FA-94911 / Warehouse slotting and bin packing / Open access

Replenishment: empty small face never refilled · case 01

An empty pick face whose max is smaller than one case pack is never replenished.

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

ROOT CAUSE

The emergency one-case rule for stocked-out faces is missing.

VERIFIED REPAIR

When the face is empty and no full case fits under max, send one case if reserve holds a full case.

Unsuccessful approach: Sending the emergency case without checking reserve creates tasks for stock that does not exist.

Case contract

faces [[loc, on_hand, min, max, case_pack, reserve_units]], min >= 1. Replenish when on_hand <= min. Quantity is the largest number of full cases that keeps on_hand <= max, limited to full cases available in reserve. A stocked-out face whose max leaves no room for a full case still gets one case if reserve has one. Zero-quantity tasks are dropped. Tasks are ordered by on_hand/min ascending, then loc.

Why this case matters

Min/max replenishment keeps forward pick faces stocked from reserve.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(faces):
    tasks = []
    for loc, oh, mn, mx, cp, reserve in faces:
        if oh > mn:
            continue
        avail = reserve // cp * cp
        qty = (mx - oh) // cp * cp
        qty = min(qty, avail)
        if qty == 0:
            continue
        tasks.append((Fraction(oh, mn), loc, qty))
    tasks.sort()
    return [[loc, qty] for _, loc, qty in tasks]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 6', [[['F0', 1, 12, 18, 6, 12], ['F1', 10, 10, 10, 1, 100], ['F2', 0, 6, 9, 12, 3]]], [['F0', 12]]], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['generated mix 9', [[['F0', 6, 6, 9, 1, 100], ['F1', 1, 12, 18, 6, 0]]], [['F0', 3]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 26', [[['F0', 7, 6, 6, 12, 48], ['F1', 0, 4, 28, 6, 12], ['F2', 0, 6, 30, 6, 0], ['F3', 1, 6, 6, 1, 3]]], [['F1', 12], ['F3', 3]]], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['generated mix 11', [[['F0', 5, 6, 9, 4, 100]]], [['F0', 4]]], ['generated mix 19', [[['F0', 7, 6, 6, 1, 12], ['F1', 0, 4, 16, 6, 0], ['F2', 4, 4, 28, 12, 48]]], [['F2', 24]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 45', [[['F0', 1, 4, 7, 6, 100], ['F1', 13, 12, 12, 6, 3], ['F2', 5, 6, 9, 4, 3], ['F3', 0, 6, 36, 6, 0]]], [['F0', 6]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['generated mix 22', [[['F0', 5, 6, 12, 4, 0], ['F1', 9, 10, 13, 1, 24], ['F2', 0, 10, 16, 1, 48]]], [['F2', 16], ['F1', 4]]], ['generated mix 30', [[['F0', 0, 12, 18, 6, 48], ['F1', 0, 6, 30, 12, 24]]], [['F0', 18], ['F1', 24]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 62', [[['F0', 0, 10, 34, 12, 3], ['F1', 5, 4, 28, 4, 100]]], []], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['generated mix 33', [[['F0', 13, 12, 36, 12, 48], ['F1', 5, 4, 10, 6, 100], ['F2', 4, 4, 10, 12, 24]]], []], ['generated mix 41', [[['F0', 0, 4, 16, 1, 12], ['F1', 7, 6, 30, 1, 100], ['F2', 5, 6, 18, 12, 24]]], [['F0', 12], ['F2', 12]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 76', [[['F0', 0, 10, 40, 1, 0]]], []], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['generated mix 44', [[['F0', 4, 4, 4, 6, 3], ['F1', 11, 10, 10, 1, 48], ['F2', 11, 12, 24, 4, 48], ['F3', 3, 6, 9, 4, 3]]], [['F2', 12]]], ['generated mix 52', [[['F0', 11, 10, 16, 6, 3], ['F1', 10, 10, 13, 4, 24], ['F2', 0, 4, 28, 1, 100], ['F3', 12, 12, 42, 4, 0]]], [['F2', 28]]]]]
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
stockout small max	`[]`	`[['B', 6]]`	Failed
generated mix 6	`[['F0', 12]]`	`[['F0', 12]]`	Passed
at min triggers	`[['A', 24]]`	`[['A', 24]]`	Passed
reserve partial case	`[['A', 12]]`	`[['A', 12]]`	Passed
priority by ratio	`[['Z', 40], ['Y', 35], ['X', 35]]`	`[['Z', 40], ['Y', 35], ['X', 35]]`	Passed
above min idle	`[]`	`[]`	Passed
stockout no reserve	`[]`	`[]`	Passed
generated mix 9	`[['F0', 3]]`	`[['F0', 3]]`	Passed

SHA-256 / 126e01fccc692abbd6047808eba87e5856460845f46322fe03b37da4329d2efa

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(faces):
    tasks = []
    for loc, oh, mn, mx, cp, reserve in faces:
        if oh > mn:
            continue
        avail = reserve // cp * cp
        qty = (mx - oh) // cp * cp
        qty = min(qty, avail)
        if qty == 0 and oh == 0:
            qty = cp
        if qty == 0:
            continue
        tasks.append((Fraction(oh, mn), loc, qty))
    tasks.sort()
    return [[loc, qty] for _, loc, qty in tasks]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 6', [[['F0', 1, 12, 18, 6, 12], ['F1', 10, 10, 10, 1, 100], ['F2', 0, 6, 9, 12, 3]]], [['F0', 12]]], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['generated mix 9', [[['F0', 6, 6, 9, 1, 100], ['F1', 1, 12, 18, 6, 0]]], [['F0', 3]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 26', [[['F0', 7, 6, 6, 12, 48], ['F1', 0, 4, 28, 6, 12], ['F2', 0, 6, 30, 6, 0], ['F3', 1, 6, 6, 1, 3]]], [['F1', 12], ['F3', 3]]], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['generated mix 11', [[['F0', 5, 6, 9, 4, 100]]], [['F0', 4]]], ['generated mix 19', [[['F0', 7, 6, 6, 1, 12], ['F1', 0, 4, 16, 6, 0], ['F2', 4, 4, 28, 12, 48]]], [['F2', 24]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 45', [[['F0', 1, 4, 7, 6, 100], ['F1', 13, 12, 12, 6, 3], ['F2', 5, 6, 9, 4, 3], ['F3', 0, 6, 36, 6, 0]]], [['F0', 6]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['generated mix 22', [[['F0', 5, 6, 12, 4, 0], ['F1', 9, 10, 13, 1, 24], ['F2', 0, 10, 16, 1, 48]]], [['F2', 16], ['F1', 4]]], ['generated mix 30', [[['F0', 0, 12, 18, 6, 48], ['F1', 0, 6, 30, 12, 24]]], [['F0', 18], ['F1', 24]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 62', [[['F0', 0, 10, 34, 12, 3], ['F1', 5, 4, 28, 4, 100]]], []], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['generated mix 33', [[['F0', 13, 12, 36, 12, 48], ['F1', 5, 4, 10, 6, 100], ['F2', 4, 4, 10, 12, 24]]], []], ['generated mix 41', [[['F0', 0, 4, 16, 1, 12], ['F1', 7, 6, 30, 1, 100], ['F2', 5, 6, 18, 12, 24]]], [['F0', 12], ['F2', 12]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 76', [[['F0', 0, 10, 40, 1, 0]]], []], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['generated mix 44', [[['F0', 4, 4, 4, 6, 3], ['F1', 11, 10, 10, 1, 48], ['F2', 11, 12, 24, 4, 48], ['F3', 3, 6, 9, 4, 3]]], [['F2', 12]]], ['generated mix 52', [[['F0', 11, 10, 16, 6, 3], ['F1', 10, 10, 13, 4, 24], ['F2', 0, 4, 28, 1, 100], ['F3', 12, 12, 42, 4, 0]]], [['F2', 28]]]]]
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
stockout small max	`[['B', 6]]`	`[['B', 6]]`	Passed
generated mix 6	`[['F2', 12], ['F0', 12]]`	`[['F0', 12]]`	Failed
at min triggers	`[['A', 24]]`	`[['A', 24]]`	Passed
reserve partial case	`[['A', 12]]`	`[['A', 12]]`	Passed
priority by ratio	`[['Z', 40], ['Y', 35], ['X', 35]]`	`[['Z', 40], ['Y', 35], ['X', 35]]`	Passed
above min idle	`[]`	`[]`	Passed
stockout no reserve	`[['B', 6]]`	`[]`	Failed
generated mix 9	`[['F0', 3]]`	`[['F0', 3]]`	Passed

SHA-256 / e94f09979eab57e2820037cf55d0196351c48e327653a37d4afd9161144e58f0

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(faces):
    tasks = []
    for loc, oh, mn, mx, cp, reserve in faces:
        if oh > mn:
            continue
        avail = reserve // cp * cp
        qty = (mx - oh) // cp * cp
        qty = min(qty, avail)
        if qty == 0 and oh == 0 and avail >= cp:
            qty = cp
        if qty == 0:
            continue
        tasks.append((Fraction(oh, mn), loc, qty))
    tasks.sort()
    return [[loc, qty] for _, loc, qty in tasks]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 6', [[['F0', 1, 12, 18, 6, 12], ['F1', 10, 10, 10, 1, 100], ['F2', 0, 6, 9, 12, 3]]], [['F0', 12]]], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['generated mix 9', [[['F0', 6, 6, 9, 1, 100], ['F1', 1, 12, 18, 6, 0]]], [['F0', 3]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 26', [[['F0', 7, 6, 6, 12, 48], ['F1', 0, 4, 28, 6, 12], ['F2', 0, 6, 30, 6, 0], ['F3', 1, 6, 6, 1, 3]]], [['F1', 12], ['F3', 3]]], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['generated mix 11', [[['F0', 5, 6, 9, 4, 100]]], [['F0', 4]]], ['generated mix 19', [[['F0', 7, 6, 6, 1, 12], ['F1', 0, 4, 16, 6, 0], ['F2', 4, 4, 28, 12, 48]]], [['F2', 24]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 45', [[['F0', 1, 4, 7, 6, 100], ['F1', 13, 12, 12, 6, 3], ['F2', 5, 6, 9, 4, 3], ['F3', 0, 6, 36, 6, 0]]], [['F0', 6]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['generated mix 22', [[['F0', 5, 6, 12, 4, 0], ['F1', 9, 10, 13, 1, 24], ['F2', 0, 10, 16, 1, 48]]], [['F2', 16], ['F1', 4]]], ['generated mix 30', [[['F0', 0, 12, 18, 6, 48], ['F1', 0, 6, 30, 12, 24]]], [['F0', 18], ['F1', 24]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 62', [[['F0', 0, 10, 34, 12, 3], ['F1', 5, 4, 28, 4, 100]]], []], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['generated mix 33', [[['F0', 13, 12, 36, 12, 48], ['F1', 5, 4, 10, 6, 100], ['F2', 4, 4, 10, 12, 24]]], []], ['generated mix 41', [[['F0', 0, 4, 16, 1, 12], ['F1', 7, 6, 30, 1, 100], ['F2', 5, 6, 18, 12, 24]]], [['F0', 12], ['F2', 12]]]], [['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 76', [[['F0', 0, 10, 40, 1, 0]]], []], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['priority by ratio', [[['X', 5, 10, 40, 5, 100], ['Y', 2, 8, 40, 5, 100], ['Z', 0, 6, 40, 5, 100]]], [['Z', 40], ['Y', 35], ['X', 35]]], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['generated mix 44', [[['F0', 4, 4, 4, 6, 3], ['F1', 11, 10, 10, 1, 48], ['F2', 11, 12, 24, 4, 48], ['F3', 3, 6, 9, 4, 3]]], [['F2', 12]]], ['generated mix 52', [[['F0', 11, 10, 16, 6, 3], ['F1', 10, 10, 13, 4, 24], ['F2', 0, 4, 28, 1, 100], ['F3', 12, 12, 42, 4, 0]]], [['F2', 28]]]]]
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
stockout small max	`[['B', 6]]`	`[['B', 6]]`	Passed
generated mix 6	`[['F0', 12]]`	`[['F0', 12]]`	Passed
at min triggers	`[['A', 24]]`	`[['A', 24]]`	Passed
reserve partial case	`[['A', 12]]`	`[['A', 12]]`	Passed
priority by ratio	`[['Z', 40], ['Y', 35], ['X', 35]]`	`[['Z', 40], ['Y', 35], ['X', 35]]`	Passed
above min idle	`[]`	`[]`	Passed
stockout no reserve	`[]`	`[]`	Passed
generated mix 9	`[['F0', 3]]`	`[['F0', 3]]`	Passed

SHA-256 / 8710226297fa104a1f32191860ca36d28cb74a5492ee9a8044225609e256a2e5

Verification & scope

Stipulated min/max policy with whole-case moves only. 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 2026-09-29T14:52:08.819913+00:00.

Case digest / 0dd9fb693a5022dd5cc05156171d9eeb2d3ff141ee9b36744d14a623f78ac766