I’m a Data Scientist with a strong mathematical background but don’t know much apart from textbook material about Operations Research. I’m dealing with a logistics problem which I don’t know how to approach. I’ve been reading the literature a bit and I think it might be a combination of a bin packing and of a cutting stock problem, but I would very appreciate if someone familiar with OR has already heard of a similar type of problem.

The idea is that we have a certain number m of items each with defined weight, length, width and a certain number k of customers. Typically, m is rather small (around 50) while k is large (around 30,000). Each customer can order a fixed quantity of each item, and we have that information in a matrix X=(x_{ij}) where each coefficient represents the demand of customer i for item j.

We have N (N is rather small too, less than 6) machines that can pack objects into boxes called kits of 2 different types, with maximal length, width and weight capacity known. Each machine can only pack one particular kit, meaning the same machine will always prepare the same type of kit with the same contents.

We’re trying to find an optimal combination of kits that allows us to satisfy the demand of all customers while minimizing costs (manufacturing the kits themselves comes with a certain cost that is increasing with the number of items contained in it).
The idea is that, in order to satisfy a customer demand, one must resort to a linear combination of the kits :

• e.g. if kit number 1 contains 2 items A and kit number 2 contains 3 items B :
• a customer asking for 3 items A and 5 items B will get 2 kits number 1 and 2 kits number 2
• while a customer asking for 4 items B will get 2 kits of type 1

This is not a classical bin packing problem as there are a limited number of kits, all of which are of fixed size content.
This is not a classical cutting stock problem as well, as the number of kits is limited and not infinite.
This might look like a scheduling or an assignment problem, but I have no idea where to start from in the literature about this type of problem.

Does someone have already encountered this type of problem, or know what it’s called, or have encountered literature about it and can provide references to help me approach the problem?
Thanks for any help provided!