# Walkability vs durability: the frontier (model v2)

Every point uses Scenario A's schools, DLI placements and 9-12 lines, and the same hard rule: at least as many schools at target as Scenario A in every year 2031-32 → 2040-41. What changes is how hard the solver pushes for schools that stay at target in **all ten years**: no reward (k17), a required minimum (k19, k21), or option1_durable's reward of 3,000 kid-miles per durable school. Numbers from `build/solver/out_v2/<point>/scorecard.json`; generated by `report_v2.py frontier`.

**Status, 2026-10-12: only the two end points ran.** Paul deferred `frontier_k19` and `frontier_k21` for speed. Both points use the newer rules (K-5 nested in Scenario A's high-school lines, the middle→high feeder floor) and shortened solver limits. `frontier_k17`'s 6-8 level was re-solved with the original limits after its first 6-8 solve broke Scenario A's count in 2034-36.

**What it shows: not a clean frontier yet.** Going from no durability reward (k17) to the full reward (option1_durable) adds **1 K-5 school at target all 10 years (18 → 19)**. That's within run-to-run noise: the earlier v2 solve without the feeder and nesting rules (`option1_durable_msfeed_off`) reached 24 schools at 0.949 mi average K-5 walk. K-5 walking barely differs between the two end points (0.989 vs 0.982 mi). Past a closer school is 1,667 vs 1,788. At 6-8, k17 walks less (1.70 vs 1.96 mi) but splits 18 elementary zones between middle schools (vs 0). So the line below should be read as noise-level, not as a price.

**For Paul:** a usable frontier needs longer solver limits, or several seeds per point, so that the gap between points exceeds the noise. Or switch the frontier's base rules back to the walkable `msfeed_off` setup, where the reward visibly mattered (24 vs 17 durable schools for Scenario A).

## K-5

| Plan | At target all 10 years | Avg walk (mi) | % within 1 mi | Over the bus line | Past a closer school | Kids reassigned vs No changes | Size shortfall left in 2031-32 (kids) |
|---|---|---|---|---|---|---|---|
| PPS Scenario A | 17 of 35 | 0.975 | 62.7 | 4,703 | 1,970 | 2,935 | – |
| Shortest walks that still last | 18 of 35 | 0.989 | 64.2 | 4,547 | 1,667 | 5,031 | 497.9 |
| Most schools that last to 2040-41 | 19 of 35 | 0.982 | 63.7 | 4,620 | 1,788 | 5,000 | 333.0 |

**What each extra K-5 school at target all 10 years costs** (from Shortest walks that still last to Most schools that last to 2040-41, +1 schools): about +73 kids over the bus line, +121 kids past a closer school, -37 ft of average walk and -31 kids reassigned, per extra school.

## 6-8

| Plan | At target all 10 years | Avg walk (mi) | % within 1 mi | Over the bus line | Past a closer school | Kids reassigned vs No changes | Size shortfall left in 2031-32 (kids) |
|---|---|---|---|---|---|---|---|
| PPS Scenario A | 6 of 13 | 1.758 | 30.3 | 2,731 | 1,259 | 1,972 | – |
| Shortest walks that still last | 7 of 13 | 1.698 | 30.3 | 2,708 | 1,094 | 2,207 | 0 |
| Most schools that last to 2040-41 | 7 of 13 | 1.963 | 23.5 | 3,405 | 2,059 | 3,006 | 76.0 |