Pallets, part pallets and cartons calculator

This is not as complicated as you might think. Before I help you with some code: why don't you try to write down (in human readable language) which steps you would take yourself when you have a number of items and want to know how much of each kind of packaging is required. These are the steps you'll have to automate! (And I'm happy to help you with that.)

Also think of the format in which you want to have the result returned after entering an amount of items in your formula or function. Are there any cells to be filled with the different number of cartons and pallets, or do you want a message box to show the result? etc. And: where is the amount of items entered? Is it the value of a specific cell on a worksheet, or do you want to enter it in an input box?

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If you want to know how many packages fit on a pallet, don't worry. We'll explain everything you need to know 😊

To find the maximum number of packages/boxes we can fit on a pallet within a limited volume, we need to test each possible pallet stacking pattern and keep the one with the highest package count.

Possible pallet stacking patterns

Picture yourself looking at an empty pallet from the top: What are all the possible ways to arrange the packages on the first layer?

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Let's begin by describing one of these possible arrangements for a single package.

Assume we first position the package on the top left corner so that its width is parallel to the pallet's width and one of the other sides is parallel to the pallet's length. We keep placing packages next to each other using this orientation until we run out of space on the pallet's width. This is our first row. Parallel to this row, we place an equal row of packages and repeat until we run out of space on the pallet's length. That completes our first layer and is one of the possible arrangements.

Remember, we didn't specify which side was parallel to the pallet's length. By placing the package's width parallel to the pallet's width, we can choose either the package's length or height to be parallel to the pallet's length, with the remaining side parallel to a vertical plane.

We can repeat this thought process and conclude that we have two possible arrangements for each side we choose to be parallel to the pallet's width. That leaves us with six possible arrangements:

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