FA-94986 / Warehouse slotting and bin packing / Open access

Pallet build: rotated layer pattern never tried · case 01

Pallets are built with fewer cases per layer than a 90-degree rotated pattern allows.

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

ROOT CAUSE

Cases per layer only evaluates the case footprint in its listed orientation.

VERIFIED REPAIR

Take the better of the two upright orientations of the case footprint.

Unsuccessful approach: Area division ignores that cases are rigid rectangles and promises layers that cannot be built.

Case contract

case [l, w, h, kg], pallet [L, W]; cases stay upright but may rotate 90 degrees; all layers share one orientation. Pallet base adds 15 height and 25 kg tare. Cases per pallet are bounded by whole layers within max_h and by max_kg (a partial top layer is allowed). Return [per_layer, layers used, cases, height, weight].

Why this case matters

Pallet build limits govern reserve storage heights and floor loading.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(case, pallet, max_h, max_kg):
    l, w, h, kg = case
    L, W = pallet
    per_layer = (L // l) * (W // w)
    if per_layer == 0:
        return [0, 0, 0, 15, 25]
    layers = (max_h - 15) // h
    by_weight = (max_kg - 25) // kg
    cases = min(per_layer * layers, by_weight)
    if cases <= 0:
        return [per_layer, 0, 0, 15, 25]
    full = -(-cases // per_layer)
    return [per_layer, full, cases, 15 + full * h, 25 + cases * kg]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['rotation wins', [[50, 30, 20, 5], [120, 100], 115, 1000], [8, 5, 40, 115, 225]], ['weight bound partial layer', [[40, 30, 25, 20], [120, 100], 190, 425], [9, 3, 20, 90, 425]], ['listed orientation wins', [[30, 20, 20, 5], [120, 100], 115, 1000], [20, 5, 100, 115, 525]], ['too big', [[130, 30, 25, 2], [120, 100], 190, 425], [0, 0, 0, 15, 25]], ['square', [[25, 25, 30, 5], [120, 80], 165, 900], [12, 5, 60, 165, 325]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['generated mix 8', [[40, 15, 30, 8], [120, 80], 100, 800], [16, 2, 32, 75, 281]]], [['generated mix 12', [[40, 15, 30, 12], [120, 80], 140, 1200], [16, 4, 64, 135, 793]], ['generated mix 10', [[30, 15, 20, 5], [120, 80], 190, 1025], [20, 8, 160, 175, 825]], ['weight bound partial layer', [[40, 30, 25, 20], [120, 100], 190, 425], [9, 3, 20, 90, 425]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['listed orientation wins', [[30, 20, 20, 5], [120, 100], 115, 1000], [20, 5, 100, 115, 525]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['generated mix 9', [[50, 20, 25, 12], [120, 100], 115, 1200], [12, 4, 48, 115, 601]], ['generated mix 19', [[30, 20, 20, 5], [120, 100], 190, 800], [20, 8, 155, 175, 800]]], [['generated mix 33', [[40, 30, 10, 20], [120, 80], 165, 800], [8, 5, 38, 65, 785]], ['generated mix 16', [[25, 20, 30, 5], [120, 80], 140, 800], [18, 4, 72, 135, 385]], ['square', [[25, 25, 30, 5], [120, 80], 165, 900], [12, 5, 60, 165, 325]], ['rotation wins', [[50, 30, 20, 5], [120, 100], 115, 1000], [8, 5, 40, 115, 225]], ['weight bound partial layer', [[40, 30, 25, 20], [120, 100], 190, 425], [9, 3, 20, 90, 425]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['generated mix 21', [[25, 20, 30, 2], [120, 80], 140, 300], [18, 4, 72, 135, 169]], ['generated mix 29', [[50, 30, 30, 20], [120, 100], 190, 300], [8, 2, 13, 75, 285]]], [['generated mix 43', [[25, 20, 20, 12], [120, 100], 140, 1200], [24, 5, 97, 115, 1189]], ['generated mix 25', [[25, 25, 25, 20], [120, 80], 190, 1200], [12, 5, 58, 140, 1185]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['too big', [[130, 30, 25, 2], [120, 100], 190, 425], [0, 0, 0, 15, 25]], ['square', [[25, 25, 30, 5], [120, 80], 165, 900], [12, 5, 60, 165, 325]], ['rotation wins', [[50, 30, 20, 5], [120, 100], 115, 1000], [8, 5, 40, 115, 225]], ['generated mix 32', [[40, 30, 10, 8], [120, 100], 165, 300], [9, 4, 34, 55, 297]], ['generated mix 40', [[20, 15, 30, 20], [120, 80], 190, 500], [32, 1, 23, 45, 485]]], [['generated mix 55', [[50, 30, 30, 5], [120, 100], 190, 1200], [8, 5, 40, 165, 225]], ['generated mix 41', [[25, 25, 10, 20], [120, 100], 165, 1200], [16, 4, 58, 55, 1185]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['listed orientation wins', [[30, 20, 20, 5], [120, 100], 115, 1000], [20, 5, 100, 115, 525]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['too big', [[130, 30, 25, 2], [120, 100], 190, 425], [0, 0, 0, 15, 25]], ['generated mix 43', [[25, 20, 20, 12], [120, 100], 140, 1200], [24, 5, 97, 115, 1189]], ['generated mix 51', [[25, 15, 10, 8], [120, 80], 165, 500], [24, 3, 59, 45, 497]]]]
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
rotation wins	`[6, 5, 30, 115, 175]`	`[8, 5, 40, 115, 225]`	Failed
weight bound partial layer	`[9, 3, 20, 90, 425]`	`[9, 3, 20, 90, 425]`	Passed
listed orientation wins	`[20, 5, 100, 115, 525]`	`[20, 5, 100, 115, 525]`	Passed
too big	`[0, 0, 0, 15, 25]`	`[0, 0, 0, 15, 25]`	Passed
square	`[12, 5, 60, 165, 325]`	`[12, 5, 60, 165, 325]`	Passed
height exact	`[9, 5, 45, 140, 115]`	`[9, 5, 45, 140, 115]`	Passed
too heavy for one	`[9, 0, 0, 15, 25]`	`[9, 0, 0, 15, 25]`	Passed
generated mix 8	`[15, 2, 30, 75, 265]`	`[16, 2, 32, 75, 281]`	Failed

SHA-256 / 78f5767aeaaa59a9ae3fb5c625721317b8c84758a3e14c4a700d294fbf037836

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(case, pallet, max_h, max_kg):
    l, w, h, kg = case
    L, W = pallet
    per_layer = (L * W) // (l * w)
    if per_layer == 0:
        return [0, 0, 0, 15, 25]
    layers = (max_h - 15) // h
    by_weight = (max_kg - 25) // kg
    cases = min(per_layer * layers, by_weight)
    if cases <= 0:
        return [per_layer, 0, 0, 15, 25]
    full = -(-cases // per_layer)
    return [per_layer, full, cases, 15 + full * h, 25 + cases * kg]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['rotation wins', [[50, 30, 20, 5], [120, 100], 115, 1000], [8, 5, 40, 115, 225]], ['weight bound partial layer', [[40, 30, 25, 20], [120, 100], 190, 425], [9, 3, 20, 90, 425]], ['listed orientation wins', [[30, 20, 20, 5], [120, 100], 115, 1000], [20, 5, 100, 115, 525]], ['too big', [[130, 30, 25, 2], [120, 100], 190, 425], [0, 0, 0, 15, 25]], ['square', [[25, 25, 30, 5], [120, 80], 165, 900], [12, 5, 60, 165, 325]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['generated mix 8', [[40, 15, 30, 8], [120, 80], 100, 800], [16, 2, 32, 75, 281]]], [['generated mix 12', [[40, 15, 30, 12], [120, 80], 140, 1200], [16, 4, 64, 135, 793]], ['generated mix 10', [[30, 15, 20, 5], [120, 80], 190, 1025], [20, 8, 160, 175, 825]], ['weight bound partial layer', [[40, 30, 25, 20], [120, 100], 190, 425], [9, 3, 20, 90, 425]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['listed orientation wins', [[30, 20, 20, 5], [120, 100], 115, 1000], [20, 5, 100, 115, 525]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['generated mix 9', [[50, 20, 25, 12], [120, 100], 115, 1200], [12, 4, 48, 115, 601]], ['generated mix 19', [[30, 20, 20, 5], [120, 100], 190, 800], [20, 8, 155, 175, 800]]], [['generated mix 33', [[40, 30, 10, 20], [120, 80], 165, 800], [8, 5, 38, 65, 785]], ['generated mix 16', [[25, 20, 30, 5], [120, 80], 140, 800], [18, 4, 72, 135, 385]], ['square', [[25, 25, 30, 5], [120, 80], 165, 900], [12, 5, 60, 165, 325]], ['rotation wins', [[50, 30, 20, 5], [120, 100], 115, 1000], [8, 5, 40, 115, 225]], ['weight bound partial layer', [[40, 30, 25, 20], [120, 100], 190, 425], [9, 3, 20, 90, 425]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['generated mix 21', [[25, 20, 30, 2], [120, 80], 140, 300], [18, 4, 72, 135, 169]], ['generated mix 29', [[50, 30, 30, 20], [120, 100], 190, 300], [8, 2, 13, 75, 285]]], [['generated mix 43', [[25, 20, 20, 12], [120, 100], 140, 1200], [24, 5, 97, 115, 1189]], ['generated mix 25', [[25, 25, 25, 20], [120, 80], 190, 1200], [12, 5, 58, 140, 1185]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['too big', [[130, 30, 25, 2], [120, 100], 190, 425], [0, 0, 0, 15, 25]], ['square', [[25, 25, 30, 5], [120, 80], 165, 900], [12, 5, 60, 165, 325]], ['rotation wins', [[50, 30, 20, 5], [120, 100], 115, 1000], [8, 5, 40, 115, 225]], ['generated mix 32', [[40, 30, 10, 8], [120, 100], 165, 300], [9, 4, 34, 55, 297]], ['generated mix 40', [[20, 15, 30, 20], [120, 80], 190, 500], [32, 1, 23, 45, 485]]], [['generated mix 55', [[50, 30, 30, 5], [120, 100], 190, 1200], [8, 5, 40, 165, 225]], ['generated mix 41', [[25, 25, 10, 20], [120, 100], 165, 1200], [16, 4, 58, 55, 1185]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['listed orientation wins', [[30, 20, 20, 5], [120, 100], 115, 1000], [20, 5, 100, 115, 525]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['too big', [[130, 30, 25, 2], [120, 100], 190, 425], [0, 0, 0, 15, 25]], ['generated mix 43', [[25, 20, 20, 12], [120, 100], 140, 1200], [24, 5, 97, 115, 1189]], ['generated mix 51', [[25, 15, 10, 8], [120, 80], 165, 500], [24, 3, 59, 45, 497]]]]
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
rotation wins	`[8, 5, 40, 115, 225]`	`[8, 5, 40, 115, 225]`	Passed
weight bound partial layer	`[10, 2, 20, 65, 425]`	`[9, 3, 20, 90, 425]`	Failed
listed orientation wins	`[20, 5, 100, 115, 525]`	`[20, 5, 100, 115, 525]`	Passed
too big	`[3, 7, 21, 190, 67]`	`[0, 0, 0, 15, 25]`	Failed
square	`[15, 5, 75, 165, 400]`	`[12, 5, 60, 165, 325]`	Failed
height exact	`[10, 5, 50, 140, 125]`	`[9, 5, 45, 140, 115]`	Failed
too heavy for one	`[10, 0, 0, 15, 25]`	`[9, 0, 0, 15, 25]`	Failed
generated mix 8	`[16, 2, 32, 75, 281]`	`[16, 2, 32, 75, 281]`	Passed

SHA-256 / 07867fdc0a341126fcc7768d40816ec2c4d738afa055146f0cd4e2820588f155

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(case, pallet, max_h, max_kg):
    l, w, h, kg = case
    L, W = pallet
    per_layer = max((L // l) * (W // w), (L // w) * (W // l))
    if per_layer == 0:
        return [0, 0, 0, 15, 25]
    layers = (max_h - 15) // h
    by_weight = (max_kg - 25) // kg
    cases = min(per_layer * layers, by_weight)
    if cases <= 0:
        return [per_layer, 0, 0, 15, 25]
    full = -(-cases // per_layer)
    return [per_layer, full, cases, 15 + full * h, 25 + cases * kg]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['rotation wins', [[50, 30, 20, 5], [120, 100], 115, 1000], [8, 5, 40, 115, 225]], ['weight bound partial layer', [[40, 30, 25, 20], [120, 100], 190, 425], [9, 3, 20, 90, 425]], ['listed orientation wins', [[30, 20, 20, 5], [120, 100], 115, 1000], [20, 5, 100, 115, 525]], ['too big', [[130, 30, 25, 2], [120, 100], 190, 425], [0, 0, 0, 15, 25]], ['square', [[25, 25, 30, 5], [120, 80], 165, 900], [12, 5, 60, 165, 325]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['generated mix 8', [[40, 15, 30, 8], [120, 80], 100, 800], [16, 2, 32, 75, 281]]], [['generated mix 12', [[40, 15, 30, 12], [120, 80], 140, 1200], [16, 4, 64, 135, 793]], ['generated mix 10', [[30, 15, 20, 5], [120, 80], 190, 1025], [20, 8, 160, 175, 825]], ['weight bound partial layer', [[40, 30, 25, 20], [120, 100], 190, 425], [9, 3, 20, 90, 425]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['listed orientation wins', [[30, 20, 20, 5], [120, 100], 115, 1000], [20, 5, 100, 115, 525]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['generated mix 9', [[50, 20, 25, 12], [120, 100], 115, 1200], [12, 4, 48, 115, 601]], ['generated mix 19', [[30, 20, 20, 5], [120, 100], 190, 800], [20, 8, 155, 175, 800]]], [['generated mix 33', [[40, 30, 10, 20], [120, 80], 165, 800], [8, 5, 38, 65, 785]], ['generated mix 16', [[25, 20, 30, 5], [120, 80], 140, 800], [18, 4, 72, 135, 385]], ['square', [[25, 25, 30, 5], [120, 80], 165, 900], [12, 5, 60, 165, 325]], ['rotation wins', [[50, 30, 20, 5], [120, 100], 115, 1000], [8, 5, 40, 115, 225]], ['weight bound partial layer', [[40, 30, 25, 20], [120, 100], 190, 425], [9, 3, 20, 90, 425]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['generated mix 21', [[25, 20, 30, 2], [120, 80], 140, 300], [18, 4, 72, 135, 169]], ['generated mix 29', [[50, 30, 30, 20], [120, 100], 190, 300], [8, 2, 13, 75, 285]]], [['generated mix 43', [[25, 20, 20, 12], [120, 100], 140, 1200], [24, 5, 97, 115, 1189]], ['generated mix 25', [[25, 25, 25, 20], [120, 80], 190, 1200], [12, 5, 58, 140, 1185]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['too big', [[130, 30, 25, 2], [120, 100], 190, 425], [0, 0, 0, 15, 25]], ['square', [[25, 25, 30, 5], [120, 80], 165, 900], [12, 5, 60, 165, 325]], ['rotation wins', [[50, 30, 20, 5], [120, 100], 115, 1000], [8, 5, 40, 115, 225]], ['generated mix 32', [[40, 30, 10, 8], [120, 100], 165, 300], [9, 4, 34, 55, 297]], ['generated mix 40', [[20, 15, 30, 20], [120, 80], 190, 500], [32, 1, 23, 45, 485]]], [['generated mix 55', [[50, 30, 30, 5], [120, 100], 190, 1200], [8, 5, 40, 165, 225]], ['generated mix 41', [[25, 25, 10, 20], [120, 100], 165, 1200], [16, 4, 58, 55, 1185]], ['too heavy for one', [[40, 30, 25, 500], [120, 100], 190, 425], [9, 0, 0, 15, 25]], ['listed orientation wins', [[30, 20, 20, 5], [120, 100], 115, 1000], [20, 5, 100, 115, 525]], ['height exact', [[40, 30, 25, 2], [120, 100], 140, 2000], [9, 5, 45, 140, 115]], ['too big', [[130, 30, 25, 2], [120, 100], 190, 425], [0, 0, 0, 15, 25]], ['generated mix 43', [[25, 20, 20, 12], [120, 100], 140, 1200], [24, 5, 97, 115, 1189]], ['generated mix 51', [[25, 15, 10, 8], [120, 80], 165, 500], [24, 3, 59, 45, 497]]]]
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
rotation wins	`[8, 5, 40, 115, 225]`	`[8, 5, 40, 115, 225]`	Passed
weight bound partial layer	`[9, 3, 20, 90, 425]`	`[9, 3, 20, 90, 425]`	Passed
listed orientation wins	`[20, 5, 100, 115, 525]`	`[20, 5, 100, 115, 525]`	Passed
too big	`[0, 0, 0, 15, 25]`	`[0, 0, 0, 15, 25]`	Passed
square	`[12, 5, 60, 165, 325]`	`[12, 5, 60, 165, 325]`	Passed
height exact	`[9, 5, 45, 140, 115]`	`[9, 5, 45, 140, 115]`	Passed
too heavy for one	`[9, 0, 0, 15, 25]`	`[9, 0, 0, 15, 25]`	Passed
generated mix 8	`[16, 2, 32, 75, 281]`	`[16, 2, 32, 75, 281]`	Passed

SHA-256 / 4329fa3b41ec833dd048b73fc8d45b5f6c050c4c6c356b6afe6813e5c7e90286

Verification & scope

Uniform-case, single-orientation layer model; no interlocking patterns. 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 2026-09-29T14:52:09.501660+00:00.

Case digest / b9f27a6dda2f220b8a232f52654252fb3d24acabb065ea96022a5d6ae93fb45b