Decide whether a quoted capacity has placement evidence
A planning sheet divides pallet area by case area and rounds down. The resulting number can look like a capacity, but it is only an upper bound for identical rectangles. It says that more than this many case areas cannot fit in the usable area. It does not say that the rectangles can be placed without overlap. Before accepting the quantity, ask for coordinates or a construction that places every case inside the boundary.
The distinction matters when unused space is fragmented into narrow strips. Summing their areas does not merge them into a new case-shaped rectangle. This guide uses hypothetical dimensions to make that issue reproducible. It supplies no pallet rating or package approval. Its examples are geometric statements about the declared rectangles.
Start with a ceiling that cannot be attained
Take a 1000 by 1000 mm usable square and identical cases with 600 by 600 mm footprints. The area is 1,000,000 square millimetres and each case occupies 360,000. The area ceiling is floor(1,000,000 / 360,000) = 2. The actual engine returns one placement, with best-found status and upper bound two.
For this particular axis-aligned square example, one can prove separately that two cannot fit. Two nonoverlapping rectangles must be separated along at least one horizontal axis. Two 600 mm extents require 1200 mm along whichever axis separates them, exceeding 1000. Rotation makes no difference to a square. That hand proof establishes the geometry, even though the engine's general status does not recognize this proof condition and continues to say best found.
Compare a different loose bound after clearance
For a 1200 by 800 mm pallet, 400 by 300 mm cases, 10 mm edge clearance, and a 10 mm case gap, usable dimensions are 1180 by 780. Their area is 920,400 square millimetres. Dividing by 120,000 gives floor(7.67) = 7. The engine returns six placements and reports best found. Unlike the square counterexample, the area arithmetic alone does not prove whether seven is possible.
| Case | Usable dimensions | Case footprint | Area ceiling | Returned count | Engine status |
|---|---|---|---|---|---|
| Large square cases | 1000 by 1000 mm | 600 by 600 mm | 2 | 1 | Best found |
| Cleared mixed layer | 1180 by 780 mm | 400 by 300 mm | 7 | 6 | Best found |
The area bound counts case area but does not fully allocate the requested gaps. That makes it a valid, potentially loose ceiling. A gap should not be subtracted as a guessed percentage of area, because its space depends on the arrangement. Coordinates must respect it between the placed rectangles. A ceiling of seven is not permission to insert a seventh case into the six-case proposal.
Reproduce the examples and preserve both numbers
Open the square-case counterexample. The one-layer height inputs simply make the layer quantity visible; they do not add a physical stacking claim. Inspect the unused L-shaped area around the returned case. Its total area exceeds another case area, but its shape cannot admit another 600 mm square.
Then open the six-case cleared proposal. Keep TI six and upper bound seven in separate fields. The candidate is a demonstrated geometric count; the ceiling identifies remaining optimization uncertainty. Both pieces are useful in reviewing a capacity statement.
Use a count only at the evidence level it supports
A returned valid count is a lower bound on the maximum: at least that many rectangles fit under the declared assumptions. An upper bound is a possible ceiling. If both are equal, the count is proven for the model. If they differ, do not load the ceiling or assume that the gap automatically means the heuristic missed a feasible pattern. The square example shows that a loose bound can exceed the true maximum.
For an order estimate, use a reviewed valid layer count, then calculate whole layers from confirmed constraints. With six cases per layer and five height-derived layers, capacity is thirty, not thirty-five. Seventy-eight cases need three thirty-case pallets. A report using seven solely because of the area bound would forecast a configuration for which this run supplies no placement evidence.
Recognize a necessary check that still leaves shape unresolved
If the total case area exceeds usable area, the proposed quantity cannot fit under this rectangle model. If it does not exceed usable area, the area test merely stops rejecting the quantity; it has not established placement. This asymmetry is useful when screening a proposal. Apply the easy area rejection first, then request the construction for quantities that pass it. A spreadsheet cell labelled “capacity” should specify whether it contains that ceiling or a validated placed count.
Check the area definition in the percentage
The cleared six-case result uses 720,000 square millimetres of case area. Relative to 920,400 usable square millimetres, utilization is about 78.23 percent. Relative to the entire 960,000-square-millimetre pallet, the same case area is 75 percent. These percentages answer different questions. The displayed usable-area coverage is not the same as proof that the residual area can hold another case.
Bound review record
For the cleared example, retain pallet 1200 by 800, case 400 by 300, units mm, edge clearance 10, case gap 10, and rotation allowed. Usable rectangle: 1180 by 780. Case area: 120,000 mm². Area ceiling: 7. Valid returned TI: 6. Engine status: best found. Save all six coordinates and their validation. A seven-case count requires new placement evidence; this record does not contain it.
The methodology explains how candidates are validated. When reviewing another capacity figure, request its dimensions, allowances, coordinates, and proof basis rather than accepting an area ratio as a load plan. That request targets the missing evidence directly and avoids inventing a universal utilization allowance.