1,000
Reproducible weekly trials
Operations Lab · Recovery-risk instrument
Will the recovery plan survive contact with reality?
Average arithmetic can make a fragile plan look certain. Model the queue, add real operating variability, and see median timing, four-in-five timing, conservative timing, target-miss risk, and the throughput shortfall that stalls recovery entirely.
P50–P95
Recovery timing
0
Data stored unless submitted
No signup
Sample scenarios
Shareable assumptions
Transparent model logic
Working data
The calculator opens with sample inputs. Scenario values remain in the page and may be encoded in a share link; scenario and contact details leave the browser only when the visitor explicitly submits them.
Decision boundary
This is a transparent scenario distribution, not a fitted forecast or optimization engine. Validate the queue definition, operating assumptions, and high-utilization behavior before acting.
Build the operating case
Test the promise—not just the arithmetic.
Replace the example with observed operating data, select how volatile the operation really is, and compare leadership’s target with the distribution of plausible recovery paths.
LUNA-BRM-3.0 · Working recovery-risk instrument
The deterministic simulation, share state, exports, telemetry, and inquiry handoff remain in the coded application.
The verified runtime executes 1,000 reproducible trials through a 104-week horizon, encodes versioned scenarios in URL hashes, creates a local decision brief, respects Do Not Track for anonymous events, and submits contact details only after explicit action. The Framer shell does not iframe or imitate those contracts.
Sample scenarios
Support tickets · Insurance claims · Order fulfillment · Permit review · Grading submissions
Each preset can be tested at Low 10%, Moderate 20%, or High 35% operating volatility.
11 numeric controls
Current backlog · Control threshold · Weekly inbound · Rated weekly capacity · Capacity utilization
Rework / defect loss · Aging-work mix · Net surge output · Planned productivity gain · Target window · Estimated cost per unit-week.
Evidence-aware, not evidence-substituting
Built from an operating engagement. Bounded by what public evidence can prove.
The model generalizes recovery mechanics used during Ryan Miller’s 2026 PSA advisory engagement. Public reporting documented a queue near 14 million units in mid-June and PSA’s official July 14 update reported 11 million. Those checkpoints demonstrate the operating context; they do not prove that Luna Sol alone produced PSA’s recovery.
01 · Source
Official operating checkpoint
PSA’s management-reviewed tracker is the primary source for its published backlog, throughput, quality, and capacity updates.
02 · Corroboration
Dated external reporting
Sports Illustrated reported the July 14 checkpoint of 11 million units and June output exceeding May by 10%.
03 · Attribution
Operating results are collaborative
Published outcomes reflect PSA leadership and operating teams. This tool contains no confidential PSA data and makes no sole-attribution claim.
Methodology
Transparent math before executive judgment.
The calculator is designed to expose the few assumptions that determine whether a queue shrinks, stalls, or grows.
01
Establish effective weekly throughput
Rated capacity is adjusted by realized utilization and the planned productivity gain, then reduced for rework. The aging factor applies an 8% maximum drag in proportion to the aged-work mix: a 50% aged mix produces a 4% throughput drag. Any temporary surge capacity is added last. This creates an effective-throughput estimate rather than treating theoretical capacity as available output.
02
Compare output with incoming demand
Weekly inbound is subtracted from effective throughput. A positive difference is net backlog burn. A zero or negative result means there is no modeled recovery at the current assumptions, regardless of the target date.
03
Test the commitment
The model calculates the throughput required to move from the current queue to the control threshold within the selected window. Any difference between required and effective throughput becomes the capacity gap leadership must fund, remove, or renegotiate.
04
Stress the execution case
The sensitivity range varies effective throughput by ±12% before inbound demand is subtracted. The recovery-risk view then runs 1,000 reproducible weekly trials with independent variation around demand and output, reporting P50, P80, P95, and target-miss risk.
05
Read the fragility—not only the date
Margin of safety equals net burn divided by effective output. The inverse operating problem is the amplification factor: effective output divided by net burn. When the margin is thin, a routine percentage change in output creates a much larger percentage change in backlog burn.
06
Treat high utilization as a warning, not a free multiplier
The input model uses utilization as a transparent throughput multiplier, but real queues become nonlinear near saturation: variability and waiting time rise sharply as utilization approaches 100%. The model does not implement Kingman’s approximation or a service-time distribution, so high-utilization scenarios require direct queueing analysis before commitment.
Trust boundary
This is a transparent scenario distribution, not a fitted forecast or optimization engine. It does not learn from historical data or model correlation, seasonality, service times, congestion, or structural breaks. Validate those mechanisms before acting.
What the product produces
The date, the odds, and the point where the plan breaks.
01
Risk-adjusted timing
P50, P80, and P95 recovery timing plus the share of simulated paths that miss leadership’s target window.
02
Fragility
Margin of safety, net-burn amplification, and the throughput shortfall that stalls recovery completely.
03
Decision gap
The effective and rated capacity required to turn the target from a hope into a controlled operating path.
When the answer is “no recovery”
Do not negotiate the date before identifying the constraint.
Use the hypothesis map to determine which operating mechanism deserves evidence first. If the recovery path crosses functions, governance, or material financial risk, Ryan can translate the scenario into an implementation plan.
Fixed-scope entry engagement
Two-week Backlog Reality Check.
Move from a browser scenario to an evidence-backed operating decision. Ryan validates the queue definition, tests the recovery assumptions against operating evidence, and converts the result into an accountable action path.
01
Validate the operating baseline
Reconcile intake, demonstrated output, yield loss, aging, and the control threshold with the people and data closest to the work.
02
Identify the three binding constraints
Separate symptoms from mechanisms and define the evidence, falsifier, owner, and decision attached to each leading constraint.
03
Sequence the recovery decision
Deliver a practical action plan with scenario ranges, leading indicators, governance cadence, and the first implementation gates.
Working window
Two focused weeks
Delivery model
Principal-led
Commercial boundary
Fixed fee agreed before kickoff
The exact fee, acceptance criteria, access requirements, and exclusions are confirmed in writing. No performance outcome is implied by this page.
How does the backlog recovery model calculate effective throughput?
Rated capacity is adjusted for realized utilization, planned productivity gain, rework loss, and a disclosed aging-work drag, then surge capacity is added. Weekly inbound demand is subtracted from that effective throughput to calculate net backlog burn.
Why does the calculator show a sensitivity range?
The transparent range applies plus or minus 12 percent variation to effective throughput before inbound is subtracted. The separate recovery-risk view runs 1,000 reproducible weekly scenarios at low, moderate, or high operating volatility and reports P50, P80, and P95 timing plus target-miss risk. Neither is a fitted forecast or confidence interval.
What does “No recovery” mean?
It means the assumptions provided do not create positive net backlog burn: effective weekly throughput does not exceed weekly inbound demand. The operating question then shifts from timing to constraint removal, capacity design, or demand control.
When should this model not be used on its own?
Do not use it as a substitute for direct observation, validated operating data, workforce planning, demand forecasting, financial approval, or safety and compliance review. Use it to make assumptions explicit and identify the next decision to validate.
Model questions
How to interpret the result.
The operator behind the model
Ryan Miller, EMBA
Founder and Principal of Luna Sol Group. Ryan’s work spans last-mile transformation, capacity planning, network operations, customer experience, and large-scale frontline execution. This calculator makes that operating lens inspectable before a conversation begins.
A specific exchange, not a generic lead form.
Send the scenario above and Ryan will reply with 2–3 operating observations within one business day—no deck and no pitch.