FA-94901 / Warehouse slotting and bin packing / Open access

Replenishment: rounding cases up overfills · case 01

Replenishment tasks overfill the pick face above its maximum.

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

ROOT CAUSE

The room-to-max is rounded up to whole cases instead of down.

THE FAILURE

The room-to-max is rounded up to whole cases instead of down.

Unsuccessful approach: Using the raw unit room breaks case integrity by requesting partial cases.

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 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 = [[['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]]], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 8', [[['F0', 0, 12, 15, 6, 0], ['F1', 1, 10, 22, 6, 12]]], [['F1', 12]]], ['generated mix 16', [[['F0', 6, 6, 36, 1, 0], ['F1', 1, 10, 22, 1, 3], ['F2', 5, 4, 16, 6, 24], ['F3', 7, 6, 36, 6, 24]]], [['F1', 3]]]], [['generated mix 21', [[['F0', 0, 4, 16, 1, 24], ['F1', 11, 10, 22, 6, 12], ['F2', 0, 6, 18, 4, 24], ['F3', 3, 4, 34, 6, 48], ['F4', 12, 12, 24, 12, 100]]], [['F0', 16], ['F2', 16], ['F3', 30], ['F4', 12]]], ['generated mix 14', [[['F0', 13, 12, 24, 6, 3], ['F1', 0, 6, 9, 4, 48], ['F2', 0, 12, 18, 4, 48]]], [['F1', 8], ['F2', 16]]], ['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['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]]], []], ['generated mix 9', [[['F0', 6, 6, 9, 1, 100], ['F1', 1, 12, 18, 6, 0]]], [['F0', 3]]], ['generated mix 18', [[['F0', 5, 6, 9, 6, 24], ['F1', 1, 12, 15, 4, 3], ['F2', 3, 12, 15, 12, 0], ['F3', 7, 6, 30, 6, 24]]], []], ['generated mix 27', [[['F0', 1, 12, 24, 6, 24]]], [['F0', 18]]]], [['generated mix 32', [[['F0', 5, 4, 34, 4, 0], ['F1', 9, 10, 40, 12, 24], ['F2', 6, 6, 9, 12, 24], ['F3', 3, 6, 9, 6, 0]]], [['F1', 24]]], ['generated mix 24', [[['F0', 3, 10, 10, 4, 48], ['F1', 0, 6, 9, 4, 12], ['F2', 0, 10, 13, 12, 100], ['F3', 6, 6, 6, 4, 12]]], [['F1', 8], ['F2', 12], ['F0', 4]]], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['generated mix 20', [[['F0', 0, 12, 36, 4, 48]]], [['F0', 36]]], ['generated mix 29', [[['F0', 1, 12, 36, 1, 100], ['F1', 0, 4, 16, 1, 100], ['F2', 3, 12, 18, 4, 24], ['F3', 7, 6, 6, 1, 48]]], [['F1', 16], ['F0', 35], ['F2', 12]]], ['generated mix 38', [[['F0', 7, 6, 9, 6, 3], ['F1', 9, 10, 13, 12, 0], ['F2', 12, 12, 12, 4, 24], ['F3', 1, 12, 15, 12, 48], ['F4', 0, 10, 16, 6, 12]]], [['F4', 12], ['F3', 12]]]], [['generated mix 42', [[['F0', 3, 4, 7, 6, 100], ['F1', 11, 12, 42, 6, 48], ['F2', 0, 6, 30, 6, 0]]], [['F1', 30]]], ['generated mix 31', [[['F0', 9, 10, 10, 4, 100], ['F1', 5, 6, 36, 1, 24]]], [['F1', 24]]], ['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['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]]], []], ['generated mix 32', [[['F0', 5, 4, 34, 4, 0], ['F1', 9, 10, 40, 12, 24], ['F2', 6, 6, 9, 12, 24], ['F3', 3, 6, 9, 6, 0]]], [['F1', 24]]], ['generated mix 40', [[['F0', 7, 6, 18, 6, 48], ['F1', 13, 12, 24, 1, 0], ['F2', 7, 6, 12, 12, 24]]], []], ['generated mix 49', [[['F0', 1, 12, 36, 6, 100], ['F1', 0, 12, 18, 12, 12], ['F2', 0, 10, 10, 1, 48], ['F3', 1, 6, 18, 1, 100]]], [['F1', 12], ['F2', 10], ['F0', 30], ['F3', 17]]]], [['generated mix 57', [[['F0', 1, 12, 36, 1, 100], ['F1', 0, 4, 28, 6, 0], ['F2', 9, 10, 40, 6, 48], ['F3', 11, 10, 13, 6, 48], ['F4', 3, 6, 18, 6, 100]]], [['F0', 35], ['F4', 12], ['F2', 30]]], ['generated mix 36', [[['F0', 0, 6, 6, 4, 3], ['F1', 5, 6, 12, 12, 48]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['generated mix 43', [[['F0', 0, 6, 18, 4, 24], ['F1', 3, 4, 34, 4, 48], ['F2', 1, 4, 10, 12, 0], ['F3', 1, 4, 34, 12, 12]]], [['F0', 16], ['F3', 12], ['F1', 28]]], ['generated mix 51', [[['F0', 4, 4, 28, 6, 12], ['F1', 1, 6, 30, 12, 0], ['F2', 9, 10, 34, 6, 3]]], [['F0', 12]]], ['generated mix 60', [[['F0', 0, 10, 40, 1, 24], ['F1', 3, 6, 30, 4, 100], ['F2', 4, 4, 4, 6, 100]]], [['F0', 24], ['F1', 24]]]]]
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
priority by ratio	`[['Z', 40], ['Y', 40], ['X', 35]]`	`[['Z', 40], ['Y', 35], ['X', 35]]`	Failed
at min triggers	`[['A', 24]]`	`[['A', 24]]`	Passed
reserve partial case	`[['A', 12]]`	`[['A', 12]]`	Passed
stockout no reserve	`[]`	`[]`	Passed
above min idle	`[]`	`[]`	Passed
stockout small max	`[['B', 6]]`	`[['B', 6]]`	Passed
generated mix 8	`[['F1', 12]]`	`[['F1', 12]]`	Passed
generated mix 16	`[['F1', 3]]`	`[['F1', 3]]`	Passed

SHA-256 / a601b9f6c62dfc331eccef24a3dc525e134e977458f85930472f8ed8d3dd284b

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
        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 = [[['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]]], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['above min idle', [[['A', 11, 10, 34, 12, 100]]], []], ['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['generated mix 8', [[['F0', 0, 12, 15, 6, 0], ['F1', 1, 10, 22, 6, 12]]], [['F1', 12]]], ['generated mix 16', [[['F0', 6, 6, 36, 1, 0], ['F1', 1, 10, 22, 1, 3], ['F2', 5, 4, 16, 6, 24], ['F3', 7, 6, 36, 6, 24]]], [['F1', 3]]]], [['generated mix 21', [[['F0', 0, 4, 16, 1, 24], ['F1', 11, 10, 22, 6, 12], ['F2', 0, 6, 18, 4, 24], ['F3', 3, 4, 34, 6, 48], ['F4', 12, 12, 24, 12, 100]]], [['F0', 16], ['F2', 16], ['F3', 30], ['F4', 12]]], ['generated mix 14', [[['F0', 13, 12, 24, 6, 3], ['F1', 0, 6, 9, 4, 48], ['F2', 0, 12, 18, 4, 48]]], [['F1', 8], ['F2', 16]]], ['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['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]]], []], ['generated mix 9', [[['F0', 6, 6, 9, 1, 100], ['F1', 1, 12, 18, 6, 0]]], [['F0', 3]]], ['generated mix 18', [[['F0', 5, 6, 9, 6, 24], ['F1', 1, 12, 15, 4, 3], ['F2', 3, 12, 15, 12, 0], ['F3', 7, 6, 30, 6, 24]]], []], ['generated mix 27', [[['F0', 1, 12, 24, 6, 24]]], [['F0', 18]]]], [['generated mix 32', [[['F0', 5, 4, 34, 4, 0], ['F1', 9, 10, 40, 12, 24], ['F2', 6, 6, 9, 12, 24], ['F3', 3, 6, 9, 6, 0]]], [['F1', 24]]], ['generated mix 24', [[['F0', 3, 10, 10, 4, 48], ['F1', 0, 6, 9, 4, 12], ['F2', 0, 10, 13, 12, 100], ['F3', 6, 6, 6, 4, 12]]], [['F1', 8], ['F2', 12], ['F0', 4]]], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['generated mix 20', [[['F0', 0, 12, 36, 4, 48]]], [['F0', 36]]], ['generated mix 29', [[['F0', 1, 12, 36, 1, 100], ['F1', 0, 4, 16, 1, 100], ['F2', 3, 12, 18, 4, 24], ['F3', 7, 6, 6, 1, 48]]], [['F1', 16], ['F0', 35], ['F2', 12]]], ['generated mix 38', [[['F0', 7, 6, 9, 6, 3], ['F1', 9, 10, 13, 12, 0], ['F2', 12, 12, 12, 4, 24], ['F3', 1, 12, 15, 12, 48], ['F4', 0, 10, 16, 6, 12]]], [['F4', 12], ['F3', 12]]]], [['generated mix 42', [[['F0', 3, 4, 7, 6, 100], ['F1', 11, 12, 42, 6, 48], ['F2', 0, 6, 30, 6, 0]]], [['F1', 30]]], ['generated mix 31', [[['F0', 9, 10, 10, 4, 100], ['F1', 5, 6, 36, 1, 24]]], [['F1', 24]]], ['stockout small max', [[['B', 0, 2, 5, 6, 12]]], [['B', 6]]], ['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]]], []], ['generated mix 32', [[['F0', 5, 4, 34, 4, 0], ['F1', 9, 10, 40, 12, 24], ['F2', 6, 6, 9, 12, 24], ['F3', 3, 6, 9, 6, 0]]], [['F1', 24]]], ['generated mix 40', [[['F0', 7, 6, 18, 6, 48], ['F1', 13, 12, 24, 1, 0], ['F2', 7, 6, 12, 12, 24]]], []], ['generated mix 49', [[['F0', 1, 12, 36, 6, 100], ['F1', 0, 12, 18, 12, 12], ['F2', 0, 10, 10, 1, 48], ['F3', 1, 6, 18, 1, 100]]], [['F1', 12], ['F2', 10], ['F0', 30], ['F3', 17]]]], [['generated mix 57', [[['F0', 1, 12, 36, 1, 100], ['F1', 0, 4, 28, 6, 0], ['F2', 9, 10, 40, 6, 48], ['F3', 11, 10, 13, 6, 48], ['F4', 3, 6, 18, 6, 100]]], [['F0', 35], ['F4', 12], ['F2', 30]]], ['generated mix 36', [[['F0', 0, 6, 6, 4, 3], ['F1', 5, 6, 12, 12, 48]]], []], ['at min triggers', [[['A', 10, 10, 34, 12, 100]]], [['A', 24]]], ['reserve partial case', [[['A', 0, 5, 30, 12, 20]]], [['A', 12]]], ['stockout no reserve', [[['B', 0, 2, 20, 6, 5]]], []], ['generated mix 43', [[['F0', 0, 6, 18, 4, 24], ['F1', 3, 4, 34, 4, 48], ['F2', 1, 4, 10, 12, 0], ['F3', 1, 4, 34, 12, 12]]], [['F0', 16], ['F3', 12], ['F1', 28]]], ['generated mix 51', [[['F0', 4, 4, 28, 6, 12], ['F1', 1, 6, 30, 12, 0], ['F2', 9, 10, 34, 6, 3]]], [['F0', 12]]], ['generated mix 60', [[['F0', 0, 10, 40, 1, 24], ['F1', 3, 6, 30, 4, 100], ['F2', 4, 4, 4, 6, 100]]], [['F0', 24], ['F1', 24]]]]]
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
priority by ratio	`[['Z', 40], ['Y', 38], ['X', 35]]`	`[['Z', 40], ['Y', 35], ['X', 35]]`	Failed
at min triggers	`[['A', 24]]`	`[['A', 24]]`	Passed
reserve partial case	`[['A', 12]]`	`[['A', 12]]`	Passed
stockout no reserve	`[]`	`[]`	Passed
above min idle	`[]`	`[]`	Passed
stockout small max	`[['B', 5]]`	`[['B', 6]]`	Failed
generated mix 8	`[['F1', 12]]`	`[['F1', 12]]`	Passed
generated mix 16	`[['F1', 3]]`	`[['F1', 3]]`	Passed

SHA-256 / d89f86e6ffe2eaeed506bcc67010857688f89a0d1bb974d4064eedbd64a4cc2a

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 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 2026-09-29T14:52:08.711793+00:00.

Case digest / e6ac9876c1a5a732887dfde0f0bd04a2453dafaab7766c2167d09c3e3487522e