How does one find open invention slots in Eve?

Solution 1:

Short of building and maintaining a POS, you can use this search tool to find all stations in the EVE universe with particular characteristics.

You will probably need to use in-game tools to identify stations with spare slots, but this should at least make finding the stations a bit easier.

Solution 2:

I just use the "Choose Installation" button in the invention screen. Set the "Range" dropdown to "Current Region", and you'll get a list of all stations that have invention slots in that range. I see five stations in Heimatar RIGHT NOW with open, "Now" invention slots.

In the longer term, it's not really necessary to worry about it. Wait times of a day or less are fine, once you've got your invention station stocked with the datacores and decryptors and T1 BPCs and and and. Once you've got your groove going, you'll have a supply of blueprints at your manufacturing station, and only pick up more BPCs from the invention station every few days, and all your slots will stay nice and full.

The real obstacle for the T2 industrialist is COPY slots. For those, I ended up building an alt, and sending him off to various stations in lowsec in obscure regions, and making sure he makes a LOT of copies at a time. I let him back into civilization every two weeks or so :)

Oh, and as a last resort, diversify. There are some nice profitable T2 modules, and manufacture times on those things are LONG... like, a day and a half for producing 10 cruiser guns. Things that take a long time to build, you don't mind if they also take a while to invent.