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I have a company that sells all kind of products and we have many issues with boxes. We are going to buy wholesale volumes, so we need to get the sizes right.

We are trying to develop an algorythm for optimizing box sizes. I have the data of all my products (Height-Width-Lenght) but I want to find the optimal number of boxes, N and the size of each N boxes (measured as H-W-L).

The constrains:

  • Obviosly, every product should fit in a box, that is, the ProductHeight <= BoxHeight and the same for Width and Lenght.

  • Every box size should be used for at least Z% of the products. We want to assure that every box has a minimum amount needed, so we don't do 1,000 boxes that will be used only one time.

I'm not that good at math or optimization, so any help would be great. Thanks!

Santiago Valdés
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  • Problems like this are either very easy or very hard. Much of the time, if you just make models of each product it is obvious which ones should be grouped to fit in the same box, then you order the boxes that fit. It is usually easier for a person to do it by eye than write a program. If not, it is a combinatorial mess. – Ross Millikan Apr 09 '15 at 20:04
  • @RossMillikan Considering we have 1,000+ products, I think the "eye" solution could end being far more slow and is not repeatable. We want to implement a solution that let us optimize our boxing choices for the future too. Generally a machine thinks this problems better than human eye. – Santiago Valdés Apr 09 '15 at 20:13
  • You have to define what you mean by optimal. To me, it could be that N=1 is optimal (since 1 is the smallest possible number which will solve the problem) – Johan Löfberg Apr 10 '15 at 06:21
  • Are you free to determine the sizes of the boxes entirely, or can you only select from a finite number of available boxes? – Johan Löfberg Apr 10 '15 at 07:40
  • @JohanLöfberg I'm free to determine the sizes. Maybe my problem lack constrains or should include more variables, any suggestion is welcomed. – Santiago Valdés Apr 10 '15 at 13:08
  • How do you define optimality (total cost of boxes?), and how much does a box with a certain dimension cost? – Johan Löfberg Apr 10 '15 at 15:22

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