Uniform distribution of mailboxes between servers / databases, recommend an algorithm?

Question

Algorithms

Hello,

please tell me the algorithm for solving the problem of transferring mailboxes between Exchange servers.

Task: there are Exchange servers that are being decommissioned. They have a fairly large amount of data (mailboxes of different sizes). They need to be distributed among other servers, taking into account:
The amount of data on all servers should be approximately the same. Those. servers A, B, C...Z should have approximately the same number of mailboxes in the database and the size of the databases.
For example, each server should have no more than 200 mailboxes/base and the total size of the base should not exceed 300 Gb. It is desirable that the distribution would be uniform, the delta in size is 100 Mb. There should not be a situation when all the small boxes ended up in one base, and only one, but "heavy", got into another.
At the moment, different servers have different load, i.e. the number of boxes/base varies from north to server.
What I tried: find the "average weight" of the box and create two arrays. One with mean down values, the other with mean up values. Further, choosing one element from each array fills the bases, but it turns out to be inefficient.
It seems to me that there should be another distribution algorithm, more suitable for such tasks.

The implementation of the algorithm will be in PowerShell.

Thank you!

Answer 1

https://stackoverflow.com/questions/1340153/which-...

Bin packing algorithm