I wouldn't put all three in a same city though, it would lower the price of the final product and rise the price of the raw material much more, so you'd be lowering the possible profits. Just put them far enough from each other in relatively strategic location that they cover a certain area.
The thing is I'm not sure if my own caravans pay for my own goods from my own workshops? (I assume they do)
So, for example, if Velvet is only produced in a single city it's going to be extremely expensive everywhere else just as a function of S/D, so a slight reduction in local price is irrelevant vs the global average price. But if my caravans are buying it from my own city, the cheaper it is the more profit they can make selling it on in other places, as the purchase cost vs sale price will be greater.
And there are a few cities that I've seen with hundreds of cotton in stockpile, so I'd have to experiment and see if 2 or 3 WS are better. If I wasn't so lazy, I would go and dive into the XML or DLL files to figure out what the daily resource consumption/conversion rate for each workshop is, and the typical output rate of each cotton farm, then work from there for the most min-max velvet operation.
In an ideal world (and i've been trying to fully understand the economy system to make a more indepth suggestion/writeup) - I would not have my caravans operate so "freely", I'd have an alternate setting that just made them run like trucks in transport tycoon, I'd give them exclusive rights (so no other caravans could buy the velvet up too and act as competitors) to distribute my velvet to wherever is paying most for it. I'd even let them buy the velvet for 0 gold from my workshops (so the workshops act as loss-leaders) to maximise all that profit the caravans could make in other cities.
Nice idea, I will try it out tomorrow. But why do you assume that starting a caravan from a particular city affects this caravan in any way? I once started all my caravans from vladian cities and after some time I started war with vladians. It didn't affect my caravans at all, they just started to avoid vladian cities obviously but nothing more happened
I've seen them return to the starting city more often, though I do think they can go anywhere if they want to but in general I think it weights which cities they go to most - slightly.
My strategy is all about trying to set up a monopoly in a commodity and exploit the distribution of that commodity, so if I can get my caravans to spend more time in my own "production" cities, buying up my own goods, that'll have a measurable increase in gold per day (both in the caravan and workshop profit lines).