How many cases fit, and how much air you are shipping PALLET

The obvious layout is usually one case short

Everybody works out the same thing: divide the pallet by the case both ways round and take the better of the two. On a 1200 × 1000 pallet a 600 × 400 case gives two by two (four), and four is what gets loaded.

The layouts that beat it are the ones where the cases are not all turned the same way. A block of cases in one orientation with a strip in the other fills the leftover margin that a uniform grid leaves at the edge, and that strip is frequently one or two more cases per layer. Nobody finds those by eye, because finding them means trying arrangements rather than dividing two numbers.

One more case per layer on a ten-layer pallet is ten more cases per pallet. Across a container that is a pallet you did not have to send, and the saving repeats on every shipment of the same product for as long as you make it.

What the air costs

The unused space is worth looking at directly rather than as a percentage nobody acts on. A pallet at 78% is not a fact about geometry; it is 22% of a freight charge spent moving nothing, on every pallet, every time.

That number is also the argument for changing the case. A case size chosen because it suited a printing run, or because it is what the previous supplier used, is very often within a few millimetres of one that fits the pallet exactly. Working out how much the current dimensions cost per year is the only thing that ever gets a case redesigned, and it needs a figure rather than a complaint.

The constraints the arithmetic does not know

A layout is not usable just because it fits. Check it against the things only you know:

• Overhang. Cases hanging over the pallet edge lose a large part of their compression strength, and most carriers refuse them. If the answer needs overhang, it is not an answer.
• Interlocking. Alternating the pattern between layers binds the stack and is what keeps it standing; a column stack is stronger vertically and falls over more easily. That is a real trade and it depends on your handling.
• Which way up. A case that must stay upright cannot be turned on its side to make the numbers work, whatever the arithmetic says.
• Height and weight limits. The optimal number of layers is often above what the vehicle, the racking or the bottom case will take, and the binding limit is usually not the one you were thinking of.
• Pick faces. A warehouse that picks cases by hand needs to reach them. The densest pattern can be the slowest to work.

So treat the result as the best geometric answer and the starting point for a conversation with whoever loads it. Print the pattern and give it to them. A layout that exists only in a calculation is one that will be done the old way the first time somebody is in a hurry.

Nothing here is uploaded. Nearby: CUT is the same kind of packing problem in one dimension, with the saw kerf counted; AXLE and BALANCE check what the loaded vehicle is allowed to carry and where the weight sits; and COSTS turns the saved pallets into money.