FA-94926 / Warehouse slotting and bin packing / Open access

Tote packing: smallest items loaded first · case 01

Small items fill totes first and bulky items each open a new tote, inflating tote count.

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

ROOT CAUSE

The packing sequence sorts by volume ascending rather than descending.

VERIFIED REPAIR

Sort items by volume descending, then weight descending, then id.

Unsuccessful approach: Sorting by weight alone ignores volume, the constraining dimension for most totes.

Case contract

items [[id, volume, kg, fragile]]. Sort by volume desc, kg desc, id. Place each in the first open tote (creation order) where volume and weight stay within limits (inclusive) and no fragile item shares a tote with an item over 10 kg (either direction). Items exceeding a tote alone go to oversize. Return [list of tote id lists, sorted oversize ids].

Why this case matters

Packing picked units into conveyor totes is bounded by volume, weight, and damage rules.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(items, tote_vol, tote_wt):
    order = sorted(items, key=lambda it: (it[1], it[2], it[0]))
    totes = []
    oversize = []
    for iid, vol, wt, fragile in order:
        if vol > tote_vol or wt > tote_wt:
            oversize.append(iid)
            continue
        placed = False
        for t in totes:
            if t['v'] + vol > tote_vol or t['w'] + wt > tote_wt:
                continue
            if fragile and t['heavy']:
                continue
            if wt > 10 and t['fragile']:
                continue
            t['ids'].append(iid)
            t['v'] += vol
            t['w'] += wt
            t['heavy'] = t['heavy'] or wt > 10
            t['fragile'] = t['fragile'] or fragile
            placed = True
            break
        if not placed:
            totes.append({'ids': [iid], 'v': vol, 'w': wt, 'heavy': wt > 10, 'fragile': fragile})
    return [[t['ids'] for t in totes], sorted(oversize)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['exact fill', [[['a', 30, 5, False], ['b', 20, 5, False]], 50, 20], [[['a', 'b']], []]], ['generated mix 1', [[['i0', 60, 10, False], ['i1', 25, 1, False], ['i2', 60, 3, False], ['i3', 5, 10, True], ['i4', 10, 10, True]], 60, 20], [[['i0'], ['i2'], ['i1', 'i4'], ['i3']], []]], ['fragile vs heavy', [[['h', 30, 12, False], ['f', 10, 1, True]], 50, 20], [[['h'], ['f']], []]], ['oversize weight', [[['x', 10, 30, False], ['y', 10, 1, False]], 50, 20], [[['y']], ['x']]], ['first fit not best fit', [[['a', 40, 1, False], ['b', 30, 1, False], ['c', 10, 1, False]], 50, 20], [[['a', 'c'], ['b']], []]], ['heavy after fragile', [[['f', 30, 1, True], ['h', 10, 12, False]], 50, 20], [[['f'], ['h']], []]], ['weight limit splits', [[['a', 10, 15, False], ['b', 10, 6, False]], 50, 20], [[['a'], ['b']], []]], ['generated mix 9', [[['i0', 60, 8, False], ['i1', 30, 10, False], ['i2', 50, 11, True], ['i3', 10, 15, True]], 50, 20], [[['i2'], ['i1'], ['i3']], ['i0']]]], [['generated mix 3', [[['i0', 50, 8, True], ['i1', 5, 3, False], ['i2', 10, 8, False]], 60, 25], [[['i0', 'i2'], ['i1']], []]], ['generated mix 7', [[['i0', 10, 3, False], ['i1', 50, 15, True], ['i2', 30, 8, False], ['i3', 50, 1, True], ['i4', 25, 1, False], ['i5', 20, 8, True]], 50, 20], [[['i1'], ['i3'], ['i2', 'i5'], ['i4', 'i0']], []]], ['oversize weight', [[['x', 10, 30, False], ['y', 10, 1, False]], 50, 20], [[['y']], ['x']]], ['first fit not best fit', [[['a', 40, 1, False], ['b', 30, 1, False], ['c', 10, 1, False]], 50, 20], [[['a', 'c'], ['b']], []]], ['fragile vs heavy', [[['h', 30, 12, False], ['f', 10, 1, True]], 50, 20], [[['h'], ['f']], []]], ['generated mix 11', [[['i0', 20, 3, False], ['i1', 60, 1, False]], 60, 25], [[['i1'], ['i0']], []]], ['generated mix 19', [[['i0', 30, 3, False], ['i1', 5, 11, True], ['i2', 50, 15, False], ['i3', 40, 11, False], ['i4', 60, 15, False], ['i5', 10, 15, False], ['i6', 25, 10, False], ['i7', 60, 8, True]], 50, 20], [[['i2'], ['i3'], ['i0', 'i5'], ['i6'], ['i1']], ['i4', 'i7']]], ['generated mix 27', [[['i0', 20, 10, False], ['i1', 25, 1, False], ['i2', 5, 11, True], ['i3', 20, 8, False], ['i4', 5, 10, False]], 60, 20], [[['i1', 'i0'], ['i3', 'i2'], ['i4']], []]]], [['generated mix 10', [[['i0', 5, 15, False], ['i1', 40, 11, True], ['i2', 25, 3, False], ['i3', 30, 1, False], ['i4', 20, 15, False], ['i5', 20, 10, False], ['i6', 30, 11, False]], 60, 20], [[['i1'], ['i6', 'i3'], ['i2', 'i4'], ['i5'], ['i0']], []]], ['generated mix 12', [[['i0', 10, 8, False], ['i1', 50, 11, True], ['i2', 5, 3, True], ['i3', 25, 3, True], ['i4', 60, 10, False]], 60, 20], [[['i4'], ['i1', 'i0'], ['i3', 'i2']], []]], ['exact fill', [[['a', 30, 5, False], ['b', 20, 5, False]], 50, 20], [[['a', 'b']], []]], ['heavy after fragile', [[['f', 30, 1, True], ['h', 10, 12, False]], 50, 20], [[['f'], ['h']], []]], ['weight limit splits', [[['a', 10, 15, False], ['b', 10, 6, False]], 50, 20], [[['a'], ['b']], []]], ['generated mix 22', [[['i0', 25, 1, False], ['i1', 30, 11, True], ['i2', 50, 1, False]], 50, 25], [[['i2'], ['i1'], ['i0']], []]], ['generated mix 30', [[['i0', 50, 15, True], ['i1', 30, 8, True], ['i2', 30, 10, False], ['i3', 5, 15, True], ['i4', 40, 10, True], ['i5', 40, 11, False], ['i6', 40, 1, True]], 50, 20], [[['i0'], ['i5'], ['i4'], ['i6'], ['i2'], ['i1'], ['i3']], []]], ['generated mix 38', [[['i0', 40, 10, False], ['i1', 60, 3, True], ['i2', 25, 10, True], ['i3', 10, 8, False], ['i4', 60, 11, True], ['i5', 40, 1, False]], 50, 20], [[['i0', 'i3'], ['i5'], ['i2']], ['i1', 'i4']]]], [['generated mix 17', [[['i0', 25, 1, True], ['i1', 60, 10, False], ['i2', 5, 1, True], ['i3', 10, 1, False], ['i4', 50, 8, False], ['i5', 40, 8, False]], 60, 25], [[['i1'], ['i4', 'i3'], ['i5', 'i2'], ['i0']], []]], ['oversize weight', [[['x', 10, 30, False], ['y', 10, 1, False]], 50, 20], [[['y']], ['x']]], ['first fit not best fit', [[['a', 40, 1, False], ['b', 30, 1, False], ['c', 10, 1, False]], 50, 20], [[['a', 'c'], ['b']], []]], ['fragile vs heavy', [[['h', 30, 12, False], ['f', 10, 1, True]], 50, 20], [[['h'], ['f']], []]], ['generated mix 32', [[['i0', 10, 8, False], ['i1', 50, 8, False]], 50, 20], [[['i1'], ['i0']], []]], ['generated mix 40', [[['i0', 10, 10, True], ['i1', 30, 1, False], ['i2', 30, 1, False], ['i3', 20, 10, False]], 60, 25], [[['i1', 'i2'], ['i3', 'i0']], []]], ['generated mix 48', [[['i0', 30, 3, False], ['i1', 5, 3, False], ['i2', 5, 10, False], ['i3', 60, 10, True]], 60, 20], [[['i3'], ['i0', 'i2', 'i1']], []]], ['generated mix 56', [[['i0', 10, 3, True], ['i1', 30, 8, False], ['i2', 5, 3, True], ['i3', 50, 15, True], ['i4', 40, 15, False], ['i5', 20, 11, True], ['i6', 60, 15, False]], 60, 20], [[['i6'], ['i3'], ['i4'], ['i1', 'i5'], ['i0', 'i2']], []]]], [['generated mix 24', [[['i0', 10, 3, True], ['i1', 50, 8, False], ['i2', 40, 10, True], ['i3', 10, 1, False]], 50, 20], [[['i1'], ['i2', 'i0'], ['i3']], []]], ['exact fill', [[['a', 30, 5, False], ['b', 20, 5, False]], 50, 20], [[['a', 'b']], []]], ['heavy after fragile', [[['f', 30, 1, True], ['h', 10, 12, False]], 50, 20], [[['f'], ['h']], []]], ['weight limit splits', [[['a', 10, 15, False], ['b', 10, 6, False]], 50, 20], [[['a'], ['b']], []]], ['generated mix 43', [[['i0', 5, 8, False], ['i1', 10, 3, False], ['i2', 40, 15, False], ['i3', 40, 15, False], ['i4', 20, 1, False], ['i5', 50, 11, False], ['i6', 20, 3, False]], 50, 20], [[['i5'], ['i2', 'i1'], ['i3'], ['i6', 'i4', 'i0']], []]], ['generated mix 51', [[['i0', 25, 11, False], ['i1', 40, 3, False], ['i2', 5, 15, True], ['i3', 60, 10, False], ['i4', 40, 15, False], ['i5', 40, 15, False], ['i6', 30, 15, False], ['i7', 50, 15, True]], 60, 20], [[['i3'], ['i7'], ['i4'], ['i5'], ['i1', 'i2'], ['i6'], ['i0']], []]], ['generated mix 59', [[['i0', 25, 3, False], ['i1', 50, 11, False]], 50, 25], [[['i1'], ['i0']], []]], ['generated mix 67', [[['i0', 40, 11, False], ['i1', 5, 15, False], ['i2', 10, 3, False], ['i3', 20, 11, False], ['i4', 25, 10, False], ['i5', 50, 1, False], ['i6', 10, 8, False]], 60, 25], [[['i5', 'i6'], ['i0', 'i3'], ['i4', 'i2'], ['i1']], []]]]]
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
exact fill	`[[['b', 'a']], []]`	`[[['a', 'b']], []]`	Failed
generated mix 1	`[[['i3', 'i4'], ['i1'], ['i2'], ['i0']], []]`	`[[['i0'], ['i2'], ['i1', 'i4'], ['i3']], []]`	Failed
fragile vs heavy	`[[['f'], ['h']], []]`	`[[['h'], ['f']], []]`	Failed
oversize weight	`[[['y']], ['x']]`	`[[['y']], ['x']]`	Passed
first fit not best fit	`[[['c', 'b'], ['a']], []]`	`[[['a', 'c'], ['b']], []]`	Failed
heavy after fragile	`[[['h'], ['f']], []]`	`[[['f'], ['h']], []]`	Failed
weight limit splits	`[[['b'], ['a']], []]`	`[[['a'], ['b']], []]`	Failed
generated mix 9	`[[['i3'], ['i1'], ['i2']], ['i0']]`	`[[['i2'], ['i1'], ['i3']], ['i0']]`	Failed

SHA-256 / 3632f3e40428a575f78f2ccf193ea4f6debcb00f3de056a52ea40afd82d604be

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(items, tote_vol, tote_wt):
    order = sorted(items, key=lambda it: (-it[2], it[0]))
    totes = []
    oversize = []
    for iid, vol, wt, fragile in order:
        if vol > tote_vol or wt > tote_wt:
            oversize.append(iid)
            continue
        placed = False
        for t in totes:
            if t['v'] + vol > tote_vol or t['w'] + wt > tote_wt:
                continue
            if fragile and t['heavy']:
                continue
            if wt > 10 and t['fragile']:
                continue
            t['ids'].append(iid)
            t['v'] += vol
            t['w'] += wt
            t['heavy'] = t['heavy'] or wt > 10
            t['fragile'] = t['fragile'] or fragile
            placed = True
            break
        if not placed:
            totes.append({'ids': [iid], 'v': vol, 'w': wt, 'heavy': wt > 10, 'fragile': fragile})
    return [[t['ids'] for t in totes], sorted(oversize)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['exact fill', [[['a', 30, 5, False], ['b', 20, 5, False]], 50, 20], [[['a', 'b']], []]], ['generated mix 1', [[['i0', 60, 10, False], ['i1', 25, 1, False], ['i2', 60, 3, False], ['i3', 5, 10, True], ['i4', 10, 10, True]], 60, 20], [[['i0'], ['i2'], ['i1', 'i4'], ['i3']], []]], ['fragile vs heavy', [[['h', 30, 12, False], ['f', 10, 1, True]], 50, 20], [[['h'], ['f']], []]], ['oversize weight', [[['x', 10, 30, False], ['y', 10, 1, False]], 50, 20], [[['y']], ['x']]], ['first fit not best fit', [[['a', 40, 1, False], ['b', 30, 1, False], ['c', 10, 1, False]], 50, 20], [[['a', 'c'], ['b']], []]], ['heavy after fragile', [[['f', 30, 1, True], ['h', 10, 12, False]], 50, 20], [[['f'], ['h']], []]], ['weight limit splits', [[['a', 10, 15, False], ['b', 10, 6, False]], 50, 20], [[['a'], ['b']], []]], ['generated mix 9', [[['i0', 60, 8, False], ['i1', 30, 10, False], ['i2', 50, 11, True], ['i3', 10, 15, True]], 50, 20], [[['i2'], ['i1'], ['i3']], ['i0']]]], [['generated mix 3', [[['i0', 50, 8, True], ['i1', 5, 3, False], ['i2', 10, 8, False]], 60, 25], [[['i0', 'i2'], ['i1']], []]], ['generated mix 7', [[['i0', 10, 3, False], ['i1', 50, 15, True], ['i2', 30, 8, False], ['i3', 50, 1, True], ['i4', 25, 1, False], ['i5', 20, 8, True]], 50, 20], [[['i1'], ['i3'], ['i2', 'i5'], ['i4', 'i0']], []]], ['oversize weight', [[['x', 10, 30, False], ['y', 10, 1, False]], 50, 20], [[['y']], ['x']]], ['first fit not best fit', [[['a', 40, 1, False], ['b', 30, 1, False], ['c', 10, 1, False]], 50, 20], [[['a', 'c'], ['b']], []]], ['fragile vs heavy', [[['h', 30, 12, False], ['f', 10, 1, True]], 50, 20], [[['h'], ['f']], []]], ['generated mix 11', [[['i0', 20, 3, False], ['i1', 60, 1, False]], 60, 25], [[['i1'], ['i0']], []]], ['generated mix 19', [[['i0', 30, 3, False], ['i1', 5, 11, True], ['i2', 50, 15, False], ['i3', 40, 11, False], ['i4', 60, 15, False], ['i5', 10, 15, False], ['i6', 25, 10, False], ['i7', 60, 8, True]], 50, 20], [[['i2'], ['i3'], ['i0', 'i5'], ['i6'], ['i1']], ['i4', 'i7']]], ['generated mix 27', [[['i0', 20, 10, False], ['i1', 25, 1, False], ['i2', 5, 11, True], ['i3', 20, 8, False], ['i4', 5, 10, False]], 60, 20], [[['i1', 'i0'], ['i3', 'i2'], ['i4']], []]]], [['generated mix 10', [[['i0', 5, 15, False], ['i1', 40, 11, True], ['i2', 25, 3, False], ['i3', 30, 1, False], ['i4', 20, 15, False], ['i5', 20, 10, False], ['i6', 30, 11, False]], 60, 20], [[['i1'], ['i6', 'i3'], ['i2', 'i4'], ['i5'], ['i0']], []]], ['generated mix 12', [[['i0', 10, 8, False], ['i1', 50, 11, True], ['i2', 5, 3, True], ['i3', 25, 3, True], ['i4', 60, 10, False]], 60, 20], [[['i4'], ['i1', 'i0'], ['i3', 'i2']], []]], ['exact fill', [[['a', 30, 5, False], ['b', 20, 5, False]], 50, 20], [[['a', 'b']], []]], ['heavy after fragile', [[['f', 30, 1, True], ['h', 10, 12, False]], 50, 20], [[['f'], ['h']], []]], ['weight limit splits', [[['a', 10, 15, False], ['b', 10, 6, False]], 50, 20], [[['a'], ['b']], []]], ['generated mix 22', [[['i0', 25, 1, False], ['i1', 30, 11, True], ['i2', 50, 1, False]], 50, 25], [[['i2'], ['i1'], ['i0']], []]], ['generated mix 30', [[['i0', 50, 15, True], ['i1', 30, 8, True], ['i2', 30, 10, False], ['i3', 5, 15, True], ['i4', 40, 10, True], ['i5', 40, 11, False], ['i6', 40, 1, True]], 50, 20], [[['i0'], ['i5'], ['i4'], ['i6'], ['i2'], ['i1'], ['i3']], []]], ['generated mix 38', [[['i0', 40, 10, False], ['i1', 60, 3, True], ['i2', 25, 10, True], ['i3', 10, 8, False], ['i4', 60, 11, True], ['i5', 40, 1, False]], 50, 20], [[['i0', 'i3'], ['i5'], ['i2']], ['i1', 'i4']]]], [['generated mix 17', [[['i0', 25, 1, True], ['i1', 60, 10, False], ['i2', 5, 1, True], ['i3', 10, 1, False], ['i4', 50, 8, False], ['i5', 40, 8, False]], 60, 25], [[['i1'], ['i4', 'i3'], ['i5', 'i2'], ['i0']], []]], ['oversize weight', [[['x', 10, 30, False], ['y', 10, 1, False]], 50, 20], [[['y']], ['x']]], ['first fit not best fit', [[['a', 40, 1, False], ['b', 30, 1, False], ['c', 10, 1, False]], 50, 20], [[['a', 'c'], ['b']], []]], ['fragile vs heavy', [[['h', 30, 12, False], ['f', 10, 1, True]], 50, 20], [[['h'], ['f']], []]], ['generated mix 32', [[['i0', 10, 8, False], ['i1', 50, 8, False]], 50, 20], [[['i1'], ['i0']], []]], ['generated mix 40', [[['i0', 10, 10, True], ['i1', 30, 1, False], ['i2', 30, 1, False], ['i3', 20, 10, False]], 60, 25], [[['i1', 'i2'], ['i3', 'i0']], []]], ['generated mix 48', [[['i0', 30, 3, False], ['i1', 5, 3, False], ['i2', 5, 10, False], ['i3', 60, 10, True]], 60, 20], [[['i3'], ['i0', 'i2', 'i1']], []]], ['generated mix 56', [[['i0', 10, 3, True], ['i1', 30, 8, False], ['i2', 5, 3, True], ['i3', 50, 15, True], ['i4', 40, 15, False], ['i5', 20, 11, True], ['i6', 60, 15, False]], 60, 20], [[['i6'], ['i3'], ['i4'], ['i1', 'i5'], ['i0', 'i2']], []]]], [['generated mix 24', [[['i0', 10, 3, True], ['i1', 50, 8, False], ['i2', 40, 10, True], ['i3', 10, 1, False]], 50, 20], [[['i1'], ['i2', 'i0'], ['i3']], []]], ['exact fill', [[['a', 30, 5, False], ['b', 20, 5, False]], 50, 20], [[['a', 'b']], []]], ['heavy after fragile', [[['f', 30, 1, True], ['h', 10, 12, False]], 50, 20], [[['f'], ['h']], []]], ['weight limit splits', [[['a', 10, 15, False], ['b', 10, 6, False]], 50, 20], [[['a'], ['b']], []]], ['generated mix 43', [[['i0', 5, 8, False], ['i1', 10, 3, False], ['i2', 40, 15, False], ['i3', 40, 15, False], ['i4', 20, 1, False], ['i5', 50, 11, False], ['i6', 20, 3, False]], 50, 20], [[['i5'], ['i2', 'i1'], ['i3'], ['i6', 'i4', 'i0']], []]], ['generated mix 51', [[['i0', 25, 11, False], ['i1', 40, 3, False], ['i2', 5, 15, True], ['i3', 60, 10, False], ['i4', 40, 15, False], ['i5', 40, 15, False], ['i6', 30, 15, False], ['i7', 50, 15, True]], 60, 20], [[['i3'], ['i7'], ['i4'], ['i5'], ['i1', 'i2'], ['i6'], ['i0']], []]], ['generated mix 59', [[['i0', 25, 3, False], ['i1', 50, 11, False]], 50, 25], [[['i1'], ['i0']], []]], ['generated mix 67', [[['i0', 40, 11, False], ['i1', 5, 15, False], ['i2', 10, 3, False], ['i3', 20, 11, False], ['i4', 25, 10, False], ['i5', 50, 1, False], ['i6', 10, 8, False]], 60, 25], [[['i5', 'i6'], ['i0', 'i3'], ['i4', 'i2'], ['i1']], []]]]]
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
exact fill	`[[['a', 'b']], []]`	`[[['a', 'b']], []]`	Passed
generated mix 1	`[[['i0'], ['i3', 'i4'], ['i2'], ['i1']], []]`	`[[['i0'], ['i2'], ['i1', 'i4'], ['i3']], []]`	Failed
fragile vs heavy	`[[['h'], ['f']], []]`	`[[['h'], ['f']], []]`	Passed
oversize weight	`[[['y']], ['x']]`	`[[['y']], ['x']]`	Passed
first fit not best fit	`[[['a', 'c'], ['b']], []]`	`[[['a', 'c'], ['b']], []]`	Passed
heavy after fragile	`[[['h'], ['f']], []]`	`[[['f'], ['h']], []]`	Failed
weight limit splits	`[[['a'], ['b']], []]`	`[[['a'], ['b']], []]`	Passed
generated mix 9	`[[['i3'], ['i2'], ['i1']], ['i0']]`	`[[['i2'], ['i1'], ['i3']], ['i0']]`	Failed

SHA-256 / 40a3f3a7cef721e663b3d8043e7dbf2eb6169ffab9a98bd79a9a83017f704769

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(items, tote_vol, tote_wt):
    order = sorted(items, key=lambda it: (-it[1], -it[2], it[0]))
    totes = []
    oversize = []
    for iid, vol, wt, fragile in order:
        if vol > tote_vol or wt > tote_wt:
            oversize.append(iid)
            continue
        placed = False
        for t in totes:
            if t['v'] + vol > tote_vol or t['w'] + wt > tote_wt:
                continue
            if fragile and t['heavy']:
                continue
            if wt > 10 and t['fragile']:
                continue
            t['ids'].append(iid)
            t['v'] += vol
            t['w'] += wt
            t['heavy'] = t['heavy'] or wt > 10
            t['fragile'] = t['fragile'] or fragile
            placed = True
            break
        if not placed:
            totes.append({'ids': [iid], 'v': vol, 'w': wt, 'heavy': wt > 10, 'fragile': fragile})
    return [[t['ids'] for t in totes], sorted(oversize)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['exact fill', [[['a', 30, 5, False], ['b', 20, 5, False]], 50, 20], [[['a', 'b']], []]], ['generated mix 1', [[['i0', 60, 10, False], ['i1', 25, 1, False], ['i2', 60, 3, False], ['i3', 5, 10, True], ['i4', 10, 10, True]], 60, 20], [[['i0'], ['i2'], ['i1', 'i4'], ['i3']], []]], ['fragile vs heavy', [[['h', 30, 12, False], ['f', 10, 1, True]], 50, 20], [[['h'], ['f']], []]], ['oversize weight', [[['x', 10, 30, False], ['y', 10, 1, False]], 50, 20], [[['y']], ['x']]], ['first fit not best fit', [[['a', 40, 1, False], ['b', 30, 1, False], ['c', 10, 1, False]], 50, 20], [[['a', 'c'], ['b']], []]], ['heavy after fragile', [[['f', 30, 1, True], ['h', 10, 12, False]], 50, 20], [[['f'], ['h']], []]], ['weight limit splits', [[['a', 10, 15, False], ['b', 10, 6, False]], 50, 20], [[['a'], ['b']], []]], ['generated mix 9', [[['i0', 60, 8, False], ['i1', 30, 10, False], ['i2', 50, 11, True], ['i3', 10, 15, True]], 50, 20], [[['i2'], ['i1'], ['i3']], ['i0']]]], [['generated mix 3', [[['i0', 50, 8, True], ['i1', 5, 3, False], ['i2', 10, 8, False]], 60, 25], [[['i0', 'i2'], ['i1']], []]], ['generated mix 7', [[['i0', 10, 3, False], ['i1', 50, 15, True], ['i2', 30, 8, False], ['i3', 50, 1, True], ['i4', 25, 1, False], ['i5', 20, 8, True]], 50, 20], [[['i1'], ['i3'], ['i2', 'i5'], ['i4', 'i0']], []]], ['oversize weight', [[['x', 10, 30, False], ['y', 10, 1, False]], 50, 20], [[['y']], ['x']]], ['first fit not best fit', [[['a', 40, 1, False], ['b', 30, 1, False], ['c', 10, 1, False]], 50, 20], [[['a', 'c'], ['b']], []]], ['fragile vs heavy', [[['h', 30, 12, False], ['f', 10, 1, True]], 50, 20], [[['h'], ['f']], []]], ['generated mix 11', [[['i0', 20, 3, False], ['i1', 60, 1, False]], 60, 25], [[['i1'], ['i0']], []]], ['generated mix 19', [[['i0', 30, 3, False], ['i1', 5, 11, True], ['i2', 50, 15, False], ['i3', 40, 11, False], ['i4', 60, 15, False], ['i5', 10, 15, False], ['i6', 25, 10, False], ['i7', 60, 8, True]], 50, 20], [[['i2'], ['i3'], ['i0', 'i5'], ['i6'], ['i1']], ['i4', 'i7']]], ['generated mix 27', [[['i0', 20, 10, False], ['i1', 25, 1, False], ['i2', 5, 11, True], ['i3', 20, 8, False], ['i4', 5, 10, False]], 60, 20], [[['i1', 'i0'], ['i3', 'i2'], ['i4']], []]]], [['generated mix 10', [[['i0', 5, 15, False], ['i1', 40, 11, True], ['i2', 25, 3, False], ['i3', 30, 1, False], ['i4', 20, 15, False], ['i5', 20, 10, False], ['i6', 30, 11, False]], 60, 20], [[['i1'], ['i6', 'i3'], ['i2', 'i4'], ['i5'], ['i0']], []]], ['generated mix 12', [[['i0', 10, 8, False], ['i1', 50, 11, True], ['i2', 5, 3, True], ['i3', 25, 3, True], ['i4', 60, 10, False]], 60, 20], [[['i4'], ['i1', 'i0'], ['i3', 'i2']], []]], ['exact fill', [[['a', 30, 5, False], ['b', 20, 5, False]], 50, 20], [[['a', 'b']], []]], ['heavy after fragile', [[['f', 30, 1, True], ['h', 10, 12, False]], 50, 20], [[['f'], ['h']], []]], ['weight limit splits', [[['a', 10, 15, False], ['b', 10, 6, False]], 50, 20], [[['a'], ['b']], []]], ['generated mix 22', [[['i0', 25, 1, False], ['i1', 30, 11, True], ['i2', 50, 1, False]], 50, 25], [[['i2'], ['i1'], ['i0']], []]], ['generated mix 30', [[['i0', 50, 15, True], ['i1', 30, 8, True], ['i2', 30, 10, False], ['i3', 5, 15, True], ['i4', 40, 10, True], ['i5', 40, 11, False], ['i6', 40, 1, True]], 50, 20], [[['i0'], ['i5'], ['i4'], ['i6'], ['i2'], ['i1'], ['i3']], []]], ['generated mix 38', [[['i0', 40, 10, False], ['i1', 60, 3, True], ['i2', 25, 10, True], ['i3', 10, 8, False], ['i4', 60, 11, True], ['i5', 40, 1, False]], 50, 20], [[['i0', 'i3'], ['i5'], ['i2']], ['i1', 'i4']]]], [['generated mix 17', [[['i0', 25, 1, True], ['i1', 60, 10, False], ['i2', 5, 1, True], ['i3', 10, 1, False], ['i4', 50, 8, False], ['i5', 40, 8, False]], 60, 25], [[['i1'], ['i4', 'i3'], ['i5', 'i2'], ['i0']], []]], ['oversize weight', [[['x', 10, 30, False], ['y', 10, 1, False]], 50, 20], [[['y']], ['x']]], ['first fit not best fit', [[['a', 40, 1, False], ['b', 30, 1, False], ['c', 10, 1, False]], 50, 20], [[['a', 'c'], ['b']], []]], ['fragile vs heavy', [[['h', 30, 12, False], ['f', 10, 1, True]], 50, 20], [[['h'], ['f']], []]], ['generated mix 32', [[['i0', 10, 8, False], ['i1', 50, 8, False]], 50, 20], [[['i1'], ['i0']], []]], ['generated mix 40', [[['i0', 10, 10, True], ['i1', 30, 1, False], ['i2', 30, 1, False], ['i3', 20, 10, False]], 60, 25], [[['i1', 'i2'], ['i3', 'i0']], []]], ['generated mix 48', [[['i0', 30, 3, False], ['i1', 5, 3, False], ['i2', 5, 10, False], ['i3', 60, 10, True]], 60, 20], [[['i3'], ['i0', 'i2', 'i1']], []]], ['generated mix 56', [[['i0', 10, 3, True], ['i1', 30, 8, False], ['i2', 5, 3, True], ['i3', 50, 15, True], ['i4', 40, 15, False], ['i5', 20, 11, True], ['i6', 60, 15, False]], 60, 20], [[['i6'], ['i3'], ['i4'], ['i1', 'i5'], ['i0', 'i2']], []]]], [['generated mix 24', [[['i0', 10, 3, True], ['i1', 50, 8, False], ['i2', 40, 10, True], ['i3', 10, 1, False]], 50, 20], [[['i1'], ['i2', 'i0'], ['i3']], []]], ['exact fill', [[['a', 30, 5, False], ['b', 20, 5, False]], 50, 20], [[['a', 'b']], []]], ['heavy after fragile', [[['f', 30, 1, True], ['h', 10, 12, False]], 50, 20], [[['f'], ['h']], []]], ['weight limit splits', [[['a', 10, 15, False], ['b', 10, 6, False]], 50, 20], [[['a'], ['b']], []]], ['generated mix 43', [[['i0', 5, 8, False], ['i1', 10, 3, False], ['i2', 40, 15, False], ['i3', 40, 15, False], ['i4', 20, 1, False], ['i5', 50, 11, False], ['i6', 20, 3, False]], 50, 20], [[['i5'], ['i2', 'i1'], ['i3'], ['i6', 'i4', 'i0']], []]], ['generated mix 51', [[['i0', 25, 11, False], ['i1', 40, 3, False], ['i2', 5, 15, True], ['i3', 60, 10, False], ['i4', 40, 15, False], ['i5', 40, 15, False], ['i6', 30, 15, False], ['i7', 50, 15, True]], 60, 20], [[['i3'], ['i7'], ['i4'], ['i5'], ['i1', 'i2'], ['i6'], ['i0']], []]], ['generated mix 59', [[['i0', 25, 3, False], ['i1', 50, 11, False]], 50, 25], [[['i1'], ['i0']], []]], ['generated mix 67', [[['i0', 40, 11, False], ['i1', 5, 15, False], ['i2', 10, 3, False], ['i3', 20, 11, False], ['i4', 25, 10, False], ['i5', 50, 1, False], ['i6', 10, 8, False]], 60, 25], [[['i5', 'i6'], ['i0', 'i3'], ['i4', 'i2'], ['i1']], []]]]]
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
exact fill	`[[['a', 'b']], []]`	`[[['a', 'b']], []]`	Passed
generated mix 1	`[[['i0'], ['i2'], ['i1', 'i4'], ['i3']], []]`	`[[['i0'], ['i2'], ['i1', 'i4'], ['i3']], []]`	Passed
fragile vs heavy	`[[['h'], ['f']], []]`	`[[['h'], ['f']], []]`	Passed
oversize weight	`[[['y']], ['x']]`	`[[['y']], ['x']]`	Passed
first fit not best fit	`[[['a', 'c'], ['b']], []]`	`[[['a', 'c'], ['b']], []]`	Passed
heavy after fragile	`[[['f'], ['h']], []]`	`[[['f'], ['h']], []]`	Passed
weight limit splits	`[[['a'], ['b']], []]`	`[[['a'], ['b']], []]`	Passed
generated mix 9	`[[['i2'], ['i1'], ['i3']], ['i0']]`	`[[['i2'], ['i1'], ['i3']], ['i0']]`	Passed

SHA-256 / 351b396de1fa45ebcf9463dd9e386e20b3caed11d72b2de434a3aabdeef74b6a

Verification & scope

Stipulated first-fit rule; 10 kg heavy threshold is a toy contract constant. 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 2026-09-29T14:52:08.962045+00:00.

Case digest / fd930cb35f63815b09093eff8c3a748d984dcbbac980a16f2823f5980de77b99