FA-94961 / Warehouse slotting and bin packing / Open access

Carton selection: dunnage on one side only · case 01

Cartons are chosen with no room for dunnage on one face, so items arrive crushed.

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

ROOT CAUSE

Only one unit of dunnage is added per dimension instead of one per side.

THE FAILURE

Only one unit of dunnage is added per dimension instead of one per side.

Unsuccessful approach: Padding only the height leaves no dunnage around the footprint.

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 + 1 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 = [[['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 14', [[6, 8, 5], 9.5, False, [['C0', 6, 6, 20, 10, 55], ['C1', 16, 6, 6, 10, 40], ['C2', 12, 20, 4, 30, 40], ['C3', 10, 16, 6, 30, 70]]], 'NO_FIT'], ['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 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'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['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 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']], [['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 28', [[12, 7, 14], 10.5, False, [['C0', 10, 12, 30, 20, 90], ['C1', 32, 6, 20, 30, 55], ['C2', 32, 6, 12, 10, 90], ['C3', 6, 20, 6, 10, 70]]], 'NO_FIT'], ['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'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['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 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']], [['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 51', [[12, 13, 13], 20, False, [['C0', 20, 20, 30, 30, 55], ['C1', 16, 16, 8, 5, 70], ['C2', 20, 16, 12, 30, 55], ['C3', 24, 12, 4, 30, 70], ['C4', 32, 6, 30, 5, 55], ['C5', 16, 12, 6, 30, 40]]], 'C0'], ['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 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'], ['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']], [['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 66', [[9, 9, 9], 5, False, [['C0', 32, 6, 30, 10, 90], ['C1', 12, 12, 8, 30, 40], ['C2', 24, 8, 6, 5, 90], ['C3', 10, 12, 12, 30, 40], ['C4', 32, 12, 4, 10, 90]]], 'NO_FIT'], ['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'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['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']], [['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 14', [[6, 8, 5], 9.5, False, [['C0', 6, 6, 20, 10, 55], ['C1', 16, 6, 6, 10, 40], ['C2', 12, 20, 4, 30, 40], ['C3', 10, 16, 6, 30, 70]]], 'NO_FIT'], ['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'], ['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 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'], ['generated mix 42', [[9, 13, 6], 4.5, False, [['C0', 6, 12, 12, 5, 90], ['C1', 24, 6, 6, 5, 70]]], 'NO_FIT'], ['generated mix 50', [[4, 4, 13], 20, False, [['C0', 12, 8, 12, 10, 70], ['C1', 20, 20, 6, 30, 90], ['C2', 32, 12, 12, 5, 70], ['C3', 32, 8, 30, 5, 70], ['C4', 24, 16, 20, 20, 90], ['C5', 12, 12, 6, 5, 40]]], '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
padding pushes to M	`S`	`M`	Failed
generated mix 14	`C3`	`NO_FIT`	Failed
rotated fit	`S`	`S`	Passed
weight over limit	`M`	`M`	Passed
no fit	`NO_FIT`	`NO_FIT`	Passed
cheap but bulky	`SMALL`	`SMALL`	Passed
weight at limit	`S`	`S`	Passed
generated mix 5	`C0`	`C0`	Passed

SHA-256 / 649ef50177313e0ceb4b4442d9246943ebcd08536229c06c0cbfe69cfb8f6ac3

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(dims[:2]) + [dims[2] + 2]
    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 = [[['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 14', [[6, 8, 5], 9.5, False, [['C0', 6, 6, 20, 10, 55], ['C1', 16, 6, 6, 10, 40], ['C2', 12, 20, 4, 30, 40], ['C3', 10, 16, 6, 30, 70]]], 'NO_FIT'], ['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 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'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['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 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']], [['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 28', [[12, 7, 14], 10.5, False, [['C0', 10, 12, 30, 20, 90], ['C1', 32, 6, 20, 30, 55], ['C2', 32, 6, 12, 10, 90], ['C3', 6, 20, 6, 10, 70]]], 'NO_FIT'], ['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'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['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 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']], [['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 51', [[12, 13, 13], 20, False, [['C0', 20, 20, 30, 30, 55], ['C1', 16, 16, 8, 5, 70], ['C2', 20, 16, 12, 30, 55], ['C3', 24, 12, 4, 30, 70], ['C4', 32, 6, 30, 5, 55], ['C5', 16, 12, 6, 30, 40]]], 'C0'], ['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 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'], ['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']], [['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 66', [[9, 9, 9], 5, False, [['C0', 32, 6, 30, 10, 90], ['C1', 12, 12, 8, 30, 40], ['C2', 24, 8, 6, 5, 90], ['C3', 10, 12, 12, 30, 40], ['C4', 32, 12, 4, 10, 90]]], 'NO_FIT'], ['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'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['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']], [['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 14', [[6, 8, 5], 9.5, False, [['C0', 6, 6, 20, 10, 55], ['C1', 16, 6, 6, 10, 40], ['C2', 12, 20, 4, 30, 40], ['C3', 10, 16, 6, 30, 70]]], 'NO_FIT'], ['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'], ['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 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'], ['generated mix 42', [[9, 13, 6], 4.5, False, [['C0', 6, 12, 12, 5, 90], ['C1', 24, 6, 6, 5, 70]]], 'NO_FIT'], ['generated mix 50', [[4, 4, 13], 20, False, [['C0', 12, 8, 12, 10, 70], ['C1', 20, 20, 6, 30, 90], ['C2', 32, 12, 12, 5, 70], ['C3', 32, 8, 30, 5, 70], ['C4', 24, 16, 20, 20, 90], ['C5', 12, 12, 6, 5, 40]]], '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
padding pushes to M	`M`	`M`	Passed
generated mix 14	`C3`	`NO_FIT`	Failed
rotated fit	`S`	`S`	Passed
weight over limit	`M`	`M`	Passed
no fit	`NO_FIT`	`NO_FIT`	Passed
cheap but bulky	`SMALL`	`SMALL`	Passed
weight at limit	`S`	`S`	Passed
generated mix 5	`C0`	`C0`	Passed

SHA-256 / 9db89122e254fa24554b0328fb297be0ea003290f7405325e1655173289ceff9

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:52:09.273945+00:00.

Case digest / 912f197bd24e20050678cfefa9f406870abbf33a925c6526b556b02070dd761d