FA-94981 / Warehouse slotting and bin packing / Open access

Carton selection: equal-volume tie ignores cost · case 01

Between two cartons of equal inner volume the more expensive one is chosen when its id sorts first.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The tie-break after volume skips cost and falls straight to id.

THE FAILURE

The tie-break after volume skips cost and falls straight to id.

Unsuccessful approach: Breaking ties by cost descending chooses the most expensive equal-volume carton.

Case contract

Item dims [a,b,c], weight kg, sioc flag (ships in own container). cartons [[id, L, W, H, max_kg, cost]]. SIOC items return "SIOC". Otherwise add 1 unit of dunnage per side (2 per dimension); the item fits a carton if the sorted padded dims are each <= the sorted inner dims (any orientation) and kg <= max_kg. Choose the smallest inner volume, then cost, then id. None -> "NO_FIT".

Why this case matters

Cartonization picks the shipping box, which drives material cost and dimensional weight.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(dims, kg, sioc, cartons):
    if sioc:
        return 'SIOC'
    need = sorted(d + 2 for d in dims)
    best = None
    for cid, L, W, H, max_kg, cost in cartons:
        inner = sorted([L, W, H])
        if any(n > c for n, c in zip(need, inner)):
            continue
        if kg > max_kg:
            continue
        key = (L * W * H, cid)
        if best is None or key < best[0]:
            best = (key, cid)
    return best[1] if best else 'NO_FIT'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['generated mix 5', [[6, 2, 8], 4.5, False, [['C0', 20, 12, 4, 30, 70], ['C1', 20, 16, 20, 20, 90], ['C2', 20, 16, 20, 20, 70]]], 'C0'], ['generated mix 13', [[5, 2, 14], 5, False, [['C0', 20, 20, 6, 5, 55], ['C1', 32, 16, 8, 20, 90]]], 'C0']], [['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['no fit', [[40, 3, 3], 1, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'NO_FIT'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['generated mix 8', [[5, 7, 8], 10.5, False, [['C0', 10, 20, 6, 10, 70], ['C1', 12, 6, 12, 10, 40], ['C2', 10, 20, 4, 20, 40]]], 'NO_FIT'], ['generated mix 16', [[6, 4, 3], 19, False, [['C0', 12, 16, 4, 5, 40], ['C1', 32, 16, 4, 10, 90], ['C2', 20, 16, 20, 10, 70], ['C3', 20, 12, 8, 10, 90]]], 'NO_FIT'], ['generated mix 24', [[14, 2, 13], 4.5, False, [['C0', 24, 8, 12, 30, 55], ['C1', 10, 8, 30, 30, 70]]], 'NO_FIT']], [['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['generated mix 19', [[11, 3, 5], 1, False, [['C0', 6, 20, 4, 20, 90], ['C1', 20, 20, 6, 5, 40], ['C2', 32, 6, 4, 20, 55], ['C3', 12, 8, 30, 20, 90], ['C4', 32, 20, 8, 10, 55], ['C5', 20, 6, 12, 20, 40]]], 'C5'], ['generated mix 27', [[10, 11, 6], 10, False, [['C0', 20, 20, 8, 30, 90], ['C1', 24, 20, 20, 5, 90], ['C2', 32, 16, 4, 5, 55], ['C3', 10, 16, 30, 5, 55], ['C4', 10, 6, 4, 10, 90], ['C5', 16, 20, 30, 5, 70]]], 'C0'], ['generated mix 35', [[10, 2, 4], 20, False, [['C0', 10, 20, 4, 5, 70], ['C1', 32, 12, 20, 5, 70], ['C2', 10, 12, 6, 20, 40], ['C3', 16, 20, 8, 20, 55], ['C4', 12, 20, 30, 30, 55], ['C5', 10, 6, 8, 5, 70]]], 'C2']], [['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['no fit', [[40, 3, 3], 1, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'NO_FIT'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['generated mix 30', [[14, 13, 10], 1, False, [['C0', 16, 8, 8, 10, 55], ['C1', 20, 20, 20, 5, 55], ['C2', 32, 20, 20, 20, 40], ['C3', 24, 20, 4, 20, 40], ['C4', 16, 12, 4, 20, 55]]], 'C1'], ['generated mix 38', [[8, 8, 5], 10, False, [['C0', 24, 16, 4, 5, 70], ['C1', 20, 16, 12, 20, 70]]], 'C1'], ['generated mix 46', [[12, 7, 5], 5, False, [['C0', 24, 16, 30, 10, 70], ['C1', 24, 16, 8, 5, 40]]], 'C1']], [['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['generated mix 41', [[11, 14, 6], 19, False, [['C0', 6, 12, 20, 30, 90], ['C1', 6, 6, 4, 20, 70]]], 'NO_FIT'], ['generated mix 49', [[5, 14, 9], 1, False, [['C0', 32, 20, 8, 5, 70], ['C1', 12, 8, 12, 5, 55], ['C2', 20, 6, 8, 5, 90], ['C3', 12, 20, 20, 30, 40], ['C4', 6, 12, 30, 20, 40], ['C5', 10, 16, 8, 5, 90]]], 'C3'], ['generated mix 57', [[2, 2, 8], 20, False, [['C0', 32, 20, 20, 30, 55], ['C1', 32, 20, 4, 20, 90], ['C2', 12, 12, 20, 30, 55]]], 'C1']]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
volume tie by cost	`A`	`B`	Failed
rotated fit	`S`	`S`	Passed
weight at limit	`S`	`S`	Passed
sioc	`SIOC`	`SIOC`	Passed
cheap but bulky	`SMALL`	`SMALL`	Passed
padding pushes to M	`M`	`M`	Passed
generated mix 5	`C0`	`C0`	Passed
generated mix 13	`C0`	`C0`	Passed

SHA-256 / 6591de8189de631b5678051d194558d7d48c8c8cbfef762fe5ad1dd9aa90ea49

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(dims, kg, sioc, cartons):
    if sioc:
        return 'SIOC'
    need = sorted(d + 2 for d in dims)
    best = None
    for cid, L, W, H, max_kg, cost in cartons:
        inner = sorted([L, W, H])
        if any(n > c for n, c in zip(need, inner)):
            continue
        if kg > max_kg:
            continue
        key = (L * W * H, -cost, cid)
        if best is None or key < best[0]:
            best = (key, cid)
    return best[1] if best else 'NO_FIT'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['generated mix 5', [[6, 2, 8], 4.5, False, [['C0', 20, 12, 4, 30, 70], ['C1', 20, 16, 20, 20, 90], ['C2', 20, 16, 20, 20, 70]]], 'C0'], ['generated mix 13', [[5, 2, 14], 5, False, [['C0', 20, 20, 6, 5, 55], ['C1', 32, 16, 8, 20, 90]]], 'C0']], [['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['no fit', [[40, 3, 3], 1, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'NO_FIT'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['generated mix 8', [[5, 7, 8], 10.5, False, [['C0', 10, 20, 6, 10, 70], ['C1', 12, 6, 12, 10, 40], ['C2', 10, 20, 4, 20, 40]]], 'NO_FIT'], ['generated mix 16', [[6, 4, 3], 19, False, [['C0', 12, 16, 4, 5, 40], ['C1', 32, 16, 4, 10, 90], ['C2', 20, 16, 20, 10, 70], ['C3', 20, 12, 8, 10, 90]]], 'NO_FIT'], ['generated mix 24', [[14, 2, 13], 4.5, False, [['C0', 24, 8, 12, 30, 55], ['C1', 10, 8, 30, 30, 70]]], 'NO_FIT']], [['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['generated mix 19', [[11, 3, 5], 1, False, [['C0', 6, 20, 4, 20, 90], ['C1', 20, 20, 6, 5, 40], ['C2', 32, 6, 4, 20, 55], ['C3', 12, 8, 30, 20, 90], ['C4', 32, 20, 8, 10, 55], ['C5', 20, 6, 12, 20, 40]]], 'C5'], ['generated mix 27', [[10, 11, 6], 10, False, [['C0', 20, 20, 8, 30, 90], ['C1', 24, 20, 20, 5, 90], ['C2', 32, 16, 4, 5, 55], ['C3', 10, 16, 30, 5, 55], ['C4', 10, 6, 4, 10, 90], ['C5', 16, 20, 30, 5, 70]]], 'C0'], ['generated mix 35', [[10, 2, 4], 20, False, [['C0', 10, 20, 4, 5, 70], ['C1', 32, 12, 20, 5, 70], ['C2', 10, 12, 6, 20, 40], ['C3', 16, 20, 8, 20, 55], ['C4', 12, 20, 30, 30, 55], ['C5', 10, 6, 8, 5, 70]]], 'C2']], [['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['no fit', [[40, 3, 3], 1, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'NO_FIT'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['generated mix 30', [[14, 13, 10], 1, False, [['C0', 16, 8, 8, 10, 55], ['C1', 20, 20, 20, 5, 55], ['C2', 32, 20, 20, 20, 40], ['C3', 24, 20, 4, 20, 40], ['C4', 16, 12, 4, 20, 55]]], 'C1'], ['generated mix 38', [[8, 8, 5], 10, False, [['C0', 24, 16, 4, 5, 70], ['C1', 20, 16, 12, 20, 70]]], 'C1'], ['generated mix 46', [[12, 7, 5], 5, False, [['C0', 24, 16, 30, 10, 70], ['C1', 24, 16, 8, 5, 40]]], 'C1']], [['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['generated mix 41', [[11, 14, 6], 19, False, [['C0', 6, 12, 20, 30, 90], ['C1', 6, 6, 4, 20, 70]]], 'NO_FIT'], ['generated mix 49', [[5, 14, 9], 1, False, [['C0', 32, 20, 8, 5, 70], ['C1', 12, 8, 12, 5, 55], ['C2', 20, 6, 8, 5, 90], ['C3', 12, 20, 20, 30, 40], ['C4', 6, 12, 30, 20, 40], ['C5', 10, 16, 8, 5, 90]]], 'C3'], ['generated mix 57', [[2, 2, 8], 20, False, [['C0', 32, 20, 20, 30, 55], ['C1', 32, 20, 4, 20, 90], ['C2', 12, 12, 20, 30, 55]]], 'C1']]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
volume tie by cost	`A`	`B`	Failed
rotated fit	`S`	`S`	Passed
weight at limit	`S`	`S`	Passed
sioc	`SIOC`	`SIOC`	Passed
cheap but bulky	`SMALL`	`SMALL`	Passed
padding pushes to M	`M`	`M`	Passed
generated mix 5	`C0`	`C0`	Passed
generated mix 13	`C0`	`C0`	Passed

SHA-256 / d5d5b3bf850064c6da6fa4b33fdd770832bdd16ad8b32745bd8262c7a16c7eef

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

Stipulated fit rule with uniform dunnage; no void-fill or multi-item cartonization. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:52:09.483634+00:00.

Case digest / 2ba6a56e63ba625bccbb6dc1e14118640e8192b879c07bcf4578a9161a55de80