But the solution is easy for some non-perishable good that's scarce and you need to hand them out in some order. Hand them out on an oldest-first basis.
Interesting idea actually.
But how would you account for preferences? For instance, what if there were white toilets and tan ones? How do you decide who gets what color? What happens if you have more variables, like single vs dual flush, round vs elongated bowl, etc.
I suppose if we live in a manufacturing utopia what you would hand out is not a good itself, but an order fulfillment slot? That is "it's now your turn for a new X. Please select the options you want and it will be delivered on <date>."
I could see that as a possibility actually. It gets more interesting when it's not "durable goods" but something where the ordering timespan is much shorter than the production timespan, like food. Maybe you'd have to just get the average consumer to better understand the concept of lead time?
There's also the question of how to deal with "warranty". Maybe if your product breaks between the normal ordering cycle time, you would get inserted into the queue early.
The other thought is - what about people who want things updated more often than the standard ordering cycle time? Would you allow people to trade their slots? Could you avoid abuse if you only allowed a one-for-one trade? I don't think you'd be able to "store" production slots.
Actually to expand on that - I wonder if you could improve things today (e.g., lessen the severity of business cycles) if we went more toward an order fulfillment culture instead of a retail "buy off the shelf" culture. That way manufacturers wouldn't be guessing about their sales, they would just be fulfilling orders.
Anyway, this is getting rambling and I don't think it's really in the realm of politics so much as economic theorizing...