effort with both schedules.
Five foundations
Finish line
Countable target condition.
Residual work
Target less current and one-off units.
Effective throughput
Raw rate times usable share.
Availability share
One partner’s hours divided by total hours.
Capacity gap
Required minus available hours.
Deep dives
Substitutability
Proportional allocation assumes either person can produce at the same effective rate.
Scope creep
Any new accepted unit raises required hours unless the horizon or rate changes.
Negative gap
A negative gap is headroom, not a reason to fill every available hour.
Evidence
Use an approved scope list, acceptance log, comparable time sample, and actual calendar availability. A positive gap signals infeasibility under assumptions; zero means no slack; negative means arithmetic spare capacity.
Limits
- Common productivity rate for both people.
- No sequential dependencies.
- One-off units assumed certain.
- No fatigue curve.
- No fairness or obligation inference.
Glossary
- Back-solve
- Derive inputs required for a fixed output.
- Residual
- Unfinished units.
- Effective throughput
- Accepted output per usable hour.
- Capacity gap
- Required hours less available hours.
- Headroom
- Available hours beyond requirement.
- Substitutability
- Ability to exchange one person’s effort for another’s.
Cases
Photo archive: a two-hour weekly gap leads to a longer horizon.
Volunteer guide: one partner has zero availability, so the proportional allocation makes the ownership constraint visible.
Important note
Do not turn proportional hours into a moral or contractual obligation; agree responsibilities separately.
Result interpretation
A solved workload can still be infeasible
The default requires ten combined hours each week but declares only eight available, so the proportional assignments are demand allocations, not feasible commitments. The two-hour weekly gap equals 40 hours over the horizon and, at two usable units per hour, exactly explains 80 unsupported target units.
Decision and sensitivity
Usable share controls the hours faster than rounding does
Raising usable share from 80% to 85% lowers required effort from 10 to about 9.41 hours/week; lowering it to 75% raises effort to about 10.67. Because the plan remains above eight available hours in each case, the decision requires scope, time, rate, or capacity change rather than a cosmetic allocation adjustment.
Questions
Why solve hours instead of projecting units?
The page starts with a fixed finish line and back-solves the weekly effort it requires. This makes the target and deadline governing inputs rather than optimistic outputs.
Is the proportional split mandatory?
No. It is a neutral allocation based on entered availability. Partners can choose another split after checking skills, constraints, preferences, and non-project work.
Can one partner take all required hours?
Yes, set the other availability to zero if that reflects the plan. Confirm that the remaining partner can perform every required task rather than assuming perfect substitution.
Why must usable share exceed zero?
A zero productive share cannot solve a positive remaining goal. If work is temporarily blocked, record zero availability and move the horizon instead of inventing productivity.
Does availability prove willingness?
No. It is a user-entered capacity assumption. Consent, energy, competing obligations, and relationship equity are outside the formula.
When is this result invalid?
When units differ in size, work is not substitutable, or dependencies dominate. In those cases use task-class estimates and a dependency-aware schedule.
Why subtract one-off units before solving hours?
A documented non-repeating contribution reduces remaining scope but should not inflate the weekly production rate. Keep its evidence and completion date with the record.
What if required hours exceed combined availability?
The plan has an arithmetic capacity gap. Extend the horizon, reduce scope, improve evidenced throughput, or add appropriate capacity rather than silently allocating unavailable hours.
Can the proportional split change over time?
Yes. Recalculate by phase or review period when availability changes. A single horizon-wide split can conceal a short-term bottleneck.
How precise should weekly hours be?
Use planning increments that match the scheduling decision and avoid false precision. Preserve unrounded required hours for reconciliation even if calendars use half-hour blocks.