Evenly Distributing Workload Based on Capacity

Hi all,

I've lurked on the forum for a while now and have always been able to find solutions to any problems I've encountered, so first off, thank you for the amazing work you all do!

I've now encountered an issue I'd like some help with, and can't find an instance where this has been addressed before, though it's a variation on a pretty common scenario.

I am working on a project where I need to distribute work assignments evenly (like I said, common enough scenario). Where it gets a little bit trickier is that the assumptions are a bit different than normal: 1) each assignment is roughly equal (i.e. there's no different amount of time or expertise required). 2) Capacity is pre-determined based on already-assigned work and won't always be binary. So, if I have a group of 20 people, on a given day one of them may have capacity to take on 2 assignments, while another may need to pass off 2 assignments on that day...or they may have no capacity in either direction. I'd like to automate these distributions...I've attached a worksheet showing how I think this should work, but I can't quite figure it out.

A1:D10 shows a manual version of total assignments to be made - in the real thing this will be automated and I'm able to get that set up with no problems - this will show each person's capacity for the day, in such a way that total number of assignments received will automatically equal total number given.

What I can't figure out is how to automate the distribution process given the varying capacity for each person. My thought was to use Solver, but typical work/team assignment scenarios I can find use a binary option that I don't believe will work due to the fact that capacity isn't binary, and I can't figure out a way to use an integer constraint in a way that will work. I'm assuming I'll need some sort of matrix, and F1:L9 shows my manual solution, but from there I'm stuck. Is anyone able to help me out with this? Let me know if I can provide any additional detail that would be helpful!

How about this setup?

I limited the integer to 4 but I realize 2 would be enough and make it run faster. Or maybe even 1.
Also I used the Minimize feature which may or may not take longer if it tries to go below zero, maybe just putting zero as goal is faster.

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Someone whispered to me that you can make it run a lot faster by changing the parameters in the Solver Evolutionary options. Reducing the maximum time without improvements makes a big difference but reducing it too much makes Solver stop before a solution is found.

It seems to me using Minimize as a goal makes Solver keep searching for lower values after a zero solution is found.
However, setting zero as a goal value makes it not find zero at all...