When I moved to New York, I - like an idiot - brought a full set of very heavy bedroom furniture with me. It probably cost me more to rent the bigger UHaul than it would have to replace it with IKEA products - and would definitely have been cheaper to just not have a bunch of furniture cluttering the place up.
As I recall, it all ended up on the street - although it was gone within a day, so I hope someone's enjoying my "donation".
There's an interesting startup called Campaign Living: https://www.campaignliving.com that's trying to solve some of this problem by making furniture that looks good and can be disassembled quickly and easily. I wish I'd bought one of their couches instead of the one I got.
That furniture lasted one more move, from Staten Island to Bushwick, Brooklyn, two years later. Probably worth it, but I've moved across the country four more times since then, and I've never moved anything I couldn't fit in a box since that move to Brooklyn.
I do like his descriptions of the art of packing a trailer. It really is a thing of beauty [0].
[0]https://www.movebuddha.com/blog/moving-cross-country-cost/
And we didn't have an idea of the complete contents in our heads ahead of time either; we just had to deal with whatever came down the chute one piece at a time. (Though you might be able to store 5-6 pieces off to the side, but that gets clumsy fast.)
One strategy to try to accommodate that randomness would be to have a lower row for one size-range, progressing horizontally, then another row on top of that in the same tier, for some other size-range. Going even further you could even start a second tier in front of that, with two more sizes. But that also could screw you if the one in front (or on top) starts to get too far ahead of the one behind (or on the bottom). Then you're back to setting packages aside and tripping on shit...
You'd have to get full dimensional info about each package... probably not that hard. But to change the order, you've now got a storage problem. Where previously your analysis was confined to just one package, now you're dealing with groups of N packages, and depending how far you want to take the optimization, N could be as big as "all packages destined for that truck." So maybe you have some kind of sort area between the inbound & outbound areas. Or maybe you use the conveyor itself as the storage - i.e. if something is out of order, it just makes a circuit around the building until its turn comes. That would probably require a bigger/longer conveyor, and to compensate for lower "density" of chute-appropriate packages, it would have to move faster.
Suddenly this seems akin to the problem of optimizing spinning disc drives, starting from slow ones in the old days and moving forward. What you're essentially calling for is something akin to random access, but instead of bytes we're accessing packages!
Edit: Or the hybrid version: you create multiple, smaller sorting areas somehow, one for each bay, located near the bay.
That proved really useful when, some months later, I received a frantic call in the early morning from a friend who had rented a U-Haul and had some friends from church coming by, but was otherwise completely unprepared.
And a few times, since. The last, this spring, when I was able to advise a friend to e.g. put that many hundred pound commercial air compressor in first, up front, so that it wouldn't crush everything else in the event of a panic stop.
I imagine the description goes far beyond what I know, but there are some basics that you can learn in an hour and that will make such packing and moving go much better and more smoothly.
There's more money in corporate relocations and military moves than I would have expected.
My big takeaway from it wasn't anything to do with trucking (the author is a professional house mover) - it was about the accumulation of stuff and how the mover took down all of this heavy furniture for customers from the northern states to Florida, only to find that they didn't really want their old stuff down there anyway.